water flooding

SPE SPE 10024 Society of Petroleum Engineer'S

Waterflood Design (Pattern, Rate, and Timing)

by Surendra P. Singh, * Conoco Inc. and O. Gerald Kiel* Conoco Inc.

'Member SPE-AIME

Copyright 1982, Society of Petroleum Engineers This paper was presented at the International Petroleum Exhibition and Technical Symposium of the Society of Petroleum Engineers held in BeJlng, China, 18-26 March, 1982. The material is subject to correction by the author. Permission to copy is restricted to an abstract of not more than 300 words. Write SPE, 6200 North Central Expressway, Dallas, Texas, 75206 USA. Telex 730989

ABSTRACT

Waterflooding is the oldest and by far the most important method used by the petroleum industry to increase recovery from both onshore and offshore reservoirs. Waterflood design is a complex problem that must ultimately be handled on an individual reservoir basis. This paper presents factors that should be considered in designing both onshore and offshore waterfloods.

The need for careful examination of the following factors is discussed:

1.

2.

3.

4.

5.

Reservoir geology deposition

Primary production of depletion

Reservoir and fluid

Reservoir pressure

Well spacing and patterns

and method of

mechanisms and stage

properties

possible waterflood

After these factors are discussed, the effects that pattern selection, timing and injection/producing rates have on project economics are discussed. A spec ial emphasis is placed on offshore waterflooding since it is now of significant concern.

INTRODUCTION

Waterflooding was first used over 100 years ago, but it was not until the 1950's that it gained popularity when field applications increased at a rapid rate. At the present time, waterflooding is so well regarded as a reliable and economic oil recovery technique that almost every field that does not have a natural water drive, is being or soon will be waterflooded. Waterflood projects from a reservoir engineering viewpoint, are very tedious and require detailed data. There are two basic classifications of water injection projects: References and illustrations at end of paper.

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(i) Waterflooding - those which displace oil from semi-depleted and depleted reservoirs, that is, increasing recovery through the more efficient displacement process.

(ii) Pressure maintenance - those which maintain a pressure in new or part ially depleted reservoirs for sustaining the production rate.

The main difference between secondary recovery (waterflooding) and pressure maintenance operations is the amount of reservoir pressure existing at the time the operations are begun. If the reservoir pressure is fairly high, the operation is called pressure maintenance, but, if the pressure has been substantially depleted, the operation is called secondary recovery. Both operations should increase ultimate recovery from the affected reservoir. Under normal circumstances, pressure maintenance operations will not bring about the rate increase that a waterflood will since it is installed when the reservoir producing rate is at a higher level.

Many factors important to waterflooding are also important to pressure maintenance, so that it is difficult to define a definite point of separation between the two processes. Accordingly, a major portion of the information presented in this paper is applicable to both waterflooding and pressure maintenance by water injection.

In this paper, we have made an attempt to review the reservoir engineering and geological parameters which control waterflood recovery. Also included is a discussion of criteria used in selecting a water injection rate, pattern and the timing of water injection. No attempt has been made to provide details of methods of forecasting waterflood recovery; however, the types of techniques generally used today are mentioned.

2 WATERFLOOD DESIGN (PATTERN, RATE, TIMING) SPE 10024

EVALUATING WATERFLOOD PROSPECTS

There are a number of reservoir factors which have a profound influence upon the success of a waterflood project and unfavorable values for any one or two of these factors can result in the complete failure of a flood, even though other factors may be quite favorable. These engineering factors involved in evaluating potential waterflood recovery normally fall into two general categories, primary and secondary variables (1). The primary variables are utilized directly in the arithmetic calculation of recoverable reserves, while the secondary variables affect the estimate of these reserves indirectly through the primary variables. The primary variables are:

1. Primary recovery efficiency

2. Connate water saturation

Volumetric sweep efficiency

4. Residual oil saturation to waterflooding

5. Crude oil shrinkage

6. Floodable reservoir pore volume

The secondary variables are listed below, with the numbers in parentheses indicating the primary variables they affect:

1.

2.

3.

4.

Geologic (structure, considerations (1, 3, 6).

continuity)

Permeability magnitude and its variation (1,3,4). Oil viscosity (1, 3, 4). Relative permeability (1, 3, 4).

5. Flood pattern (3, 4). 6. Reservoir pressure (5).

7. Economic factors such as crude price, depth of reservoir, well spacing, operating costs, etc. (1,3,4,6). Callaway (1) developed a relationship for

estimating total waterflood recoverable reserves:

Npwf V12 ( 1

- Swc) x {1 - Rp - Boi x ( 1 - Ev x Ed)} =

Boi Bof

and (1)

Ed = 1 - (Sorl (1 - Swc (2) where:

Vp = Floodable reservoir pore volume (7758Ahl6), barrels Boi = Original formation volume factor,

RB/STB.

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Bof =

Swc =

Sor =

=

Ev =

Ed =

Npwf =

Formation volume factor during water-flooding, RB/STB.

Connate water saturation, fraction.

Residual oil saturation after waterflooding, fraction.

Primary recovery efficiency, fraction of original oil in place (OOIP).

Overall volumetric sweep efficiency, fraction of reservoir volume, fraction.

Maximum unit disp~acement efficiency (to be defined later), fraction. Waterflood reserves, STB.

A sensitivity analysis of waterflood recovery using equation (1) can be performed to examine the effect of the primary variables on oil recovery.

Certain of the six primary variables are more directly susceptible to evaluation than are others under most field condit ions. The crude shrinkage can usually be determined or estimated fairly closely. Log and core data can provide reasonably accurate estimates for connate water and residual oil saturations. Detailed geologic studies are needed to determine floodable reservoir pore volume. The remaining factor, overall sweep efficiency, has been the subject of a tremendous amount of experimental and theoretical discussion.

As related to waterflooding, a brief discussion of geological and depositional environment factors, primary production mechanisms and stage of depletion, fluid and rock properties, and of factors

affectin~ recovery efficiency (Ev x Ed) is given below.

GEOLOGICAL FACTORS AFFECTING WATERFLOODING

One of the first steps in organizing reservoir information for waterflooding is to determine the geometry of the reservoir. The structure and stratigraphy of the reservoir control the location of wells, and to a large extent, dictate the methods by which a reservoir may be waterflooded. For example, if a suitable structure exists and the remaining oil saturation is sufficient, a peripheral type flood may result in a higher areal sweep efficiency than conventional pattern or line drive floods.

