Well-Testing Characterization of Heavy-Oil Naturally Fractured Vuggy Reservoirs

SPE-171078-MS

Well Testing Characterization of Heavy-Oil Naturally Fractured VuggyReservoirs

Camacho-V. Rodolfo, Pemex E&P; Susana Gómez, IIMAS-UNAM; Vásquez-C. Mario, Pemex E&P/IPN-ESIA;Fuenleal-M. Norma and Castillo-R. Tomás, Pemex E&P; Gustavo Ramos and Minutti M. Carlos, IIMAS-UNAM;Alejandro Mesejo, MatCom-UH; Fuentes-C. Gorgonio, Texas A&M University/IMP

Copyright 2014, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Heavy and Extra Heavy Oil Conference - Latin America held in Medellin, Colombia, 24–26 September 2014.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contentsof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the writtenconsent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations maynot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

This paper presents the advances on the characterization of Naturally Fractured Vuggy Reservoirs(NFVR) located in the South East Gulf of Mexico. Halos, fractures and vugs were characterized throughwell tests using the triple porosity–double permeability (3!-2k) model. Through the analysis of well andimagelogs was determined the predominance of high vuggyporosity producing intervals, so that thepressure data were analyzed using a triple porosity-double permeability (3! -2k) approach, with total andpartial penetration. These NFVRs have vuggy and fracture porosity, with triple porosity, matrix, fractures,and vugs, or matrix, vugs with their halos. In both cases, the 3!-2k model is appropriate to characterizethese fields. These models, recently presented involve the determination of 9 and 13 parameters, for totaland partial penetration, respectively, which implies challenges in terms of the uniqueness of the results.In this way, it is suggested to consider information from other sources like cores, well logs, and imagelogs, in order to select characteristic values for some of the parameters of the model of interpretation,specifically the storage ratios for vugs and fractures, "v and "f, and in this way to eliminate thenon-uniqueness problem. Thus, the integration of static and dynamic information is a key element for acomplete description of NFVR.

The 3!-2k model allows better data fits than the classical dual-porosity model, obtaining moreinformation related to the interactions of the three different media. The sum of vuggy and fracture porosityobtained from 3!-2k model is not equal to the secondary porosity obtained from the dual-porosity model.

If partial penetration effects are present, it is recommended to perform the analysis taking into accountthese effects because information on the vertical communication of vugs and fractures can be obtainedwith the 3!-2k model. It is confirmed through the analysis of well-tests with partial penetration that thevertical communication of vugs can be more important than the horizontal communication. It is crucialto obtain fracture and vug connectivity in both horizontal and vertical direction, mainly because thesereservoirs are sharing a common aquifer.

The objective of this work is to demonstrate the application of a 3!-2k model to determine severalparameters related to reserves and productivity of NFVR. Vertical connectivity of both vugs and fractures

are important parameters when an aquifer is underlying heavy oil NFVR, because these areas couldestablish preferential routes for the advancement of water.

IntroductionThe main producing fieldsin the world are associated with carbonate Naturally Fractured VuggyReser-voirs (NFVR), involving a heterogeneous and anisotropic porous system, mainly due to carbonate rocksbeing particularly sensitive to post-depositional diagenesis, including dissolution, dolomiting and frac-turing processes1. For the purpose of this work, there is not distinction between vugs, caverns andchannels, so that all of them will be denoted only with the term vug. Thus, the diameter of theseheterogeneities can vary from millimeters to meters.

Vugs are a result of the dissolution of carbonate or sulfate. From observations in cores, it has beendetermined that the matrix porosity around vugs contains microfractures elongated by dissolution andimproved intercrystalline porosity due to dissolution. Thus, it is possible to have an increase ofpermeability in areas adjacent to vugs.

Vugular porosity is common in carbonate reservoirs and its importance on the productive andpetrophysical characteristics of the porous medium has been recognized in several works. This porositymay be associated with connected and disconnectedvugs. In this way, the effect of vugs on thepermeability is related to its conectivity2. Thus, the high permeability in vuggyareas is controlledby theincrease in the dissolution of pore throats, creating aninterconnected system of vugs. The porosity ofmatrix, fractures and vugs are usually present in naturally fractured-vuggy carbonate reservoirs. Thedetermination of porosity and permeability in vuggyareas from core measurements are pessimistic due tosampling problems. In areas lacking cores, open hole logs can be used to help identify vuggy areas;however, vugs are not always recognized by conventional logs due to its limited vertical resolution3.Dissolution cavities and fractures are difficult to characterize because of their natural irregularities alongthe carbonate rocks. An approach to the determination of these characteristics is to analyze digital imagesof cores and study the FMI logs for distributions of size and area of dissolution cavities. In Ref. 4 it isoutlined some conditions for the transport of fluids through the dissolution cavities in laboratoryexperiments in cores and using the percolation theory; however, in the literature has been observed thatvuggy areas strongly influence the production behavior2, 5. For this reason, it is critical to determine thecharacteristics of fractures and vugs networks in early field development stages.

