Integrated Reservoir Characterization Study of a Carbonate Ramp Reservoir: Seminole San Andres Unit, Gaines County, Texas

Integrated Reservoir Characterization Study of a Carbonate Ramp Reservoir: Seminole San Andres Unit, Gaines County, Texas F.P. Wang,* SPE,  F. Jerry Lucia,  SPE, and  Charles Kerans,  SPE, Bureau of Economic Geology, The U. of Texas at Austin

Summary

One of the important issues in constructing geologic and reservoir models is to define geologic frameworks. A geologic framework is fundamental to defining flow units, to interpolating well data, and thereby to modeling fluid flow. For the Seminole San Andres Unit (SSAU), the high-frequency cycles (HFC’s) and rock-fabric facies identified ident ified on outcr outcrop op analogs and cores were used to correlate wireline logs. Reservoir and simulation models of the outcrop and a two two-se -secti ction on are areaa of SSA SSAU U wer weree con constr struct ucted ed wit with h roc rock-f k-fabr abric ic uni units ts within wit hin the HFC HFC’s ’s as a geo geolog logic ic fra framew mework ork.. Sim Simula ulatio tions ns wer weree performed using these models to investigate critical factors affecting recovery. HFC’s HFC ’s and rock-fab rock-fabric ric units are the two cri critic tical al sca scales les for modeling shallow-water carbonate ramp reservoirs. Descriptions of  rock-fabric facies stacked within HFC’s provide the most accurate framework for constructing geologic and reservoir models, because discrete petrophysical functions can be fit to rock fabrics and fluid flow can be approximated by the  k  kh h  ratios among rock-fabric flow units. Permeability is calculated using rock-fabric-specific transforms between interparticle porosity and permeability. Core analysis data showed that separate-vug porosity has a very strong effect on relative permeability and capillary pressure measurements. The effect of stratigraphic constraints on stochastic simulation was studied. Geologic models gener generated ated by a conve convention ntional al linea linearr interpolation, a stochastic simulation with stratigraphic constraints, and a stoch stochastic astic simulation without stratigraphic stratigraphic cons constraint traintss were compared. The stratigraphic features of carbonates can be observed in stoch stochastic astic realizations realizations only when they are constrained constrained by rockfabricc flow units. Simul fabri Simulation ation results from these realizations realizations are similar in recovery but different in production and injection rates. Scale-up of permeability in the vertical direction was investigated in terms of the ratio of vertical permeability to horizontal permeabili perme ability ty ( k vh ). Thi Thiss rat ratio io dec decrea reases ses exp expone onenti ntiall ally y with the vertical gridblock size up to the average cycle size of 20 ft (6.1 m) and remains at a value of 0.06 for a gridblock size of more than 20 ft (6.1 m), which is the average thickness of HFC’s. Simulation results showed that the critical factors affecting recovery efficiency are stacking patterns of rock-fabric flow units,  k vh  ratio, and dense mudstone distribution. Introduction

The SSAU lies on the northeastern margin of Central Basin Platform (Fig. (Fig. 1) 1) immediately south of the San Simon Channel. 1 It covers cov ers app approx roxima imately23 tely23 sq mile miless andconta andcontains ins mor moree tha than n 600 wel wells. ls. The field, discovered in 1936, is a solution-gas-drive reservoir with a small initial gas cap, and it has an estimated original oil in place (OOIP) of 1,100 MMSTB. 2 Production comes from the Upper San Andres Formation and the upper part of the Lower San Andres Format For mation ion.. The cru crude de is 35° 35°API API andhas an ini initialforma tialformatio tion n vol volume ume factor (FVF) of 1.39 and a solution/gas ratio of 684 scf/STB. * Now with PGS Reservoir. Copyright 1998 Society of Petroleum Engineers Original SPE manuscript received for review 8 October 1996. Revised manuscript received 10 November 1997. Paper peer approved 19 December 1998. Paper (SPE 36515) first presented at the 1996 SPE Annual Technical Conference and Exhibition, Denver, 6–9 October.

