Water-Injection Pressure Maintenance and Waterflood Processes

Chapter 44

Water-Injection Pressure Maintenance and Waterflood Processes C.E. Thomas, Care Laboratorim Inc.* Carroll F. Mahoney, Core Laboratone\ tnc. George W. Winter, Core Laboratories Inc.

Introduction Many factors that are important to waterflooding are also important in water-pressure maintenance, so it is difficult to define the point of separation between the two processes. Accordingly, a major portion of the information presented in this chapter applies to both waterflooding and water-pressure-maintenance operations. For our purposes, waterflooding and water-pressure maintenance are defined as follows.

Wurrfl~&ing is a secondary-recovery method by which water is injected into a reservoir to obtain additional oil recovery through movement of reservoir oil to a producing well, after the reservoir has approached its economically productive limit by primary-recovery methods.

Water-pressure muintrnclnce is a process whereby water is injected into an oil-producing reservoir to supplement the natural energy that is indigenous to the reservoir and to improve the oil-producing characteristics of the field before the economically productive limits are reached.

General History and Development of Waterflooding The first recognition of the benefits that can be obtained from water injection came as a result of accidental flooding when water was inadvertently admitted to producin oil sands through abandoned wells. In 1880. Carl1 ?

reported increased oil production following accidental flooding in the Pithole City (PA) area, and suggested the use of intentional flooding. Although waterflooding was illegal in Pennsylvania before 1921 and in New York before 1919. water-injection operations in these areas were reported as early as the 1890’s.’ Since it was illegal, limited information is available on operations before 1922; ‘Orlglnal chapter in the 1962 editon was wtten by H.C Osborne. C E Thomas J F Armslrong, L L Cratn. C.F Mahoney, F C Kelton 0111 Lafayette and J E Smith

however, increased production was noted in 1907 in Penn- sylvania’s Bradford field and in 1912 in New York.’ The linedrive pattern was introduced in 1922 and the five-spot pattern in 1924. The use of pattern injection programs, when combined with surface pressure injection, provided a more effective and efficient method of moving oil to the producing wells.

The initial success of watertlooding in the Bradford area can be attributed to a number of favorable factors. The Bradford sand generally had no natural water encroachment, contained a relatively low-viscosity crude, and had a low initial gas saturation. As a result, primary recovery was limited, and the oil recovery by water injection was significantly larger than that achieved by natural pres- surcl depletion.

Waterflooding was slow to expand outside the Pennsyl- vania-New York area. The first waterflood was initiated in Oklahoma in 1931 in a shallow Bartlesville sand in Nowata County. In 1936, waterflooding was introduced in Texas when injection was applied to the Fry pool in Brown County. Within 10 years, watcrflooding was in operation in most of the oil-producing areas. However, it was not until the early 1950’s that the general applica- bility of waterflooding was recognized. a

There are no generally reliable records of water- injection operations in areas outside the U.S. during this developmental period, but sufficient data have been published to indicate a comparable growth pattern in other parts of the world.

Waterflooding currently is accepted worldwide as a reliable and economic recovery technique; almost every significant oil field that does not have a natural water drive has been, is being, or will be considered for waterflooding.

44-2 PETROLEUM ENGINEERING HANDBOOK

Important Factors in Waterflooding or Water-Injection Pressure Maintenance In determining the suitability of a given reservoir for waterflooding or pressure maintenance, these factors must be considered: (1) reservoir geometry, (2) lithology, (3) reservoir depth, (4) porosity, (5) permeability (magnitude and degree of variation), (6) continuity of reservoir rock properties, (7) magnitude and distribution of fluid saturations, (8) fluid properties and relative- permeability relationships, and (9) optimal time to waterflood.

Generally, the influence of all these factors on ultimate recovery, rate of return, and ultimate economic return must be considered collectively to evaluate the economic feasibility of conducting waterflood and/or water- pressure-maintenance operations in a particular reservoir. Factors other than reservoir characteristics also will have a great influence. These include the price of oil, market- ing conditions, operating expenses, and availability of water.

Reservoir Geometry

One of the first steps in organizing reservoir information to determine whether water injection is feasible is to establish the geometry of the reservoir. The structure and stratigraphy of the reservoir control the location of the wells and, to a large extent, dictate the methods by which a reservoir may be produced through water-injection practices.

Structure is a principal factor in governing gravitational segregation. In the presence of high permeabilities, recovery by gravity segregation, particularly in old pools, may reduce oil saturation to a value at which the application of water injection may be uneconomical. If a suitable structure exists and the remaining oil saturation proves sufficient for secondary operations, the adaptation of a peripheral flood may result in a higher areal sweep efficiency than would the conventional pattern or linedrive floods. High relief also would suggest investigation of a companion gas-injection program. The shape of’ the field and the presence or absence of a gas cap would also influence this decision.

Most water-injection operations conducted to date have taken place in fields that exhibit only moderate structural relief. Many floods are located in pools where the oil accumulation occurs in reservoirs of the stratigraphic-trap type. Since these pools, as a rule, have been produced by dissolved-gas drive and have not received any benefits from natural-water encroachment or other displacement- energy mechanisms, high oil saturations usually remain after primary-recovery operations, making these reservoirs most attractive for secondary-recovery operations.

In such pools, the dip of the strata may be so slight as to have no noticeable effect on secondary-recovery operations. Thus, the location of the injection and producing wells may be made to conform to property lines and to known sand conditions. Whether such a practice would prove successful in pools where oil and gas distribution has been controlled by a high-relief structure is ques- tionable.

An analysis of reservoir geometry and past reservoir performance is often important in defining the presence and strength of a natural-water drive and, thus, in defining the need for supplementing injection. If a natural-water

drive is determined to be strong, injection may be unnecessary. Structural features such as faults, or stratigraphic features such as shale-outs, or any other permeability bar- rier usually will influence these decisions. An otherwise suitable reservoir may be so highly faulted as to make any injection program economically unattractive.

Lithology Lithology has a profound influence on the efficiency of water injection in a particular reservoir. Lithological factors that affect floodability are porosity, permeability, and clay content. In some complex reservoir systems, only a small portion of the total porosity, such as fracture porosity, will have sufficient permeability to be effective in water-injection operations. In these cases, a water- injection program will have only a minor impact on the matrix porosity, which might be crystalline, granular, or vugular in nature. Evaluation of such effects requires an extensive laboratory investigation and a somewhat comprehensive reservoir study. Evaluations can be sup- plemented by experimental pilot injection operations.

There is laboratory evidence that a difference between the mineralogical compositions of the sand grains and ce- menting material of various oil-producing formations may account for differences in the residual oil saturation (ROS) that have been observed subsequent to waterflooding. These differences in oil saturation are indicated to be dependent not only on the mineralogical composition of the reservoir rock but also on the composition of the hydrocar- bons within the rock. Benner and Bartell’ have shown that, under certain conditions, the basic constituents of some types of petroleum cause quartz to become hydrophobic because of the adsorption of these constituents by the surface of the sand grains. In a similar manner, the acidic constituents of other types of petroleum render calcite hydrophobic. At present, there are not enough data available to permit valid predictions regarding the effects on recovery when the pore walls are made wet to various degrees by water and petroleum, but it appears probable that there is some effect.

Although there is evidence that the clay minerals that are present in some oil sands may clog the pores by swelling and deflocculating when waterflooding is used, no exact data are available as to the extent to which this may occur. The effect depends on the nature of the clay minerals; however, an approximation of the pore-clogging impact may be determined through laboratory investigations. The montmorillonite group is most likely to cause a reduction in permeability by swelling; kaolinite is least likely to cause a reaction. The extent to which such a reduction in permeability will occur also depends on the salinity of the water that is injected. Brines are usually preferable to fresh water for flooding purposes.

Reservoir Depth The depth of the reservoir is another factor that should be considered in waterflooding. If the depth of the reservoir is too great to permit redrilling economically and if old wells have to be used as injection and producing wells, lower recoveries may be expected than in cases in which new wells can be drilled. This is particularly true in old fields where regular well spacings were not observed and where infill development was not as extensive as lease- line development. Also, after primary operations, ROS’s

WATER-INJECTION PRESSURE MAINTENANCE & WATERFLOOD PROCESSES 44-3

in most deep pools probably are lower than in shallow pools, because a greater volume of solution gas was generally available to expel the oil and because shrinkage factors are higher. Therefore, less oil remains. Greater depth, on the other hand, permits the use of higher pressures and wider well spacings. provided the reservoir rock possesses a sufficient degree of lateral uniformity.

Caution should be exercised in shallow-depth fields since the maximum pressure that can be applied in a secondary-recovery operation is limited by the depth of the reservoir. In waterflood operations, it has been found that there is a critical pressure (usually approximating that of the static pressure of the column of rock overlying the productive sand, or about 1 psi/ft of sand depth) which, if exceeded, apparently permits the penetrating water to expand openings along fractures or other planes of weak- ness, such as joints and, possibly. bedding planes. This results in the channeling of the injected water or the bypassing of large portions of the reservoir matrix. Con- sequently, an operational pressure gradient of 0.75 psi/ft of depth normally is allowed to provide a sufficient mar- gin of safety to prevent pressure parting. However, to remove as much doubt as possible. information regarding fracture pressures or breakdown pressures in a given lo- cality should be studied. Either pressure should be considered as an upper limit for injection. These considerations will also influence equipment selection and plant design. as well as the number and location of injection wells.

Porosity The total recovery of oil from a reservoir is a direct function of the porosity, because the porosity determines the amount of oil that is present for any given percent of oil saturation. Since the fluid content of reservoir rock varies from 775.8 to 1,551.6 bbliacre-ft for porosities of IO and 20%. respectively, it is important that reliable porosity data be assembled, Porosities sometimes vary from IO to 35% in an individual zone. In limestones and dolomites, pinpoint and fractured porosities may vary from 2 to 11% ; honeycombed and cavernous porosities may vary from 15 to 35 %. In establishing an average porosity, the arith- metic average of the porosities determined from core samples has proved acceptable. If there are sufficient data, isoporosity maps are used when the distribution of porosity is important-as, for instance, when some fields are unitized. These maps may be areally or volumetrically weighted to give a very good total porosity value. If enough core data are available, statistical analyses of porosity and permeability may be used to improve the use of these data.

To date, the most satisfactory method of measuring this important property has been through laboratory measurements of core samples. Various logging methods have been quite satisfactory in many cases. The logs may include a “microlog” or “contact log,” neutron log, density log, or sonic log.

Permeability (Magnitude and Degree of Variation) The magnitude of the permeability of the reservoir rock controls, to a large degree. the rate of water injection that can be sustained in an injection well for a specific pressure at the sandface. Therefore. in determining the suitability of a given reservoir for waterflooding, it is necessary to determine (I) the maximum permissible injection pres-

sure from depth considerations. and (2) the rate vs. spacing relationships from the pressure/permeability data. This should indicate roughly the additional drilling that would be required to complete the proposed flood program in a reasonable length of time. An approximation of the expected recovery then can be compared with the monetary expenditure for this development program, so as to indiL cate quickly the suitability of the reservoir as a flood pros- pect. If the project profitability is favorable, more detailed work may be warranted.

The degree of variation in permeability has justifiably received much attention in recent years. Reasonably uniform permeability is essential for a successful waterflood. because this determines the quantities of injected water that must be handled. If great variations in the permeability of the individual strata within the reservoir are noted, and if these strata maintain continuity over substantial areas, injected water will break through early in high-permeability streaks and will transport large quantities of injected water before the low-permeability streaks have been swept effectively. This, of course, will influence the ec- onomics of the project and thus the suitability of the reservoir for flooding. Not to be overlooked is that continuity of these streaks or strata is as important as the pcrmea- bility variation. If there is no correlation between the permeability profiles of the individual wells, the chances are good that the high-permeability zones are not continuous and that the channeling of injected fluids will be less severe than indicated by performance calculations.

Continuity of Reservoir-Rock Properties The importance of reservoir-rock continuity in relation to permeability and vertical uniformity in determining the suitability of a reservoir for waterflooding has been mentioned previously. Since the flow of fluids in a reservoir is essentially in the direction of bedding planes, horizontal (along bedding planes) continuity is of primary interest. If the reservoir body is split into layers by partings of shale or dense rock. a study of a cross section of the producing horizon should indicate whether individual layers have a tendency to shale out in relatively short lateral distances, or whether sand development is uniform. Also, evidence of crossbedding and fracturing should bc collected from core data. These features should be considered in determining well-spacing and flood patterns, and in estimating the volume of the reservoir that will be affected during the injection program. The presence of shale partings is not necessarily detrimental, provided the individual layers of reservoir rock exhibit a reasonable degree of continuity and uniformity with respect to permeability, porosity, and oil saturation. When vertical discontinuities exist (i.e., when there is a water- or gas-bearing stratum in the producing formation), shale partings will sometimes permit a selective completion; such a completion allows the exclusion or reduction of water or gas production and permits selective water injection.

Fluid Saturations and Distributions In determining the suitability of a reservoir for waterflooding, a high oil saturation certainly would be considered more suitable than a low oil saturation. Usually, the higher the oil saturation at the beginning of flood operations, the higher the recovery efficiency will be. Also, ultimate


recovery will be higher, the bypassing of water will be less, and the economic return per dollar risked will be greater. Also involved in the suitability determination is the ROS after passage of the water front. Methods for ascertaining this saturation are discussed later in this chapter. The more this value can be reduced. the greater the ultimate oil recovery and economic gain. Most of the new- er, more specialized displacement techniques that are currently under development and experimentation are aimed solely at reducing the value of ROS behind the displacing medium (see Chap. 42).

Also of great interest is the initial saturation mcasurc- ment of the interstitial water. A knowledge of this quantity is essential in determining the initial oil saturation. Leverett and Lewis ’ and other investigators ‘J have shown experimentally that, as a fraction of PV, oil recovery by solution-gas drive is essentially independent of connate-water saturations. Therefore. the amount of residual oil after the solution-gas depletion varies inversely with the water saturation. Worthy of mention here is the effect that initial water saturation has on the formation of an oil bank in front of the advancing water front. If the water saturation exceeds some critical value, an oil bank may not form: although substantial oil recovery may be achieved, oil will be produced at high water cuts. The water saturation that would preclude the formation of an oil bank may be determined from the fractional-flow equation, as illustrated later. This value may vary greatly from field to field. The fractional-flow equation also will indicate the amount of water that may be expected in the total flow stream at any particular saturation.

In the U.S. midcontinent area. waterflood programs have resulted in substantial oil recoveries being obtained from sands that have water saturations ranging from 22 to 40%. The average saturation in the Bartlesville sand of Oklahoma is about 30%. In the Bradford field, gas injection has proved unprofitable with oil saturations of 40% and water saturations of 30%; however, waterflooding has been very successful.

The Venango fields of Pennsylvania have responded more favorably to gas injection than to waterflooding because of high interstitial-water saturations. Oil saturations in cores range from 20 to 35%, with interstitial water varying from 40 to 60%. Waterflood oil recoveries have been uneconomical in these fields, but gas injection has resulted in additional recoveries of up to 100 bbliacre-ft. 9

An exception to the rule concerning the uneconomical flooding of sands with high water content occurred in the Woodsen Shallow field, Throckmorton County, TX; a successful waterflood program was carried out in this field where the sands have an average water saturation of 54%. ‘O

Interstitial water content may be estimated from cores that are obtained with an oil-based mud system, through electrical log interpretations, laboratory restored-state floods, or capillary-pressure tests.

Another factor that is instrumental in determining the susceptibility of a reservoir to waterflood operations is the free-gas saturation. The pore space occupied by free gas in the reservoir is dependent on the voidage created by the produced stock-tank oil and gas, provided no in- flux of edge water has occurred. If accurate production data are known. the pore space depleted by the produced oil and gas may be determined. For solution-gas-drive

reservoirs. the portion of pore space occupied by gas may be determined by

s,v =(loo@s,,.) NBni - (N-Np)B,,

. . NB,,i

where S,? = gas saturation, fraction, S,,. = water saturation. fraction,

N = initial oil in place, STB. N,, = oil produced, STB, B,,; = initial oil FVF, RBISTB, and B,, = OII FVF, RBISTB.

Several authors have shown through experiments that. for a given oil saturation, the percent of recovery by waterflood increases as gas saturations increase to about 30 % , but the benefits decline as gas saturations go beyond the 30% level. The effect of free gas has been to cause lower ROS’s behind the front than could be obtained by waterflooding the same systems in the absence of such gas. The increased recovery obtained because of the presence of gas during a waterflood has been variously attributed to changes in the physical characteristics of the oil, to the selective plugging action of the gas, to inclusion of oil mist in the free-gas phase, and to replacement of residual oil by residual gas. The degree of improvement in recovery has not been established in the field: however, an investigation ’ ’ into the influence of a free-gas saturation on recovery by water drive indicated that the optimal gas saturation could be determined for maximum oil recovery by water displacement. Some operators who have injected gas ahead of water have reported that floods have benefited in one way or another. Besides the advantages of increased oil and gas production, benefits such as increased water-injection rates, more efficient flooding, and decreased paraffin problems have been reported.

The effects of free-gas saturations on oil recovery in waterflooding remain an academic problem. Until the merits of injecting gas ahead of (or with) water can be proved practicable in both the laboratory and in the field, caution should be used in applying this method to any large field operation.

Fluid Properties and Relative- Permeability Relationships The physical properties of the reservoir fluids also have pronounced effects on the advisability of waterflooding a given reservoir. Of major importance among these effects is the viscosity of the oil. The viscosity of the oil affects the mobility ratio. The relative permeability of the reservoir rock to the displacing and displaced fluids is also a factor in the mobility ratio, as is the viscosity of the displacing fluid-water, in this case (refer to Chap. 43). The mobility of any single phase (e.g., oil) is the ratio of the permeability of that phase to its viscosity. k,,/p(, The mobility ratio, M, is the ratio of the mobility of the displacing fluid to that of the displaced fluid. The larger the mobility ratio, the lower will be recovery at breakthrough; hence, more water must be produced to recover a fixed amount of oil. This is because (I) a smaller area is swept at breakthrough, and (2) the stratification effect is enhanced.


With high-viscosity (low-gravity) crudes, primary recovery normally is lower and shrinkage is less than with low-viscosity crudes. This tends to offset the bad effects of high-viscosity crudes since it often results in higher oil saturations at the beginning of water-injection operations.

Optimal Time to Waterflood The optimal time to waterflood a particular reservoir depends on the operator’s primary objective in waterflooding. Among these objectives might be (1) maximum oil recovery, (2) maximum number of dollars of future net income, (3) maximum number of dollars of future net income per dollar invested, (4) stabilized rate of monetary return, or (5) maximum discounted present worth. Certainly all these objectives are desirable, and all seem to call for an early beginning of water-injection operations; however, that is not always the case. The most common way to determine the optimal time to begin flooding is to compute the anticipated oil recovery, production rate, monetary investment, and income for several assumed times of initiation-and then observe the effect of these factors on the most desirable goal.

In a homogeneous reservoir, maximum oil recovery can be expected if flooding is begun at the precise time bubblepoint pressure is reached. This is because residual oil after waterflooding will have the maximum amount of gas in solution and, at the bubblepoint, oil viscosity is most favorable. If the effect of a free-gas saturation on ROS is ignored, heterogeneity causes the optimal pressure for highest recovery to be lower than the bubblepoint pressure. If the bubblepoint pressure is quite low, production rates may have substantially declined and the operator may prefer an earlier flood. Water-injection operations initiated above the bubblepoint in a heterogeneous recovery may ultimately result in less oil recovery but may be justified economically.

Objective 1, maximum oil recovery, is important to all operators or agencies who are concerned primarily with the best interests of the public. Objectives 2, 3, and 5, involving certain financial goals, are most important to privately owned companies, either independent or major; in these cases, the choice would depend on a company’s size and financial position and on whether it is planning to sell the property. Objective 4, stabilized rate of monetary return, becomes important when financing, such as production loans and oil payments, and federal taxes are considered. This last point, federal taxes, is particularly important to small operators who are subject to large variations in a tax rate that depends on their tax bracket. Also, some money-lending agencies are particularly interested in properties that are anticipated to have long producing lives-i.e., to have a production rate that has been stabilized somewhat below the attainable rate. Other agencies are more interested in a fast return on investment.