In the South-East Gulf of Mexico, there is a heavy crude development project that includes 18 fields.The closest one to the coast is 130 km, and the farther one is 145 km from the coast. Up to date, tworeservoirs have been found, one in the Cretaceous and another one in anoolitic bank of the upper JurassicKimmeridgian. In the Cretaceous, the main productive formation is a breccia, with intercrystallineporosity, and secondary porosity in networks of fractures and cavities of dissolution (vugs). The porosityin the matrix is low, but the secondary porosity due to diagenetic processes is high, especially vuggyporosity is abundant, observing in some cases dissolution caves.

Ref. 6 presents a description of the different existing diageneticfaciespresent in the fields of this project.Cretaceous rock is mainly a breccia, which is made up of fragments of mudstone-wackestone andpackstone, with secondary porosity in fractures and dissolution cavities. In particular, T-1 well drilled witha thick Cretaceous package of 580 m, of which 150 m belong to the breccia in the upper Cretaceous, 130m are rocks of the KM and 300 m from KI. Dolomitized breccias with intercrystallineand vuggy porositywere deposited on top of the KS. The presence of vugs is common in most cores cut in the breccia. Fig.1 presents the core 1 of T-1 well, demonstrating the above.

In the diageneticfaciesBTPKS B, the porosity evolves by dissolution to vuggy porosity. It also presentsremnant porosity associated with fractures, which is preserved when the fracture is partially cemented. Itis also important to the porosity in fractures widened by dissolution and porosity associated to intersection

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of fractures, which can generate vugs. Also, it pres-ents intercrystalline porosity restricted to dissolu-tion halos around vugs impregnated with oil asshown in Fig. 2.

In the BTPKS-C facies, the diagenetic character-istics are penetrating dolomitization, inherited po-rosity, moderate fracturing, dissolution and vuggyporosity as well as intercrystalline porosity. Thesefacies are present toward the bottom of the brecciaBTPKS. At this level, the zoning of diageneticproperties is primarily vertical. The tendency inBTPKS is that it presents better characteristics inthe dolomitized zone, but also the vertical behavioris important because it was observed the best reser-voir conditions in BTPKS are presented in the mid-dle and lower part of this unit, represented for theBTPKS B and BTPKS C facies, see Fig. 3.

The diagenetic facies KMA is defined by dolo-mitization of penetrating replacement, fracture po-rosity, and intercrystalline porosity. In KMB facies,the representative diagenetic features are the dolo-mitization by penetrating replacement, remnants ofopen fractures and fracture porosity. Porosity in theKMA facies is basically intercrystalline, containingfew open fractures. Facie KMB presents remnantsof fracture porosity although vuggyporosity associ-ated with fractures and open fractures is also evi-dent, see Fig. 4.

KI has an abundant vuggy porosity, where somedissolution caverns are observed, which may cause good porosity6. KM is characterized by rocks rangingfrom mudstone to wackestone, fractured, as well as silty mudstone-wackestone with interbedded sandyand silty shale. KS is constituted by calcareous breccias, dolomitized and fractured, with powerfulthickness and porosity ranging between 6% and 12%.

BackgroundPorosity and permeability of vugs and fractures can be contrasting and can dominate the overall systemresponse by the processes that occur in the two systems at different times. Fractures always occupy a smallportion of the volume of the reservoir, while 28% porosity values may correspond to vuggy porosity5.

The presence of connected vugs contributes both to the effective porosity and permeability. Quinteroet al.8 explained that in some reservoirs vuggy permeability may be even more important than thepermeability of fractures. In this way, for the construction of different models5 is common to find that thepermeabilities of vugs were set up by 3 to 5.5 Darcy.

