Miscible Gas Research Articles

Effective potential approach to bulk thermodynamic properties and surface tension of molecular fluids: II. Binary mixtures of n-alkanes and miscible gas

A representation of alkanes and alkane/gas mixtures is proposed in terms of simple fluids interacting through pairwise square well potentials parameterised by the range of attractive forces. Using the model, vapour–liquid equilibria and interfacial tension (IFT) are studied both for pure alkane fluids (C4, C5, C6, C8, C10 and C14) and their high pressure binary mixtures formed with methane, nitrogen or carbon dioxide. Potential parameters for the isolated components are first determined from the critical parameters, Pitzer’s acentric factor and one surface tension datum at a chosen temperature. Cross-term interactions between species are obtained from modified Lorentz–Berthelot rules which provide good fits to the vapour–liquid coexistence densities as functions of mixture composition. At a general state point, the interfacial tension is predicted using generalised van der Waals (gvdW) theory, which is a mean field free energy density functional theory. This semiempirical procedure typically produces very satisfactory agreement with experimental interfacial tension data.

EOS tuning to model full field crude oil properties using multiple well fluid PVT analysis

Equations of State (EOS) are increasingly being used to model fluid properties of crude oil and gas reservoirs. This technique offers the advantage of an improved fluid property prediction over conventional black oil models. Once the crude oil or condensate fluid system has been probably characterized, its PVT behavior under a variety of conditions can easily be studied. This description is then used, within a compositional simulator, to study and choose among different scenarios for EOR schemes, such as miscible gas injection for oil reservoirs or liquid recovery under lean gas injection for condensate reservoirs. In this paper, crude oil from a reservoir in the United Arab Emirates (UAE) was characterized using the Peng–Robinson Equation of State (PR-EOS) to arrive at one EOS model that accurately describes the PVT behavior of crude oil produced from the different wells in the reservoir. The multi-sample characterization method is used to arrive at one consistent model for crude oil for the whole reservoir. The fluid samples are first analyzed for consistency to make sure that they are representative of oil produced, and then they are used to obtain parameters for EOS model. The tuning procedure for the EOS is done systematically by matching the volumetric and phase behavior results with laboratory results. Also, a consistent C 7+ pseudo-component split using the Whitson splitting method is used for all samples to arrive at a consistent model for crude oil for the whole reservoir. Results showed a very good match of PVT properties predicted using the EOS model with laboratory tests for this field. These results demonstrate the usefulness of the multi-sample method in providing one EOS model for the crude oil using PVT test results from different wells. The EOS model developed for this particular field may be used in reservoir simulation studies to optimize hydrocarbon recovery.

Application of a New Technique to Optimize Injection Gas Composition For the Rainbow Keg River F Pool Miscible Flood

Abstract A new experimental technique, called the Vanishing Interfacial Tension (VIT) technique, has been successfully utilized in this study to optimize solvent composition for the miscible gas injection project being considered for the Rainbow Keg River F Pool. The VIT technique consists of measuring the interfacial tension between the injected gas phase and the reservoir crude oil at the temperature of the particular oil containing formation and at varying pressures and/or enrichment levels of the gas phase. These interfacial tension measurements are carried out by computer digitization of the image of the profiles of sessile and pendant drops of crude oil enclosed in a surrounding medium of the injection gas. By fitting these experimental drop profiles with the iterative solution of the Laplace capillary equation, the value of the interfacial tension is obtained at each pressure or enrichment level. By making a plot of the interfacial tension against the independent variable (either pressure or enrichment), accurate values of the minimum miscibility pressure (MMP) and/or the minimum miscibility composition (MMC) are obtained by extrapolation to zero interfacial tension. This paper describes the new VIT technique and provides experimental evidence for its validity by comparing the VIT-MMP with slim-tube-MMP. Each MMP determination using the VIT technique was accomplished within 4 – 6 hours, while 4 – 6 weeks were required for the slim-tube technique. The paper also describes the application of the VIT technique to the problem of optimizing the injection gas composition at the Rainbow Keg River F Pool miscible flood. For this field application of the technique, live reservoir crude oil as well as lean and rich gas mixtures, matching field gases in composition, were used in the experiments. Gas/oil interfacial tension measurements were made in "first contact" as well as "equilibrium" modes. The optimized solvent composition was then verified by a single slim-tube test and compared with equation of state predictions. It has been demonstrated through this study that the new VIT technique is a reliable, accurate and fast technique for cost effective determination of MMPs and optimum injection gas compositions. Introduction Hydrocarbon miscible flooding is by far the most important conventional oil EOR process in Canada. It accounts for 83% of the 164,600 b/d of Canadian conventional oil EOR production(1). Furthermore, it is worth noting that most of the 104,300 b/d EOR production increase in 1992 (over that in 1990) in the US was also due to miscible projects based on both CO2 and hydrocarbon gases(1). Further improvements in the economics of miscible flooding could be accomplished by minimizing the cost of solvent blends and the cost of their injection. These can be achieved by (1) optimizing the solvent composition so that minimum enrichment of the dry gas by the C2+ fraction would yield cheaper solvents for injection and enable increased sales of the natural gas liquids, (2) increasing the accuracy of determination of minimum miscibility pressures for a given solvent composition and reservoir temperature which, in turn, would enable operation at near miscible conditions resulting in considerable compression cost savings.