In summary, then, the optimal time to begin water- injection operations depends on which of the objectives is of primary concern.

Determination of Residual Oil After Waterflooding Perhaps the most commonly used technique for calculating total waterflood recovery is to subtract the ROS after waterflooding from the oil saturation before flooding, then

to multiply the difference by the appropriate factors to convert the displaced portion to barrels of stock-tank oil, after making adjustments for such things as area1 pattern efficiency and vertical conformance. If original reservoir saturation conditions and fluid properties are known or can be determined, current saturation conditions may be computed at any time from the pressure and production history. The determination of the ROS resulting from displacement by an advancing water front can be determined satisfactorily only from laboratory measurements made on representative samples of the reservoir rock. These samples must be subjected to a displacement process that is similar to that expected under waterflood. Such tests of waterflood susceptibility, or potential, are run on both fresh cores and on restored-state samples. Interpretation of the data is often difficult, particularly when fresh-core techniques are used or when there are not enough data available to establish its reliability.

Fresh-Core Techniques The fresh-core technique has the advantage of being quick- er and cheaper than the restored-state technique. In applying this technique, a core sample that is fresh from the field is subjected to waterflooding and the residual oil is determined. This procedure is meaningful only when coring conditions have ensured that flushing and contamination by drilling fluid has been virtually eliminated, as is the case when a depleted sand is cored with cable tools. Contamination of cores by the drilling fluid, which often contains surface-active agents and other chemicals as well as contaminating solids, can drastically change wettability characteristics and reduce ROS’s to considerably below the naturally occurring value. Any ROS that has been determined in this manner should be regarded suspiciously and be used only if the reported values can be verified by other means. ‘*

Interpretation of Conventional Core-Analysis Data

In the absence of more dependable data, some authors rec- ommend that the oil saturation measurement that is derived from conventional core analysis of cores taken with water-based drilling fluids be used as a reasonable estimate of the ROS after waterflooding. This procedure is valid only after the saturation value is increased by the FVF at the existing reservoir pressure. The resulting measurement is believed to be more dependable than the saturation value that is determined from further flooding this same core sample with more water, as is done with the fresh-core technique.

Laboratory tests I3 indicate that an additional correction should be made for the reduction in oil saturation that results from gas expansion as the core is being pulled. The actual reservoir ROS would be represented by the term S,,, B,, C,, , where S,,, is the residual oil measured at the surface, Bog is the oil FVF at current reservoir conditions, and C,, is the correction for gas expansion. (A value for C,,, of 10.0% is acceptable in the absence of measured data.)

Restored-State Technique

Probably the most dependable means of determining the ROS behind an advancing front is to study the results of waterflood susceptibility tests that are performed by the


restored-state technique on representative samples of the reservoir rock. This requires the obtaining of enough data to establish dependably that the core samples represent all the permeability ranges contained in the reservoir. This ideal situation is very rarely available to the engineer, so interpretations must be made with less than the ideal data. In the restored-state technique, the sample is first extracted and then dried in an effort to remove all contaminants. Then, the irreducible water saturation is determined by the capillary-pressure method. After this, the sample is saturated with brine, which is usually of approximately the same composition as that of the reservoir. All mobile water then is displaced with an oil of about the same viscosity as the reservoir oil, leaving the core sample in its original condition. Then the core sample is sub,jected to a water-displacement process until the effluent IS essentially 100% water. At this point, the oil saturation is determined in the normal manner and called the ROS.

Relative-Permeability Curves ROS’s also may be determined from relative-permeability curves, but the normal purpose of these curves is to give more data for the area that lies between the two extreme conditions of interstitial water and ROS. Since the measurements for the area between those two conditions are made on rather small samples of the reservoir rock, they are normally performed with an oil of substantially greater viscosity than that of the reservoir oil. The more viscous oil facilitates accurate measurement of the pressure gradients that are necessary for dependable relative-permeability determination. Therefore, relative-permeability curves should be used primarily for fractional-flow and rate/pressure calculations, with more weight being given to the middle saturation range than to those on either end. This view seems to support the practice of arbitrarily reshaping the experimental k,, curve in the vicinity of the ROS and the experimental k, curve in the vicinity of the irreducible water saturation so as to confirm more dependable determinations of these saturations. Further, it seems to indicate that considerable error might be introduced by using an ROS taken from relative-permeability measurements alone.

Effect of Initial Saturations Initial saturations of water, oil, and gas on reservoir suitability have been discussed previously in this chapter. The effect of these saturations on the ROS behind the water front will be considered here.

As previously mentioned in the discussion of fluid saturation and distributions, an initial water saturation that is above the “critical” value will cause the displacement mechanism to be of the “subordinate-phase” variety that normally prevails after breakthrough. This means that a frontal displacement will be impossible; still, considerable quantities of oil may be recovered if it is economical to use large volumes of water. For predictions of this type of performance, a fractional flow evaluation is necessary-rather than reliance on the concept of an ROS behind an advancing front, or “piston,” of water.

The effect of an initial gas saturation has been investigated by several authors, most of whom report increasing beneficial results in reducing the ROS left by the displacing water when an initial gas saturation up to 30% has been found. 14-16 Some authors 14,” have reported

substantial benefits from an initial gas saturation of more than 30%; however, these benefits begin to decline as the gas saturation increases. True benefits were also found to vary with the properties of the reservoir rock as well as with the properties of the reservoir fluids. All authors report substantial increases in ROS’s as the oil/water viscosity ratio increased. Accurate predictions of the amount by which the ROS may be reduced as a result of any initial gas saturation is a matter for laboratory determination or for calculation from field performance data. ” Craft and Hawkins I2 state that the total residual hydrocarbon saturation will be about the same value, whether for oil or gas, or a combination of oil and gas. This view is not rigidly supported by laboratory data but the value may be used as an approximation.

Influence of Wettability It has been shown that wettability has an influence on the interstitial water saturation, ROS, capillary pressure, relative permeability, waterflood performance, and the resistivity index of oilfield cores. In short, any property that is influenced by saturation conditions and/or interfacial relationships also will be influenced by wettability. This indicates the importance of assuring that all measurements of such properties are made under the correct conditions. Any laboratory measurements that are made under improper wettability conditions will give results that will differ to a potentially large degree from the true magnitude of the property as it exists in the reservoir. The importance of wettability in reservoir-rock-fluid behavior has been increasingly emphasized in recent literature. “-”

In most cases, the laboratory data, engineering calculations, and field experience will indicate that water is generally more efficient than gas in displacing oil from reservoir rocks. There are two primary reasons for this: (1) the viscosity of water is much nearer that of oil than is the viscosity of gas, and (2) the water occupies the less conductive portions of the pore spaces whereas the gas occupies the more conductive portions. Thus, in water displacement, the oil is left to the central and more conductive portions of the pore channels. This circumstance is true only for reservoir rocks that are preferentially water-wet (hydrophilic), as is the case for most reservoir rocks. Where the rock is preferentially oil-wet (hydrophobic), the displacing water will invade the more conductive portions first (just as the gas does), thus resulting in lower displacement efficiencies. However, the efficiency by water displacement still exceeds that by gas displacement because of the viscosity advantage. This effect is accounted for in capillary-pressure and relative- permeability measurements only if the rock samples in the laboratory exhibit the same number and degree of hydrophilic and/or hydrophobic qualities as those that pre- vail in the reservoir. Waterflood oil-recovery predictions that were based on core-analysis data have shown recoveries from water-wet rock to exceed recoveries from oil- wet rock by as much as 15% of the original oil in place (OOIP). ” Apparently, coring fluids and core-handling techniques can disturb the native wettability characteristics of reservoir rock surfaces and may render undepend- able the laboratory measurements that are made on any particular core. However, a few coring fluids, brine in particular, have been found not to affect core wettability, and core handling and preserving procedures have been


TABLE 44.1-EXAMPLES OF THE STILES CALCULATION

k= PermeabtlIty at End 01 Group

= 1% khM,o (kh), -kh (Eql+(f%+ 1

IV = '(58'; vo = IW, - (51

(9) 2100 2475- 7.725 1662 4620 7.530 167 1 652 5 7,175 146 4 1.3695 6,705 129 5 I,6315 6,295 1089 2,466 0 5,690

Average Permeablllty of Group

(md) = (W2) (6)

225 0 1950 1775 ,567

water cut (fracllon) =(6)1(10)

(11) 0 031 0 057 0106 0 170 0 226 0 304 0419 0 564

Recovery Recovery m ,f‘ZllO”)

=(3)+(12) =(13)/h, 1131 (14) 37 6 0310 42 4 0 348 46 9 cl 384 52 2 0 428 58 5 0 480 67 2 0551 77 0 0631 86 6 0 710

Capaclly \n Group (md-It) (4) 225 195 355 470 420

kh , -h/l/i = (9Vl7) 1121 36 6

khM,o +w, - kh = ,6) + (9)

1101 7.972 5 7.992 0 8.027 5 8.074 5 8.1165 9.176 0 6.265 0

("WI) (5) 225 420 775

1.245

40 4 42 9 45 2 48 5 52 2 53 0 48 6

t 665 1400 1190 2.260

3.150 4.300 5,600

96 9 82 1 68 0 53 0

SO 5 3,465 0 4,600 75 I 4,730 0 3,650 60 5 6.226 0 2.290 45 5 7,566 0 1.070 31 5 8,277 5 425 163 8,662 5 75 - 0.745 0 0

8.360 0 6.516 0 6,636 0 6.702 5 9,737 5

0 731 37 9 95 9 0 786 0 676 23.5 ,045 0 6571 0951 135 111 5 0914

,166 0 956 0991 1 000

46 00 1220 1 000

10 45 60 to 23 1, 30 45 10 17 12 15 to30 14 13 oto 15 10

h.=122

I.220 645

6.660 7.525 7.875 7,950

379 25 0 75

350 75

c.=7,950

9,745 0

k M wo

~,lio(~)~o.2oo~~(,100)=1100.

k ro fib+ 0 600 0 90

developed to preserve wettability characteristics during storage and laboratory testing.

Predicting Water Injection Oil Recovery and Performance Predictions of future oil recovery and reservoir performance for waterflood and water injection projects provide the basis for the economic evaluation of the profitability of proposed projects. These performance and recovery projections should be made in sufficient detail to define the economic viability of the project. This definition should be made after consideration is given to the investment requirements, cost of operations, projected recovery, and the return that is expected on the investment. In some cases, an estimate of the ultimate oil recovery that is expected from the operation may be sufficient; in fact, it may be the only estimate possible if basic reservoir and past production data are limited or are of ques- tionable reliability. However, in most cases, detailed projections are required for making economic evaluations. These include the projection of future well requirements and recompletions, individual well injection and producing rates, reservoir and injection pressures, producing WOR’s, and oil recovery throughout the course of the project. Detailed projections require complex predictive methods and complete and detailed reservoir data. It is the responsibility of the reservoir engineer to choose the detail and complexity of the performance projections- following consideration of the management requirements, the cost of developing the projections, and the amount and reliability of the basic reservoir and economic data that are available.

Displacement Calculation Procedures

There are a number of methods presented in the literature for calculating the performance of a waterflood project. Two of the early methods that were developed for application in stratified reservoirs are the Stiles I9 and Dykstra-Parsons. I5 The Stiles method is based on the assumptions that fluid displacement occurs in a piston-like manner, in a linear bed of a specific permeability, and that the rate of advance of the flood front is proportional to the permeability of the bed. The Dykstra-Parsons method for predicting waterflood performance includes

consideration of actual fluid mobilities rather than an assumption of equal mobility for the displacing and displaced fluids. With this exception, the basic assumptions made in the development of both techniques are essentially the same.

For the description of water/oil displacement in homogeneous reservoirs, two methods are of primary importance: the Buckley-Leverett’O frontal advance thee and a subsequent extension of this work by % Welge. These two techniques provide the fundamental basis for describing the water/oil displacement characteristics of a linear reservoir segment with homogeneous properties.

Stiles Calculation. In the Stiles I9 method, the following assumptions are made. The rate of flood advance in a linear bed is proportional to the permeability of that bed. After breakthrough, the water/oil production rates are governed by, respectively, the water and the oil mobility ratios of the beds that produce the water and oil in the output well. This latter point is equivalent to the assumption that the rate of fluid movement in each bed is proportional to the oil mobility if breakthrough has not occurred, or proportional to the water permeability if breakthrough has occurred, and that there is no crossflow between beds. The Stiles method involves a calculation procedure that gives recovery values for a “unit” of the total reservoir.

The data needed for the calculations are the individual, measured, permeability values for the reservoir unit being considered, the water/oil mobility ratio, and the oil FVF at flood conditions. The Stiles calculations give the values of produced watercut vs. oil recovery as a fraction of the total recoverable oil. In practical applications, the total recoverable oil is determined independently, as the difference between the amount of oil in the reservoir at the start of the waterflood and the amount of oil remaining after the flood has been completed (to 100% water cut); this difference is then adjusted by an area1 coverage factor for the flood unit.

For convenience in calculating, the permeability values are arranged in a numerically descending sequence. If there are a great many values. they may be grouped by permeability ranges and the total millidarcy-foot capacity and footage for each range is computed. In the case of such grouped values, it is preferable to set the ranges


.- 80

to

40 I

I I

11’ ” “I” ‘I’ )’ 12 5 10 20 M405oM)7080 w 95 98 9999.5

PORTION Of TOTAL SAMPLE HAVING HIGHER PERMEABILITY

Fig. 44.1-Log-normal permeability distribution.

so that there will be approximately equal capacities in the middle permeability ranges and somewhat smaller capacities in the high and low permeability ranges.

Values for cumulative capacity and cumulative thickness, as well as the average permeability for each group, then are calculated. The fractional cumulative capacity may be plotted vs. fractional cumulative thickness; the result of this procedure is referred to as a capacity- distribution curve. In the original Stiles method. the permeability data are plotted at the midpoint values of cumulative thickness, a smooth curve is drawn through the points. and a new set of permeability values are read at the thickness values to be used in the final calculations. In the equivalent calculation method presented in this chapter, the plotting may be eliminated because the smoothing of permeability values is accomplished by for- ward interpolation between successive permeability values. The calculation of fractional capacity and thickness also may be eliminated if the capacity-distribution curve is not required.

An example of a water-cut recovery calculation is shown in Table 44.1, In that. table, the letters h and HI, in Cols. 3 and 5, represent cumulative foot and millidarcy- foot capacity, respectively; h, and (kh), , inCols. 2 and 4, represent the corresponding totals; and k, in Col. 7, designates the interpolated average permeability in millidarcies. The equations for the fractional water cut and recovery, at the time when h feet are producing water, are as follows.

f,, = khM,w,

t khM,,,, +(kh), -kh

and

N,,‘,L k-t (kh)r-kh , . h, k 1

where M,,, equals the water/oil mobility ratio multiplied by the FVF of the reservoir oil at the time of flooding:

where k,,./k, = water/oil relative permeability ratio, fiL,/p, = oil/water viscosity ratio,

B = FVF, N

1; = recovery to depletion (abandonment), = capacity of flowing water, and

1 -kh = capacity of flowing oil.

The resulting recovery vs. water-cut data may be used as the starting point for further calculations in connection with the flood unit. For example, if the unit is a five-spot in a depleted field and an estimate of the gas space in the reservoir is available, calculations of the time behavior of the flood may be made for an assumed injection-rate schedule. These calculations would involve determination of the fill-up time and a subsequent application of the water-cut recovery curve so as to calculate the oil production rate vs. time.

As noted previously, the Stiles method gives recovery vs. water-cut data for a hypothetical flood unit, in which breakthrough into various producing wells of the unit occurs at the same time. The information could be expected to approximate that for the behavior of a five-spot pattern or that for a group of five-spots, provided an appropriate area1 coverage factor is applied.

Dykstra-Parsons Calculation. Dykstra and Parsons I5 performed a series of laboratory waterflooding tests on field core samples and concluded that oil recovery by waterflooding is a function of both mobility ratio and permeability distribution, with the mobility ratio being defined as follows.

M- kw PO , . . . . . . . . . . . . . . . . . . . . . (4) P I,’ kc,

where k, is the permeability to water in the water- contacted portions of the reservoirs, and k, is the permeability to oil ahead of the waterfront (or mobility of swept to unswept region).

On the basis of the laboratory test results, and calculations made on a layered linear model in which it was assumed there was no crossflow, a correlation that related waterflood recovery to both mobility ratio and permeability distribution was developed. Permeability distribution was measured by the efficiency of permeability variation EK, as follows.

k -k, EK=-, . . ___ _. (5)

k

where k is the mean permeability and k, is the permeability value at 84.1% of the cumulative sample, as shown in Fig. 44.1.4


KrwYo M=--

k ro P w

Fig. 44.2-Permeability variation vs. mobility ratio, showing lines of constant E,(l -S,) for a producing WOR of 1.

The correlations developed by Dykstra and Parsons were for WOR’s of 1, 5, 25, and 100, with recovery related to permeability variation, interstitial water saturation, ROS, and mobility ratio. The basic equations used in developing the correlations were based on the following approach.

At the beginning of injection, the mobility in a layer is determined by the oil and gas phases. As water advances into a layer, the mobility is a composite of oil, gas, and water mobilities; after fill-up, the mobility is determined by the relative permeability and the viscosity ratios. The varying nature of the overall mobility results in a continuously changing injectivity. This method assumes that the permeability distribution is log-normal.

By use of the linear Darcy flow equation for incompressible fluids, the following equations for “coverage” or “conformance efficiency” and WOR were developed:

and

“Br c ki i=l

F,,.,, =

i ki

l=(llH, + I) J

1

(6)

. . . .._....................... (7)

Fig. 44.3-Permeability variation vs. mobility ratio, showing lines of constant ER(l -0.72.S,,) for a producing WOR of 5.

where EC =

F M’O = n=

k; = k, =

M= nBT =

fractional coverage or conformance efficiency,

WOR, number of layers, permeability of layer, permeability of x layer, or the layer that

has just been flooded, mobility ratio, and number of layers in which water has

broken through (varies from 1 to n).

When the coverage and F,,(, are known, it is possible to predict oil recovery and water cut as a function of time, provided the injection rates can be determined adequately.

To develop the relationship between the producing WOR and coverage, or fractional oil recovery, the equations must be solved for breakthrough conditions in each layer of the system, or at least for a substantial number of layers. This method is laborious for hand calculations and, in a later paper, Johnson22 presented a graphical technique for applying the Dykstra-Parsons method that was based on the plots shown in Figs. 44.2 through 44.5, where ER is the fractional recovery of OIP at a given producing WOR. An example of the manner in which these plots were used in applying the Dykstra-Parsons technique was presented by Craig.’

Both the Stiles and the Dykstra-Parsons methods were developed for linear, piston-like displacement in a stratified system, and the results that are obtained when applying these techniques must be interpreted within the context of the limitations imposed by the basic assumptions. However, the concepts established as a result of this early work provided the basis for a number of predictive techniques that have since been developed.

Frontal Advance Calculation. The frontal advance calculation was derived from the concept of fractional flow presented by Leverett 23 in his classic 1941 paper. The fractional flow equation was developed from Darcy’s law for water and oil and, in generalized form, it is as follows.


k ,WPO M=-

k ml”*

Fig. 44.4-Permeability variation vs. mobility ratio, showing lines of constant E,(l -0.52.S,,) for a producing WOR of 25.

k rwPo M=- k roPw

Fig. 44.5-Permeability variation vs. mobility ratio, showing lines of constant E,(l -0.4OS,,) for a producing WOR of 100.

1 -(ko/p,q) ap, Z-gAp sin 0

> . . . (8) fw=-

where fit, =

k,,k,,. = fraction of water in the flowing stream, effective formation permeability to the

specific phase, kk, and kk,,, oil viscosity, water viscosity, fluid volumetric flow rate per unit cross-

sectional area, P,. =

L= Ap =

capillary pressure, p. -pn distance along direction of measurement, density difference between water and oil,

PLI -PO> @=

g=

angle of formation dip referenced to horizontal, and

acceleration caused by gravity.