Most water injection operations to date have been conducted in fields exhibiting only moderate structural relief. In such pools, the dip may be so small that it has no not iceable effect on waterflooding. Thus, the location of injection and producing wells may be made to conform to property lines and known sand conditions. Such a practice may not prove successful in reservoirs where oil and gas distribution has been controlled by a high relief structure.

SPE 10024 S. P. SIOOH, O. G. KIEL

Structural features such as faults, or stratigraphic features such as shale outs, or any other permeability barriers, will usually influence waterflood design. An otherwise suitable reservoir may be so highly faulted as to make any injection program unattractive. For efficient production each fault block must be considered a separate reservoir.

Vertical permeabilities, which may be less than horizontal permeabilities because of grain orientation and cementing material, can be measured on core samples. But, it is also necessary to determine distribution of non-pay intervals because small amounts of impermeable rock can profoundly affect vertical permeabilities (2) even if it is discontinuous and randomly distributed. Proper description requires knowledge of the depositional environment. Natural fractures can cause serious by-passing of the injected water unless patterns are carefully oriented (see discussion of factors affecting areal sweep efficiency).

Conditions of the depositional environment (e.g. deltaic, reef, etc.) determine the type of deposit which will occur. For example, layering caused by depositional sequence and facies change both affect lateral cont inuity. A thorough understanding of these environments is essential for determining distribution, continuity and internal characteristics such as porosity, permeability, silt/clay interbedding, and flow barriers, etc. of reservoir rock. As an example, a depositional study (3) of the Boundary Lake field in British Columbia (Canada) showed that the reservoir is comprised of thin continuous porous zones confined above and below by dense beds. This type of reservoir lends itself to a pattern type waterflood. Detailed correlation and mapping of individual zones is a prerequisite for assuring that every zone is being waterflooded.

A dramatic change occurred in continuity concepts (Figure 1) when surface and subsurface studies of the San Andres formation in the Wasson Field in West, Texas showed that gross modeling of continuity was not adequate (4). The revised model consists of 10 mappable pay units, some of which are not continuous between wells drilled on 40-acre spacing. The pay intervals are, at places, separated by impermeable barries that prevent cross flow. On the basis of this concept of "continuous" and "non-continuous" pay, infill drilling on 20 acres spacing was initiated. The work of George and Stiles (5) also illustrates the techniques used to quantify the discontinuous nature of porosity zones within the gross reservoir section by constructing a relationship between pay continuity and well spacing (Figure 2). They also attempted to show that floodable pay, even though continuous, is not necessarily floodable because of irregularities in bed geometry between wells. Pract ical applicat ion of the floodable pay concept shows that as the average distance between injectors and producers decreases, floodable pay increases. This concept becomes important when evaluating infill drilling and pattern changes.

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PRIMARY PRODUCTION MECHANISMS AND STAGE OF DEPLETION

The driving forces which cause oil and gas to flow to the wellbore can be divided into four basic types: depletion drive, gas cap drive, water drive and gravity drainage. If more than one of the above forces is a major contributing factor, the reservoir is called a "combination drive" reservoir, e.g., a reservoir with both a free gas cap and an external water drive.

One would usually expect a reservoir wi th a strong natural water drive not to be subjected to water injection unless there are some very unusual circumstances such as tremendous reservoir size or a lower rate of production. Another primary recovery mechanism where water flooding would not normally be attempted is in reservoirs with large gas caps. These reservoirs have sufficient natural reservoir energy so an external source of energy is not required for efficient oil recovery. Here, it is assumed that there are no unfavorable flow barriers to stop gas cap expansion to provide pressure support in the oil zone. Also, in general, reservoirs with gas caps and thin oil rings are often not good candidates for waterflooding because downdip (or bottom) water injection may force oil into the gas cap area where it frequently is unrecoverable.

A reservoir with good gravity drainage is another example of reservoirs which probably should not be waterflooded if we are attempting to maximize recovery. Gravity drainage is a much more efficient recovery mechanism as compared to displacement by water. In the case of fair gravity drainage reservoirs, water injection probably should be used only to increase producing rates.

In depletion drive (dissolved gas drive) reservoirs natural energy is less efficient than that provided by water injection. Such reservoirs are good candidates for waterflooding. Also reservoirs with inefficient water drives, and those with small gas caps can benefit from water injection.

In depletion or weak combination drive reservoirs, distribution of free gas saturation depends on the stage of the reservoir's depletion (pressure reduction). A higher gas saturation would require larger water volumes for reservoir fill up and oil production response would be delayed. If gas saturation is fairly high, it may not be possible to form an oil bank and oil production will occur at high water cuts. Several authors (6) have experimentally shown that, for a given oil saturation, recovery by waterflooding increases with increasing gas saturation up to a certain limit. The effect of gas has been to cause lower residual oil saturations behind the front than could be obtained by waterflooding the same system in the absence of gas. However, the degree of improvement in oil recovery has not been established quantitatively to any degree of accuracy.

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4 WATERFLOOD DESIGN (PATTERN, RATE, TIMING) SPE 10024

FLUID AND ROCK PROPERTIES

The most important fluid and rock properties which affect the susceptibility of a reservoir to waterflooding are formation volume factor (FVF), oil viscosity, rock permeability and its distribution, and relative permeability. The effect of FVF on waterflood recovery can be evaluated by assuming the residual oil saturation behind the front is the same regardless of when water injection starts. We then calculate the number of stock tank barrels of oil in the swept portion of the reservoir which will remain as residual oil saturation at different pressures for the project. It can be shown that stock tank barrels of oil left in the swept area is minimum if the waterflood is started when the reservoir is at bubble point pressure.