Effect of oil saturation on foam propagation in Snorre reservoir core

A series of foam floods was conducted in Snorre reservoir core at 90°C and 300 bar, at different oil saturations. The rate of foam propagation decreased and the time required to reach the maximum attainable apparent foam viscosity increased strongly with oil saturation. Apparent foam viscosity decreased steeply at a “critical” oil saturation of 13% to 15%. Extremely high apparent foam viscosities, up to 1000 cP, were generated at miscible gas flood residual oil saturation (13%). Above the critical oil saturation, strong foams with apparent viscosities of about 200 cP were still formed, compared to apparent gas viscosities in the absence of surfactant of 0.5 to 0.7 cP. The effect of gas composition (Snorre field gas, methane, nitrogen) on foam performance was minor. Significant residual gas mobility reduction was observed during gas injection into the foam-filled core.

Reservoir management of the Wytch Farm Oil Field, Dorset, UK: providing options for growth into later field life

The Wytch Farm Oil Field, currently on plateau, produces up to 110 × 10 3 BOPD, 17.6 × 10 6 SCF gas and 725 tonnes LPG per day. Original reserves are 450 × 10 6 BBL with a proven 230 × 10 6 BBL oil equivalent remaining. The Triassic fluvio-lacustrine Sherwood Sandstone, at 1535mTVDSS (true vertical depth, subsea), is the largest and most prolific reservoir. Approximately half the reserves are in an offshore extension being developed by extended reach drilling (ERD) at step-outs of up to 10.1 km from onshore Poole Harbour. Projects to increase reserves, extend plateau and slow decline include: additional ERD wells; infill drilling; miscible gas injection; and pattern water flooding of the low nett: gross Upper Sherwood all whilst maintaining reservoir pressure. Reservoir description is central to realizing these opportunities for growth. Structural uncertainty has been reduced through acquisition of the first transition-zone 3D seismic survey in the UK. An extensive RFT (repeat formation test) and production log database has been acquired in the onshore and ERD wells. These dynamic data, together with static data from core and outcrop studies, and >21km of ERD formation evaluation logs, are used to develop a high-resolution, fluvio–lacustrine sequence architecture of the Sherwood. The deterministic model enhances predictability of flow barriers, baffles and high permeability intervals. This understanding of fluid flow and recovery provides the framework for economic evaluation, which, with clear communication of uncertainty across disciplines, is the key to successful management of the reservoir into later field life.

A Case Study in Scaleup for Multicontact Miscible Hydrocarbon Gas Injection

SummaryWe describe the strategy and results of scaleup done to simulate a multicontact miscible hydrocarbon water alternating gas (WAG) injection process. To adequately model both oil recovery and solvent retention in WAG, one must model three-phase flow including gas trapping. Scaleup of the multicontact miscible gas process is particularly difficult because of the very fine-scale structure of the gas fingers and the miscible front. The case studied is a heterogeneous mixed wet reservoir with a transition zone down to an underlying aquifer. The objective was to develop pseudo relative permeability curves and other parameters that are suitable for running in a full-field limited compositional model with three hydrocarbon components.Both history-matching and systematic approaches were used to generate pseudo relative permeability curves that reproduced results of high-resolution, fully compositional (FC) reference simulations. Dynamic pseudoization techniques were used to derive first guesses at pseudos, but required further calibration to reproduce reference simulations successfully. In matching incremental miscible gas/oil recovery timing and solvent retention, varying three-phase water relative permeability was much more effective than varying the mixing parameter.The predictive capability of pseudos was tested for changes with respect to slug size, WAG ratio, and solvent enrichment. Pseudos derived for one pattern or cross section were tested in other patterns or cross sections. Pseudos worked well with respect to changes in WAG ratio, fairly well with respect to changes in solvent enrichment, and moderately well for changes in slug size. They were less robust with respect to changes in description.