In practical units, the equation becomes

1 +0.001127L!!L

.fw = CJtPo 2 -0.434A.p sin 0)

where fit = kc, = k,,. =

A= 41 =

P,. = Ap =

a= !-l= L=

, + CL ,I’ kc,

~0 kw . . . . . . . . . . . . . . . . . . I. (9)

fractional flow of the displacing fluid, effective permeability to oil, md, effective permeability to water, md cross-sectional area of flow, sq ft, total flow rate, (qM.+qo), BID, capillary pressure, p. -p ,,,, psi, density difference, g/cm3, p,,, -po, dip angle, positive updip, phase viscosity, cp, and distance. ft.

In the case of a water drive, neglecting the effects of the capillary pressure gradient and the dip of the reservoir, the terms dP,/aL and gAp sin f3 become insignifi- cant. The fractional flow equation then reduces to

1 fw =

l+(k,/k,,,)(p,,,/,u,)’ “““““‘.“” . . (10)

which states that the fraction of water in the flow stream is a function of the relative-permeability relationships in which p0 and CL, are constant for a given reservoir pressure. Since k,/k, is a function of saturation, Buckley and Leverett20 derived the following frontal-advance equation on the basis of relative-permeability concepts.

s,~) . . . . . . (11)

where L = distance, ft,

9, = total flow rate, B/D, f$ = porosity, A = cross-sectional area, sq ft, and t = time, days.

This states that the distance a plane of constant saturation (S,) advances is directly proportional to time and to the derivative (afJaS,) at that saturation. The value of the derivative may be obtained for any value of water saturation by plotting f,b, from Eq. 9 vs. S,,. and graphi- cally taking the slopes at values of S,,. Fig. 44.6 shows a plot off,. vs. S,,, in addition to the resultant df,,,./dS, vs. S,. relationships for the S,, vs. k,/k,,, data at a viscosity ratio of water to oil of 0.50 (see Table 44.2).

If the df,,ldS, values found in Fig. 44.6 are substituted into Eq. 11, the distance that a given water-saturation plane or front will advance for any time f can be calculated for the known throughput q in barrels per day, fractional porosity, and cross-sectional area (in sq ft).

WATER-INJECTION PRESSURE MAINTENANCE 8. WATERFLOOD PROCESSES 44-11

Fig. 44.7 represents the water-saturation profile or frontal-advance curves for a bed that is 1,320 ft wide and 20 ft thick, and has a porosity of 20% and a throughput of 900 B/D for 60. 120, and 240 days with the f,,,, L3f,,,/&S,,. vs. S,,. relationship shown in Fig. 44.6 The curves shown in Fig. 44.7 are characteristically double- valued or triple-valued. For example, the water saturation after 240 days at 400 ft is 20, 36, and 60%. The saturation can have only one value at any place and time, and the difficulty is resolved by dropping perpendiculars so that the areas to the right (A) equal the areas to the left (B).

Fig. 44.8 represents the initial water and oil distributions in the example reservoir and also the distributions after 240 days. The area to the right is the flood front or “oil bank,” and the area to the left is the water-invaded zone. The area above the 240-day curve and below the 90% water-saturation curve represents oil that may be recovered by the displacement of additional volumes of water through the area. The area above the 90% water saturation curve represents unrecoverable oil because the ROS is 10%.

Welge Calculations. In 1952, We1 e*’ extended the earlier work of Buckley and 30 Leverett to derive a simplified method for calculating fractional flow and recovery performance after water breakthrough. The basic equations developed by Welge are as follows:

S,*,-S,,.* =wif<,* (12)

and

wi=-, 1 dSw

H

, . . . . . (13)

dSw s,1!

where S, = average water saturation. fraction of PV,

S w2 = water saturation at the producing end of the system,

IV; = cumulative PV’s of water injected, fraction, and

f02 = fraction of oil flowing at the producing end of the system.

An example of the use of the Welge technique for calculating waterflood displacement performance was presented by Craig. 4 Basic data used in the example calculation are average permeability, 50 md; porosity, 20%; irreducible water saturation, 10% of PV; oil viscosity, 1.0 cp; and water viscosity, 0.5 cp (see Table 44.3).

By Eq. 10,

The fractional flow vs. water saturation relationship is calculated from basic data, such as those given in Table 44.4.

TABLE 44.2-S, vs. k,/k, DATA AT A VISCOSITY RATIO OF WATER TO OIL OF 0.50

S w ko’kw 0.20 0.30 GO 0.40 5.5 0.50 1.70

0.60 0.55 0.70 0.17 0.80 0.0055 0.90 0.0000

Fig. 44.6-Plot of t, vs. S,.

Fig. 44.7-Fluid distribution at initial conditions and at 60. 120, and 240 days.

Fig. 44.8-Waler saturation distributions as a function of distance.


TABLE 44.3--RELATIVE PERMEABILITY CHARACTERISTICS

Water Saturation, Relative Permeability

(fra%on) Oil, k

(fractidon) ~fZrtio”n~

0.10 1.000 0.000 0.30 0.373 0.070 0.40 0.210 0.169 0.45 0.148 0.226 0.50 0.100 0.300 0.55 0.061 0.376 0.60 0.033 0.476 0.65 0.012 0.600 0.70 0.000 0.740

TABLE 44.4-FRACTIONAL FLOW DATA

Water Saturation,

(0,: b”) Fractional Flow of Water,

f&v 10 0.0000 30 0.2729 40 0.6168 45 0.7533 50 0.8571 55 0.9250 60 0.9665 65 0.9901 70 1 .oooo

The fractional flow curve from this calculation is shown in Fig. 44.9. For water breakthrough, the tangent to the fractional flow curve from the point of irreducible water saturation defines (1) S ,,., the average water saturation behind the front, (2) S,,.z. the water saturation at the producing end of the system, and (3)f,., the fractional flow of water at the downstream end of the system.

s,, = 0.563 PV, S. ,,BT = average water saturation at water

breakthrough, % PV, S,,.,; = water saturation at upstream end of the

stabilized zone, % PV, S,,.z = 0.469 PV, and frc* = 0.798.

From the fractional flow curve, df,ldS,, is determined for water saturations that are higher than S,,.? at water

9

0 IO 20 30 40 50 60 70

S,. WATER SATURATION, % PV

Fig. 44.9-Fractional flow curve, example problem.

breakthrough conditions, and the df,,./dS,,. vs. S, curve is developed, as shown by Fig. 44.10. From Eq. 13, Wi is calculated for increasing values of S,,z andf,,z and cor- - respondmg values of SW2 are calculated from Eq. 12.

The results for the calculations of the example problem are shown in Table 44.5.

Areal Sweep and Pattern Effkiency The previous discussion dealt with fundamental techniques for defining water/oil displacement characteristics in linear reservoir segments in stratified reservoirs and in homogeneous reservoir rock systems. However, from a practical standpoint, a truly linear displacement is never used in waterflood operations. In practice, water is injected into some wells and oil and water are produced from others, and often portions of the reservoir are never contacted by the injected water. Therefore. it is necessary to consider the area1 sweep efficiency so as to make esti-

25

10, __--

05.

..,.....‘ . . ,

.

O- I 40 50

S,,WATER SAT”RAT%N,%P” 70

Fig. 44.10-Plot of df,/dS, example problem.


TABLE 44.5-WATERFLOOD DISPLACEMENT PERFORMANCE (Example Problem)

f s

Exit-&d Exi%d S

Flowing Stream df,/dS,, Ave;Yalge Water Consisting of Slope of W,, Water

Saturation Water Fractional PV of Cumulative Saturation (fraction PV) (fraction) Flow Curve Injected Water (fraction PV)

0.469 0.798 2.16 0.463 0.563 0.495 0.848 1.75 0.572 0.562 0.520 0.688 1.41 0.711 0.600 0.546 0.920 1.13 0.887 0.617 0.572 0.946 0.851 1.176 0.636 0.597 0.965 0.649 1.540 0.652 0.622 0.980 0.477 2.100 0.666 0.649 0.990 0.317 3.157 0.681 0.674 0.996 0.195 5.13 0.694 0.700 1.000 0.102 9.80 0.700

mates of recoverable oil for a particular project and to predict reservoir performance for waterflood operations.

The purpose of this section is (1) to present methods for determining area1 sweep efficiency for pattern flood projects, (2) to discuss factors that affect areal floodout patterns, and (3) to present correlating factors that are used to define areal sweep efficiency.

Methods of Determining Areal Sweep Efficiency. To conduct waterflood operations in a continuous reservoir with a relatively large area1 extent, it is common practice to locate injection and producing wells in a regular geometric pattern so that a symmetrical and interconnective network is formed. Five of these basic patterns will be discussed: (1) direct line drive, (2) staggered line drive, (3) five-spot, (4) seven-spot, and (5) nine-spot. 24.25 Figs. 44.llA through 44.llE are diagrammatic representations of these basic waterflood patterns. The dashed areas represent the basic symmetrical elements that are used in both analytical and model determinations of sweepout patterns.

It is often impractical or even impossible to design waterflood operations that correspond to one of the standard geometrical flood patterns. In such a case, the operator must select a less sophisticated well network-the choice being either a peripheral or random injection pattern.

The random flood pattern will not be considered specifically in this work because that type of flood is required only in certain explicit cases; it is used only when it is impossible to arrive at an arrangement of the peripheral or geometric type of pattern. Most of the material deal- ing with peripheral floods will apply generally to random waterflood networks. Fig. 44.12 is an illustration of the typical peripheral flood network. 26 It is obvious from this figure that there is no symmetrical element that could be considered for analysis, and that reservoir simulation techniques are necessary to obtain reliable future performance predictions for random or peripheral injection patterns. l7

Mathematical Analysis of Area1 Pattern Efficiency. Most practical mathematical analyses of flood coverage are based on Darcy’s law when it is assumed that steady- state single-phase flow occurs through large areas of homogeneous reservoir rock.

Muskat presents a comprehensive review of this theory in his early discussions of the steady-state flow ca-

Y

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 oPRODUClNG WELLS

4 2 ^ dg “‘C’C 2 0 0 0 T-1 o_ 0 0lNJECTlON WELLS

2 mx

0 0 0 0 0 0 0 0 0

Cl 0 0 0 0 0 0 0 0

0000 0 0 0 0

Fig. 44.1 l A-A diagrammatic representation of a direct-linedrive well network. Dashed segment represents basic symmetry element.

Y 1 0 0 0 0 0

T 0 0 0 0 0 0 0 0 0 0 0 0 Cl

0 0 0 0

d ,,_ a _

+X

Fig. 44.11B-A diagrammatic representation of the staggered- line-drive network.


0

0

0

0

0

0

0

---E 0 0 0

0 0

0 0

0 d !!I----

X

0

0

0 0

0

Fig. 44.11C-The five-spot well network. Dashed segment represents basic symmetry element.

pacity of the various pattern networks. As early as 1934, Muskat and Wyckoff28 presented a theoretical means of calculating area1 sweep efficiency for basic flood patterns. Fig. 44.13 is taken from their early work and it shows the variation in calculated steady-state homogeneous-fluid sweep efficiencies for linedrive networks with different values of d/u, where d is the distance between rows of

t--*--t--*---+--*--t--*--T

I I I I I

i o i o i o i o i

Fig. 44.1 lE-Nine-spot injection system showing the reservoir element represented by the model.

Y

t

Fig. 44.11D-The seven-spot well network. Dashed segment represents basic symmetry element.

wells and a is the difference between adjacent wells in a single row. The graph shows a curve for both direct linedrive and staggered linedrive patterns with d/u values from 0.45 to 4.0. Even though the absolute values of pattern efficiency presented in this illustration apply to a simplified system, there are two conclusions that can be drawn from the information: (1) at breakthrough, the staggered

0 0 0 0 0 0 0 0

( 0 0 0 0 0 0 0 0

( 0 0 0 0 0 0-a

( 0 0 x d d*:-? 0

0 0 0 ( 0 0 0 0

0 0 0 0 < 0 0 0 0

0 0 0 0

0 0 o-o- -”

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

) 0 0 0 0 c 0 0 0

0 500’ 1000’ SCALE W

Fig. 44.12-Typical random flood network

WATER-INJECTION PRESSURE MAINTENANCE & WATERFLOOD PROCESSES

04 /

I/ 02,

01 I I I I I I I I 0 04 08 1.2 1.6 2.0 24 28 32 36 40

Fig. 44.13-The variation of the calculated steady-state, homogeneous-fluid sweep efficiencies of line-drive networks with d/a = distance between the injection and producing lines/(well spacing within the lines). I = direct line drive and II = staggered line drive.

line drive will always result in a greater pattern efficiency than the direct line drive regardless of the value of d/u, and (2) the increase in pattern efficiency is rather insig- nificant for d/u values that are greater than 2.4.

Muskat presents steady-state equations for computing breakthrough time and breakthrough sweep efficiency for the several waterflooding networks. The numerical values of these idealized flow capacities and sweep efficiencies are the result of complex pressure distributions within the flood pattern. As the flood front advances through the pattern, the isopotential lines, which control the streamlines and pressure gradients, are constantly changing. How- ever, for the special case of a mobility ratio of one, it is possible to predict the pressure distribution and streamlines of a given pattern by reasonably simple analytical

56

55

54

53

52

51

50

49

48

47

Fig. 44.14-The steady-state, homogeneous-fluid equipressure contours and streamlines In a Iwo-well element of a direct-line-drive network. Numbers represent percentages of the total pressure drop.

Fig. 44.16-The steady-state, homogeneous-fluid equipressure contours and streamlines in a quadrant of a five-spot network element. Numbers represent percentages of the total pressure drop.

38 36 343228 0253033 35 37

Fig. 44.15-The steady-state, homogeneous-fluid equipressure contours and streamlines in a two-well element of a staggered-line-drive network. Numbers represent percentages of the total pressure drop.


Fig. 44.17-The steady-state, homogeneous-fluid equipressure contours and streamlines in a segment of a seven- spot-network element. Numbers represent percentages of the total pressure drop.

techniques. Figs. 44.14 through 44.17 are taken from Muskat and Wyckoffz8 and represent steady-state isopotential contours and streamlines for systems with homogeneous fluids that have direct linedrive, staggered

linedrive, five-spot, and seven-spot networks, respectively. When the isopotential lines and streamlines are known,

it is easy to determine the fluid interface position at any time during the flood by using the methods described by Craft and Hawkins. I2 In the particular case analyzed for a tive-spot pattern and a mobility ratio of 1 .O, depicted by Fig. 44.18, the calculated breakthrough sweep efficiency is 72 %. This corresponds to a value of 7 1.5 % that

52

54

55

56

57 58

2:

62 5

66

70

80

Fig. 44.18-Potentiometric model study of the five-spot network, showing the isopotential lines, the flow lines, and two flood fronts.

,. - . -- . .

Fig. 44.19-Flood between alternate lines of input and output wells

Fig. 44.20-Flood in five-spot array.


Fig. 44.21-Flood in inverted seven-spot array Fig. 44.22-Flood m seven-spot array

was computed by Muskat as the steady-state breakthrough sweep efficiency for the five-spot pattern at a mobility ratio of 1.0.

Analog Methods for Investigating Area1 Sweep Effi- ciency. Several types of analog models have been used in the petroleum industry to study the shape of injection- fluid fronts and to evaluate areal sweep efficiencies. All the models depend on the analogy between Darcy’s law and Ohm’s law for a conductive medium that is scaled to represent the reservoir geometry. One of the earliest of these analo Wyckoff et al. 59

s is an electrolytic model designed by Its operation is based on the movement

of copper ammonium and zinc ammonium ions in a medium such as blotting paper or gelatin. Figs. 44. I9 through 44.22 are photographic histories of various pattern floods under steady-state, homogeneous-fluid flow conditions, as obtained by using a blotter-type electrolytic model. Fig. 44.23 shows the same type of photographic history but it represents an irregular well network and was obtained with the gelatin type of electrolytic model. 3o

The potentiometric model was introduced to the industry in 1939 by Swearingen3’ as a method for studying sweep efficiency in gas-cycling operations; the model has been further refined for waterflood studies by Hurst and McCarty 32 and Lee33 The potentiometric model is based on the same basic principle as the electrolytic model except that electron flow, rather than ionic flow, is measured.

Porous Reservoir Models. The approach presented by Slobod and CaudleM is another that has been used by the petroleum industry for studying areal pattern efficiency; this involves scaled porous models of the reservoir element. The model initially is saturated with a fluid that rep-

resents the reservoir oil. Injected fluid in this case contains an X-ray-absorbing material and the displacing front can be followed on a fluorescent screen or X-ray film. Fig. 44.24 is an X-ray shadowgra

7! h study of the five-spot

model by Slobod and Caudle.. An areal sweep efticien- cy at breakthrough for the 1 : I mobility system is indicated as 69%

Two-Dimensional (20) Numerical Models. In an early paper describing the use of numerical models in predicting flood coverage for a peripheral, or random, water injection program, McCarty and BarfieldZh presented results obtained for two typical field studies, as shown in Figs. 44.25 and 44.26. In this approach, the computer is used to perform essentially the same calculations as those described by Muskat, with the reservoir defined by a grid network. A valid method of numerical analysis is used to allow solution of the basic differential equations that describe the simultaneous flow of oil and water. As is true of the methods described by Muskat and Wyck- off, 28 Stahl, 35 and Craft and Hawkins, I2 the digital computer calculates the pressure distribution in the reservoir and then tracks the progress of the interface between the displacing and displaced phases.

This calculation can be done for any combination of injection and producing rates. The approach will allow the calculation of the optimal sweep efficiency under a particular pattern as a function of reservoir injection and producing rate distribution.

Mobility-Ratio Effects. In the previous discussion of various methods of studying areal sweep efficiency, it is important to realize that each technique is based on the assumption that isopotential lines remain fixed during the advance of the front; that is. that the mobility of the dis-

PETROLEUM ENGINEERING HANDBOOK

lnput=30.8% of Area 1

hput = 82 % of Area 2

Input 130% of Area 3

Composite Flood 5

Input 195% of Area 4

Fig. 44.23-The photographic history of the injection-fluid fronts in an injection project of limited area and with an irregular well distribution, under steady-state, homogeneous-fluid-flow conditions as obtained with a gelatin electrolytic model. Double circles indicate injection wells.

Fig. 44.24-Typical radiograph showing areal sweepout efficiency for the five-spot well spacing. Mobility ratio = 1.

0 INJECTION WELL

. PRODUCTION WELL

t, EQUAL-TIME LINE

Fig. 44.25-Typical flood pattern resulting from field study.

placing fluid is the same as that of the displaced phase. However, it is well known that isopotential lines change constantly during most injection operations. Consequent- ly, the actual pattern efficiency that will result in the reservoir can be quite different from that indicated by a simplified analysis that assumes a mobility ratio of 1.

The mobility ratio is probably the most important factor involved in determining pattern efficiency. Even though the methods previously cited were based on the assumption of a mobility ratio of unity, it does not mean that they are not of practical use, and the resulting information has served as a basis for further experimental investigations of certain geometrical characteristics that come into play during waterflood operations.

Although the early analog models that were used for studying pattern efficiency did not take into consideration the mobility-ratio effects, later investigations have made use of ingenious ideas to circumvent this restric- tion. Burton and Crawford36 described an electrolytic model that has been used to estimate flood coverage by mobility ratios of 0.5,0.85, 1.2, and 3. In that work, the

WATER-INJECTION PRESSURE MAINTENANCE 8. WATERFLOOD PROCESSES 44-1s

INJECTION WELL

PRODUCTION WELL

EQUAL-TIME LiNE

Fig. 44.26-Typical flood pattern resulting from field study.

adjustment for mobility ratios was accomplished through the use of metallic complex ammonium ions other than the copper and zinc compounds used by Wyckoff et al. 29 Aronofsky 37 has been able to include mobility ratios other than unity in a special ada

P tation of the potentio-

metric model. Nobles and Janzen 8 have presented a variation of the potentiometric model by replacing the liquid with a system of interconnecting resistors; by changing the values of these resistors, they were able to introduce mobility-ratio effects.