The viscosity of oil and water ( Mo. Mw ) and the relative permeability characteristics of the rock (kro, krw) affect the mobility ratio. In terms of waterflooding, the mobility rat io is the water mobility in the water swept portion of the reservoir divided by the oil mobility in the unswept portion. Mathematically:

M = krw x.!:!:!L Mw kro

The reservoir oil viscosity appears explicity in the above equation. Figure 3 shows the effect of oil viscosity on mobility ratio for strongly water wet and strongly oil wet rock (6). Regardless of rock wetability preference, the mobility ratio increases with increasing oil viscosity. The oil and water viscosities and rock relative permeability characteristics also enter into the fractional flow equat ion, which for a horizontal system can be written as:

fw = --~--~-----1 + kro Mw

krwMo (4)

The oil recovery efficiency at breakthrough, following breakthrough and cumulative pore volumes of water required to produce oil up to a given water cut are strongly influenced by this fractional flow relationship. Figures 4 and 5 show the effect of oil viscosity and fractional flow curves for strongly water wet and strongly oil wet rock, respectively. It can be shown that, regardless of wettability, a higher oil viscosity results in less efficient displacement; that is, there is a lower recovery at any water-oil ratio and increased injected water volume is required to achieve that recovery.

The magnitude of permeability of the reservoir rock controls, to a large degree, the rate of water inject ion which can be sus tained for a specified pressure at the sand face. Reasonably uniform permeability distribution is essential for a successful waterflood since this determines to a great degree the quantities of injected water that must be handled. If great variations in the permeability of individual continuous strata within the reservoir exist, injected water will break through early in high permeability streaks and will cycle large volumes of water before lower permeability streaks have been effectively swept.

206

Directional trends in permeability in a given strata will also cause early breakthrough if patterns are not aligned properly (to be discussed later). REVIEW OF FACTORS AFFECTING DISPLACEMENT, AREAL AND VERTICAL SWEEP EFFICIENCIES

The fraction of oil that will be removed by waterflooding is a function of the following efficiency factors:

1. Areal sweep efficiency, Ea

2. Invasion or vertical sweep efficiency, Ei

Unit displacement efficiency, Ed

Figure 6 depicts these three efficiencies (7). Areal sweep efficiency is the pattern area that

has been displaced by water divided by the total pattern area. Vertical sweep or invasion efficiency is a measure of the uniformity of water invasion and is defined as the cross sectional area contacted by the injected fluid divided by the cross sect ional area of the entire reservoir thickness behind the injected fluid front. The unit displacement efficiency is that fraction of initial oil saturat ion that has been displaced from pores by water, thus:

Soi Sor Soi (5)

Other efficiency factors can be defined by a combination of the above efficiencies. For example, volumetric sweep efficiency Ev, is given by:

Overall recovery efficiency ER, displacement process can be written as:

AREAL SWEEP

(6) by the

Numerous studies have shown that the areal sweep efficiency is a function of the following reservoir and operating variables:

1. Flood pattern; that is well arrangement in relation to one another and with respect to reservoir boundaries.

2. Mobility ratio

Permeability orientation

4. Fracturing and fracture orientation

5. Formation dip

6. Depleted zones

7. Volume of water injected

SPE 10024 S. P. SINGH, O. G. KIEL

A wide variety of flood patterns (injection -production well arrangement) have been studied. Figure 7 shows the arrangement of various patterns and Table 1 summarizes the characteristics of these patterns (6). The efficiencies listed in Table 2 for various confined well patterns at breakthrough indicate the effect of the type of pattern. A comparison of the data for the two direct line drive patterns indicate that sweep is a function of spacing ratio, the greater ratio resulting in higher breakthrough sweep efficiency. The areal sweep efficiency of a developed pattern continue to increase after water breakthrough. This has been shown for five spot and line drives (8) and for nine spots (9). The effect of off-pattern wells was studied by Prats et al (10) and they found that the oil recovery at breakthrough is always lower with an off-pattern injection well. Sweepout beyond normal pattern was studied by Caudle et al (11). They found that at least 90 percent of the area lying outside the last row of wells and within one well spacing of these wells would ultimately be swept by the injected water.

The patterns discussed above are geometrically repeated arrangements for developing an entire field or for pilot flooding. Another type of flood pattern which is often utilized is the end to end flood pattern or a form of peripheral flood pattern where the producing wells are either shut-in or converted to water injection once the injection water breaks through. Ferrell et al (12) showed that when producers are shut in at water breakthrough, efficient areal sweep is obtained and less injected water is required to recover the oil. Operators of peripheral waterfloods often use this technique, taking oil production from wells ahead of the flood front and producing only the last well or row of wells to high water-oil ratios.

The effect of mobility ratio on areal sweep efficiency has been studied extensively with the aid of reservoir models for different injection patterns. The breakthrough sweep efficiency is significantly affected by mobility ratio (decreases with increasing ratio) and, following breakthrough, the areal sweep increases by continued injection of water. Figure 8 shows the fraction of a five spot that will be swept at water breakthrough and at increasing water cuts of the produced fluid for different values of mobility ratio (3). Water cuts can be related to cummulative volume of water injected.

Landrum and Crawford (14) have studied the effect of direct ional permeability on sweep efficiency at unit mobility ratio, for a five spot and direct line drive (square pattern). Their results are shown in Figure 9 for two relative positions of directional permeability. A 45 0 rotation of patterns could result in approximately 100 percent sweep for the five spot and approximately zero sweep for a line drive.

207

The effect of vertical fractures on the sweep of a pattern in the five spot well network has been studied by Dyes, et al (15). They found the effect of fractures to be a function of fracture length and orientation for a given mobility ratio. Figure 10 present results for two cases, that where the vertical fracture is in the line with the breakthrough streamline (unfavorable), and that where the vertical fracture is 45 degrees displaced from this streamline (most favorable orientation). Also presented is the effect of fracture length for the unfavorable cases. Dyes, et al concluded that fractures up to one half the distance between wells had little practical effect on the areal sweep efficiency or values of the order of 90 to 98% sweep could be achieved by operat ing to 90% water cut. Also, the general conclusion to be drawn from these results is that the producing wells should be arrayed parallel to the fracture orientation or maximum permeability axis.

Peripheral injection programs are often used in dipping beds, but the high viscosity for some crudes (low mobility) may dictate closer spacing of pattern floods if economical producing rates are to be obtained. Prats et al (16) have shown that in addition to formation dip and the orientation of a well array with respect to dip, operational procedures affect the areal sweep even though injection and production rates are balanced. If the injection and producing wells are maintained at constant injection and production heads, respectively, the dip has no effect (horizontal data apply). However, if the producing wells are maintained at constant pressure, sweep efficiency is reduced. In a partially depleted system, three regions of differing mobil it ies could be present. These are the un invaded depleted zone in which gas is flowing, an oil bank, and the water bank. The favorable mobility of the gas displacement by oil results in improved sweep over that obtained if oil and injected water are present (17).