SPE Reservoir Evaluation Evaluation & Engin Engineering eering,, April 1998

The field was developed during the 1940’s and produced 120 MMSTB (about 11% of OOIP) during the primary recovery from 1936 to 1969, in which time the reservoir pressure dropped from 2,020 to about 1,100 psig. Waterflooding was initiated in late 1969 using usi ng alt altern ernati ating ng row rowss of 160 160-ac -acre re inv invert erted ed nin nine-s e-spot pot pat patter terns. ns. Inf Infill ill drilling occurred in 1976, converting the pattern to a mixed 80- and 160-acre inverted nine spot. Waterflooding increased oil recovery to 388 MMSTB. The characteristics of waterflooding are a short fill-up time, a sharp increase in pressure, and a sharp decrease in gas/oil ratio. A second infill drilling program that converted the patter pat tern n to an 8080-acr acree inv invert erted ed nin ninee spo spott occ occurr urred ed dur during ing 198 1984 4 through 1985. Fieldwide CO 2   flooding began in 1985. The CO 2 flooding further increased oil production, and the cumulative oil production was about 539 MMSTB in 1994. The SSAU has an excellent suite of cores and a large amount of  core, wireline log, and production data. A two-section area, Tract 23–28, which has 33 wells with complete porosity log suites and 11 cored wells covering nearly the entire reservoir interval, was selected for detailed geologic, petrophysical, and engineering characterization. This paper summarizes the results of this integrated outcrop outcr op and subsu subsurface rface characterizatio characterization. n. More compl complete ete studie studiess were reported by Senger  et al.,3 Kerans  et al.,1 Wang  et al.,4 and Lucia  et al.5 The objectives of this study were (1) to define critical scales for constructing reservoir and simulation models for carbonate ramp reservoirs, (2) to study the effects of rock fabrics on petrophysical properties, (3) to determine important geostatistical parameters from outcrop and subsurface data, (4) to investigate the effectt of stratig effec stratigraphi raphicc const constraint raintss on stoch stochastic astic simulation and recovery recov ery efficiency, efficiency, and (5) to study factors affecting affecting recov recovery ery efficiency, such as the stacking patterns of rock-fabric units and  k vh ratio using outcr outcrop op and subsurface subsurface model models. s. Rock-Fabric and Petrophysical-Property Relationships

Petrophysical properties of porosity, permeability, and saturation are a function of pore-size distribution, which is related directly to rock fabrics. 6 The Seminole San Andres reservoir produces from anhydr anh ydritic itic vug vuggy gy and non nonvug vuggy gy dol dolomi omites tes and con contai tains ns thr three ee rock-fabric/petrophysical classes 7: (1) dolograinstone; (2) graindominated packstone and medium-crystalline mud-dominated dolostone; and (3) fine-crystalline mud-dominated dolostone ( Table 1). These fabrics have unique stratigraphic locations and petrophysical characteristics. Core Porosity and Core Permeability. The effect of rock fabrics on poros porosity-p ity-permea ermeability bility transforms transforms was shown by Lucia6 and subsequently was modified by Lucia  et al.5 Data from the SSAU 2505 250 5 wel welll and Lawyer Lawyer Can Canyon yon outcrop outcrop wer weree use used d to dev develo elop p porosity-permeability transforms for the SSAU. Rock fabrics and pore types were described by point counting thin sections.  Fig. 2 shows core porosity and permeability from the SSAU 2505 well. For a given porosity, permeability varies with rock fabric by one to two orders of magnitudes. Within a specific rock fabric, the permeability increases with interparticle porosity. Alternative Altern atively, ly, these poros porosity-p ity-permea ermeability bility transf transforms orms can be used to estimate separate-vug porosity, 4 because separate-vug porosity contributes contributes little to perme permeabilit ability. y. Norma Normally, lly, separ separate-v ate-vug ug 105

Fig. 1—Location map of Seminole San Andres Unit (SSAU) in the Permian Basin, West Texas, and two section area (bold outline).

TABLE 1—ROCK-FABRIC/PETROPHYSICAL CLASSES COMMON IN THE SEMINOLE SAN ANDRES STUDY 

Class

Rock Fabric

Particle Size (PS)

I

Dolograinstone



100

II

Grain-dominated dolopackstone and medium-crystalline dolowackestone

20

III

Mud-dominated dolopackstone and fine-crystalline dolowackestone





20

m

PS



100

m

m

Fig. 2—Porosity, permeability, and rock-fabric relationships for grainstone, dolopackstone, and dolowackestone having crystal sizes of 20 m or less. Data from SSAU 2505 well.