The most logical model with which to study mobility- ratio effects is a porous model, or, specifically, a porous model that uses X-ray shadowgraph techniques. In this type of analysis, the injection and displaced phases may be selected so that almost any mobility ratio can be fixed in the reservoir model. Experimental studies by Slobod and Caudle34 take advantage of this feature of the X-ray shadowgraph technique, so that liquids of different viscosities can be used as the displaced and displacing phases and the effect of mobility ratios can be evaluated. Their original work has been extended by Caudle et al. 3y Fig.

RECIPROCAL OF MOBILITY RATIO ~2.2

RECIPROCAL OF

/

RECIPROCAL OF MOBILITY RATIO=O.B

Fig. 44.27-Areal sweepout patterns, five-spot well spacing.

RECIPROCAL OF MOBILITY RATIO

Fig. 44.28-Sweepout pattern efficiency vs. reciprocal of mobility ratio for the five-spot well spacing.

44.27 is an X-ray shadowgraph that shows the effects of the reciprocal of mobility ratio on sweep efficiency at breakthrough for three different reciprocals of mobility ratios. Fig. 44.28 is a plot of the reciprocal mobility ratio vs. five-spot pattern sweepout efficiency at breakthrough. It is apparent from these illustrations that there is little change in breakthrough efficiency for reciprocal mobility ratios that are greater than 7.

In his monograph, Craig4 has summarized the area1 sweep efficiency studies that have been presented in the literature for various flooding patterns. These summaries are listed in Tables 44.6 through 44.12.

Fig. 44.29 is a plot of the area1 sweep efficiencies at breakthrough that were developed as a function of mobility ratio by the various investigations referenced in Ta- ble 44.7. As indicated, there is good agreement in the region below a mobility ratio of 1 .O; however, considerable deviation exists at higher mobility ratios. Craig4 points out that potentiometric model data obtained for high mobility ratios may yield high sweep efficiency values and that miscible displacement methods may give low re-


TABLE 44.6-AREAL SWEEP EFFICIENCY STUDIES-LINEDRIVE PATTERNS

Date Author(s) Method

1933 Wyckoff et a/. electrolytic model 1934 Muskat and Wyckoff electrolytic model

1952 Aronofsky numerical and potentiometric model

1952 Slobod and Caudle X-ray shadowgraph using miscible fluids

1954 Dyes et al. * X-ray shadowgraph using miscible fluids

1955 Cheek and Menzie fluid mapper 1956 Prats numerical approach 1956 Burton and Crawford gelatin model

Line Drive

direct direct

staggered

direct

direct direct

staggered direct

staggered direct

d/a

1.0 0.5 to 4.0 0.5 to 4.0

1.5

1.5 1 .o 1 .o 2.0

.O to 6.0 1 .o

Mobility Ratio

1.0 1 .o

0.1. 1.0. 10

0.1 to 10 0.1 to 17

0.04 to 11.0 1.0

0.5 to 3.0

‘After-breakthrough perlormance also presented I” these references

Reference

29 28

37

34 40

41 42 36

TABLE 44.7-AREAL SWEEP EFFICIENCY STUDIES-DEVELOPED FIVE-SPOT

Date Author(s) Method

1933 Wyckoff et al. electrolytic model 1934 Muskat and Wyckoff electrolytic model 1951 Fay and Prats numerical 1952 Slobod and Caudle X-rav shadoworaph using

1953 Hurst 1954 Dyes et al. *

1955 Craig et al. ’

1955 Cheek and Menzie 1956 Aronofsky and Ramey 1958 Nobles and Janzen 1960 Habermann

1961 Bradley et al.

‘After-b reakthrough performance also ,,re sented ,n these references

miscible-fluids - numerical

X-ray shadowgraph using miscible fluids

X-ray shadowgraph using immiscible fluids

fluid mapper potentiometric model

resistance network fluid flow model using

dyed fluids potentiometric model

using conductive cloth

Mobilitv Ratio’

1.0 1.0 4.0

0.1 to 10 1.0

0.6 to 10

0.16 to 5.0 0.04 to 10.0

10 to 10.0 0.1 to 6.0

0.037 to 130 46

0.25 to 4 47

Reference

29 28 43

34 44

40

45 41 37 38

TABLE 44.6-AREAL SWEEP EFFICIENCY STUDIES-NORMAL AND INVERTED FIVE-SPOT PILOT’

Mobility Date Author(s) Method Type Ratio

1958 Paulsell’ * fluid mapper inverted 0.319 1.0 2.01

1959 Moss et al. potentiometric inverted 1960 Caudle and Loncaric” X-ray shadowgraph normal 0.1 tom10.0 1962 Neilson and Flock rock flow model inverted 0.423

Areal Sweep Efficiency at Breakthrough

(W Reference

117.0 48 105.0 99.0 92.0 49 t 50

110.0 51

‘iNote base area=a’. where a IS the distance between adwent producing wells) “After.breakthraugh performance also presented !n these relerences ‘Depends on ratlo of ,“,ect,on rate to prodwng rate.

suits because of mixing. As a result, he concluded that the most probable value of sweep efficiency at high mobility ratios for the five-spot pattern is represented by the solid line of Fig. 44.29. Breakthrough sweep efficiencies obtained later, from investigations with numerical methods conducted in 1979 by Martin and Wegner,s6 are in agreement with this conclusion.

There are insufficient data for patterns other than the five-spot to allow a comparison of the results obtained by various investigators: however, the correlations shown

in Figs. 44.30 through 44.48 are standards in the industry for determining areal sweep efficiency relationships for the normal patterns. In these figures,

Vd = displaceable PV’s injected. fraction, f, = fraction of total flow coming from the

swept portion of the pattern, fjc,l, = corner well producing water cut, and fj,r,l, = side well producing water cut.

WATER-INJECTION PRESSURE MAINTENANCE 8. WATERFLOOD PROCESSES 44-21

TABLE 44.9-AREAL SWEEP EFFICIENCY STUDIES-DEVELOPED NORMAL SEVEN-SPOT PATTERN

Mobility Date Author(s) Method Ratio

1933 Wyckoff et al. electrolytic model 1.0 1934 Muskat and Wyckoff electrolytic model 1.0 1956 Burton and Crawford* gelatin model 0.33

0.85 2.0

1981 Guckert’ X-ray shadowgraph using 0.25 miscible fluids 0.33

0.5 1.0 2.0 3.0 4.0

‘After-breakthrough performance also presented I” these references

Areal Sweep Efficiency at Breakthrough

W) Reference

82.0 29 74.0 28 80 5 36 77.0 74.5

88.1 to 88.2 52 88.4 to 88.6 80.3 to 80.5 72.8 to 73.6 68.1 to 69.5 66.0 to 67.3 64.0 to 64.6

TABLE 44.10-AREAL SWEEP EFFICIENCY STUDIES-DEVELOPED INVERTED (SINGLE INJECTION WELL) SEVEN-SPOT PATTERN

Date Author(s)

1933 Wyckoff et al.

Method

electrolytic model

Ratio*

1.0

Areal Sweep Efficiency at Breakthrouah

(%) -

82.2

Reference

29 1956 Burton and Crawford” gelatin model 0.5 77.0 36

1.3 76.0 2.5 75.0

1961 Guckert* X-ray shadowgraph using 0.25 87.7 to 89.0 52 miscible fluids 0.33 84.0 to 84.7

0.50 79.0 to 80.5 1.0 72.8 to 73.7 2.0 68.8 to 69.0 3.0 66.3 to 67.2 4.0 63.0 to 63.6

‘After-breakthrough performance also presented m these references

TABLE 44.11 -AREAL SWEEP EFFICIENCY STUDIES- DEVELOPED NORMAL NINE-SPOT PATTERN

Mobility Date Author Method Ratio Reference

1939- Krutter Electrolytic 1961 Guckert’ modet 1.0 53

X-ray shadowgraph using miscible fluids 1.0 and 2.0 52

‘After breakthrough performance also presented m this reference

TABLE 44.12-AREAL SWEEP EFFICIENCY STUDIES-INVERTED (SINGLE INJECTION WELL) NINE-SPOT PATTERN

Date Author Method

1964 Kimbler et al.’ X-ray shadowgraph using miscible fluids 1964 Watson et al.’ fluid flow model using dyed fluid

‘Afler-breakthrough performance also presented in these references

Mobility Ratio Reference

0.1 to 10.0 25 0.1 to 10.0 54


PATTERN AREA

Fig. 44.29-Areal sweep efficiency at breakthrough, developed five-spot pattern.

I.0 MOBILITY RAT?l

100

0 r-b-7 0

! ,

0 L.-,-l A

PATTERN AREA

REF. . 29 x 40 0 36

Fig. 44.30-Areal sweep efficiency at breakthrough, developed Fig. 44.33-Effect of reciprocal mobility ratio on oil production direct line drive, d/a = 1 .O. for the direct line drive (square pattern); d/a = I.

I I 4o0.1

Ill1 I IllI I !I11 I.0 MOBILITY PA:&

I.9”

0 r-O-7 0 I I Id h--a--h

PATTERN AREA

REF. - 0 26 0 40 . 36

Fig. 44.31-Areal sweep efficiency at breakthrough, developed staggered line drive, d/a = 1 .O.

0.1 02 04 0.608 I 2 456 810 20 30 RECIPROCAL OF MOBILITY RATIO

Fig. 44.32-Effect of reciprocal mobility ratio on the displaceable volumes injected for the direct line drive (square pattern); d/a = 1.

100

90

l-80 b Y m”70

G

, 1 /IIt I

060.610 20 40 608010 20 30 RECIPROCAL OF MOBILITY RATIO

01 0.2 0.4 0.60.8 1.0 20 40 6.08010 20 30 RECIPROCAL OF MOBILITY RATIO

Fig. 44.34-Effect of reciprocal mobility ratio on the displaceable volumes injected for the staggered line drive; d/a = 1.



Fig. 44.35-Effect of reciprocal mobility ratio on oil production for the staggered line drive; d/a = 1


Fig. 44.36-Effect of reciprocal mobility ratio on the displaceable volumes injected for the five-spot pattern.

90

60

50 01 0.2 0.4 0608lO 20 40 601


Fig. 44.37-Effect 01 reciprocal mobility ratio on oil production for the five-spot pattern.

PATTERN AREA

REf. - 29 : 28 . 36 0 52

0

Fig. 44.36-Areal sweep efficiency at breakthrough, developed normal seven-spot pattern.

o-- 4, ,’ i

d’ n ‘0 \

\ i’ ‘O-- -+’

PATTERN AREA

REF.

. 29 3 36 ’ 52

Fig. 44.39-Areal sweep efficiency at breakthrough, developed inverted seven-spot pattern.

Fig. 44.40-Sweepout pattern efficiency as a function of mobility ratio for the nine-spot pattern at various displaceable volumes injected.


Fig. 44.41-Sweepout pattern efficiency as a function of mobility ratio for the nine-spot pattern at various side-well producing cuts ( f,,).

PRODUClNG RATE RATIO no.5 SIDE WELL ABANDONED AT 11,. *0.99

Fig. 44.42-Sweepout pattern efficiency as a function of mobility ratio for the nine-spot pattern at various corner- well producing cuts ( f,C,).

PRODUCING RATE RATIO . ,.O SIDE WELL ABANDONED AT 11,. * 0.99

Fig. 44.43-Sweepout pattern efficiency as a function of mobility ratio for the nine-spot pattern at various displaceable volumes injected.

PRODUCING RAlE RATIO I I.0 SIK WELL ADANDOWEO AT I,,. * 0.99

1.0

Fig. 44.44-Sweepout pattern efficiency as a function of mobility ratio for the nine-spot pattern at various side-well producing cuts ( f,,,).

Fig. 44.45-Sweepout pattern efficiency as a function of mobility ratio for the nine-spot pattern at various corner- well producing cuts ( f,,,).

pnoDucIN0 RATC RATIO .0.0 910~ WELL AOANDOWLD LT (I,. * 0.~3

Fig. 44.46-Sweepout pattern efficiency as a function of mobility ratio for the nine-spot pattern at various corner- well producing cuts ( f,,,).


PRODUCING RATE RATIO .J.,,

SIDE WELL A8ANDONEO AT f,,. . 0 95

Fig. 44.47-Sweepout pattern efficiency as a function of mobility ratio for the nine-spot pattern at various side-well producing cuts ( f,,,).

Effect of Reservoir Dip. The effect of reservoir dip on five-spot sweep patterns has been investigated by Mat- thews and Fischer. 57 It was found that distortion would occur in the normal sweepout patterns in dipping reservoirs. Most of this distortion was attributed to gravitational effects. The conclusion reached in this study was that pattern flooding is practical for dipping reservoirs but that the pattern should be shifted to allow for dip. Figs. 44.49 through 44.52 are charts that show how to locate wells correctly for pilot and field five-spot floods in reservoirs that

N= SF =

ha;e substantial dip. In these figures,

ratio of square root of production rates, position of center of unflooded area at

moment of fill-up (correct drilling location) fraction of length of side or diagonal,

FF = ratio of viscous to gravity forces defined by

P= 4=

F = “8

fluid viscosity, poise, injection rate before interference,

so -so,

s, -s,, 3

so = so, = s, =

s,, =

oil saturation at start of flood, fraction, ROS, fraction, gas saturation at start of flood, fraction,

and residual gas saturation, fraction.

Prats er al. 58 have made analytical studies of the same problem. Van der Poe1 and Killian have made analytical and analog studies to investigate the area that can be swept out in dipping reservoirs by using water drive around the structurally highest wells.

Fig. 44.48-Sweepout pattern efficiency as a function of mobility ratio for the nine-spot pattern at various corner- well producing cuts ( f,,).

Effect of Directional Permeability. Some formations exhibit differences in reservoir permeability in one horizontal direction relative to another. When this situation is encountered, it is apparent that pattern sweep efficiencies will be affected adversely when the direction of high permeability is between an injector and a producing well. The initial study to determine the effect of directional permeability on the area1 sweep performance of a five-spot pattern flood was made by Hutchinson. 6o If the X-ray shadowgraph technique is used and a directional permeability difference of 16 to 1 is considered, the data shown in Figs. 44.53 and 44.54 are obtained for mobility ratios varying from 0.1 to 10. It is apparent from these data that improved sweep efficiency results when the pattern is oriented with the direction of maximum permeability, parallel to a line passing through the injection wells. In later investigations, Landrum and Crawford6’ and Mortada and Nabor6* also studied the effects of directional permeability on five-spot and linedrive patterns. The results of their studies confirm the data obtained by Hutchinson. ho

Effect of Reservoir Fractures

In 1958, Dyes et ~1. 63 presented one of the most comprehensive studies of the effect of vertical fractures on sweepout pattern efficiencies. Their investigations showed that relatively long and highly conductive vertical fractures, not usually obtained from fracturing operations, are required to affect sweep efficiencies substantially. Other investigations 64-67 have confirmed the results of Dyes et al. ; these show that vertical fracturing can affect breakthrough sweep efficiency significantly, but that sweep efficiency at higher water cuts is influenced to a much lesser degree. Table 44.13 is a summary of the results obtained by Dyes et al. 63

Landrum and Crawford68 have investigated the effect of horizontal fractures on sweep efficiency in thick reservoirs. The results of their studies, along with those of other investigators, 36,69,70 show that the adverse effect


Fig. 44.49-Correct location of production well in pilot five-spot-side along strike

Fig. 44.50-Correct location of production well in pilot five-spot-diagonal along strike

of horizontal fractures on areal sweep efficiency is a direct function of fracture radii; that is, only small effects were observed on sweep efficiency when the fractures had small radii. However, as the fracture radius increases, sweep efficiency will be reduced drastically.

Methods for Predicting Waterflood Performance There are many papers and articles in the petroleum industry literature that present or discuss methods for predicting waterflood or water-injection performance. Most

of the classic prediction techniques that have been developed since the early work by Muskat, Stiles, I9 Buckley-Everett, 2o Dykstra-Parsons, I5 and others have been modifications, enhancements, or extensions of those pioneering techniques, which were discussed in the ini-

tial part of this section. In many cases, those techniques, when combined with data obtained from area1 sweep investigations, provided the basis from which several of the methods were conceived and developed.


Fig. 44.51-Correct location of production wells in a field of five-spots-side along strike.

Fig. 44.52-Correct location of production wells in a field of five-spots-diagonal along strike.

In his monograph, Craig4 has described and compared the classic prediction methods that were presented before 197 1, and has included recommendations for selecting the appropriate waterflood prediction technique to obtain the desired results. The methods that were considered were categorized into five groups, which may be summarized as follows: (1) reservoir heterogeneity (Refs. 15, 19, 22, and 71 through 80), (2) area1 sweep methods (Refs. 25, 28, 34, 37, 40. 50, 55, and 81 through 85), (3) displacement mechanism (Refs. 20, 21, 45, and 86 through 97), (4) numerical methods (Refs. 98 through 103), and (5) empirical approaches (Refs. 104 through 107).

Craig’s monograph is certainly the most comprehensive review and evaluation of the techniques for predicting waterflood performance that has appeared in the petroleum industry literature.

Craig compared the capabilities of each method that was evaluated to the capabilities of the “perfect method,” in which the calculation procedures would allow consideration of all pertinent fluid-flow, well-pattern, and heterogeneity effects-i.e., the influence of relative permeability characteristics, wettability, pore size distribution, and initial and final water and oil saturations; the effect of different well arrangements and mobility ratio on injection rate


Fig. 44.53-Sweepout pattern efficiency in a five-spot pattern of anisotropic horizontal permeability. The most favorable arrangement has the direction of maximum permeability parallel to lines through injection wells, as illustrated here.

'"r

Fig. 44.54-Sweepout pattern efficiency in a five-spot pattern operating under the least favorable arrangement; i.e., with the direction of maximum permeability parallel 10 a line from an injection well direct to a producing well.

and area1 sweep efficiency; and the effect of the heterogeneity of the reservoir rock recovery and performance.

Table 44.14 shows Craig’s evaluation of these techniques, as compared to the “perfect method.”

Of the many classic methods that were evaluated, Craig has concluded that the three that most closely meet the requirements of the “perfect method” are Hi ins- Leighton, 93-95.97 Craig et al. 4.108 and Prats et al. !G, 108

The Higgins-Leighton method can be used for: various flooding patterns or for irregular well patterns;while the other two can be applied only for the five-spot pattern. Computer programs for the Higgins-Leighton and Craig et al. techniques are available in the literature. Examples of the calculation procedures and compbe descriptions of the techniques also can be found in the literature. The

best, detailed description of the Higgings-Leighton technique is given in Ref. 97. Complete and detailed calculations for an example waterflooding problem that was solved by the Crai

zi et al. technique are

B resented in

Craig’s monograph and by Timmerman. ’ 8 An example of the use of the Prats et al. technique is also presented by Timmerman. lo8

Other authors have compared results obtained by a num-

ber of the classic methods with actual field performance. Abernathy ‘09 compared the observed performance of five-spot waterfloods in three carbonate reservoirs in west Texas with the performance predicted by the Stiles,‘” Craig et al.,45 and Hendricksongo techniques. Figs. 44.55 through 44.57 show these comparisons.

TABLE 44.13-EFFECT OF VERiTlCAL FRACTURES ON FIVE-SPOT PATTERN SWEEP PERFORMANCE: FRACTURES IN IYNE WITH INJECTION-PRODUCTION WELL DIRECTION

Fracture Length (Fraction of Distance Between

Fractured Injector and Producer)

Unfractured

M 0.1 1.1 3.0 0.1 1.1 3.0 0.1 1.1 3.0 0.1 1.1 3.0 0.1 1.1 3.0 0.1 1.1 3.0 0.1 1.1 3.0

Areal Sweep Efficiency (%)

90% Breakthrough Watercut

99 99 72 99 56 92 93 98 45 96 39 92 88 98 37 96 28 92 33 97 14 93 IO 83 78 98 43 95 40 88 38 98 24 96 22 92 18 98 13 94 9 07

Throughput at 90% Watercut (Displaceable PV)

1.0 1.8 2.2 1 .o 1.7 2.2 1.1 I .a 2.7 1.2 2.3 3.8 1.1 1.6 1.9 1.2 1.7 2.1 1 .a 2.3 3.3



Fig. 44.55-Calculated vs. actual performance of Panhandle field.