Operating methods have an effect on the breakthrough sweep effic iency, even in horizontal systems, for example, in the case of an inverted nine spot (Figure 11), the ratio of producing rates of the corner wells to the side wells (18). Unbalanced injection rates in five spots arrays have been shown by Crawford to vary the breakthrough sweep efficiency from 45 to 72 percent.

VERTICAL SWEEP

Variations in vertical sweep may be caused by lensing, faulting, shale barriers, permeability variations, and other reservoir heterogeneities. Vertical sweep values in the range of 70% to 90% are considered to be common in typical reservoirs. Reservoirs with an extensive network of fractures and/or areally widespread gas caps provide short circuits for injected water thus drast ically re-ducing vertical sweep.

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6 WATERFLOOD DESIGN (PATTERN, RATE, TIMING) SPE 10024

A detailed discussion of all the factors affecting vertical sweep is beyond the scope of this paper. However, factors affecting vertical sweep are listed in Table 3 along with general statements regarding their effect on this parameter. In brief, formation stratification, permeability stratifica-tion, mobility ratio, relative magnitudes of gravity, capillary, and viscous forces (inject ion rate), cross flow, and total fluid injected determine the vertical sweep which can be achieved in a waterflood. Figure 12 shows volumetric sweep efficiency product of areal and vertical sweep at breakthrough as a function of permeability variation and mobility ratio for a five spot pattern with no gas saturation (19).

UNIT DISPLACEMENT EFFICIENCY

The unit displacement efficiency, expressed as the fraction of oil displaced from a volume of rock which have been contacted by the injection water, depends on many physical parameters. Some of these are:

1. Rock wettability - water wet, oil wet, or neutral.

2. Pore size and its distribution (permeability) .

3. Viscosity of fluids.

4. Gravity forces.

The wetability of a rock determines which fluid coats its surface. In general, water as a displacing fluid is more efficient in a water wet system as compared to an oil wet system. In preferentially water wet rock the oil remaining at floodout exists as trapped isolated globules in most of the flow channels. In preferentially oil wet rock, at conditions approaching flood out, the residual oil exists in the smaller flow channels and as a film in larger water filled pores.

The pore size and its distribution controls the magnitude of permeability, capillary pressure, and fluid distribution in a multifluid system. Unfortunately, this parameter can' not be measured directly and only approximations have been obtained

~y ~ean of capillary pressure studies. Fortunately, It lS not necessary for us to determine wetability, and pore size distribution of the reservoir rock to determine unit displacement efficiency during waterflooding. The effect of these factors is included in the water - oil flow characteristics (relative permeability) of the reservoir rock. Relative permeabilities, when measured on native state reservoir rock samples at reservoir temperatures, show the composite effect of pore geometry, wetability, and the direction of saturation change (drainage or imbibition).

The unit displacement efficiency is related to oil-water relative permeability, viscosity, capillary pressure, and gravity forces by the following generalized fractional flow equation (20):

1 +0.001l27 K x kro x~ { aPe fw

~L - 0.433 b,p Sin ad} )10 qt a

208

where:

fw =

K =

kro =

krw =

)10 =

)1w =

qt =

ad =

b,p =

)1w kro +--)10 krw (8)

Fractional flow of water in the flowing stream at any point in rock (water cut)

Formation permeability, md

Relative permeability to oil

Relative permeability to oil

Oil viscosity, cp

Water viscosity, cp

Flow rate, bid

Angle of formation dip to the horizontal

Water oil density difference, ( p w - p 0), gmlcc

Pc = Capillary pressure - pressure in oil phase minus pressure in water phase

L = Distance along direction of movement

A Area of cross section normal to flow direction

It should be noted that above the fract ional flow equat ion reduces to the simpler form given earlier (Equation 4) when capillary and gravity forces are neglected:

(~ a L =

o 0 and ad=O.O)

The unit displacement efficiency at water breakthrough is found by constructing a fractional flow curve assuming a negligible capillary pressure term and by drawing a tangent to the fractional flow curve from a value of fw = 0.0 and a value of water saturation corresponding to the connate water saturation (assuming connate water saturation is irreducible water saturation also). This tangent construct ion is shown in Figure 13. The value of the water saturation at which the tangent intersects fw = 1.0 line is the average water saturation in the water invaded zone at breakthrough, S wbt). The unit displacement efficiency at this time is (21):

= S wbt - Swc

1.0 - Swc (9)

SPE 10024 S. P. SI~H, o. G. KIEL

The maximum unit displacement efficiency by waterflooding is:

Sor (10) - Swc

This value of unit displacement efficiency was used earlier in Equation which is used to calculate waterflood reserves.

As can be seen from Equation 8 , for inclined reservoirs the fractional flow curve is dependent upon the formation permeability, the total flow rate, the density difference, and dip angle in addition to water - oil relative permeabilities and viscosities. Also, by constructing fractional flow curves, it can be shown that water displacing oil up dip will result in a lower value of fw at any water saturation than water displacing oil down dip. The value of dip Rngle is measured from the horizontal with flow moving up dip assigned a positive angle and flow moving downdip assigned a negative angle.

Furthermore, worthy of mention here is the effect initial wRter saturation has on the formation of an oil bank in front of an advancing water front. If the initial water saturation exceeds some critical value, (such that it is no longer possible to constrict a tangent to the fractional flow curve), an oil bank may not form; and although substantial oil recovery may be achieved, oil will be produced at high water cut values.

EFFECT OF INJECTION AND PRODUCING RATES ON OIL RECOVERY'

During the late 1950's, a controversy existed on the effect of injection or producing rate on the oil recovery of a waterflood. Let us consider the following factors which have been mentioned in some detail earlier:

(i) In horizontal reservoirs the displacement efficiency is independent of rate.

(ii) The vertical sweep efficiency is influenced by viscous, capillary and gravity forces. The viscous forces result from the pressure gradient and thus are proportional to the flow rate. In water wet rocks, capillary forces can be efficient in displacing oil from less permeable portions of the reservoir. With lower injection rates more time is available for imbibition. However, published information (22) suggests that rate variations of five-fold or more have little effect on recovery. The degree of gravity segregation depends on the injection rate - lower values enhance the tendency for water to under run the oil and cause earlier water breakthrough. However, the degree of gravity segregation also depends upon horizontal and vertical transmissibilities to fluid movement. Again, published information (23) supports that a significant change in flow rate is required to effect small changes in volumetric sweep resulting from gravity forces.