porosity can be point counted from thin sections or estimated from core slab surfaces. Because thin sections are often too small to represent whole cores or sometimes are unavailable (which is commonly the case with relative permeability data), separate-vug porosity can be estimated by subtracting interparticle porosity from total porosity where total porosity is the core porosity and interparticle porosity is obtained from the porosity-permeability transform for a specific rock fabric at a given permeability value. Effect of Separate-Vug Porosity on Relative Permeability. The effect of separate-vug porosity on capillary pressure and relative permeability has not been studied extensively. Wang  et al.,4 using laboratory data measured on Lawyer Canyon outcrop and SSAU core samples, showed that separate-vug porosity has a strong effect on waterflood recovery and residual oil saturation. With additional SSAU data, the correlation between waterflood recovery and separate-vug porosity is improved. Although special core analyses were performed in 1981 on core plugs from two wells—SSAU 2310 and 4902—these core plugs were not available for this study in 1992. Whole cores were therefore sampled immediately adjacent to locations of the original core plugs used for special core analyses, and thin sections were made and rock fabrics were determined. Three sets of relative permeability curves ( Fig. 3a) measured from SSAU 2310 cores show that the relative permeability increases with core permeability. Without examining the cores, the low relative permeabilities of oil for samples 4WC and 9WC would probably be explained as mixed and strongly oil wet. However, the core porosity of 19.5% and a permeability of 5.6 md for sample 9WC indicate a high separate-vug porosity; the separate-vug porosity estimated from rock fabric, permeability, and porosity data is 9%. The photomicrograph from thin sections adjacent to core plug 9WC (Fig. 3b) clearly shows many separate intrafusulinid 106

Fig. 3—(a) Three relative permeability curves from SSAU 2310, and (b) photomicrograph of thin section at 5,229 ft adjacent to core plug 9WC, showing both intrafusulinid (separate-vug) and interparticle pores. SPE Reservoir Evaluation & Engineering, April 1998

vugs and interparticle pores. The core data and the photomicrograph thus suggest that the separate-vug porosity is another factor other than wettability that is controlling the relative permeabilities. All the relative permeability data from SSAU 2310 and 4902 were summarized in terms of recovery and residual oil saturation (Fig. 4a). Recovery by waterflooding decreases with an increase in the ratio of separate-vug porosity to total porosity (vug porosity ratio, or R vp ), whereas residual oil saturation increases with  R vp . Residual oil saturations determined from steady-state experiments are much lower than those determined from unsteady-state experiments (Fig. 4b), because the real residual oil saturations were not reached in the unsteady-state method. Capillary Pressures.   Capillary pressure data from the SSAU 2310 well are separated into grain-dominated dolopackstone and medium-crystalline mud-dominated dolostone (Fig. 5). In both rock  fabrics the capillary pressure decreases with an increase of porosity but not of permeability. For example, vuggy carbonates have low permeability and high porosity, but relatively low capillary pressure. Reservoir Modeling

One of the important issues in constructing geologic and reservoir models is to define geologic frameworks. A geologic framework is fundamental to defining flow units, interpolating well data into interwell regions, and thereby modeling fluid flow. Scales of  reservoir and flow simulation models vary considerably. However, simulations using too coarsely scaled models are not representative, whereas simulations using fine-scaled models are costly. Critical scales are the scales at which depositional facies can be properly correlated and petrophysical properties and fluid flow can be properly modeled. For carbonates, two critical scales are HFC’s and rock-fabric units.1,8,9 The stacking of rock-fabric units in an HFC defines the framework.

Fig. 4—(a) Waterflooding recovery and (b) residual oil saturation as a function of vuggy porosity ratio (  Rvp ). SPE Reservoir Evaluation & Engineering, April 1998

Fig. 5—Capillary pressure, water saturation, and rock-fabric relationships for medium-crystalline mud-dominated dolowackestone. Data from SSAU 2310 well.

The reason for using rock-fabric/petrophysical classes to define flow units is that many petrophysical properties and correlations, such as porosity-permeability transforms, capillary pressure, relative permeability, and residual oil saturation, can be better grouped according to rock-fabric/petrophysical classes than to strict depositional facies groupings.7 For example, fusulinid packstone, ooidpeloid packstone, and dasycladacean-mollusk wackestone may all behave petrophysically as mud-dominated rock-fabric facies and therefore can be grouped into a single rock-fabric/petrophysical class. Geologic Framework. A detailed reservoir characterization study was carried out on a two-section area, Tract 23–28 of the SSAU. The depositional model used is of a carbonate ramp, a simple 0.2° to 2° seaward-sloping depositional interface that extends from just above sea level to a depth of several hundred feet. Discrete environmental belts on this ramp from landward to seaward include inner ramp, ramp crest, and outer ramp. The ramp crest is the critical belt where the fair-weather wave base intersects the depositional profile, creating a 1- to 2-mile-wide belt of higher energy, grain-dominated rock-fabric facies. This belt, which occupies a water-depth range of 0 to 30 ft, separates lower energy 0- to 10-ft water-depth inner-ramp deposits landward from outer-ramp deposits seaward. The outer-ramp environment extends from 30 to 200 ft of water depth and is characterized by heterolithic mud-dominated rock-fabric facies. Eleven cores covering the reservoir were described in detail. Twelve HFC’s and flow units as shown in  Fig. 6 of the Amerada Hess SSAU 2505 well were identified in cores and uncored wells. The upper 9 HFC’s (Cycles 1 to 9) record progradation of the ramp-crest facies tract over the outer ramp during lower San Andres composite sequence progradation. These HFC’s are typical upward-shallowing cycles having basal mudstones and wackestones grading upward into grain-dominated packstones and grainstones. Rock-fabric variability includes thin intercalation of Classes I, II, and III rock fabrics. 7 The lower producing interval (Cycles 10 to 12) is composed of outer-ramp facies. The HFC’s are composed of  dolowackestone and grain-dominated packstone fabrics. However, pore size in these wackestone facies has been significantly enhanced by dolomitization, and thus rock fabrics fall largely within petrophysical Class II. 7 Petrophysics and Reservoir Model.   To construct the reservoir model, core data were calibrated with log data using neutron, density, acoustic, and resistivity logs. Total porosity was calculated using the neutron, density, and acoustic logs. Separate–vug porosity was calculated using a calibration of separate-vug porosity to total porosity and acoustic transit time9 (Fig. 7). A Z-plot of total porosity, water saturation, and rock fabric was used to define rock-fabric fields. Petrophysical properties of total porosity, separate-vug porosity, water saturation, permeability, and rock fabrics were calculated for 33 wells, and the results of the petrophysical evaluation of the SSAU 2309 well are shown in   Fig. 8. The 107