Fig. 44.56-Calculated vs. actual performance of Foster field pilot.

Fig. 44.56-Comparison of actual and predicted recovery history, Flood 1.

Fig. 44.59-;;m$~~ of actual and predicted oil recovery,

Guerrero and Earlougher lo6 compared the actual and predicted performance of two floods. The predictive methods that were compared included Stiles’, modified Stiles’, Dykstra-Parsons’, Prats et al. ‘s, and the empirical approach developed by Guerrero and Earlougher. The results of these comparisons are shown in Figs. 44.58 through 44.61. (Also see Ref. 4, Figs. 8.16 through 8.19.) Higgins and Leighton% compared the results obtained by using their method with actual field performance and with predicted performance obtained by the methods of Prats el al. and Slider.74 This comparison is shown in Fig. 44.62. (Also see Ref. 4, Fig. 8.20.)

It is obvious from these comparisons that the fields do not always perform as predicted regardless of the method that is used to estimate future performance. This is true for many reasons, including (1) an incorrect or inadequate description of the reservoir rock, fluid, and water/oil flow properties, (2) a prediction technique that does not have the capability to consider all the factors that affect waterflood performance, and (3) the fact that there is always a question of the reliability of the estimates of the inter- well character of the reservoir rock and the vertical and horizontal variations that exist in reservoir rock and fluid properties.


Fig. 44.60-Comparison of actual and predicted recovery history, Flood 2.

Fig. 44.61-Comparison of actual and predicted oil recovery, Flood 2

The prediction techniques selected as most promising by Craig4 appear to deserve primary consideration when one of the classic techniques is being selected for pro- jecting future reservoir performance under waterflood operations. The comparisons made by Abernathy lo9 show the Craig-Stiles multilayer method to be capable of making predictions that yield a good match with actual reservoir performance. In the Guerrero and Earlougher comparison, the Prats et al. method performed very well in the case of Flood 2 but erred badly with respect to oil recovery in the prediction of the behavior of Flood 1. The Hig- gins and Leighton method gave a good comparison with respect to actual performance in the case presented.

Since the time when Craig made his evaluation and comparison of the classic prediction methods that were available, reservoir simulation models have continued to be improved and expanded to the point that, today, there are models available for prediction of waterflood or water- injection performance under a variety of conditions. The reservoir simulation models that are available to the industry at present are capable of considering any type of flooding pattern, as well as gravity, capillary, and viscous forces, with virtually any type of three-dimensional (3D) reservoir description. The initial developments of the numerical methods were made by Douglas et al. 98 in 1958, and this work was later extended to two dimen- sions by Douglas ef al. Iw in 1959. Since that time, numerical models and reservoir simulation techniques have improved continuously, in step with the increased speed and storage capacity of the computing systems that have become available.

Although the subject of reservoir simulator development and application has been covered in another section of this handbook, it is important to emphasize that the simulation models and techniques that are presently available to the industry are capable of modeling the most complex reservoir systems. With the use of these tools, predictions of waterflood and water-injection performance can be made in such detail that almost every factor that affects reservoir and individual well behavior can be considered and simulated.

Selection of the Waterflood Prediction Method When choosing the appropriate waterflood prediction method, the engineer must bear in mind the objective in

‘r, PRATS ET AL. METHOD

d 0.2 04 0.6 0.6 1.0 1.4

CUMULATIVE INJECTION IN FLOODABLE ::LUMES

Fig. 44.62-Comparison of field behavior with predicted perfor- mances by the Prats et al., Slider, and Higgins- Leighton methods.

making the recovery predictions, the amount and quality of basic data that are available, and the resources that are available for performing the calculations in light of both the manpower that will be necessary and the actual costs for computer use or data processing. In some instances, a simple estimate of ultimate oil recovery may be sufficient and, in fact, it may be the only reliable estimate possible because of data limitations. However, in most cases, more detailed projections will be required to evaluate the economic potential of the proposed project; and a method must be used that will allow the estimation of future well requirements, producing WOR’s, producing rates, oil recovery, injection well requirements, and injection rates and distribution, all as functions of time.

The methods available to the reservoir engineer range in complexity from those that provide an estimate of ultimate recovery to those that use sophisticated reservoir simulation models that are capable of predicting both reservoir and individual well performance for water injection operations. However, the time requirements and costs for making the calculations are in direct proportion


16

2 14

”

i? F 12

6 ” >- 10 t-

8

fi 0.8 REINHOLD PUBLISHING CORR

5 P 3 06

4

: 0.4

0.2

0 0 50 loo 150 200 250 300 350

TEMPERATURE DEG F

Fig. 44.63-Viscosity of water at oilfield temperatures and pressures.

to the complexity of the technique used. The engineer must choose the method for predicting performance while taking into account the availability of time and resources and the reliability and quantity of the basic data at hand.

The most basic evaluation is that of defining the ultimate oil recovery to be expected from the project. This can be determined by using the Welge*’ technique or by estimating ROS’s and conformance. Empirical approaches are also available to provide these estimates if data are limited. Guthrie and Greenberger ‘04 have developed an equation, based on waterflooding experience in a number of sandstone reservoirs, that has proven effective for estimating the ultimately recoverable oil. The equation is as follows:

ER =0.2719 log k+0.25569S,.--0.1355 log p0

- 1.5380$-0.0003488h+0.11403, . . . . . (14)

where ER is the oil recovery efficiency, fraction, and h is the formation thickness, ft.

Another equation that is applicable in estimating the ultimate recoverable oil was developed by an API committee. lo7 The relationship developed by this committee is as follows.

ER co.54898 [ “;;w)] “04** (%) “O”

-0.2159 )((S )-0.1903

w (13

where pi is the initial pressure and p(, is the pressure at depletion (abandonment).

When a projection of producing WOR as a function of oil recovery is required, the basic methods that are available are those developed by Stiles, I9 Slider,74 and others. These procedures allow a prediction of the water- cut performance of the waterflood as well as the ultimate recovery. The published correlation charts of Johnson,” based on the data developed by Dykstra-Parsons, I5 will allow a quick prediction of future waterflood performance.

For a more detailed projection of future performance, Craig4 has suggested the technl;$ues proposed “,x Higgins-Leighton,93-97 Craig et al., and Prats et ul. These techniques require considerably more engineering time and more reservoir data than do the basic calculations, but they will enable projections to be made in sufficient detail so that an economic analysis of the project can be made for comparison with the projected return that might be expected as a result of alternative operational programs.

The complex reservoir simulation models that are available to the industry today can produce projections of water injection performance that consider all the factors that influence the behavior of the injection operation. Their use requires a detailed description of the reservoir rock, fluid, and fluid-flow properties, as well as the characterization of individual wells. When the basic data are available for future performance predictions, there is no doubt that the simulation approach will produce the highest confidence level that is attainable with today’s technology. When compared to the other alternatives that are available, reservoir simulation approaches are expensive; however, if used properly, these techniques will enable a complete evaluation of the potential of a proposed water injection project.

The engineer has many choices available in selecting the approach that he will use to evaluate a prospective water injection operation. To repeat, the selection should be made while bearing in mind the overall objectives of the evaluation, the resources that are available, and the data that are either immediately available or that can be obtained within the imposed time or monetary limitations.

Water-Injection Well Behavior The initial water-injection rate of a well depends on the (I) effective permeability, (2) oil and water viscosity, (3) sand thickness, (4) effective well radius, (5) reservoir pressure, and (6) injection pressure at the sandface. As water begins to fill the reservoir, other factors are introduced to affect the behavior of the injection well. These factors are influenced by the increase in flow resistance as water extends into the reservoir and by the quality of the injection water.

The fundamental equation 24 for the rate of water injection into a well is expressed as

1 h, = 0.00708k,h(Pi,f-p,)

. . . . . CLn ln(r,,r,) (16)

There are numerous uncertainties that make quantitative applications of the equation difficult. They do not, however, impair its usefulness in ex laining the relative importance of each of the factors. ’ P o


I. Effective Permeability. The symbol k,,. denotes the effective permeability (millidarcies) of the sand to water. According to laboratory work on clean sands, the relative permeability to water ranges from 30 to 60% of the dry permeability as the water saturation varies from 70 to 85 % Tests on virgin and artiticially oil-saturated cores show that the effective permeability of the sand to water is often less than one-tenth ofthe dry permeability. When- ever possible, the effective permeability to water should be determined on representative cores from the field.

2. Viscosity. The viscosity (centipoise) of the injected water, pa., can be measured, or a value approximated, from Fig. 44.63.

3. Sand Thickness. The sand thickness, h, is the net effective sand thickness (feet) of the interval that is open for injection.

4. Pressure. The bottomhole flowing injection pressure, pi,,:f, (pounds per square inch) at the sand face can be estimated from the wellhead pressure, the depth of the well, the density of the water, and the flowing pressure gradients. pr is the effective reservoir pressure (external boundary pressure).

5. Well Radius. The effective radius of a well, rw. (feet) may vary from a few inches to several feet, depending on the type of completion.

6. Pressure Radius. The pressure radius (external boundary radius), r,, can be estimated, at least roughly, from the amount of water that is injected and from the available pore space, and is the distance from the injection well where the pressure is pe. The available pore space is defined as the total PV less that occupied by interstitial water and oil. As more and more water is injected, the pressure radius, re, in Eq. 16 increases and, therefore, the injection rate, i,,, must decrease with time.

The pressure radius, rc, depends on the cumulative volume of water that is injected into the space that is available, in accordance with the equation

) . . . . . (17)

where Wj is the cumulative water injected, bbl. The oil may or may not be moved by the advancing

water. If the oil is not moved, the water will fill the gas space. If the oil is moved ahead of the water bank. the volume of injected water that is required to fill the reservoir with liquids (oil and water), for a given distance (to external radius), will still be the same as that which was originally necessary to fill the gas space.

If a large percentage of oil is being moved, Eq. I6 does not hold strictly true, and a more exact expression prior to interference is

I ,,. = 0.00708hk,,,(P,,,5-Pr)

(~,,,lk,,.)ln(R,,/r,, )+(~L,/k,)ln(R,lR,,.) ’ (18)

where R ,,. is the outer radius of the waterflood front and R, is the outer radius of the oil bank.

As a rule, the width of the oil bank is small in comparison to the radius of the encroached water so that very little error will be introduced by considering the simpler

c3 2 8 ;;8 B E7 a &6 a $5 a ?I4 E a 3

9 1

r 2

9 1

e 2 7 40 80 120 160 200 240 280 320 360 400 440 480 =

TIME-DAYS

Fig. 44.64-Five-spot pattern computed input well history

case. The change in intake rate with time can be calculated by Eq. 19.

0.0253kApt =I+

0.0142khAp

/-h.4q(h4* -1

P II’ 1 M’ >

x 1@00617WNy.,, I,,) . . . . . . . . . . . . . . . . . . (19)

Eqs. 16, 18, and 19 can be applied to a single-well system (radial flow); however, they are not valid for pattern floods after interference has occurred between injection wells. When interference occurs, the advancing liquid converges on the producing well and, for mobility ratios near unity, finally stabilizes at the steady-state conductivity of the specific pattern. The effect of interference on a five-spot pattern for a system with a favorable mobility ratio (MS 1) is as shown in Fig. 44.64.

Muskat and Deppe 84 have developed equations for calculating the steady-state injectivities for the normal flooding patterns when a mobility ratio of one is considered. These equations are as follows.

Five-spot pattern24 :

O.O01538k,hAp 1 MI = . . . .

>

(20)

Direct line drive24 :

for drl, a

O.O01538k,,,hAp I ,I’ = (21)

p,,. log? f0.6821-0.798 rI,, a >

PETROLEUM ENGINEERING HANDBOOK

' il

01

j

01 10 IO

Fig. 44.65-Conductance ratio as a function of mobility ratio and the pattern area swept (E,), five-spot pattern.

Staggered line drive24 :

for !>l, a

O.O01583k,hAp I, - , . . . . (22)

pLw log? +0.682! -0.748 rH a >

where d is the distance between rows of wells, ft and a is the distance between wells in a row, ft.

Seven-spot pattern 84 :

O.O02051k,,hAp I,<, = . . . . . . . . . . . .

>

(23)

Inverted nine-spot patterns4 :

. . . . . . . . . . . . . . . . . . . (25)

where d=

FP =

AP;~ =

@is =

distance between rows of wells, corner-to-side-well producing-rate ratio, pressure differential between injection well

and corner well, and pressure differential between injection well

and side well.

These equations allow the determination of the steady- state injectivities for the normal patterns if it is assumed the system is completely filled with liquid and has a mobility ratio of one.

There are a number of papers that report the results of investigations to define the variation of injectivities for the five-spot pattern at mobility ratios that are other than one. Various techni ues were used. Deppeg4 and

95 Aronofsky and Ramey used potentiometric model techniques; Caudle and Witte8* used the X-ray shadowgraph technique and a porous model of the reservoir element. In the Caudle and Witte study, ‘* one-eighth of the five- spot pattern was modeled. Nobles and Janzen used resistance networks to simulate mobility differences, and Prats et al. *’ used an analytical solution. Qualitatively, all investigators arrived at the same conclusion-i.e., if the mobility ratio is favorable (MI l), injectivities will decline continuously during the entire operation; however, if the mobility ratio is unfavorable (M> I), injectivities will increase continuously.

In their work, Caudle and Witte determined the variation in injectivity for the five-spot pattern as a function of the mobility ratio that exists before and after water breakthrough. Fig. 44.65 shows the results of their studies, in the form of the relationships between the conductance ratio, the mobility ratio, and the fractional areas of the reservoir that are contacted by the injected fluid.

Craig4 points out that, subsequent to fill-up, the relationships developed by Caudle and Witte can be used along with Eq. 20 to calculate water injection rates for the five-spot pattern:

’ W’ . = FcXib,

where . = water-injection rate,

i: = Caudle and Witte conductance ratio, and ib = the injection rate of fluid that has the same

mobility as the reservoir oil in a liquid- filled (base) pattern, as calculated from Eq. 20.

As the intake rate declines in the early stages of injection, it is important to be able to tell whether the decline results from the plugging of the sand (a situation that requires remedial work), from natural reservoir fill-up, or from mobility ratio effects. Consequently, a method is required to determine the intake capacity of the well itself without regard to the conductivity of the well system surrounding it. Such a method would be achieved by conducting periodic tests on certain selected wells scattered across the flood area. A close check of the efflclency of the input of the wells could then be maintained.

One practical method of determining the efficiency of the input wells is to use the calculated injectivity index

WATER-INJECTION PRESSURE MAINTENANCE & WATERFLOOD PROCESSES

Fig. 44.66-Composite type log, Hewitt field, Carter County, OK. Flg. 44.67-Hewitt unit, Chubbee structure map.

of the well. The injectivity index is defined as the number of barrels per day of gross liquid that is pumped into an injection well per pound per square inch of pressure differential between the mean injection pressure and the mean formation pressure associated with a specific subsurface datum, usually the mean formation depth. To be most valuable in a study of the behavior of the individual input wells, use of the injectivity-index concept should be restricted to defining the conductivity of an individual well; it should not be used to determine the general conductivity of the well system. This restricted injectivity index, which may be called a “localized injectivity index,” is best used in measuring the conductivity of the cylinder of sand surrounding the well-most of the pressure drop takes place in this cylinder, whose inside wall is the sandface.

The localized injectivity index can be calculated from a modified Eq. 16:

0.@-)7@%h(Pi,~-Pbp) I &, = cLw ln(ri,r,) 3 . . ‘. . . . (26)

where p@ is the transient backpressure and ri is the distance from the well to the point of pressure equalization at Pbp.

Differentiating, the localized injectivity index, with pbP being constant, is expressed as

I-di,- O.O0708k,h y, ln(rj,r,). . . . .

dp,w . . (27)

Experimentally, it has been found that, for small volumes of injected water, di ,,A$ iw is constant. If small volumes of water are injected during the course of a test, r; changes only slightly; r; is considerably greater than rw and the logarithm of ri/rw is practically constant. If, however, larger volumes are injected during the course of the test, the In r,/r, will no longer be constant and the localized injectivity index, di,ldpi,, will not be constant. If large enough volumes are injected so that equi-

librium conditions are obtained, the corresponding pattern formula is applicable. In the case of a five-spot pattern, the change in intake rate for each change in pressure can be approximated by

I- diw - O.O03541k,,,h

dpiw pW [ln(d/r,)-0.61901 ’ ’ . . (28)

where d is the distance between unlike wells. The transient backpressure, pbP, is a pressure

phenomenon that occurs when the intake rate of an injection well is changed. Theoretically, the flow of water from a well into the surrounding formation will continue until the intensity of the sandface pressure is reduced to that of the reservoir pressure. In practice, if the pressure on an input well suddenly is reduced to the atmospheric pressure at the surface, the well backflows for a period of time that varies from a few minutes to several hours. The pressure that caused the backflow of water from the well is defined as the transient backpressure. This pressure, which occurs near the wellbore, is greater than the average reservoir pressure and has been attributed qualitatively to the compressibility of water and gas near the wellbore. When the injection is terminated, the backflow is caused by the expansion of the water and gas that results from the decrease in pressure. Quantitative treatment of this phenomenon has been given by Nowak and Lester ’ ’ ’ and Hazebroek et aZ. ’ I2 The transient backpressure gradually dissipates and approaches the reservoir pressure. The localized injectivity index should be determined after the transient pressure has started falling very slowly or is in equilibrium with the reservoir pressure.

A comparison of the injectivity indices for injection wells in the waterflood will give an indication as to the wells that are not performing satisfactorily, and investigations should be made to determine whether the remedial measures are necessary to improve the injectivity rate. The intake rate of a normal well declines during its life, at least until a constant steady-state pressure distribution is established in the part of the reservoir affected by the well. In addition to the normal well decline, the sandface


TABLE 44.15-HEWITT UNIT RESERVOIR DATA

General

Unit area, acre Floodable net sand volume, acre-ft Average composite thickness, ft Original oil in place, MMbbl

Rock Properties

2,610 284,700

109 350.8

Permeability, md Porosity, % Interstitial water, % Lorenz coefficient Permeability variation

Fluid Properties

Mobility ratio Original reservoir pressure, psig Reservoir temperature, “F Original FVF, RBlSTB Flood start FVF, RBlSTB Oil stock-tank gravity, “API Oil viscosity, cp Original dissolved GOR, cu ft/STB

Primary recovery mechanism

184 21 .o 23.0 0.49

0.726

4.0 905

96 1.13 1.02

35 8.7 253

solution gas drive gravity drainage

gradually becomes plugged by suspended solids in the injected water. These suspended solids include materials like clay, silt, iron oxide, and hydroxides. In addition to suspended solids, dissolved and organic growths may con- tribute to the plugging of the formation sandface. Plugging of the sandface by these materials may be minimized with the proper treatment of the injection water. This treatment is covered in this chapter under the heading Water Treating.

By means of rate/pressure curves established at intervals of a few months, it is possible to distinguish between the decrease in intake rate caused by plugging and that caused by fill-up of the reservoir as mobility ratio effects. Rate/pressure curves are helpful also in indicating the value of the critical breakthrough pressure at which rup- ture of the formation occurs. If plugging is occurring and the injection rate declines, backflow of the well may be induced to remove the material from the sandface. Or if the plugging material on the sandface cannot be removed by backflowing, then perhaps it can be dissolved through the use of various types of acids. If necessary, fracturing may be used to increase the injectivity rate in the well.

Water-Injection Case Histories Many examples of field case histories of water-injection projects can be found in the literature. Seven case histories of waterfloods in both sandstone and limestone reservoirs, using pattern as well as peripheral injection, are detailed in SPE Reprint Series No. Za, Waterflooding (1973). SPEReprintSeriesNo~.4(1962)and4a(1975), Field Case Histories and Oil and Gas Reservoirs, also describe the history of several typical waterflood and pressure-maintenance projects.