209

As concluded by Craig (6), it is impossible to make a general statement as to an optimum water injection rate because of the wide range of rock and fluid properties in oil reservoirs. Furthermore, technical studies suggest that injection rate changes of five - fold or more are required to significantly alter the effects of reservoir capillary and/or gravity forces. TlJus, in reservoirs with only a small amount of dip, oil recovery should not be sil'nificantly affected by variations in injection and production rates within pract ical limits. In steeply dipping reservoirs, when downdip peripheral injection is utilized, slower rates should result in higher oil recovery. In such cases, economic factors must be considered in selecting an optimum injection rate. OPTIMUM TIME TO START A WATERFLOOD

The optimum time to start a waterflood depends on several factors. In the following discussion, it is assumed that the objective is to maximize oil recovery, although other economic objectives such as maximum discounted rate of return may be desirable in many cases.

As discussed by Tarr et al (24), two types of factors dictate the optimum time to start wa terflood:

1. Pressure dependent factors

2. Other factors such as permeability variation, reservoir geometry, etc.

Since the formation volume factor has its highest value at the bubble point pressure, a water-flood initiated when the reservoir pressure reaches this pressure, will leave minimum stock tank barrels of oil trapped in the reservoir, provided pressure during waterflooding is never allowed to go below the bubble point. Thus when considering oil shrinkage alone, one can say that optimum time to start a h'aterflood is at the bubble point pressure.

At this pressure also, the reservoir oil viscosity is at its minimum value, which improves the mobility ratio and areal sweep. Other factors which favor waterflooding at the original bubble point pressure are (i) the producing wells have the maximum producitivity index and (ii) flood response occurs with minimum delay because the reservoir is liquid filled at the start of the flood.

Reservoir geometry and permeability variations can affect optimum timing for waterflooding if recovery by water injection is expected to be severely reduced due to a poor volumetric sweep. In such cases, the actual method to determine the optimum time for water injection should involve calculations of ultimate recovery (primary plus waterflood) as a function of the pressure at which waterflood is to be started. A plot of recovery vs. pressure can be used to determine the optimum pressure, and hence the time to start water injection.

7

8 WATERFLOOD DESIGN (PATTERN, RATE, TIMING) SPE 10024

If water injection is started to optimize some economic criterion (e.g. maximum present worth), then the only way to determine the optimum time to begin water injection is to compute total recovery, rate, investment and income for several assumed times of initiation. By comparing the results of these calculations the best alternative can be selected.

WATERFLOOD PREDICTION METHODS

Over 30 calculation techniques have been discussed in the waterflooding literature. A monograph (6) published a decade ago provides an excellent description and comparison of these methods. The most desirable method of predict ing waterflood performance would, of course, include all pertinent fluid flow, well pattern and heterogeneity effect s. It appears that mathemat ical reservoir simulators have approached close to such a method. These models require detailed reservoir data and the expense of running performance predictions could be substantial for some complex three dimensional models. Other simple analytical methods, which many times work reasonably well, have been presented by Higgins and Leighton (25), Craig et al (26), and Prats (27).

DESIGN OF WATERFLOODS

The reservoir engineering design of waterfloods involves:

1. Specifying the rate of water injection. 2. Establishing the waterflood pattern.

3. Estimation of producing rates and expected oil recovery.

The interrelated factors affecting oil recovery have been discussed earlier. It is difficult to estimate water injection rates with any accuracy using analytical methods. Frequently, the most reliable injection data is obtained from pilot tests or from similar waterfloods located nearby.

SELECTION OF A FLOODING PATTERN

The regular waterflood patterns yield areal sweep efficiencies in the high permeability layers approaching 100 percent at economic water-oil ratios. The proposed optimum waterflood pattern should (6):

1. Provide desired oil production rate.

2.

3.

4.

Provide a sufficient water injection rate to support this oil production rate.

Maximize oil recovery with a minimum of water production to lift, handle and dispose of.

Take advantage of known reservoir rock characteristics such as directional permeability, fractures, dip, etc.

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5. utilize existing wells and thus minimize drilling of new wells.

6. Be compatible with the flooding patterns of operators on other leases.

At first, basically two different choices are available:

(a) Treatment of the reservoir as a whole using a peripheral flood.

(b) Waterflooding utilizing a repeating pattern such as five spot, nine spot, etc.

PHERIPHERAL FLOODING

As the name implies, this technique ut ilizes wells along the flanks of a reservoir for water injection. For example, one of the worlds largest offshore waterfloods is the Umm Shaif field (27) of Ahu Dhabi which has 25 peripheral injection wells. In such a flood, production wells can be shut in at or shortly after water breakthrough, and the oil recoverable at these wells will be recovered at the next row of producers. Of course, the operator of a peripheral flood may choose to convert watered - out producers to injectors and thus keep injection wells as close as possible to the water front without by-passing any oil. In dipping reservoirs this type of flooding is preferred to take advantage of the formation dip to even out of the waterflood front. Some of the advantages and disadvantages of peripheral flooding are as follows:

1. Generally maximum oil recovery is obtained with a minimum of produced water. Also, production of significant quantities of water can be delayed until only the last row of producers remains.

2.

3.

Because of the limited number of injectors as compared to the number of producers, total water injection tends to be limited as well as the number of producers responding to anyone time. Also, it takes a long time for injected water to fill up the gas space, with the result that production rate increases are delayed beyond what they would be for a pa t t ern flood.

Sufficiently high permeability is required to move water at the desired rate over a distance of several well spacings if the operator does not wish to convert watered out producers to injectors.

WATERFLOODING USING REPEATED PATTERNS

If a pattern waterflood is indicated, the engineer must decide the type of pattern. Where the wells are on square spacing, as is usual, five spots and nine spots are the most common flooding patterns. Laboratory studies (28, 18) have shown that both of these patterns yield nearly the same oil recovery and HOR performance. The choice can be made primarily on the basis of water injectivity,

SPE 10024 S. P. SIOOH, o. G. KIEL

although reservoir heterogeneity is an important factor. (See Table 1 for ratio of injectors to producers for different types of patterns.)