Fig. 7—Wireline log/separate-vug porosity and rock-fabric relationships. Relationship between acoustic transit time and separate-vug porosity form thin-section point counts.

one simulation. This method is easy and fast, but the realizations are too random to accurately depict realistic stratigraphic distributions. One of the recent trends in stochastic simulation is to generate geologically realistic models using statistical techniques and engineering data. In several examples we found that deterministic stratigraphic constraints are the most applicable. Two stratigraphic constraints used are the rock-fabric flow units and HFC’s. Stochastic simulations were performed separately for each rock-fabric unit using rock-fabric-specific geostatistical parameters. The realization for the entire reservoir is accomplished by combining all realizations of individual rock-fabric units.  Fig. 11 compares permeability distributions in Cycles 9 to 11 along a cross section on the SSAU 2309 well, Tract 23-28. This comparison includes examples generated by a conventional linear interpolation and by stochastic simulations with and without stratigraphic constraints. The linearly interpolated permeability patterns are smooth and continuous (Fig. 11a); the stochastically generated permeability data without stratigraphic constraints (Fig. 11b) are toorandom, and Fig. 6—Twelve high-frequency cycles and rock-fabric facies in  Amerada Hess SSAU 2505 well.

calculated permeability matches the core permeability better in Cycles 6 and 8a than in Cycle 5 because of the differences in rock  fabric calculated from logs and from core data. A three-dimensional (3D) reservoir model of the two-section study area was constructed using a 3D geocellular modeling software. In modeling, the geologic framework was first built by mapping the tops of 12 HFC’s. Porosity, permeability, and water saturation values calculated from petrophysical analyses of each well location were interpolated among wells. At each location, the vertical block sizes are the same within each cycle but are different among cycles. The permeability distribution in a west-to-east cross section shows that the permeability is generally more uniform and higher in Cycles 9 to 12 than in Cycles 1 to 8 ( Fig. 9). The 3D porosity distributions in Cycles 8 and 9 ( Fig. 10) show the upwardshallowing patterns and significant lateral variability within a rock-fabric flow unit. Because most reservoir simulation programs do not allow for discontinuous layers, all flow-unit boundaries must be continuous within the model. This results in rock-fabric flow layers containing more than one rock-fabric facies. No sharp boundaries are placed between the facies because no sharp boundaries have been found in analog outcrops, and the average petrophysical values are interpolated between wells to fill the HFC framework. Stochastic Simulation

One method commonly used in stochastic simulation is the generation of stochastically distributed data over the entire reservoir in 108

Fig. 8 —Comparison between core data and calculated porosity, water saturation, permeability, and rock-fabric values from petrophysical analysis of SSAU 2309. SPE Reservoir Evaluation & Engineering, April 1998

Fig. 9 —East–west cross section of permeability distribution.