For this chapter, three recently reported water-injection- project case histories were selected from the literature as a means of illustrating the use of contemporary technolo-

TABLE 44.16-SUMMARY OF ROCK AND FLUID PROPERTIES, RESERVOIR PROPERTIES, AND

PRODUCTION-INJECTION DATA, JAY/LITTLE ESCAMBIA CREEK (LEC) WATERFLOOD

Rock and Fluid Properties

Porosity, O/O

Permeability, md Water saturation, O/O

Oil FVF, RBlSTB Oil viscosity, cp Oil gravity, OAPI Sol&on &OR, scf/STB Hydrogen sulfide content, mol% Mobility ratio (water/oil)

Reservoir Properties

Datum, ft subsea Original pressure, psia Current pressure, psia Saturation pressure, psia Temperature, OF Production area, acres Net thickness, ft OOIP, MMSTB

Production/Injection (Jan. 1, 1981)

Oil production rate, MSTBlD Cumulative oil production, MMSTB Water injection rate, Mbbl Cumulative water injection, MMbbl

14.0 35.4 12.7 1.76 0.18

51 1,806

8.8 0.3

15,400 7,850 5,750 2,830

285 14,415

95 728

90 296 250 524

gy and reservoir engineering methods to solve some of the more complex problems encountered in many oil fields today. Summarized in the following discussion are results of projects involving (1) an older field with multiple sands, (2) a deep carbonate reservoir, and (3) an offshore field.

The effects of extensive waterflooding operations in the Hewitt field unit, Carter County, OK, were reported in 1982 by Ruble. ‘I3 The project described in that paper is a pattern waterflood in multiple sands that had been essentially depleted through 50 years of primary operations. The project is a good example of a simultaneous waterflooding of numerous sands containing relatively high-viscosity oil at shallow depths, as shown in Fig. 44.66. A structure map of the Hewitt unit is shown in Fig. 44.67. A summary of the reservoir performance data is given in Table 44.15. The additional oil recovery by waterflooding has been estimated to be 34.9~ lo6 STB (123 bbllacre-ft) as compared to a primary recovery of 109.6~ lo6 STB (385 bbl/acre-ft). These numbers represent approximately 10 and 31% of the OOIP, respectively. Among the outstanding features of this project are (1) the use of triple completion injection wells with tubing and packer installations for control of the water that is injected into as many as 22 individual sands, (2) the plugging of 680 old wells and drilling of 149 new wells, and (3) the use of surveillance and selective injection programs to optimize oil recovery.

Langston et al. ’ I4 have reported on a large-scale water- injection project in the Jay/Little Escambia Creek field in Florida and Alabama. The project is a good example of a pressure- and rate-maintained project in a deep, undersaturated, carbonate reservoir. A summary of the production performance data for the field is presented in Table 44.16. The injection pattern is a 3 : 1 staggered line drive, as shown in Fig. 44.68. Reservoir pressure and

WATER-INJECTION PRESSURE MAINTENANCE l? WATERFLOOD PROCESSES 44-37

oil production rates, shown in Fig. 44.69, were maintained at constant levels for 6 years before they began to decline. Ultimate oil recovery is expected to be 346 x lo6 STB, or 47.5% of the OOIP. This represents 222~ lo6 STB more recovery than from primary operations-i.e., water-injection procedures will account for 64% of the total anticipated recovery. A great number of rock and fluid property data were acquired during the early development phase of the field. Use of these data provided the basis for decisions concerning unitization and the subsequent injection program.

Although water injection programs are being carried out in many offshore fields, primarily in the Persian Gulf area, in the North Sea, on the Louisiana-Texas gulf coast, and on the California coast, case histories have been reported on only a few. Jordan et al. ‘I5 reported on injection operations in the Bay Marchand field, offshore Louisiana, in April 1969.

Initial reservoir pressures in individual sands of the Bay Marchand field ranged from 4,600 to 5,29 1 psig. Reser- voir temperatures varied from 182 to 197°F. Initial GOR’s averaged 450 scf/STB and oil gravities were between 21 and 30”API. PVT properties varied with depth and the oil columns were undersaturated at their volumetric midpoints. Oil viscosities ranged from 1.1 to 1.9 cp, indicating favorable mobility ratios.

Porosities were rather uniform and averaged 29%. However, permeabilities exhibited wide variations; three reservoirs had geometric-mean air permeabilities of less than 100 md, while the remaining sands had values up to 2,000 md. Initial water saturations exhibited a corresponding variation, from 40 to 15 %

Pressure maintenance using seawater for injection began in 1963. According to McCune, ‘I6 who reported on operations in the Bay Marchand field in Oct. 1982, successful injection operations have been carried out over a 20-year period in six major sand reservoirs. A typical sand unit structure map and pressure-production history are illustrated in Figs. 44.70a and 44.70b, respectively.

The techniques used to test, treat, filter, and pump seawater are discussed in detail in the papers by Jordan et al. ‘I5 and McCune. ‘I6 The basic methods used in the Bay Marchand field, which include both coarse and fine filtration of solids, oxygen removal, and chemical treatment for control of corrosion and bacteria, have since been adopted in many other seawater injection projects.

Pilot Floods A pilot waterflood is conducted to provide a means of evaluating the feasibility of a full-field implementation of the waterflood process. Both reservoir performance and’ operational procedures can be evaluated during the pilot flood. This experience is helpful in performing the engineering and economic studies that are necessary in deciding whether expanded waterflood operations should be carried out.

It is important to understand that a pilot flood should be designed to assure engineering success rather than economic success. Any small economic loss sustained by the pilot flood can be weighed directly against the much greater economic loss that would result from expanded waterflood operations that are undertaken without accurate pilot performance data. Such economic losses can result

o PRODUCING WELL WELL

Fig. 44.68-Jay/Little Escambia Creek waterflood well location map.

Fig. 44.68-Jay/Little Escambia Creek unit performance.

from the project capital investments or from a reduction in the ultimately recoverable oil reserves.

Caudle and Loncaric 5o has suggested several aspects of field pilot operations that need to be considered to achieve the greatest amount of useful data from the project. Fluid movement is most critical; one cannot isolate a segment (pilot area) of a reservoir and confine assess- ments of fluid movement to that segment.

A commonly used pilot flood pattern is the inverted five- spot, in which there is one injection well and four producing wells; all other nearby wells are shut in. The popular- ity of this pattern is mostly because only one injection well is required. The inherent problem with this pattern is that


WEI ORLEMS

- ‘\ r, ‘:I :r I I : I

i

-

Fig. 44.70A-Typical unit structure map, Bay Marchand field.

80

0

Fig. 44.70B-Pressure production history vs. time. Typical unit reservoir, Bay Marchand field.

three-fourths of the produced fluid comes from outside the “pilot area” while, at the same time, fluid leaves the pilot area from the regions between the producing wells. The re!ative volumes are affected by the ratio of production rates to injection rates.

A “volumetric balance” can be maintained in the pilot area by allocating only one-fourth the rate of the injection well to each production well. Although the volumes are balanced, the production history will still reflect the fact that only one-fourth of the oil that is produced actually comes from inside the pilot area. Therefore, no reliable estimate of the amount of recoverable oil in the pilot area can be made. Computer model studies show that the production history for this pilot pattern is so greatly affected by conditions outside the pilot area that correction factors are probably inadequate to compensate for the errors. This is especially true if there is a gas saturation in the reservoir at the start of injection.

The considerations noted previously suggest that a reversal of that pattern, in which one producing well is surrounded by four injection wells, could be a more accurate mechanism for evaluating the performance of a pilot flood. This pattern would minimize the escape of the oil originally contained in the pilot area as well as the en- try of outside oil into the pilot area. The conventional tive- spot pattern, as it is known, is probably the most simple and useful pilot pattern. While it is true that three-fourths of the injected fluid will not enter the pilot area, the production from the center producer will be much more useful for predicting total fluid recoveries.

The purpose of the pilot flood is to facilitate an evaluation of the performance of a small section of the reservoir so that the resulting information can be used to estimate the behavior of a much more extensive operation. If the production history of the individual pilot well does not generate data that are representative of the entire area to be flooded, a correction factor can be used to adjust the actual production history in order that the potential production of a fully developed or “confined” pattern flood element can be estimated.

Such a pilot (or pilot production well) must operate as if it were in a confined area (i.e., in one that is surrounded by many similar areas). In reality, such a situation could occur only if the pilot area composed the entire proposed flood project. However, if a sufficient number of similar elements are operated around the pilot, results that would closely approximate those of the confined case could be achieved. The number of similar elements around the pilot area that are necessary to generate results that are us- able without correction depends on the mobility ratio and initial gas saturation.

Model studies”‘,“* have shown that, in general, the single conventional five-spot pilot is adequate for mobility ratios below one. More complex pilot patterns are necessary at higher mobility ratios.

Certain considerations should be weighed in deciding the location of the pilot area. Knowledge of the reservoir’s geometrical configuration, its structural data, and its stratigraphic data are necessary to make the selection. A partially confined or bounded area will increase the value

WATER-INJECTION PRESSURE MAINTENANCE 8 WATERFLOOD PROCESSES 44-39

of the pilot in predicting the behavior of an expanded flood. The boundaries to be sought are as follows: (1) oil/water contacts with respect to monoclinal or an- ticlinal structures, (2) fault planes, (3) small fault blocks, (4) structural or permeability pinchouts, and (5) shale-outs to the side.

Reservoir and well conditions must be evaluated before initiation of the pilot flood. In selecting the portion of the reservoir in which the pilot flood is to begin, it is important to be informed concerning these elements: (1) the pattern and spacing of injection and producing wells with respect to the formation structure and the distribution of formation properties, (2) the type of well completions, completion intervals, and the repair and workovers that have occurred in the past, and (3) the productivity factors that have been measured for producing oil wells.

Reservoir conditions and other related data provide information that is necessary before, and at the initiation of, the pilot flood. Some characteristics and categories of data that are valuable in determining the magnitude and distribution of oil, water, and gas saturations before the start of the pilot flood are (1) the development and production history, (2) total oil recoveries during primary operations, (3) encroachment of water or gas, (4) reservoir pressures within and surrounding the selected pilot flood area, and (5) distribution of fluids through gravity drainage.

The behavior of the reservoir and the wells should be evaluated continually throughout the life of the pilot flood. The records of this monitpring should include information about the following matters: (1) water-injection history on each well, including the time the injection began; (2) cumulative volumes of water and the rate of injection, by well, for the flood; (3) injection pressures and the iden- tities of the sections taking water; (4) fluid production history, by well, for the total area within the flood region and for wells in the surrounding area; included should be the rate of production and the cumulative volumes of oil, water, and gas; (5) WOR and GOR trends; (6) reservoir pressure distribution inside, and surrounding, the flood area; (7) the frontal advance and associated displacement efficiency of water, as evidenced by the time and location at which water appears in individual wells; (8) workover history of both injection and producing wells; and (9) any pertinent changes in the pilot flood program.

There are two efficiency factors that may be calculated and used in evaluating the effectiveness of the pilot flood. One involves a displacement efficiency, determined on the basis of the ratio of the volume of total fluids produced to the volume of water injected. This ratio will indicate whether the injected water is effectively moving fluids from the injection well to the producing well (or wells) within the pilot area. The second factor involves the sweep efficiency within the flood pattern and the fractional depletion of the oil zone, which determine the economic life of the reservoir as well as the ultimate oil recovery.

Production data in the form of production-decline curves may be used to evaluate the pilot flood performance. The usual procedure in presenting the history of oil production in pilot flood operations has been to plot the logarithm of oil production vs. time or the logarithm of time. The advantages of using production-decline curves are that

they indicate the time of fill-up and the current oil- production response with respect to the injection program. However, there are limitations in using production-decline curves to evaluate injection efficiencies and the future behavior of the pilot. Among these limitations is the fact that true decline conditions seldom exist because fluid production is controlled by water-injection rates. There is no basis for assuming any particular shape with regard to a production-decline curve because the oil rate does not necessarily vary with time; the oil production rate is directly dependent on the rate at which water is injected and on the physical characteristics of the reservoir rock and the fluids it contains.

During the development and operation of the pilot test, certain conclusions regarding the performance of an expanded waterflood may be drawn. For example, if the reservoir has a high water saturation, the water may be more mobile than the oil, which would soon result in a high WOR in the pilot area. Because of the permeability reductions around the wellbores of the input wells, the formation itself might not take a satisfactory injection rate without exceeding the maximum pressure. Again, exces- sive pressure would produce adverse conditions. Water- cut data, used in conjunction with the Stiles calculation I9 or other similar conformance calculations, will indicate whether the pilot is performing as expected.

Surface-Active Agents in Waterflooding Surface-active agents in waterflooding are used to improve oil recovery by (1) improving mobility, (2) reducing interfacial tension, and (3) altering the rock wettability.

Laboratory investigations and field tests in which various surface-active agents and other chemicals are used will be discussed in Chap. 45, “Miscible Displacement,” and Chap. 47, “Chemical Flooding.” The large number of technological advances that have taken place during the past decade and the voluminous publications on the use of surface-active agents allow only a brief reference to the subject in this chapter.

Mobility Improvement Control of the mobility of the injected water, along with the use of surface-active agents and chemicals to alter the wettability characteristics of the reservoir rock, are among the techniques now being used in certain waterflood projects to improve oil displacement efficiencies. The addition of an acrylamide polymer or some similar chemical to increase the viscosity of water causes area1 and vertical coverage in the reservoir to be increased as a result of a reduction in the mobility ratio between the displaced and displacing fluids. This addition of a polymer also reduces the volume of injected fluids required in the oil displacement process that lowers the saturation in the swept portion of the reservoir to its residual value. The first field studies involving the use of polymers for mobility control were reported by Sandiford in 1964. ‘I9

The injection of a high-molecular-weight polyacrylamide polymer to increase waterflood sweep efficiencies through improved mobility ratios was considered to be unprofitable in two reported case histories ‘20.‘2’ that are summarized below. In the Wilmington field, CA, ‘*O a large-scale injection program was initiated during 1969 in relatively unconsolidated sands that contained an


18”API gravity crude oil with a reservoir oil viscosity of 30.8 cp, The mobility ratio of brine/oil was 14.2, compared to a mobility ratio of 1.33 for a 250-ppm polymer/ oil. After injection of 1,300,OOO Ibm of polymer over a period of 2.5 years at an average concentration of 213 ppm, the injection of polymer was discontinued because no increase in oil recovery could be attributed to the polymer injection. The poor response was believed to be caused by (1) a polymer concentration that was too low; (2) injection rates that decreased by an average of 25% (as a result of scale formation), accumulation of undissolved polymer on the face of the formation, and possible reduction in the reservoir permeability from adsorption of the polymer (85 lbm/acre-ft); and (3) a premature breakthrough of the polymer solution through highly permeable intervals.

A pilot project 12’ in the Pembina field of Alberta, Canada, was started in Nov. 1971 with two la-acre, five- spot patterns composed of six injection wells and two producing wells. The producing interval consisted of a conglomerate zone underlain by a sandstone, and these zones had average permeabilities of 63.6 and 25.3 md, respectively.

The viscosity of the 37”API crude oil, at reservoir conditions, was 1.05 cp. A total of 217,400 lbm of polymer was injected, with the first 124,750 lbm being injected at a concentration of 1,000 ppm and the remaining 92,650 Ibm being injected at decreasing concentrations from 1,000 to 100 ppm. The conclusions reached from the Pem- bina pilot project were as follows.

1. The overall performance of the producing wells in the pilot area showed no permanent improvement.

2. Early breakthrough of polymer through the conglomerate zone indicated that the polymer did not significantly reduce the effects of the highly permeable interval.

3. Water/rock interaction and formation water com- mingling reduced the effective viscosity level of the polymer solution to approximately 25 % of the designed value.

4. There was a significant reduction in the injection rates of two injection wells during polymer injection.

5. Adsorption of the polyacrylamide polymer was about 2 mg/m’ of surface area.

The injection of polymer solutions to improve oil recovery through mobility control has not yet been well established for general application. Laboratory displacement tests should be performed on reservoir rock samples, and the reservoir crude oil and formation water should be used as a guide in selecting the type of polymer and the concentrations necessary for scaling the formulation to field conditions. Of particular significance is the effect of the formation water’s salinity on reducing both the viscosity of the polymer solution and its adsorption by the reservoir rock.

Published reports “‘-‘24 about various field applications of polymer solutions have indicated improvements in oil recovery efficiencies of 5 to 15% above recoveries from conventional waterfloods.

Reduction in Interfacial Tension Early laboratory tests ‘25m’27 indicated that dilute solutions of surfactants would remove more oil from sandstone cores than would untreated water. The economic feasibility of using this process in a waterflood has been ques-

tioned because of the loss of the surfactant by adsorption at the rock/liquid interfaces. The adsorption is especially problematical with both anionic and cationic surfactants, and it occurs to a lesser degree with nonionic surfactants. In one field project, the results of which were published’28 in 1968, a nonionic surfactant was injected at concentrations of 25 to 250 ppm into a sandstone reservoir at an advanced stage of waterflooding; an additional oil recovery of approximately 9% was attributed to the use of the surfactant.

Alteration of Rock Wettability Recognition of the use of alkaline salts to improve oil recovery was first disclosed by Squires ‘29 and patented by Atkinson I30 in 1927. Wagner and Leach, 13’ in 1959, presented laboratory results that showed improved oil recovery through the injection of water containing chemicals that altered the pH of the injected water. Acidic injection water resulted in an improvement in WOR and a corresponding increase in recovery; however, its use as an injection medium has not proved practical because of chemical reactions with most reservoir rocks. Subse- quent laboratory tests 13* established similarly improved oil recovery results with sodium hydroxide.

Laboratory tests have indicated that the injection of caustic solutions can result in improved oil recovery, primarily as a result of lowering the water relative permeability, ‘33 pH control ‘34 and the oil/water interfacial tension. ‘35 These effect;, though, are dependent on the water salinity, ‘34 the temperature, ‘36 and the type of crude oil.

In 1974, there was a report ‘34 of a field trial in which a solution containing 3.2 wt% sodium carbonate was injected into a previously waterflooded Miocene sand in southeast Texas. The test involved two wells located 36 ft apart. Some improvement in oil cuts was noted at the producing well before alkaline water breakthrough, sug- gesting the formation of a low-mobility water-in-oil emul- sion bank. No economic evaluation of the test was reported.

The first field test of the caustic flooding recess was mentioned by Nutting 13’ in 1925. A report’& published in 1962 of a field trial in which sodium hydroxide was used in the Muddy “J” sand, Harrisburg field. West Har- risburg Unit, Banner County, NE. The injection of a 40,000-bbl slug of 2.0 wt% sodium hydroxide resulted in a recovery of approximately 8,700 bbl of oil from an area that previously had been flooded out by normal water injection operations. In another case, an 8% PV slug of 2.0 wt% sodium hydroxide was injected into a portion of the Singleton field, Banner County, NE. The test was in an area under waterflood that had not been completely watered out. Increased oil recovery, reported ‘38 in 1970, amounted to 17,600 bbl, or 2.34% PV.

The only description of a large-scale field trial of caustic flooding that has been published ‘39 involved a 63-acre area in the Whittier field, CA. The area had been under waterflood for 2.5 years before caustic was injected. A 0.2 wt% sodium hydroxide slug, equal in volume to 23% PV, was injected. The slug was followed by plain water. The increase in oil recovery beyond that by waterflooding was estimated to be from 350,ooO to 470,000 bbl, or 5.03 to 6.75% PV.


Water Source and Requirements During the planning stages of a waterflood program, these basic steps must be taken: (1) the water requirements should be determined as accurately as the data will permit; (2) all possible water sources should be surveyed with special attention given to satisfying the quantitative requirements: and (3) the selected source should be developed in the most economical manner permitted by good engineering practice.

Waterflood Requirements Daily Water-Injection Rates. The largest daily demand for water from the water source occurs during the fill-up period when there is no return water available. During the early life of the reservoir’s injection program, or during the fill-up period, it is usually advantageous to maintain a high rate of injection so as to accomplish an early fill-up (a rate between 1 and 2 B/D/acre-f1 is desirable). One author I40 states that after fill-up has been achieved, the injection rate should be maintained at about 1 B/D and not less than % B/D/acre-ft. Flood pattern, well spacing, and injection pressures should be designed to meet these requirements.