The mobility ratio is a measure of the injectivity of a well relative to its productivity. At unfavorable mobility ratios (M > 1), water injectivity exceeds the oil productivity of a producer after fill up and the reverse is true at favorable mobility ratios. Thus, at an unfavorable mobility ratio, a pattern having more producers than injectors is indicated to maintain balanced injection and production rates. For favorable mobility ratios, the recommended pattern should have more injectors than producers.

As discussed earlier, the choice of pattern must also consider direct ional permeability, the existence of reservoir fractures and their orientation. The prudent engineer will arrange his pattern such that the direction of maximum permeability or fracture orientation is in the same direct ion as the line joining the adjacent injectors.

In brief, the choice of either a peripheral or a repeating pattern flood is usually made on the basis of reservoir size, dip, permeability and the need for a fast initial production response.

WELL SPACING

The major factor in recovering oil by waterflooding is ,reservoir heterogeneity. In 1945, Craze and Buckley (29) concluded that recovery efficiency is independent of well spacing. Some of the leading experts in the oil industry believe that well spacing is the key to solving recovery problems caused by heterogeneity (30). It is not difficult to see that in reservoirs with limited lateral communication such as lenticular sands or discont inuous porosity development in blanket carbonate deposits, or in faulted reservoirs, there should be an improvement in oil recovery with reduced well spacing, but this is very difficult to quantify. Certainly, reduced well spacing does allow for higher total injection and oil production rates.

OFFSHORE RESERVOIRS

Waterflood operations in the offshore areas are different, not so much in reservoir characteristics, but in special operating considerations that exist in the those regions. First, a high economic limit is particular to offshore and the life of these fields is shorter than onshore reservoirs. From the standpoint of well spacing, the luxury of having wells close together does not exist. Thus, sand continuity and fault patterns may not always be completely understood. Also wells are completed into more than one sand.

The uncertain reservoir configuration, faulting, and large spacings usually preclude the possibility of a pattern -type flood. Also, since offshore operating costs are much higher than onshore, most water injection projects (in the absence of an active water drive) will be started

211

for pressure maintenance to keep oil product ion rates at the highest possible values. Also, abandonment water-oil ratios will be lower than many onshore projects. Very careful early planning is mandatory for offshore reservoir development to maximize oil recovery.

The following is a list of engineering factors, not necessarily from a reservoir engineering point of view, which should be taken into consideration in the development of offshore waterfloods:

1. Early delineation drilling, that is, sufficient wells must be drilled to obtain the best reservoir description as early as possible. Reservoir data gathering in early wells (cores, logs, well tests, etc.) must be planned to get "ball park" estimates of expected well productivities and major reservoir heterogenetics for early planning of production facilities.

2. Early coordination with Drilling Department for best directional drilling and completion program.

3. Determination of platform size to accomplish desired drilling densi ty and its capRbility to hold waterflood facilities.

4.

5.

6.

Early determination of offtake levels possible with pressure maintenance and/or artificial lift.

Determination of a facilities plan; that is, where separation will occur, the size of major separators, offshore loading or pipeline, central or widespread injection, field operating pressures and temperatures, recognttion of major long lead items such as water injection trains and gas lift compressors, early well engineering design to determine tubular sizes for maximum rates, etc.

Early "dump flood" evaluat ion prior to pressured injection.

7. Injectivity testing to confirm oil/water relative permeability measurements. Also identification of clay problems and other water injection impediments such as scale formation.

In addition to the above engineering considerations, another important factor is a team approach. Since offshore development usually requires "large" accumulations, it is very important to maintain continuity of manpower over the first few (five or so) years of a project. Here, the explorationist, engineer and project people must be continually updated on new wells and how they fit the plan. Many changes take place in the early years of a project.

9

10 WATERFLOOD DESIGN (PATTERN, RATE, TIMING) SPE 10024

SUMMARY

This paper presents important factors that should be considered in designing both onshore and offshore water injection projects. The need for carefully examining the reservoir geology, primary production mechanisms, stage of depletion, rock and fluid properties, etc. is discussed. A brief review of effects of injection and production rates, pattern type, well spacing, and injection timing on waterflood recovery is also presented. Since offshore reservoirs are of significant concern and do require speCial continued attention, a list of important engineering factors pertaining to their development is provided.

References

1.

2.

3.

4.

5.

6.

8.

Callaway, F. H.: "Evaluation of Waterflood Prospects", J. Pet. Tech., October, 1959, pp 11-16.

Richardson, J. G., Harris, D. G., Rossen, R. H., and Van Hee, G.: "The Effect of Small, Discontinuous Shale on Oil Recovery", J. Pet. Tech., November, 1978, pp 1531-1537.

Jardine, D., Andrews, D. P., Wishart, J. W., and Young, J. W.: "Distribution and Continuity of Carbonate Reservoirs", J. Pet. Tech., July, 1977, pp 873-885.

Ghauri, W. K., Osborne, A. F., and Magnuson, W. L.: "Changing Concepts in Carbonate Waterflooding -West Texas Denver Unit Project -An Illustrative Example", J. Pet. Tech., June, 1974, pp 595-606.

George, C. J., and Stiles, L. H.: Techniques for Evaluating Wa terfloods in West Texas", J. November, 1978, pp 1547-1554.

"Improved Carbonate

Pet. Tech.,

Craig, Aspects Society 1971.

F. F., Jr.: "Reservoir Engineering of Waterflooding", Monograph Series, of Petroleum Engineers, Dallas, Texas,

Herbeck, E. F., Heintz, R. C., and Hastings, J. R. : "Fundamentals of Tert iary Oil Recovery -Part I: Why Tert iary Recovery?", Petroleum Engineer, January, 1976, pp 35-46.

Dyes, A. B., Caudle, B. H. and Erickson, "Oil Production After Breakthrough Influenced by Mobility Ratio", Trans. (1954) 201, 81-86.

R. A.: As

AIME

9. Kimbler, O. K., Caudle, B. H., and Cooper H. E., Jr.: "Areal Sweepout Behavior in a Nine Spot Injection Pattern", J. Pet. Tech., (February, 1964), 199-202.

10. Prats, M., Hazebroek, P., and Allen, E. E.: "Effect of Off-Pattern Wells on the Performance of a Five Spot Flood", Trans. AIME (1962) 225, 173-178.

212

11.

12.

13.

14.