Fig. 10 —Three-dimensional image of porosity distribution of Cycles 8 and 9 in Seminole San Andres Unit, Tract 23-28.

geologic features such as upward-shoaling sequences cannot be found; and the stochastically generated permeability data with stratigraphic constraints largely preserves the features of upwardshoaling sequences (Fig. 11c). Scale-Up For Flow Model

One of the objectives of the 3D reservoir modeling is to generate flow models at various scales for reservoir simulation. To generate flow models, it is necessary to scale-up small-scale data into larger simulation blocks in both horizontal and vertical directions. Scale-up in the horizontal direction is discussed by Journel and Huijbregts10 and Perez and Kelkar11 using horizontal well data, and by Wang  et al.4 using Lawyer Canyon outcrop data. Scale-up in the vertical direction is related to topics of vertical permeability and the ratio of vertical permeability to horizontal permeability. Core analyses commonly show a ratio of vertical to horizontal permeabilityranging from 0.1 to 1. This general trend holds in SSAU core data, as illustrated in Fig. 12a, by data from the SSAU 2710 well. Open circles are data from Cycle 9, squares are data from Cycle 10, crosses are data from Cycle 11, and solid circles are data from Cycle 12. Statistically speaking, the average  k vh  ratio is about 0.3. Many formulas have been proposed for scale-up of the  k vh  ratio from core data to simulation block sizes. 12,13 Wang  et al.4 applied a simple analytical equation to illustrate interesting features in scale-up of the vertical permeability of carbonates (Fig. 12b). The k vh  (   k h /    k v) ratio decreases with the vertical gridblock size up to 20 ft (6.1 m) to a value of 0.06 and remains at a constant value at a vertical gridblock size greater than 20 ft ( 6.1 m). This limiting SPE Reservoir Evaluation & Engineering, April 1998

Fig. 11—Permeability distribution in an east-west cross sections of (a) linearly interpolated model, (b) stochastic realization without stratigraphic constraints, and (c) stochastic realization with stratigraphic with stratigraphic constraints.

value of 20 ft (6.1 m) is close to the average thickness of HFC’s and suggests that data variance increases significantly within a cycle but only slightly among cycles. Reservoir Simulation

Reservoir simulations were performed using outcrop and subsurface models to study critical factors affecting recovery efficiency. Factors studied are geometry and distribution of rock-fabric units, direction of water injection, the k vh  ratio, dense mudstone distribution, initial gas cap, and stochastic realizations. Lawyer Canyon Outcrop.  The flow model for the Lawyer Canyon window (Fig. 13a) was constructed by overlaying the rockfabric units on the stratigraphic framework and by assigning each unit an average porosity and permeability ( Table 2).3 The result is a geologically constrained description of the spatial distribution of  petrophysical properties. Grainstone flow units in Cycles 1 and 2 are continuous, and permeability is high throughout the entire model, whereas in Cycle 9 the grainstone flow unit appears only in the south-central part. A number of two-dimensional waterflood experiments were conducted using this model to show the large impact of the geometry and distribution of rock-fabric facies3,8 and, particularly, the impact of low-permeability mudstone layers on performance predictions. Geometry and Distribution of Rock-Fabric Units.   Senger et al.3 demonstrated the importance of the correct spatial permeability distribution by comparing simulation results using the outcrop model (Fig. 13a) with results using a simulated subsurface model 109

Fig. 12—(a) Vertical permeability vs. horizontal permeability  sorted by high-frequency cycles, and (b) k vh   as a function of vertical block size.

constructed by the linear interpolation of cycles and petrophysical data between the ends of the model (Fig. 13b). The difference in the predicted recovery is about 13%of the OOIP, or 48% recovery from the interpolated model and 35% from the outcrop model (Fig. 13c) because the high-permeability grainstone in the middle of Cycle 9 does not extend to either end and was missing in the linearly interpolated model. The second experiment illustrated how the position of wells relative to the spatial distribution of permeability affects recovery. 3 In   Fig. 14a and b, water saturation and recovery of two runs,

Fig. 13—Lawyer canyon flow models. (a) The rock-fabric permeability model based on continuous outcrop data. (b) A linear interpolation of permeability data taken from two pseudo-wells on either end of the Lawyer Canyon window. (c) Comparison of waterflooding performance between two models. The rockfabric permeability model gives lower recovery than the linearly  interpolated model because the permeable grainstone unit is missing in the linearly interpolated model.