Ultimate Water Requirements. The PV method has been found to give a good approximation of the ultimate water requirements for a waterflood. The volume of water required should range from 150 to 170% of the total pore space, and the measurement of such space should include the PV of any adjacent overlying gas sand or basal water sand. The ultimate water requirements, together with the average water-injection rate, will serve as a basis for estimating the total life of the waterflood.

Makeup Water. The volume of return water becomes an increasingly significant percentage of the required injection rate as a flood progresses; therefore, it is an economic necessity that produced water be injected unless the treating cost of the produced water is higher than that of the makeup water. If gas or water sands are not present, the produced water will compose 40 to 50% of the ultimate water requirements. If gas or water sands are present, less return water will be available-thus, the ultimate makeup water requirement will increase to as much as 60 to 70% of the total quantity of water that is injected. In recent years, federal and state agencies have enacted regulations that limit or prohibit disposal of oilfield waters in surface systems. Environmental regulations should be reviewed carefully when studies of the treatment and disposal of produced water are being made.

Water Sources There are three principal freshwater sources and two sources of salt water that can be used for waterflooding purposes. Freshwater supplies include surface waters, municipal water. waters from alluvium beds, and some subsurface waters. Saltwater sources include some subsurface waters and the oceans. Where economically permitted, salt water usually is preferable to fresh water.

Fresh Water-Surface Sources. Surface waters, including ponds, lakes, streams, and rivers, have been used throughout the history of oilfield waterflooding projects,

and these are the sources for which competition from other industries and from municipalities is highest. There are a number of other factors that limit the availability of this resource. For example, there is a continuing growth in the demand for fresh water, and droughts have resulted in water shortages in some areas during recent years. In addition, some states have taken legislative action to control freshwater supplies. Therefore, when fresh water is to be used in a waterflood project, it may be necessary to obtain approval from the appropriate state agency before proceeding with development of such a source. If salt water is chosen as the injection medium, legal approval for the withdrawal of the water may not be necessary

Small ponds and streams are very unreliable as a constant source of supply for all seasons of the year. Large lakes and rivers are preferable; however, these also may have limited capacity during drought periods. The principal disadvantages of surface sources are the unreliabil- ity of their quality and quantity, the high cost of treating equipment, and the cost of the chemicals that are necessary to obtain a satisfactory water.

Fresh Water-Alluvium Beds. A more favored method of using river or stream waters calls for the alluvium beds near the river to be tested with shallow wells. Use of this source in some of the world’s largest waterfloods-the Salem unit in Illinois, 14’ rhe Burbank unit, I42 and the Olympic pool in Oklahoma-indicates the high productivity that can be achieved from alluvium beds. If closed injection systems are used, chemical treatment (with the possible exception of a bactericide) normally is not required. Filtration usually is unnecessary because of the natural filtration of the alluvium beds.

Sulfate-reducing bacteria are anaerobic and thrive within a few feet of the surface, so waters from alluvium beds frequently can be highly contaminated with these bacteria. However, low-cost chemical treatment can control these organisms. Having noted this minor problem, it is safe to say that the quality of water from alluvium wells is more dependable than that from direct surface sources. Wells are not subject to extreme turbidity changes during rainy seasons or to the variable organic content of the surface waters.

The reliability of alluvium beds as a continuing source of water is slightly better than the reliability of an adjacent river or stream. The water table will drop steadily when a river dries up, but wells should go on supplying water for some time after the surface waters are depleted.

The principal advantages of alluvium-bed sources are their low development cost, low pumping cost, and the possibility that they will not need filtration. If bacteria are not a problem, corrosion rates should be low and chemical treatment unnecessary.

Fresh Water-Subsurface Formations. In certain areas, subsurface sand or carbonate formations may be tested for water production with good results. Good-quality water often is produced from certain formations whose depths range from close to the surface to 1,000 ft or more. As in the case of the alluvium wells, closed systems usually are used, thus eliminating chemical treatment and filtration requirements. When a well is completed in a freshwater subsurface formation, drawdown tests should


TABLE 44.17--RESERVOIR ENGINEERING

Dtssolved Gas Test Effects

Hydrogen sullide. H,S Odor or taste. If lab Very corrosive in the analysis desired, presence of motslure. sample is preserved parttcularly if oxygen by addihon of zinc is present. acetate and sodium hydroxide

Carbon dioxide, CO, Determine the slabillty of the carbonate- bicarbonate balance, titrate for free CO, at source point.

Oxygen Determine if the Fe + + ion is being oxidized. Dissolved 0, meter and membrane probe is used when H,S is absent.

1. Corroston Increases wtth Increasing percentages of co,.

2 Removal of CO, may cause preclpltatton of metalltc carbonates or bicarbonates.

1. Ii is largely responsible for corrosion of equipment.

2 Its reaction with metallic tons (Fe + + mostly) wtll cause plugging in the reservotr

Remedial Treatment pH Control

A decrease in DH will 1 Open aeration (poor) increase rate df

2 Synthebc or natural corrosion, but the combustton corrosion rate also exhaust gases depends on the flowtng counter- composition of the current to water contacted metal and WI packed towers. the alkalinity of the

3 Forced-draft solution. aerators.

1 Aeratton by the An increase in pH Funclton of the three methods also will decrease the carbonate and mentioned above. free CO, that IS bicarbonate stabtlity

2 Increase the present. Free CO, vs. corrosive activtty alkalinity. may not exisl in water IS caused directly by

3. Chemtcal inhibitors. wtth pH values which the CO,. Not as are greater than 8 3. corrosive as equal

porttons of O2 or H,S.

1. Use of closed No effect is to be Limtts of detection- systems will found tn either acidtc I.e., 10 ppb (Note: minimize oxygen or alkaline water. iron bacteria can use. grow in waters

2. Open systems- contatntng 0.3 vacuum aeration pm. ‘53 SRB can has been used. also live in aerobic

3. Counterflow (in conditions.) Soluble bubble lower) of 0, IS approxtmately natural gas with four times as cor- low oxygen rosive as equal mole content. volumes of COP.

Tolerance Suggested

50 ppm. “’ Corrosron rate is rapid up to 15 ppm. Hugh H,S concentrahons,may act to tnhrbil corroston.

be made to determine the initial productivity. The test should be conducted for a sufficient length of time to determine the static working fluid level, which will indicate the rate at which the well can be produced.

Optimal spacing in the water-supply wells may vary from 25 ft for sand points to as much as 1,320 ft for deep wells. The productivity will indicate how many wells are necessary to meet the daily water requirements. Where a number of deep wells are required to develop the freshwater source, the economic viability of drilling the additional wells should be carefully considered.

Pumping equipment for water wells may include surface-driven or submersible, centrihtgal (or rod) pumps. If a high-pressure gas source is available, gas-lifting methods should be considered also. Selection of the pumps should be governed by economic considerations, and these are influenced by the static fluid level, the drawdown, and the desired productivity. The advantages of freshwater wells in subsurface formations include low corrosion rates and the possible elimination of the need for chemical treating and filtration.

Salt Water-Subsurface. In most oil fields, either above or below the oil zones, there are saltwater formations that are potential sources of water supply. 143 The relatively shallow saltwater wells are similar in most respects to the shallow freshwater wells. 144.‘45 The saltwater wells are completed in the same manner and have the same advantages of being adaptable to closed injection systems. Many producing areas have deep saltwater formations that have extensive area1 coverage and a thickness of up to several hundred feet. These prolific saltwater-producing formations frequently have high working fluid levels. Such formations may contain waters with high mineral content, and have wellhead temperatures in the range of 100 to

173°F. Hydrogen sulfide may or may not be present. If the water contains significant amounts of hydrogen sulfide, open systems that incorporate aeration, sedimentation, and filtration capabilities should be used. Examples of prolific formations are the Arbuckle 146 and Mississippi limestones in Kansas and Oklahoma, the Ellenburger lime in Texas, the Tar Springs in Illinois, and the Madison lime in Wyoming. The drilling and completion costs of deep supply wells may range up to, and exceed, $500,000; however, they frequently are the most economical source of large volumes of water because of small fluid-level drawdowns. The advantages of the deep saltwater wells include their adaptability to closed systems, their high and reliable productivity, the compatibility of salt water with the oil sand, and, where high hydrostatic fluid levels are found, the relatively low lifting costs.

Salt Water-Ocean. Use of ocean water for injection purposes is confined to coastal regions and offshore fields. “6*‘47-149 Closed systems in which shallow wells on the shore are used as the source of supply are preferred. A moderately high corrosion rate should be expected, and ocean water probably will require a bactericide. The advantages of oceanwater supply include an inexhaustible source and low development and pumping costs.

Salt Water-Return Water. During the life of a flood, the return water may represent a total volume of from 30 to 60% of the injection requirements. The use of the return water for injection may improve the economic condition of the overall project. In open systems, return water generally is added to the makeup water and injected. The mixing of the waters in a pond or settling tank permits precipitation and sedimentation of the incompatible constituents. In recent years, however, it has been determined

WATER-INJECTION PRESSURE MAINTENANCE 8 WATERFLOOD PROCESSES 44-43

TABLE 44.18-WATER-INJECTION PRESSURE MAINTENANCE

Organisms GWlUS Phylum

Sulfate reducers Desulfouibrio -

Organisms Pseudomonas -

Iron bacteria Leptothrix - Crenothrix Gallienella

Algae

Fungi

Thallophyta

Thallophyia

Agents Used Enwonment for Treating

Anaerobic (though they Chlortne* cannot grow in the Quaternary presence of free ammonium oxygen, they can live; compounds will not grow In highly Other bactericides” saline waters.) Low-pH waters also stifle growth. Aerobic or facullallve Chlorine’ (usually require free Quaternary oxygen for growth) ammonium

compounds Bactena withdraw Bactencides ferrous Iron (Fe + + ) Chlorine’ that is present in their aqueous habitat and deposit It in the form of Fe(OH). Chlorophyll-contalnmg Copper sulfate plants (require presence of sunlight Sodium and moislure for pendachlorphenate growth). Oxvaen (reauire presence of’free oxygen).

Closed system Chlorine’ Closed system

‘Llmlled to Iron-free waters “Mercuric and phenolic compounds: fatly and resin amines: formaldehyde

Effect of Agents m Reducing Growth Purpose in Treating

Partiallv effective 1. To orevent Effective

Effective

coriosive activity as a result of H 2 S formation.

2. To prevent pluggmg of sandface.

Effective 1. To prevent plugging Effective. (Note, of equipment change bactericide 11 2. To prevent plugging immunization occurs.) of sandface. Effective 1. To prevent plugging Effective. (Note: slug of equipment. injection is usually 2. To prevent pluggmg sufflcient.1 of sandface

Effective, depending 1. To prevent pluggmg on water alkalinity. of equipmenl. Effective, depending on 2. To prevent plugging water alkalmlty. of sandface. Effective Effective 1. To prevent plugging Effective of equipment.

2. To prevent plugging of sandface.

that the mixing of the produced water and makeup water results in increased scale deposition and corrosion in the surface system and injection wells. Also, scale deposition in the perforations, and the transport of suspended solids (a product of corrosion) into the formation, reduce the well injectivity and necessitate frequent backwashing and acid treatments. Therefore, in many of the major waterfloods, the waters are isolated in the surface system and are injected separately into the reservoir.

In closed systems, the compatibility of the return and makeup waters is more critical than it is in an open system, but the two waters can be mixed satisfactorily in most cases. Complete analysis of the water should be made, with special attention being given to the detection of any combinations of ions that may precipitate on being mixed. The effect of the more common precipitates and the treatment of them is covered in this chapter under Water Treating.

Water Treating During the early days of waterflooding, only the quantity, not the quality, of the water was given consideration. How-ever, it was soon noted that when the quality was poor, higher injection pressures were required to maintain suitable injection rates and corrosion problems mounted. As a result, the operators of the early waterfloods began to realize that the quality of the water was equally as important as the quantity, and that poor water treating was proving disastrous to waterfloods that otherwise might have been successful. Water-treating practices have improved greatly as the waterflood industry has matured, a point that is substantiated in the literature by the many contributions on this subject. ‘45,‘50-‘64 API has published recommendations for analysis of oilfield waters I50 and biological analysis of injection waters. 15’ Successful results normally can be achieved when these recommended

procedures are followed. Standardized procedures for membrane-filterability tests, ‘52 a useful tool in water testing, also have been adopted by the industry.

After the water source is known, a water analysis is required to determine these matters: (1) compatibility of the injection water with the reservoir water (the test should include actual blends as well as theoretical combinations); (2) whether an open or closed injection facility would be the most suitable; and (3) what treatment is necessary to have an acceptable water for the reservoir and to minimize corrosion of the equipment.

Prudent operation of the waterflood requires that water analyses be conducted periodically to determine the presence of dissolved gases, certain minerals (discussed later), and microbiological growth-undesirable constituents of water. Samples of the injected water should be collected at several points in the system-for example, at any point in the system where a change in water quality could or should occur, and at the injection wells.

Sampling The importance of good sampling practices cannot be overemphasized. An extremely acccurate chemical analysis of a water sample followed by a brilliant assessment of the problems indicated by the analysis is worthless if the sample does not represent the water in the system.

Dissolved Gases To eliminate the loss of dissolved gases through changes in tempeature and pressure, testing of such gases should be carried out in the field soon after a water sample is taken. The three dissolved gases to be considered are hydrogen sulfide, CO2, and oxygen. Table 44.17 lists the test, the effects of the gas when present, remedial treatment, pH control, and tolerance permitted in ppm.


Microbiological Growth Static control of colonies of one-celled animals and plants is of much concern to operators attempting to maintain a suitable water for injection. Aerobic, anaerobic. fun- gal, and algal growths will cause reservoir and equipment plugging and corrosion. Table 44.18 lists the various organisms, their environment, the various treating agents that have been used, the results that may be expected, and the purpose of the treatment.

Special attention and control are required for sulfate- reducing bacteria (SRB). The presence of the sulfate ion is essential to the growth and reproduction of these particular bacteria. Sulfate, in turn, causes plugging. The reaction of the sulfate ion with the SRB forms the sulfide ion. which then reacts with iron. Iron sulfide is serious plugging agent and H 2 S is an extremely corrosive agent.

Early studies of SRB involved the the plate-count method, 153~1s4 a clinical practice derived for the purpose of isolating and identifying bacteria. But this technique is of little value in assessing sulfate-reducing bacteria activity, which is what really counts.

The objective of studies of SRB in a water system is to determine whether practical problems exist, and to be able to execute effective countermeasures if such problems are found. The concept of bacterial activity was developed to meet this objective. The procedures for conducting these studies are presented in the API RP 38 publication. Is’

Many organic and inorganic bactericides are now available to control this problem.

Minerals Appearance. A notation concerning the appearance of the water at the time it is sampled is important for future reference. Frequently, organic growths and precipitated material can be detected visually.

Temperature. The temperature of the water sample is important in estimating the solubilities of various materials. For example, calcium carbonate solubility decreases with increasing temperature, as does calcium sulfate and all sulfates.

Significance of pH. Simply put, pH is a measure of the acidity or caustic intensity of water. Two important points to remember are that calcium carbonate and iron solubilities both decrease with increasing pH value; therefore, the higher the pH the more difficult it is to hold iron in solution and to keep calcium scale from forming. How- ever, if iron is being removed in the water-treating program, then a high pH may be beneficial. The pH value is very important when corrosion control is considered.

Turbidity. A turbidity test measures the suspended material in a water and it is based on the intensity of light scattered by the sample in comparison with light scattered by a known concentration of a standard solution. The higher the scattered light, the higher the turbidity. Stan- dards are compared to Formazin polymer, which has gained acceptance as the turbidity reference standard sus- pension for water.

The generally accepted method of measurement is conducted with a nephelometer. Results are reported in nephelometric turbidity units (NTU), which correspond

with Formazin turbidity units (FTU) and Jackson candle units (JCU). Normal turbidity measurements are within the 0- to 50-NTU range.

Iron. Some form of iron is probably the most common plugging agent encountered in injection wells. Ferrous ;‘Foent(tF; +’ IS soluble to 100-t ppm, while ferric iron 1 .

) is insoluble except at low pH levels (3 ppm or less). Low iron contents are desirable in any water. The retention of soluble iron in solution is the prime objective in closed systems. In properly operated iron-removal plants, the iron content in the finished water should be less than 0.2 ppm. In many cases, it is possible to reduce the iron so that it is consistently less than 0.1 ppm. There should be no significant increase in iron content as the water travels from the pressure source to the injection wells.

Manganese. Soluble manganese in water reacts somewhat as iron does, except that it is more difficult to remove. In most waters, good manganese removal requires a pH level of 9.5 to 10 ppm. Manganese problems in the Ap- palachian oil fields have been very severe. Only in a few isolated cases has it been troublesome in the Illinois ba- sin; it has been of little concern in most floods in that area, or farther west. Low to moderate manganese contents are found in many waters and can be tolerated as long as the pH values remain low enough to keep it in solution.

Alkalinity. The alkalinity of water is defined by the measure of its acid-neutralizing capacity. Since the occurrence of hydroxide is quite unusual in flood waters, alkalinity generally can be taken as a measure of carbonates and bicarbonates. Calcium carbonate solubility depends on alkalinity; however, other factors, such as pH, calcium content, temperature, and total dissolved solids, influence the reaction.

Sulfates. Sulfates are of most interest from a deposition standpoint. Three generalizations may be made with regard to this class of substances.

1. An abnormally low or zero sulfate value in a brine suggests the possibility of the presence of barium and strontium. It requires practice and experience to evaluate a low-sulfate-content water.

2. In general, high-sulfate water should not be mixed with water containing appreciable amounts of barium or strontium.

3. A high-sulfate brine indicates there is a possibility of exceeding the calcium sulfate solubility. The solubility of SrS04 or CaS04 is governed by the limiting factor of either SO4 or Ca or Sr and the ionic strength or for- eign salt concentration of the brine.

Chlorides. Chlorides are the primary indication of the salinity of a water, or the ionic strength of a brine, or the presence of a fresh water. Chloride tests can be useful in tracing the progress of a waterflood.

Hardness. The term hardness refers to a measure of the amounts of calcium and magnesium that are present in the water and is expressed in ppm of calcium carbonate. Since calcium is involved, the hardness of the water is of importance in relation to calcium carbonate stability.


Calcium and Magnesium. These two minerals are grouped together because they are the principal contrib- utors to a water’s hardness. The calcium salts are less soluble than magnesium under most practical conditions. Also. the presence of an appreciable quantity of calcium is necessary for calcium sulfate and calcium carbonate scale to form. It is important to note that other factors, beyond the calcium value, must be considered in assessing calci- urn carbonate formation.

Suspended Solids. Suspended solids are a mixture of line, nonsettling particles, or precipitated material in the water. Unless suspended solids are removed, difficulties involving plugging of the injection or disposal wells can be expected.

Dissolved Solids. It is necessary to prevent precipitation of those soluble salts that are dissolved in the water, so that there will be no plugging of the sandface.

Total Solids. Technically, the term “total solids” means the combination of dissolved and suspended solids. Long experience in operating water injection systems has established that good water-quality control requires knowledge of not only the general content of the water but the constituents of the undissolved (suspended) material that exist under in-line conditions. It is this suspended material that may cause well and reservoir plugging. The suspended solids often are the result of the precipitation of constituents of the water, but the quantity and type of solids that actually are precipitating cannot be ascertained from the water analysis alone.

The MilliporeTM filter test has been developed to provide a means of measuring suspended material under injection system conditions. This test is conducted with the MF-Millipore filter of mixed esters of cellulose and a uniform pore size of, generally, 0.45pm opening. The filter diameter may be of several sizes; however, 90-mm- diameter filters are recommended because a greater volume of throughput water can be handled, thus giving a more representative test for the system being examined.

A small stream of water is taken, through suitable con- nections and the test apparatus, from the selected point in a system. The test apparatus that holds the filter will trap all the suspended material flowing through the sample line. The water effluent that passes through the filter is measured and recorded, for use in the later analysis, as volume throughput in milliliters of water. After sufficient water has passed through it and/or the initial pressure of about 10 psig has increased sufficiently to indicate plugging, the filter is removed and placed in a protective screwcap tube (preferably containing distilled water to prevent the drying out of the filter) and submitted to the laboratory for either comprehensive or selective analysis. As a safety precaution, it is highly recommended that duplicate samples be obtained through the use of a parallel- apparatus hookup.