Using X-ray tomography, Ref. 7 determined that the increase in porosity and permeability may be dueto vugs directly connected and vugs connected via parts of the matrix around them with improved porosityand permeability2. Permeability values as high as 700 md were measured in the halos around the vugs5.This difference in values suggests that the vugs are interconnected in some degree through their halos.Therefore, there are cases of vuggy porous media with different percentages of porosity in matrix, poroushalos, and vugs. Fig. 5 shows thin films of different segments of cores at different depths, showing the

Figure 1—T-1 well, core 1, interval: 3202-3207 m, recovered length 1.45m, BTP-KS, after Ref. 6.

SPE-171078-MS 3

presence of halos. Thus, in some cases even thoughfractures may be present, it is considered to have asecondary effect on vuggy areas permeability.

In order to use a double-porosity9 model to studythe behavior of NFVR, it is required that matrix,fracture, and vuggy porosity be partitioned into pri-mary and secondary porosity. Connected vugs mustbe treated as fractures in the numerical model whilethe rest of the vugs can be treated as isolated vugsand included in the matrix as an additional poros-ity10. One of the challenges of modeling this type ofreservoirs in this way is to determine percentages ofconnected vugs to the fracture network and to thematrix, respectively. Also, it is not described howthe interporosity flow parameters, #mf, #mv, and #vf,are combined to generate the parameter # of thedouble porosity model.

Tkhostov et. al.11 reported that vugs compress-ibility is approximately three times the correspond-ing one of the matrix. According to Reiss12, thefractures compressibility is in a range of 1 to 20times the matrix compressibility. Considering thatporous volume compressibility is one of the mainsources of energy for NFVR13, it is necessary todistinguish between matrix, fractures, and vugs asseparate systems but interacting among themselves.

The fluid flow nature in NFVR depends on thecharacteristics associated with fractures and disso-lution cavities (size, orientation, density, and thenetwork connectivity of fractures and vugs) and thematrix rock (permeability and porosity). In NFVRs,the data that are directly related to fractures andvugs are scarce, for example, data from cores andimage logs. Other data types as seismic informationand pressure transient tests data, although most havea greater coverage, they are usually related to thedistribution of these characteristics indirectly.Therefore, it is required that all available data areintegrated for the reservoir modeling.

The effect of dissolution cavities on permeabilityis related to its conectivity2. Therefore, high perme-ability can be present in vuggy areas, dominatingany flow in the reservoir. Also, directional perme-ability is essential in NFVR, which usually exhibitimportant vertical permeabilities, so their behavioroften is more controlled by the flow along thevertical direction than in horizontal sense14. Reser-voir areas that contain fractures and vugs provide

Figure 2—Diageneticfacies BTPKS B, after Ref. 6.

Figure 3—Diageneticfacies BTPKS C, after Ref. 6.

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high permeability paths, which contribute to highproductions; however, these areas usually are notbeneficial for secondary and enhanced recoveryprocesses, because they are areas that capture theinjected fluids. So, for NFVR both the porosity andpermeability of fractures and vugs networks areimportant factors to be considered in early stages ofthe field development.

Based on previous ideas, it is evident that thecharacterization of NFVR, with the aim of optimiz-ing their productivity and recovery, is a challengeboth from the static and dynamic points of view.Therefore, results obtained from the analysis ofpressure and production data should be combinedwith results from other static sources, such as theinterpretation of geological and seismic data, anal-ysis of cores, well and image logs.

In terms of dynamic characterization, it is obvi-ous the need for a model of interpretation of tripleporosity, which consider the interaction between therock matrix, fractures, and vugs, including the pos-sibility of modeling both primary flow through the system of vugs, in addition to the existing flow throughthe fractures network. In this way, the resulting model is a triple porosity- double permeability model.

In this work, it is used the 3!– 2k model proposed by Camacho-V. et al.15 in 2005, which considersthat the fluids transfer between the matrix, vugs and fractures is directly proportional to the difference inaverage volumetric pressure in the matrix, vugs and fractures, involving primary flow through fracturesand vugs networks. Thus, considering a cylindrical symmetry, the differential equation for fractures, interms of dimensionless variables is given in the following way:

(1)

the equation for the matrix blocks is given by:

(2)

and the equation for the vugs system by:

(3)

where all dimensionless variables are given by:

(4)

With j! fractures or vugs, and

(5)

(6)

(7)

Figure 4—Diageneticfacies KM A and B, after Ref. 6.