Caudle, B. H., Erickson, R. A., and Slobod, R. L. : "The Enchroachment of Injected Fluids Beyond the Normal Well Pattern", Trans. AIME, (1955) Vol. 204, 79-85. Ferrell, H., Irby, T. L., Pruit, G. T., and Crawford, P. B.: "Model Studies for Injection - Production Well Conversion During a Line Drive Waterflood", Trans. AIME (1960) 219, 96-98.

Caudle, B. H. and Witte, M. D.: " J. Pet. Tech., December, 1963, pp 63.

Landrum, B. L., and Crawford, P. B.: of Directional Permeability on Efficiency and Production Capacity", AIME, (1960), Vol. 219.

"Effect Sweep

Trans.

15. Dyes, A. B., Kemp, C. E., and Caudle, B. H.: "Effect of Fractures on Sweepout Patterns", Trans. AIME (1958) Vol. 213.

16. Prats, M., Strickler, W. R., and Matthews, C. S.: "Single Fluid Five Spot Floods in Dipping Reservoirs", Trans. AIME (1955) 204, 160.

17. Dyes, A. B. and Braun, P.H.: "Sweepout Patterns in Depleted and in Stratified Reservoirs", Prod. Mon. December, 1954, Vol. 19, No.2.

18. Cotman, N. T., Still, G. R., and Crawford, P.

19.

20.

21.

B.: "Laboratory Comparison of Oil Recovery in Five Spot and Nine Spot Waterflood Patterns", Prod. Monthly (December, 1962),27, No. 12, pp 10-13.

Craig, F. F., Jr.: "Effect of Permeability Variation and Mobility Ratio on Five-Spot Oil Recovery Performance Calculations", J. Pet. Tech., October 1970, pp 1239-1245.

Leverett, M. C.: "Capillary Behavior in Porous Solids", Trans. AIME (1941),142,152-169. Welge, H. J.: "A Simplified Method for Computing Oil Recovery by Gas or Water Drive", Trans. AIME (1952),195,91-98.

22. Gaucher, D. H., and Lindley, D. C.:

23.

"Waterflood Performance in a Strat Hied Five Spot Reservoir - A Scaled Model Study", Trans. AIME (1960), 219, 208-215.

Craig, F. F., Jr., W. and Geffen, T. Gravity in Frontal 210, pp 275-282.

Sanderlin, J. L., Moore, D. M., "A Laboratory Study of Drives", Trans., AIME, 1957,

24. Tarr, C. M., and Heuer, G. J.: "Factors Influencing the Optimum Time to Start Water Injection", Paper SPE 340, presented at the SPE-AIME 5th Biennial Secondary Recovery Symposium, Wichita Falls, Texas, May 7-8, 1962.

25. Higgins, R. V., and Leighton, A. J.: "Computer Method to Calculate Two Phase Flow in Any Irregularly Bounded Porous Medium", Journal of Petroleum Technology, June 1962, 679-683.

SPE 10024 S. P. SIOOH, O. G. KIEL

26. Craig, F. F., Jr., Geffen, T. M., and Morse, R. A.: "Oil Recovery Performance of Pattern Gas or Water Injection Operations from Model Tests", Trans. AIME (1955) 204, 7-15.

27. "World's Largest Offshore Waterflood Goes on Stream", World Oil, 184 (5): 89-90, April, 1977.

28. Crawford, P. B.: "Laboratory Factors Affecting l>laterflood Pat tern Performance and Select ion", J. Pet. Tech., December, 1960, pp 11-15.

213

29. Craze, R. C. and Buckley, S. E.: "A Fractural Analysis of the Effects of Well Spacing on Oil Recovery", Drill and Prod. Prac., API (1945), 144.

30. Van Everdingen, A. F. and Kriss, H. S.: "New Approach to Secondary Recovery", Petroleum Engineer International", November, 1980, pp 27-40.

11

TABLE 1

CHARACTERISTICS OF DISPERSED

INJECTION PATTERNS (6)

Pattern

Ratio of Pracucing Hells

to In jection Wells Drilling Pattern

Required

Four-spot Skewed four-spot Five-spot Seven-spot Inverted seven-spot

(single inject ion well) Nine-spot Inverted nine-spot

(single injection well) Direct line drive Staggered line drive

1/3

TABLE 2

Equilateral triangle Square SquarE' Equilateral triangle

Equilateral triangle Square

Square Rectangle Offset lines of wells

Areal sweep efficiencies at breakthrough for various confined patterns. (Homogeneous, Isoptropic, Uniform Thickness, Horizontal Formations; Unit Mobility Ratio; Equal Injection Rates.)

Type of Pattern

Direct Line Drive, d/a = 1.0

Direct Line Drive d/a = 1.5

Five Spot

Seven Spot

Staggered Line - Drive, d/a

Ea! at Breakthrough, Fract ion

1.5

TABLE 3

0.570

0.706

0.723

0.740

0.800

FACTORS AFFECTING VERTICAL SWEEP

Reservoir Parameters

1. Formation stratification (subdivision of format ion into correlative non-commun ica t ing zones)

2. Permeability variation

3. Mobility ratio

4. Gravity forces and inject ion rate

5. Capillary forces

6. Cross flow

7. Volume of water injected

Effect on Vert ical Sweep

Causes non uniform advance of water due to differences in permeability, porosity, and due to well completion technique used (select ion of wellbore interval open to wellbore, wellbore stimulation of one zone relative to other).

In a given zone, these variations also create non uniform flood front advancement prior to breakthrough and can cause significant cycling of injected water after breakthrough. In systems having permeability strat ificat ion, an unfavorable mobility ratio tends to increase the effect of permeabili ty variat ion and decrease the vertical sweep. The reverse is true when the mobility ratio is favorable. (19).

Sweep at breakthrough, in horizontal homogeneous systems, depends on the ratio of viscous forces to the gravity forces. Higher rates result in higher sweeps in horizontal systems.

In water wet systems, due to imhibi t ion, capillary forces can increase sweep in low permeability layers.

Cross flow between layers increases vert ical sweep when a favorable mobility ratio exists; the reverse occurs with unfavorable mobility ratio.

Vert ical sweep increases with increased water throughput.

214

'A

5'

II 5'

III 10'

...

PROD.

t INJ.

+ PROD

OLD GEOLOGIC CONCEPT CONTINUOUS PAY

.. t .. PROD. INJ. PROD.

[JPAY

CURRENT GEOLOGIC CONCEPT NON CONTINUOUS PAY

FIGURE 1

t INJ.

t INJ.