Identification of the solids and particle size distribution (with Coulter counter) is useful for designing facilities to treat and to remove solids from the water.

Barium. Barium ions have been quite troublesome in many cases because of the extremely low solubility of the most common form of their deposition, barium sulfate.

It is generally undesirable to mix a water with appreciable amounts of barium with a water containing high sulfates or strontium.

Strontium. This is another alkaline earth metal that occurs in small quantities and is associated with calcium and barium minerals. It is found principally in the form of celes- tite (SrS04) and strontianite (SrC03) ores; its solubility in both forms is considerably greater than its barium coun- terpart but much less than CaS04.

Sequestering and Chelating Agents. The use of sequestering and chelating agents in injection waters plays an important role in preventing the precipitation of salts of calcium, barium, strontium. iron, copper, nickel, manganese, etc. ‘55 The definition of each term is given as: (1) sequester: to set apart, to put aside, or to separate, and (2) chelute: pertaining to or designating a group or compound which, by means of two valences (principal or residual, or both), attaches itself to a central metallic atom so as to form a heterocyclic ring.

The sequestering agent will separate the metallic cat- ion from the anion by chelation. This will prevent the metallic ion from reacting with the anions to form precipitates that will cause plugging of the reservoir. If precipitation of the metallic salt ions does occur, reverse flow of the injection well and acid treatments usually will correct the situation so that normal injection rates can be continued and maintained. The requirements for desirable sequestering agents are that they Is5 (1) form chelates in the presence of other ions such as calcium, magnesium, strontium, barium, and others that are common to waters used for secondary recovery, (2) form stable water- soluble chelates or complexes with iron, (3) be compatible with other chemical compounds used for water treatment, (4) be economically feasible, and (5) be easy and safe to handle.

The most widely used sequestering agents are “Ver- sentates” (trademark for certain salts of ethylenediamine- tetraacetic acid and related compounds), citric acid, gluconic acid, organic phosphonates, and the poly- phosphates. Of these, the citric acid sequestrants have been most successful.

Corrosion Inhibitors. Corrosion inhibitors are chemicals that are used to control the corrosive activity between the metallic alloys and water. “The current interest in chemical inhibition is largely a result of the availability of organic treating compounds that possess both corrosion- inhibiting and biocidal properties. Field and laboratory tests made with organic inhibitors such as quaternary, ros- in, and fatty amine compounds have indicated favorable results in minimizing corrosion caused by dissolved acidic gases.” ‘56

Selection and Sizing of Waterflood Plants The selection and the sizing of waterflood plant facilities normally are unique to each waterflood because of the many variable parameters. The primary parameters might be the volume and pressure, while secondary parameters might include the treating requirements and the economic position of the investor. A variation in any single one of these parameters might drastically modify or completely change the selection and sizing of a waterflood plant.


The volumes of injection water to be handled will, of course, be the most important basic item of information to learn for determining the size of the plant. Here, too, there are several parameters on which the calculation is based. Essentially, the water volume is a function of the gross size of the reservoir to be flooded, the porosity of the reservoir rock, the anticipated conformity or efficiency of the flood, and the ROS at both the initiation and completion of the flood. These data will be applied to the actual reservoir calculations, and only the final gross volume and the required daily injection rate must be known by the plant designer. As a general rule of thumb, 8 to 15 bbl of injected water per barrel of secondary oil, or I % to 2 PV of injected water, will provide a reasonable estimate of the ultimate water-handling requirements. Daily injection rates may vary from 5 to 25 bblift of pay. The producing-equipment capacity may be a limiting factor in determining the maximum injection rates. A relatively high ratio between the amount of fluid that is injected and the amount of fluid that is produced can be anticipated before fill-up.

There are certain other factors that should be considered in designing the proper capacity of the plant facilities. If the available quantity of supply water is relatively small, it is usually necessary to consider produced brine along with other supply waters so that an adequate injection volume is provided. Where the original source water is not compatible with the produced water, or where the produced water is best handled in a closed system and original source water is best handled in an open or semi- open system, flexibility in capacity design will be required. This flexibility is necessary to adjust or to balance capacities between two separate injection systems (one with a constantly increasing load, the other with a constantly diminishing load).

The pressure required to inject water into a formation is a function of formation depth, rock permeability, water quality, and the injection rate that is required. The basic reservoir data and secondary-recovery study will have defined the rock properties so that the anticipated surface pressures can be defined closely, if no adverse effects are anticipated as a result of poor-quality or incompatible water. Poor quality might be because the water contains a large quantity of solids as a result of poor filtration, inadequate settling, precipitation in an unstable water, or the growth of bacteria. Incompatibility might result from mixing injection water with formation water, from the swelling of clay particles, or from chemical reactions between the rock minerals and the injected water. In general. it has been found that the pressures than initially are encountered are less than might be anticipated when the only governing factors are depth and permeability; however, increasing pressures should be expected if there is no plan to reduce the injection rate as fill-up is approached. A final factor in predicting injection rates is the method of production. If the reservoir is to be produced by natural flow, the injection pressure must be sufficient to overcome dynamic hydraulic forces and to support a flowing rate of production. If, on the other hand, production is to be by mechanical means, with producing fluid levels at or near reservoir depth, a considerable reduction in injection-pressure requirements is possible. Con- sideration should be given to what the maximum allowable injection pressures should be. As a rule of thumb, pres-

sure at the surface should not exceed 0.5 psi for every foot of reservoir depth. The maximum wellhead injection pressure will limit the resulting pressure at the perforations, which is less than the parting or fracture pressure. This pressure can be determined by an injectivity test conducted before or during pilot flood operations. Breakdown pressures are often encountered below the 0.5-psi value, and in such circumstances the maximum pressure will be defined by the breakdown pressure. In older fields, or in reservoirs located at considerable depth, the mechanical strength of the injection-well casing may be the deciding factor concerning the pressure limit. This limitation can be overcome by installation of competent tubing set on a packer.

The source and the condition of the supply water will be the most important factors in determining a treating method. It is generally good practice to plan originally on using a closed system that requires little or no treating. Subsequently, the closed system may evolve into one in which the mixing of produced water will require custom-tailoring for conditions that are unique to the particular flood being considered. By starting with a basic treating system, the unit may be expanded into a complete version that may include aeration, chemical treating, flocculation, settling, corrosion inhibition, and bacteria control.

In developing the proper treating system for a particular plant, the economic factors that are unique to the situation should be given close attention. If the flood is to be of relatively short duration, it may be profitable to use a system that is less than adequate and to anticipate more than normal maintenance demands. In other circumstances, it might prove most profitable to install corrosion- resistant equipment and to reduce the use of corrosion- inhibiting treatment. Consideration should be given to installing fiberglass tubing or internally plastic-lined tubing in injection wells. Also, if new injection wells are to be drilled, a full or partial string of fiberglass casing should be considered to minimize corrosion and scale buildup, especially in the area across the producing formation. A paper published in 1980 discusses the use of fiberglass liners and injection tubing in a west Texas waterflood. I65

Possibly the last item to be considered by many design engineers, and yet the most important item in many companies, is the financial position of the investor. It is quite possible that a particular operator may have limited investment capital and would find it desirable to keep this sum to a minimum, at the expense of higher future operation costs or additional future investment. The capital investment situation might also affect the choice of injection rate. The operator might be in a financial position in which a low, long-term, constant income would be most advantageous; in other circumstances, a short-term, high- income situation might be most desirable. Under either of these conditions, the normal approach to determining injection rates and plant design would be modified to produce the most desirable income vis-8-vis investment conditions.

When the most desirable injection rate as well as the pressure and treating technique have been determined, the plant must be designed to f’it the prescribed conditions. F0r.a closed system, the plant design may be extremely simple and yet completely automatic. With in-line, high-


pressure filtration equipment and a relatively high- discharge head source well pump, it is possible to use the supply pump as the injection pump and to inject directly from the supply well to the injection well. In this plan, individual cartridge-type well filters may be used if the supply water is relatively free of solids.

The next stage in increasing the capacity of the injection plant would be to install a booster pump downstream from the filters, so that the supply pump and filters would not have to operate at injection pressures. The step after that would be to place a gas- or oil-blanketed water surge tank between the supply and filter system and the injection pumps. With this arrangement, low-pressure equipment can be used for supply and filtration; if the supply water and produced water are found compatible, produced water can be commingled in the surge tank. Where the systems are separated, it is also possible to use injection pumps with maximum pressure capacities. Further flexibility is also possible in that both source and injection rates can be varied independently, as long as the supply rate is at least as great as the injection rate. Corrosion frequently is minimized in the low-pressure side of this type of system by use of plastics, which also results in reduced fabrication costs.

If a supply water is naturally aerated, the operation of a closed system becomes pointless. Also, because of ex- cessive amounts of dissolved acid gases and/or a high content of dissolved iron, it may be desirable to aerate the water as a treating technique. When an open treating system is being designed, consideration should be given to using natural elevation or substructures to obtain gravity flow through the system. Under these circumstances, open gravity filters are often the most economical and practical.

When a complete chemical-treating program is planned, the most common approach is to have the prefabricated mixing and sludge tank placed immediately ahead of the filters. In certain circumstances, it has been found desir- ble to deaerate the treated water before using it for injection. Chemical treatments can be used; however, chemicals are too costly except for the removal of very small quantities of oxygen. Counterflow, bubble-tray towers that use natural gas or a vacuum are sometimes used for oxygen removal. However, oxygen is not removed if it can be avoided, because of the relatively high cost of the process; the price must be weighed against the deleterious effects of the entrained oxygen.

Centrifugal pumps have proved most satisfactory for low-pressure supply water and for injection at low pressures. Among the advantages of this type of pump are the small number of its moving parts and its excellent adaptability to volume control; however, in cases in which an appreciable amount of power is to be used, the relatively low efficiencies of centrifugal pumps (particularly when they are operated at other than design conditions) may preclude their use. In selecting centrifugal pumps, the proper metals should be chosen carefully for both the case and the trim to ensure the best performance. The greatest economy may be achieved with a cheaper pump that is subject to some corrosion rather than with a much more expensive pump, even though it might not be sus- ceptible to corrosion. The positive-displacement type of injection pump is the most common one in use. Some use has been made of multistage centrifugal pumps; however,

they have not yet been widely accepted because of some limitations in flexibility and efficiency.

The most generally accepted type of pump for medium- to high-pressure water injection is of either vertical or horizontal multicylinder design. These pumps are relatively simple to operate and to maintain, and they can be purchased with a variety of corrosion-resistant parts and accessories. The selection of the proper number of pumps and their capacity is contingent on the present and future requirements for the project. It is, of course, a good practice to provide a standby capacity that is sufficient to maintain continuous injection in case one pump has a mechanical failure. This can be accomplished by distrib- uting the maximum design load over two or more units so that at least half the injection capacity can be maintained.

A considerable number of filtering techniques are now used in the oil field. These involve ceramic-, metallic-, paper-, and cloth-element pressure filters with sand, grav- el, or coal media; and rapid sand pressure filters with sand, coal, or graphite media. The choice of filters is a function of the raw water quality and volume of water required for injection. If solids in the water must be reduced to submicrometer size, one of the element-type or diatomaceous-earth filters, or a combination of the two, is recommended. For less rigorous filtration, the gravity or rapid sand pressure filters are most widely used. In general, filtration rates are considered normal at about 2 gal/min-sq ft of filter area; however, this figure will vary considerably depending on the quality of the influent and the desired quality of the effluent. Decreased rates also may be desirable if very frequent backwashing is net- essary. The rates and techniques for backwashing are prescribed by the manufacturers of the various types of filters; this function should be considered in plant design to ensure adequate clear-water storage for both backwashing and continuous injection. It may be desirable to install additional filter capacity so that filtration will not stop during backwashing. The addition of standby filtration facilities also offers a guarantee against a total shut- down in which a filter requires a complete change of the filter medium.

Refs. 116, 144, 145, 147, 148, and 149 discuss waterflood plant facilities. Also, Ref. 163 discusses waterflood plant facilities for a North Sea waterflood project.

For a more derailed discussion on plant design criter- ia, design calculations, etc., the reader is directed to Chap. 15, Surface Facilities for Waterflooding and Saltwater Disposal.

Nomenclature a = distance between wells in a row, ft A = cross-sectional area, sq ft B = FVF, RBISTB

3, = 011 FVF, RBISTB B,,, = initial oil FVF, RBlSTB

B (,R = oil FVF at current reservoir conditions, RBiSTB

C,, = correction for gas expansion d = distance between rows of wells, ft

EC = fractional coverage or conformance efficiency


E;y = efficiency of permeability variation, fraction

ER = oil recovery efficiency, fraction f,,.,, = corner well producing water cut, fraction f,,,,. = side well producing water cut, fraction f(,z = fraction of oil flowing at the producing end

of the system f, = fraction of total flow coming from the

swept portion of the pattern f,,. = fractional flow of water F, = Caudle and Witte conductance ratio FF = ratio of viscous to gravity forces

F C’S = oil/gas saturation ratio Fp = cornerto~side~well producing-rate ratio

F,,.,, = WOR g = acceleration caused by gravity, ft/sec2 h = formation thickness, ft

it, = injection rate of fluid that has same mobility as the reservoir oil in a liquid- filled (base) pattern, as calculated from Eq. 20, RB/D

i,,. = water-injection rate, RBiD k,, = effective permeability to oil, md k,,. = effective permeability to water, md k., = permeability of x layer, or the layer that

has just been flooded, md k = mean permeability, md

k, = permeability value at 84. I % of cumulative sample, md

L = distance, ft M = mobility ratio

M,,,, = water/oil mobility ratio multiplied by the FVF of the reservoir oil at the time of flooding

n = number of layers IIBT = number of layers in which water has

broken through (varies from 1 to n) N = initial oil in place, STB, or ratio of square

root of production rates N,, = oil produced, STB

N ,“I = recovery to depletion (abandonment), fraction

PO = pressure at depletion (abandonment), psi P II,, = transient backpressure. psi PC = effective reservoir pressure (external

boundary pressure), psi p, = initial pressure, psi

Api<. = pressure differential between injection well and corner well, psi

AL’,\ = pressure differential between injection well and side well, psi

P,. = capillary pressure. p,, -pII.. psi q, = total flow rate (q,,, +q,,), B/D rr = pressure radius (external boundary radius),

ft

r, = distance from well to the point of pressure equalization at p,,,), ft

ru = effective radius of a well, ft

R, = outer radius of oil bank, ft R,,. = outer radius of waterflood front, ft SF = position of center of unflooded area at

moment of fill-up (correct drilling location), fraction of length of side or diagonal

S, = gas saturation at start of flood, fraction S,,. = residual gas saturation, fraction S,, = oil saturation at start of flood, fraction

S,,,. = ROS, fraction S,,. = water saturation, fraction

S ,I 2 = water saturation at the producing end of the system, fraction

s ,,,~r = average water saturation at water breakthrough, % PV

S,,,,sZ = water saturation at upstream end of stabilized zone, % PV

r = time, days V,t = displaceable PV’s injected, fraction W, = cumulative PV’s of water injected, fraction

8 = angle of formation dip referenced to horizontal

PO = oil viscosity, cp

P II’ = water viscosity, cp Ap = density difference between water and oil,

P~,~-P~~, g/cm3 Cp = porosity

Key Equations in SI Metric Units

ER =0.2719 log k+0.2.5569S,,. -0.1355 log ,L<,

-1.53804--0.0011444h+0.52478 .(l4)

ER =93.5399 [ 44 ;,s,,‘) ] o.0422 (2) O.O”

-0.2159 . . (15)

I ),’ = 5.427x 10~4k,,,h(p;,,/-~e)

. . (16)

3.4542x 10p4kApt =1+

1.0885x10-“khAp

cl,,dSsrb? -I

CL II 1 IO >

x 104.7297~10 'klrA&,,i,, J (19)


1.178966x lo-‘k,,hAp lb, = ,,..........

>

(20)

1.572211~10-~k,,.hAp l,,. = ,.........

>

(23)

I= 2.714382x 10-4k,,.h

, . .

>

where B,i is in m”/m’,

d,h,r,,r,,. are in m, I is in m’id,

i,, is in m3id, k,k,,. are in pm’,

Pivf,Pp are in kPa, s, s,, are in fraction,

t is in days, po,p,v are in Pass, and

4 is a fraction.

References I Carll, J.F.: “The Geology of the Oil Regions of Warren, Venango,

Clarion and Butler Counties.” Second Geological Survey of Pennshmia 1875-79 (1880) 268.

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5. Benner, F.C. and Bartell. F.E.: “The Effect of Polar Impurities Upon Capillary and Surface Phenomena in Petroleum Production,” Drill and Prod. Prac., API, Dallas (1941) 341.

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1 I. Land, C.S.: “The Optimum Gas Saturation for Maximum Oik Recovery from Displacement by Water,” paper SPE 2216 presented at the 1968 SPE Annual Meeting, Houston, Sept. 29- Oct. 2.

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99. Hiatt. W.N.: “Injected-Fluid Coverage of Multi-Well Reservoirs With Permeability Stratification,” Drill. and Prod. Prac., API, Dallas (1958) 165-94.

100. Douglas, J. Jr., Peaceman, D.W., and Rachford, H.H. Jr.: “A Method for Calculating Multi-Dimensional Immiscible Displace- ment,” Trans., AIME (1959) 216, 297-306.

101. Warren, I.E. and Cosgrove, J.J.: “Prediction of Waterflood Behavior in a Stratified System,” Sot. Per. Eng. J. (June 1964) 149-57: Truns.. AIME, 231.

102. Morel-Seytoux, H.J.: “Analytical-Numerical Method in Water- flooding Predictions,” Sot. Pet. Eng. J. (Sept. 1965) 247-58: Trans., AIME, 234.

103. Morel-Seytoux, H.J.: “Unit Mobility Ratio Displacement Calculations for Pattern Floods in Homogeneous Medium,” Sot. Per. Eng. J. (Sept. 1966) 211-27; Trans., AIME, 237.

104. Guthrie, R.K. and Greenberger, M.H.: “The Use of Multiple- Correlation Analyses for Interpreting Petroleum Engineering Data,” Dn’[/. und Prod. Prac., API. Dallas (1955) 130-37.

105. Schauer, P.E.: “Applicatton of Empirical Data in Forecasting Waterflood Behavior,” paper SPE 934-G presented at the 19.57 SPE Annual Fall Meeting, Dallas, Oct. 6-9.

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123. Sloat, B.: “Polymer Treatment Boosts Production on Four Floods,” Worid Oil (March 1969) 4447.

124. Sloat, B.: “Polymer Treatment Should Be Started Early.” Prf. Eng. (July 1970) 64-72.

125. Taber. J.J.: “The Injection of Detergent Slugs in Waler Floods,” Trans. ( AIME (1958) 213. 186-92.

126. Dunnmg. H.N. and Hsiao. L.: “Laboratory Experiments with Detergents as Water-Flooding Additives,” Prod. Monrh/y (Nov. 1953) 59 l-96.

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(Oct. 1959) 11-16.

Dalton, R.L. Jr., Rapoport, L.A., and Carpenter, C.W.: “Laboratory Studies of Pilot Waterlloods,” L Per. Tech. (Feb. 1960) 24-30; Trans., AIME, 219.

Jordan, J.K.: “Reliable Interpretation of Waterllood Production Data,” J. Per. Tech. (Aug. 1958) 18-24.

Justen, J.J. and Hoenmans, P.J.: “Pembina Pilot Waterflood Proving Successful,” J. Per. Tech. (June 1958) 21-23.

Rosenbaum, M.J.F. and Matthews, C.S.: “Studies on Pilot Waterflood ing,” .I. Pet. Tech. (Nov. 1959) 316-23; Trans., AIME, 216.

Wright, F.F.: “Field Results Indicate Significant Advances in Water Flooding: Effect of Rates on Performance in Browning Unit Water Flood,” J. Pet. Tech. (Oct. 1958) 12-14.

Water-Injection Pressure Maintenance and Waterflood Processes

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