TABLE 2—PROPERTIES OF ROCK-FABRIC FLOW UNITS FOR LAWYER CANYON OUTCROP MODEL (FROM SENGER   ET AL.3 )

Flow Unit

Rock Fabric

Porosity

Permeability (md)

Initial Water Saturation

Residual Oil Saturation

1

Mudstone

0.040

0.01

0.900

0.01

2

Wackestone

0.105

0.30

0.405

0.40

3

Grain-dominated packstone I

0.085

4.50

0.214

0.35

4

Grain-dominated packstone II

0.129

1.80

0.400

0.35

5

Grain-dominated packstone III

0.118

5.30

0.243

0.35

6

Moldic grainstone I

0.145

0.70

0.091

0.40

7

Moldic grainstone II

0.159

2.20

0.077

0.40

8

Highly moldic grainstone

0.230

2.50

0.041

0.40

9

Grainstone I

0.095

9.50

0.189

0.35

10

Grainstone II

0.110

21.3

0.147

0.25

11

Grainstone III

0.135

44.0

0.103

0.25

110

SPE Reservoir Evaluation & Engineering, April 1998

This  k vh  effect on waterflooding is illustrated in  Fig. 15, which shows water saturation distributions after 20-year waterflooding for three cases: k vh    0, 0.1, and 1. When k vh   0, the noncommunicating case, severe channeling occurs through high-permeability flow units. When  k vh  0.1, crossflow increases and Cycles 3 to 7 are better swept than in the noncommunicating case. When k vh  1, increased crossflow in Cycles 3 to 7 improves the sweep and recovery efficiencies. Simulation results of these cases are summarized in terms of  recovery efficiency with respect to pore volume of water injected (Figs. 16a and b). For all k vh  ratios, recovery is higher in the model without dense mudstone layers. In Fig. 16c, recovery efficiencies at a 0.3 pore volume of water injected in both models are plotted with respect to the  k vh  ratio. The upscaled  k vh  ratios for the model without dense mudstone layers, corresponding to the same recovery in the model with dense mudstone layers at  k vh  ratios of 0.3 and 1, are, respectively, 0.02 and 0.04. The  k vh  ratio range of 0.02 to 0.04 agrees well with the  k vh  ratio reported in most large-scale reservoir simulations,4,14 where coarse-scale simulation grids are used and dense mudstone layers are averaged in. Therefore, adding dense mudstones to the flow model reduces the crossflow resulting from the artifact of scaling up from fine-scale reservoir models to coarse-scale simulation models. All the outcrop simulations were conducted using a dead oil without solution gas. However, the SSAU crude has a high initial solution gas ratio and the field had a small initial gas cap. It is

Fig. 14—Water saturation distribution after 24 years of water injection in (a) a left-to-right injection experiment and (b) a right-to-left injection experiment, showing crossflow points at the downflow termination of high permeability in Cycle 9 and oil left in the middle of Cycle 7. (c) Comparison of waterflooding performances between (a) and (b).

flooding from left to right (a) and right to left (b), are compared. In both cases, water channels through the highly permeable grainstones in Cycles 1, 2, and 9. Channeling is more severe in Cycles 1 and 2 than in Cycle 9. Water channels through the grainstone in Cycle 9 until it is laterally terminated, where it then flows down across the basal mudstone of Cycle 9 into underlying Cycles 8 and 7 and leaves oil in the middle of Cycle 7 unswept. Twelve percent more oil is trapped when water is injected right to left than when water is injected from left to right (Fig. 14c) because the upstream barrier of Cycle 9 is shorter and water is channeling faster in case (b) than in case (a). Effects of  kvh   Ratio and Dense Mudstones.   Many simulation studies have shown that the  k vh  ratio is one of the most dominant parameters affecting recovery efficiency. Determining the  k vh  ratio of flow models is one of the major issues in reservoir analysis. 14 The effect of  k vh  ratio on recovery was tested in Lawyer Canyon outcrop models with and without dense mudstone layers. The model without dense mudstone layers can be considered as an analog of the coarse-scale simulation model where dense mudstone layers are averaged in during scale-up. In each case, simulations were run with a k vh  ratio of 0.001, 0.01, 0.1, and 1. SPE Reservoir Evaluation & Engineering, April 1998

Fig. 15—Effect of k vh   value on water-saturation distributions after 20 years of water injection. The k vh  values varying from (a) 0, (b) 0.1, and (c) 1.0. 111

Fig. 17—Effect of  k vh ratio on waterflooding recovery using a 2D cross section model with an initial gas cap in SSAU, Tract 23-28.

units to study their effect on recovery and production and injection rates. Results on recovery (Fig. 18a) indicate that no significant differences occurred from the three realizations using a correlation length of 1,000 ft (300 m). This was partly because these realizations were constrained by rock-fabric units. Nevertheless, production and injection rates are different in these runs (Figs. 18b and 18c). These differences stem from the change in permeability distribution and effective permeability with realization. Conclusions

Rock fabrics are defined on the basis of grain and crystal size and sorting, interparticle porosity, separate–vug porosity, and the presence or absence of touching vugs. Petrophysical properties of  porosity, permeability, relative permeability, and capillary pressure can be grouped according to rock fabrics. Permeability profiles can be calculated using rock-fabric-specific transforms between interparticle porosity and permeability. Special core analysis data indicate that waterflood recovery decreases and residual oil saturation increases with increasing separate-vug porosity. Residual oil sat-