SPE-171078-MS 5

(8)

(9)

With kvf ! kv if pv"pf, and kvf ! kf otherwise. $ij

is the shape factor of interporous flow betweenmedium i and medium j. The parameter % has valuesbetween zero, when there is only primary flow inthe vugs network (there may be isolated fractures),and one, when there is only primary flow throughthe fractures network (there may be only isolatedvugs). Storativity ratios for fractures and vugs aregiven, respectively, by:

(10)

(11)

This model is characterized by six dimensionlessparameters instead of two for Warren and Root9

model. These parameters are the primary flow ratio,three parameters of interaction and two storativityratios. A similar approach has been used to modelNFVR in China16-18.

Fuentes-C. et al.19 presented an extension of the previous model for a partially penetrating wellproducing from a NFVR, taking into account various boundary conditions.

The objective of this work is to discuss advances focused on the characterization of the fields of a heavyoiloffshore project, specifically in regards to its rock matrix heterogeneities such as fractures and vugs,through the analysis of well and image logs, as well as pressure transient data.

ResultsThis section is divided into two parts. The first one presents information on well logs and image logs. Thesecond part presents the analysis of the behaviour of pressure transient tests ofwell T - 1, KS and KMformations, using the classical model of Warren and Root9 (2! - 1 k), with full penetration, and the modelof Camacho-V. et. al.15 (3 ! - 2 k model), with full penetration, without fixing the values of "v and"f andfixing these values obtained fromwell logs. Finally, the model of Fuentes-C. et. al.19 (3 ! - 2 k model) andits generalization presented by Gómez et. al.20 (for a finite wellbore radius), both for partial penetration,are used considering the valuesof "v and"f obtained fromwell logs as indicators.

The results with the models of Camacho-V. et. al.15, Fuentes-C. et. al.19, and Gómez et. al.20, wereobtained with a software developed by Gomez et. al.21-22.

Characterization with well and image logsWell logs are of good quality. In the case of well A-L1 it was determined the water-oil contact at a depthof 4228 m. T-1 well was 13 ° API oil producer, producing from two intervals, with a rate of 3591 bpdfrom the first interval and 5996 bpd from the second interval. The average values obtained from well logsare: !f ! 0.00413 and !v ! 0.0645 for KS, and !f ! 0.00104 and !v ! 0.0504 for KM23.

Image well logs are fundamental to resolve the small-scale heterogeneity in complex systems ofcarbonates. So a workflow is used to discretize the porosity in the three existing media, matrix-fracture

Figure 5—Thin films of different segments of cores at different depths,showing the presence of halos around the vugs7.

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-vugs or matrix-halos-vugs, using the integration of geophysical and image logs, and pressure transienttests. Once determined the porosity of each medium by means of geophysical logs, other dynamicparameters corresponding to these media by means of pressure tests can be obtained.

Image logs are used for qualitative analysis, such as determining the density and connectivity of vugsin the vertical direction, as well as the density and orientation of fractures. Of course, a fundamental partin the logs processing is a proper calibration of image logs before any quantitative petrophysical analysis.

Fig. 7 presents an image log of well T-1, where it is observed in the interval 3220-3228 m a calcareousbreccia showing vertically connected vuggy zones in the first productive interval. In the interval3276-3283 m, at depth 3280 and 3281, it is detected a cavern of 1 to 1.5 m of vertical length; the brownarea inside the cavern is drilling mud. There are also estilolites, microfractures, and a breccioid area,connecting with the dissolution cave24. Taking into account this Fig. and what is mentioned in thedescription of the diagenetic facies of the breccia in the KS and the facies of the KM, at some intervalswithin the breccia, the three predominant media are matrix, halos, and vugs; while the three media in KMare matrix, fractures and vugs.

Figure 7—Image log of T-1 well, showing good vertical communication through the vugs and a cave of 1 to 1.5 m vertical length.

SPE-171078-MS 7

Dynamic characterization using pressure transient testsAnalysis results of pressure tests at well T-1, formation KS, interval 3200-3285 m, and formation KM,interval 3340-3425 m, are presented. Table 1 shows the values of the parameters used for the analysis.

Figs. 8 and 9 show the results with the 2 ! – 1 k model, Warren and Root9 solution, with totalpenetration. Table 2 presents the corresponding results, where the storativity ratio appears in red.

Taking into account the presence of three media interacting each other, matrix-halos-vugs, for KSformation, and matrix-fractures-vugsfor KM formation, Figs. 10 and 11 show data fits obtained with themodel proposed by Camacho-V. et. al.15, 3 ! - 2 k, for the same tests of T-1 well, in KS and KM,respectively, also considering full penetration. In both cases, KS and KM, three possible data fits arepossible, which were obtained with the software developed by Gomez et. al.21-22.