Fast Procedure for Upscaling Compositional Simulation

Summary Single-phase upscaling techniques have been in use for a number of years now to incorporate subgrid reservoir description information into reservoir simulation. There have also been a number of approaches to developing two-phase upscaling algorithms suitable for black oil simulation. The key barrier to the development of compositional upscaling techniques is algorithm speed. A straightforward extension of existing two-phase upscaling approaches would consume enormous amounts of computer time because of the number of additional components modeled and the need to perform flash calculations. This paper describes an upscaling method for simulations in which compositional processes play a key role, such as miscible gas injection or gas cycling schemes. We will describe the method to generate upscaled compositional fluxes in two or three dimensions, and the way in which the upscaled fluxes are incorporated into a compositional simulator. Our approach uses a streamline technique, which provides a tremendous gain in speed for the loss of a small amount of accuracy. The streamline technique produces upscaled fluxes almost identical to those obtained from postprocessing conventional compositional model runs in a fraction of the time. The results of applying these upscaled fluxes in a realistic example show that we can obtain close agreement between fine and coarse grid models of lean gas injection into oil at residual saturation. For an example problem with a 12-component equation of state (EOS), the component recovery curves with upscaled fluxes on a 5 × 5 grid agree well with the original 100 × 20 fine grid

Geochemical comparison of reservoir solid bitumens with diverse origins

Geochemical and petrologic comparison of solid bitumens with various origins from reservoirs in Zaire, Canada and Kazakhstan were studied to provide insight into their formation processes and their physical and chemical properties. Results of this study can help develop methods for treatment and removal of solid bitumen, and evaluating producibility of associated hydrocarbon fluids. Characterization of these solid bitumens reveals a wide range in quantity and composition of extractables (soluble material) and in solid bitumen reflectance, which indicate significant differences in formation processes, hydrocarbon source and thermal maturity. The Zaire and Kazakhstan samples represent end members of the spectrum of solid bitumens studied. Solid bitumens from the Motoba Field, Zaire, are highly extractable and low in thermal maturity (0.2 – 0.3% bitumen reflectance). Reservoir mixing of a Cretaceous lacustrine sourced oil and a Tertiary marine sourced oil of different thermal maturities appears to be responsible for their formation. In contrast, solid bitumens from the Tengiz Field, Kazakhstan, are characterized by their extremely low extractables, high bitumen reflectance (> 1%) and low atomic H/C ratios (< 1.0). Thermal alteration is an important process in the formation of these highly mature bitumens (pyrobitumen). Petrographic textures of the solid bitumens complement their geochemical characterization and provide insight into their origin. Solid bitumens from the Mitsue Field, Canada, which has been under miscible gas flood for sometime, are intermediate in the yields of extractables and thermal maturity (∼0.7% bitumen reflectance). The origin of the solid bitumen may have been gas deasphaltening originating from geological processes rather than from the recovery process. A combination of pyrolysis gas chromatography and petrology (bitumen reflectance and occurrence) provides distinction between production and geologically induced reservoir solid bitumen.

ニーワットアルギャラン油田の開発

Abu Dhabi Oil Co., Ltd. (ADOC) is currently operating three oil fields; Mubarraz, Umm Al-Anbar and Neewat Al-Ghalan (GA) Fields. The oil production of Mubarraz Field commenced in 1973 and an artificial lift with ESP (electrical submersible pump) was applied. Umm Al-Anbar Field initiated the oil production in 1989 and one of EOR methods; a vaporized gas miscible drive was applied to increase an oil recovery. Neewat Al-Ghalan Field is located in the southern part of the Arabian Gulf about 100km off the coast of Abu Dhabi, U.A.E., between Umm Al-Anbar Field and Mubarraz Island where ADOC has oil processing, storage, loading and utility facilities. GA Field is marginal to be developed from its reservoir characteristics, low OOIP and so on. The development of the field became feasible by applying the vaporized gas miscible drive for achieving higher oil recovery, and utilizing the existing facilities in Umm Al-Anbar Field and Mubarraz Island. The development plan was established and the development works commenced in 1993. It has been completed in two years as scheduled and the production commenced in June 1995.This report summarizes the development of Neewat Al-Ghalan Field with presenting its exploration, field outline, development plan, development works and both production and injection performances. It also describes a sour gas injection project, which is undergoing in order to solve an environmental protection issue.