OLD AND NEW GEOLOGIC CONCEPTS(4)

5'

:;;;::

.....:::::

5'

B

A

"''WEDGE'' AREA 5' 5' "UNIFORM" AREA

(a) (b)

> !:: :;) z i= z 0 U I-z w u a: w a..

40

20 ~ ~ HORIZONTAL DISTANCE BETWEEN WELLS FEET

(c) FIGURE 2

FLOODABLE PAY CONCEPTS(4)

215

B

5'

1.0

0.9

a: 0.8 w I-oCt :i: 0.7 u. 0 :i: 0.6 0 ...I U. ...I 0.5 oCt z 0 0.4 I-u oCt 0.3 a: u.

10 .. ____ ~------~----~----.. o ~ ~~1 a: O\V 1 > d.~~

~ 1~------~~~~~~~~~------~------~ en o :2: ...I

o .1.---~~~-------+------~------~ a: w I-oCt :i:

.01 ... __ ... ___ ..... ___ ... __ .. . 1 1 10 100 1000

OIL VISCOSITY, CP

FIGURE 3 EFFECT OF OIL VISCOSITY ON WATER OIL

MOBILITY RATIO (6)

0.9

ffi 0.8 .---t--)~y+--I-I-I--t---t I-oCt :i: 0.7 ...._---1I----jr-'/ u. o :i: 0.6 ...._-1-1--1-1'-1---#--1 ~---+---I o ...I U. ...I 0.5 ...._---1I-I-iJ oCt Z o 0.4 '--111-1--1-+-+-1+---+---+--1

j 0.2 ~--Ir-~"'-+-J-4I

I-U oCt a: u.

~ 0.2I-Jr-tt-/ f--V--f--f--+--I

20 30 40 50 60 70 80 WATER SATURATION, % PORE VOL.

FIGURE 4 EFFECT OF OIL VISCOSITY ON

FRACTIONAL FLOW CURVE, STRONGLY WATER WET ROCK(6)

~

216

0.1

o .... ~...-j~-'-...-j~-'-.... 10 20 30 40 50 60 70

WATER SATURATION, % PORE VOL.

FIGURE 5 EFFECT OF OIL VISCOSITY ON

FRACTIONAL FLOW CURVE, STRONGLY OIL WET ROCK(6)

;6 If----If ,e P I ' : '

t t--a1 : : d

;6 }----}6 } p (a) DIRECT LINE DRIVE

,e p jf---/f P .... a--, , , ,

.: T : : d :

p p )Ll-} P

.,.-----.. 8

SWEEP EFFICIENCY

UNIT DISPLACEMENT

EFFICIENCY

RESIDUAL OIL-~~~

FIGURE 6 FRACTION OF OIL RECOVERY BY WATERFLOODING

AS A FUNCTION OF 1) AREAL SWEEP EFFICIENCY 2) VERTICAL SWEEP EFFICIENCY AND 3) UNIT

DISPLACEMENT EFFICIENCY (7)

.... ---- -.--- --.,.-----.... -----, I , I I I I I I I I I I

+ p ? + : CORNER: SIDE :

~_m_:~~~~ __ ~ ~ : I : : 7. 1 :

~ ~ ~ ~ ~ i INJEcTION WE~ : I ' I I I I

.... ----..----... -- ------- ...

(d) NINE SPOT

o Q 0

o " I ' , ,

, .. ;0.. ......... ,,' \" 0 ," /'" '.,4 - SPOT

Q" ,'"0 '. 0 7 - SPOT \: ,': '-

o : 6-------~-----b ,

o (b) STAGGERED LINE DRIVE 6. ,0 """"c:r'" " P p p P

P jIf-----A ;f -a ---'

' I I r I : d:

,e jJ--- --/6 p JIf , ,

(e) 5 SPOT SPECIAL CASE OF (b) WHERE d/a = 1/2

o

o

FIGURE 7

o

o o (e)

SEVEN AND FOUR SPOTS

DIAGRAMATIC REPRESENTATION OF WATERFLOOD NETWORKS

217

o

o SMALLEST AREA OF

o FLOW SYMMETRY

o

100

90

80

> u 70 Z w 60 LL LL w 50 Q,. w w

~ (I) 40

30

20

10

100

'#. I

> u z w

~ LL LL W

~ ::J 0 Q,. w w

~ (I) ..J

75~------~~~--~~~--+-----------i *-

~ 11. W

~ 501-----"~~~------------_r--~----~__1 ~ ~~ ec ~ ~ -

25~~~------+_----------+_~~--~__1 MOBILITY RATIO = 1.1

L = FRACTURE LENGTH O~ ________ ~ ______ ~ ________ ~

o 1 2 3 THROUGHPUT - DISPLACEABLE VOLUMES

(al Unfavoration Orientation

75.-------~~----------~--------_I #. t-11. W

~ 501-----#-----~----------_+----------__t w ec

251-~--------+_----------+_------~__i

> 0 100 Z !!!#. o .

80 -:I: u.C!I :b::J 11. 0 wec 60 w:l:

3:~ en~ 40 0 -w ecec

~CD 20 w~ ~ ....I 0 0 > .01

MOBILITY RATIO = 1.1 L = FRACTURE LENGTH

1 2 THROUGHPUT - DISPLACEABLE VOLUMES

(bl Favorable Orientation

FIGURE 10 EFFECT OF FRACTURE LENGTH AND ITS

ORIENTATION ON AREAL SWEEP 1151

V~O.8

.1

(PERM. VARIATION)

1.0 MOBILITY RATIO

FIGURE 12

10

3

100

VOLUMETRIC SWEEP EFFICIENCY AT BREAKTHROUGH, FIVESPOT PATTERN; ZERO INITIAL GAS SATURATION 1191

120

*- 100 I

> 80 0 z w

~ u. u. w 11. 40 w w 3: en

20

219

.02 .03

.0' .02

.03

RELATIVE PRODUCING RATIO = 03/02 FIGURE 11

EFFECT OF PRODUCING RATIOS ON SWEEP EFFICIENCY ON NINESPOT PATTERNI18)

Swbt

1.0 ... ------... ~ ...

Swt

I

"

WATER SATURATION, % PV

FIGURE 13 DETERMINATION OF AVERAGE WATER

SATURATION AT BREAKTHROUGH, Swbt