It is important to note that in each case the sum of the parameters "v and "f is not equal to thestorativity ratio, ", determined with Warren and Root9 model. Also, it is not trivial to combine theparameters #mf, #mv, and #vf to get the parameter # of Warren and Root9. Thus, the use of double-porositysimulatorsto model the behavior of NFVR is not an easy task25.

Table 1—Properties values used in well tests analysis.

Parameters T-1 KS T-1 KM

Thickness, h, ft 440.61 413.38Wellradius, rw, ft 0.7983 0.7083Rate, q, STB/D 6500 3800Viscosity, &, cp 49.8 49.8Formation volumen factor, Bo 1.12 1.12

Figures 8 and 9—Fittings with Warren and Root9 model with full penetration for T-1, KS and KM formations, with variable and fixed wellborestorage, respectively.

Table 2—Fitting results with Warren and Root9 model, total penetration.

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In order to eliminate the uncertainty of multiple fittings in the results shown of these tests, it wasdecided to fix the values of the parameters "v!0.64 and "f!0.041 for KS formation, and "v!0.63 and"f!0.013 for KM formation, determined with the porosities obtained from well logs, considering that thecompressibility of the three media values were the same. The results are shown in Figs. 12 and 13 for KSand KM formations, respectively.

As can be seen in Figs. 12 and 13, the data fit, when the values of "v and "f are fixed, are unique butthey are not as good as those obtained when these parameters are not fixed, see Figs. 10 and 11. This maybe due to two possible reasons. First, the values of "v and "f were obtained with the values of porositiesobtained from well logs, which do not necessarily remain constant within the drainage area observed inpressure tests. The second reason is that the compressibilities of the three media were considered the same,which is not necessarily correct because it is expected that the compressibilities of vugs, halos, andfractures are greater than the matrix compressibility.

Figure 10—Multiple fittings with Camacho et. al.15 model with total penetration for well T-1, formation KS, obtained by Gómez et. al.21-22

Figure 11—Multiple fittings with Camacho et. al.15 model with total penetration for well T-1, formation KM, obtained by Gómez et. al.21-22

SPE-171078-MS 9

From Figs. 10 and 11, it is observed the presence of spherical flow in both KS and KM formations,respectively; therefore these tests were also analyzed with the 3! - 2 k model presented by Fuentes-C. et.al.19, and modified by Gómez et al.20 for a finite wellbore radius and the possibility that %r and %z weredifferent from one, considering partial penetration and using the software developed by Gomez et al.21-22.In this way, Figs. 14 and 15 show the data fits, obtaining multiple solutions again. However, using thevalues "v and "f (or "v and "h), obtained from the porosities of well logs, just as indicators, it is possibleto decide which are the appropriate solutions. Thus, the appropriate solutions are shown in Table 3. Otherrelevant parameters obtained from the pressure transient analysis are %r and %z, which allow determiningthe percentage of the primary flow that occurs through the vugs and fractures or halos, the drainage areaanisotropy, as well as the interporous flow parameters between the three existing media.

Figures 12 and 13—Fittings with Camacho et. al.15 model with total penetration for well T-1, KS and KM, respectively, obtained by Gómez et. al.21-22,fixing !v and !f obtained fromwell logs.

Figure 14—Multiple fittings with Gómez et al.20 model with partial penetration for well T-1, formation KS, obtained by Gómez et. al.21-22

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Considering the Fit 2 of Fig. 14, in the KS formation, the flow of fluids in the horizontal direction iscontrolled by the halos/fractures system (%r!0.81); however, the dominant system in the vertical directionis represented by the interconnected vugs (%z !0.001). Considering the Fit 2 of Fig. 15, in the KMformation, the flow of fluids in both the vertical and horizontal directions is controlled by the fracturesystem (%r!%z!0.93).

In addition, by using the values of "v and"h,f and the porosity estimates obtained from well logs, it ispossible to estimate compressibility values for fracture/halos and vugs in terms of matrix compressibility.Thus, for KS: ch ! 0.63 cm and cv ! 1.26 cm, and for KM: cf ! 8.35 cm and cv ! 0.76 cm. Vugscompressibility for KS, and fractures compressibility for KM values appear coherent; however, haloscompressibility for KS and vugs compressibility for KM do not agree with the expected values. Certainlythe correct way to determine the total porosity-compressibility of the system is by using interference tests.Estimation of porosity-compressibility in a reservoir scale may lead to more appropriate values for thethree media. Therefore, the estimated values are considered preliminary.