Fig. 16 —Effect of dense mudstones on the  k vh value. (a) Lawyer Canyon outcrop model with dense mudstones, (b) Lawyer Can yon outcrop model without dense mudstones, and (c) the technique to determine an effective  k vh  value for the model without dense mudstones based on the  k vh  of core data.

therefore important to understand how the k vh ratio affects recovery efficiency when SSAU crude is used and an initial gas cap is present. This k vh  effect was studied using a SSAU cross-section model through SSAU 2316, 2602, 2506, 2502, 2505, and 2704 wells. Three simulation runs were performed using  k vh   0, 0.1, and 1. Recovery curves ( Fig. 17) show a trend of decreasing recovery with an increase of  k vh  ratio, which is opposite to the trend observed in the outcrop models (Fig. 16). The opposite trend stems from an initial gas cap being presented in the subsurface model. The high-mobility gas cap serves as a big conduit for water channeling, and increasing the k vh ratio increases the crossflow of water through an unperforated gas cap. The k vh  ratiocan be estimated by matching simulation results with production history. Wang  et al.4 used a  k vh ratioof 0.04 in an 80-acre 3D model to match the SSAU production. This suggests that the barrier effect in SSAU is strong. Effect of Stochastic Realization.  Because uncertainties in flow models generated from well data are high, the chances of matching field production using a linearly interpolated model are low, and history matching may be better achieved by using stochastic models. Flow simulations were performed on stochastic realizations conditioned on SSAU well data andconstrained by rock-fabric flow 112

Fig. 18 —Effect of stochastic realization on (a) waterflooding recovery, (b) production rate, and (c) injectivity. SPE Reservoir Evaluation & Engineering, April 1998

urations determined by the steady-state method are significantly lower than those determined by the unsteady-state method, because the real residual oil saturation is not reached in the fast unsteadystate method. HFC’s and rock-fabric units are the two critical scales for modeling shallow-water carbonate ramp reservoirs. Descriptions of  rock-fabric facies stacked within HFC’s provide the most accurate framework for constructing geologic and reservoir models because discrete petrophysical functions can be fit to rock-fabric units and fluid flow can be approximated scale-up within rock-fabric flow units. Stochastic simulations without stratigraphic control can be too random for generating geologically realistic models. The upwardshallowing sequences of carbonates can be observed in stochastic models only when they are constrained by rock-fabric flow units. Scale-up of permeability in the vertical direction was investigated in terms of the k vh   ratio. Because of the cyclic nature of  carbonate reservoirs, the  k vh  ratio decreases exponentially with the vertical gridblock size up to the average cycle size of 20 ft (6.1 m) and remains at a value of 0.06 for a gridblock size of more than 20 ft (6.1 m). Simulation results showed that critical factors affecting recovery efficiency are the stacking patterns of rock-fabric units, the k vh ratio, and the dense mudstone distribution. Simulations using outcrop models demonstrated that the geometry and distribution of  rock-fabric units can significantly affect recovery efficiency and the direction of water injection. The k vh   ratio and dense mudstone layers are the primary controlling parameters governing the recovery efficiency. Waterflood recovery increases with the k vh   ratio when dead oil is used and decreases with the k vh   ratio when an initial gas cap is present. When stochastic models are constrained by the rock-fabric framework, simulation results are similar in recovery but different in production and injection rates. Nomenclature h    thickness, m k     permeability, md k oi   permeability at initial oil saturation, md k ro    relative oil permeability, fraction k rw    relative water permeability, fraction k h    horizontal permeability, md    k h    arithmetic mean of horizontal permeability, md k v    vertical permeability, md    k v    harmonic mean of horizontal permeability, md k vh  ratio of vertical permeability to horizontal permeability,fraction  R vp    ratio of separate-vug porosity to total porosity, fractions Acknowledgments