The zones of high permeability, either fractured and/or vuggy, have a high impact in the production andare the primary cause of the anticipated water surgence, making it necessary the characterization of theseheterogeneities, including the definition of primary flow through them. The abrupt increase in the watercut is one of the features that characterize the NFVR26. Also, the determination of the anisotropy in theseheavy oil reservoirs is crucial, mainly because it allows to anticipate the water arrival, especially if thefractures and/or vugs networks are connected to an active aquifer, as it is the case of the reservoirs of thisproject with a very limited water imbibition, and possible problems of formation of emulsions within theporous media and throughout the production system.

Figure 15—Multiple fittings with Gómez et al.20 model with partial penetration for well T-1, formation KM, obtained by Gómez et. al.21-22

Table 3—Fitting results with Gomez model et al.20 with partial penetration for well T-1, KS and KM formations, obtained by Gómez et al.20- 21.

Formation !v !f,h "mf "mv "vf #r #z sf,h sv

KS 0.70 0.023 2.3#10-5 3.9 #10-5 1.2 #10-5 0.81 0.001 0.39 0.65KM 0.51 0.12 1.8#10-5 8.2 #10-5 5.5 #10-6 0.93 0.93 1.07 1.08

SPE-171078-MS 11

ConclusionsThe proposed workflow to determine the properties in the three existing media in NFVR, consists ofcombining the results of the petrophysical analysis of well logs and cores to determine the porosity of thethree media and thus to estimate the parameters "v and "f, which serve as indicators to overcome theproblem of non-uniqueness in the well test analysis using the 3! - 2 k. model. Also, inferences from imagelogs and cores allow assessing the situation to be resolved with the 3 ! - 2 k model, either matrix-fractures-vugs or matrix-halos-vugs. This integration of information, together with production and seismicdata, provide the basis for the prediction of heterogeneities between wells, the anisotropy of the reservoirsand the definition of the strategy of field development. In this way, the following conclusions are obtainedbased on the results shown in this work.

1. The dolomitized facies have the best diagenetic features to store fluids, with the presence of vuggyporosity and fracturing. In the breccias of the KS, there are mainly vugs and halos, which help tohorizontal and vertical communication. In the KM, matrix, fractures, and vugs are present.

2. The 3 ! - 2 k model allows most appropriate pressure data fits than the classical Warren and Root(2 ! - 1 k) model, which usually exists in the commercial software of transient pressure analysis.Obtaining more information of the porous medium relating to the interactions of the three differentmedia, i.e. for KS: matrix-halos-vugs and for KM: matrix-fractures-vugs, and the percentage ofprimary flow through fractures/halos and vugs.

3. It is shown that the sum of the vugs and fractures/halos storativity ratios obtained with the 3 ! –2 k model is not equal to the storativity ratio of the 2 ! – 1 k model.

4. In the case that there are effects of partial penetration in the well tests, it is convenient to performthe analysis taking into account these effects in order to obtain information on the verticalcommunication of vugs and fractures/halos with the 3 ! - 2 k model.

5. It is confirmed through transient pressure analysis with partial penetration that vertical commu-nication through vugs can be even more important than their horizontal communication, which isvery relevant to heavy oil fields that share a common aquifer.

AcknowledgmentsThe support of the University of Mexico (UNAM) and Pemex E&P is acknowledged.

NomenclatureA ! drainage area, L2, ft2

Bo ! oil volumen factor, RB/STBc ! compressibility, Lt2/m, (psi-1)h ! formation thickness, L, ftk ! permeability, L2, mdp ! pressure, m/Lt2, psipD ! dimensionless pressurepwD ! dimensionless wellbore pressurepwf ! wellbore pressure, m/Lt2, psiq ! oil rate, L3/t, STB/Dr ! radial distance, L, ftrD ! dimensionless radiuss ! skint ! time, T, hourstD ! dimensionless time

12 SPE-171078-MS

# ! interporous flow parameter, dimensionless& ! oil viscosity, m/Lt, cp$ ! shape factor$ ! porosity" ! storativity ratio, dimensionless

SubscriptsD ! dimensionlessf ! fracturesh ! halosm ! matrixv ! vugulosw ! well

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