This research was done at the Reservoir Characterization Research Laboratory of the Bureau of Economic Geology and was funded by industrial sponsors and by DOE Contract no. AC22-89BC1440. Publication was authorized by the Director, Bureau of Economic Geology, The U. of Texas at Austin. We thank Susan Lloyd for word processing and layout, and Tari Weaver and David M. Stephens, under the direction of Joel L. Lardon and Richard L. Dillon, for preparation of illustrations. References 1. Kerans, C.  et al.:  “Characterization of Facies and Permeability Patterns in Carbonate Reservoir Based on Outcrop Analogs,” The U. of Texas at Austin, Bureau of Economic Geology, final report, Contract No. DE-AC22–89BC14470 for the Assistant Secretary for Fossil Energy, U.S. DOE, Washington, DC (1993) 160. 2. Galloway, W.E.  et al.: Atlas of Major Texas Oil Reservoirs,  The U. of  Texas at Austin, Bureau of Economic Geology (1983) 139. 3. Senger, R.K.  et al.:  “Dominant Control on Reservoir-Flow Behavior in Carbonate Reservoirs as Determined from Outcrop Studies,” Reservoir  Characterization III,  B. Linville  et al.  (eds.),  Proc.,  Third International ReservoirCharacterization Technical Conference, Tulsa (November1993). 4. Wang,F.P. et al.: “Critical Scales, Upscaling, and Modeling of ShallowWater Carbonate Reservoirs,” paper SPE 27715 presented at the 1994 SPE Reservoir Evaluation & Engineering, April 1998

SPE Permian Basin Oil and Gas Recovery Conference, Midland, Texas, 16–18 March. 5. Lucia, F.J. et al.:  “Fluid-flow Characterization of Dolomitized Carbonate-Ramp Reservoirs: San Andres Formation (Permian) of Seminole Field and Algerita Escarpment, Permian Basin, Texas and New Mexico,”   Hydrocarbon Reservoir Characterization: Geologic Framework  and Flow Unit Modeling,   E.L. Stoudt and P.M. Harris (eds.), SEPM Short Course No. 34 (1995) 129–153. 6. Lucia, F.J.: “Petrophysical Parameters Estimated from Visual Descriptions of Carbonate Rocks: A Field Classification of Carbonate Pore Space,”  JPT   (March 1983) 629;  Trans.,  AIME,  275. 7. Lucia, F.J.: “Rock-Fabric/Petrophysical Classification of Carbonate Pore Space for Reservoir Characterization,”  American Assn. of Petroleum Geologists Bull.  (1995) 79, No. 9, 1275. 8. Kerans,   et al.:  “Integrated Characterization of Carbonate Ramp Reservoirs Using Permian San Andres Formation Outcrop Analogs,”  American Assn. of Petroleum Geologists Bull.  (1994) 78,  No. 2, 181. 9. Lucia, F.J. and Conti, R.D.:   Rock Fabric, Permeability, and Log  Relationships in an Upward-Shoaling, Vuggy Carbonate Sequence,  The U. of Texas at Austin, Bureau of Economic Geology,   Geological Circular 87-5  (1987) 22. 10. Journel, A.G. and Huijbregts, Ch.J.:   Mining Geostatistics,   second edition, Academic Press, San Diego (1978) 599. 11. Perez, G., and Kelkar, M.: “Assessing Distributions of Reservoir Properties Using Horizontal Well Data,” Reservoir Characterization III,  B. Linville   et al.   (eds.),   Proc.,  Third International Reservoir Characterization Technical Conference, Tulsa (November 1991). 12. Lishman, J.R.: “Core Permeability Anisotropy,”   J. Cdn. Pet. Tech. (April–June 1970) 79. 13. Haldorsen, H.H. and Lake, L.W.: “A New Approach to Shale Management in Field-Scale Models,” SPEJ  (1984) 447;  Trans.,  AIME, 277. 14. Harpole, K.J.: “Improved Reservoir Characterization—A Key to Future Reservoir Management for the West Seminole San Andres Unit,” JPT  (November 1980) 2009;  Trans.,  AIME,  269.

SI Metric Conversion Factors

acre  4.046 873 ft  3.048* psi  6.894 757 sq mile  2.589 988

E 03 E01 E 00 E 00

m2  m  kPa 2  km 

 

*Conversion factor is exact.

SPEREE

Fred P. Wang is a senior reservoirengineer at PGSReservoir, Inc., in Houston and previously worked at the Bureau of Economic Geology, The U. of Texas at Austin. He holds an MS degree from The U. of Texas at Austin and a PhD degree from Stanford U., both in petroleum engineering.   F. Jerry Lucia  is a Senior Research Fellow with the Bureau of Economic Geology developing new techniques and methods for characterizing carbonate reservoirs to improve recovery from existing oil fields through the integration of geological, petrophysical, engineering, and production data. Previously Lucia was a Consulting Geological Engineer forShellOil Co.assignedto theHead Officestaff when he retired in 1985 with 31 years’ experience as a geological engineer in research and operations. Currently, he holds a BS degree in engineering and an MS degree in geology from the U. of Minnesota. Charles Kerans is a seniorresearch scientist in the Bureau of Economic Geology. He holds a BS degree from St. Lawrence U. anda PhD degreefromCarletonU., both in geology.

Wang

Lucia

Kerans 113