Modeling velocity changes associated with a miscible flood in the Prudhoe Bay Field

The Prudhoe Bay Field, Alaska, is produced by a number of recovery processes. A miscible gas (MI) injection pilot was studied to see if repeated seismic surveys could detect the progress of the MI gas. Gassmann's equation was used on the injection, producing and monitor wells where a detailed reservoir simulation was available. Time‐varying saturations of the three fluid phases and the pressure were used to calculate the expected velocity of the reservoir at different stages of the injection. The differences between the modeled velocities at two extremes of gas saturation after the water‐after‐gas (WAG) range up to 500 ft/s (150 m/s). It was concluded that it have been possible to detect the fluid saturation had a baseline survey been collected early in the field's development. Unfortunately, initial production introduced 2% gas into the fluid, muting later attempts to map changes in saturation that varied from between 30% and 60%. Additionally, the use of a WAG process further complicated the gas mapping by both increasing and decreasing the reservoir fluid velocities. Collecting new seismic data over this pilot was not recommended. The modeling exercise highlighted a number of issues that are important in monitoring other reservoirs. Amongst these are the timing of data collection and the weakness of the petrophysical models caused by the numerous assumptions that are required in the absence of field observations. It was demostrated that modeling exercises can both save unnecessary field expenses and provide considerable insight in reservoir behavior.

Integrated reservoir study, Lower Eocene Misoa reservoirs, VLA-6/9/21 Area, Block I, Phase 2, Stage 2, Lagunillas Field, north‐central Lake Maracaibo, Venezuela

Twenty‐eight geologically targeted, field development opportunities, including a variety of deeper pool opportunities that could significantly add to Maraven's (affiliate of PDVSA) reserve base, are identified in Lower Eocene Misoa reservoirs in the Stage 2 Area in Block I in north‐central Lake Maracaibo, Venezuela with the help of integrated geophysical, geological, petrophysical, and engineering analyses. Seismic rms amplitudes are instrumental in detecting and mapping trends of lithofacies and were integrated into stratigraphic models. Amplitude response to net sand thickness is a linear relationship. The amplitude signature also captures hydrocarbon charge as evidenced by bright amplitudes coincident with structural, fault‐bounded culminations. These direct hydrocarbon indicators (DHI) can result from as low as 2% miscible gas fraction within the hydrocarbon column.

RESERVOIR CHARACTERISATION OF THE MOORARI/WOOLKINA FIELD COMPLEX, COOPER BASIN

The Tirrawarra Sandstone oil accumulation at the Moorari/Woolkina Field complex in the Cooper Basin, Central Australia has been under miscible gas flood EOR since 1984. A facies-based reservoir characterisation study of the field was undertaken to help explain unpredicted field performance and to provide a reliable model on which to base any future field development and necessary engineering studies prior to blow down.The reservoir is dominated by the interaction of fluvial braid-plain and glacio-lacustrine shoreface processes in a braid-delta setting. It comprises five basic facies from which eleven sub-facies are identified, eight containing oil bearing reservoir. An extensive field wide lacustrine mudstone acts as a vertical barrier and divides the reservoir into two gross sand units. The individual sub-facies were petrographically and petrophysically characterised and mapped in detail to provide a model of the field architecture, within which the residency of the original and remaining oil-in-place was determined.A substantial increase in OOIP explained the better than predicted performance from the EOR pattern and highlighted the field flanks for assessment for incremental development. This was confirmed by the engineering data review which also revealed that the poor structurally low wells were affected by relative permeability effects. As a result of this study, plans for incremental field development are in progress with the goal of increasing reserves and production.

Abstract: Evaluating Reservoir Fracture Distribution for Planned Miscible Gas Injection: Rhourde El Baguel Field, Algeria

Abstract: Evaluating Reservoir Fracture Distribution for Planned Miscible Gas Injection: Rhourde El Baguel Field, Algeria

Scale-up of near-miscible gas injection processes; integration of laboratory measurements and compositional simulation

Results from laboratory PVT measurements, special core analysis studies, and reservoir condition core-flood studies were used to develop and test the accuracy of a compositional simulation model in predicting near-multicontact miscible gas flood performance at the laboratory scale. Excellent agreement was obtained between the core-flood measured recoveries and GOR and the compositional simulation model predictions. No history matching was required to obtain this result. The choice of PVT and special core tests were critical to our ability to model the near-multicontact miscible displacement process without history matching. This result provides a high degree of confidence in using the compositional simulation model in cross-section and 3D element models to predict field-scale performance. Cross-sectional simulation sensitivities were performed in a geostatistical model of a dipping reservoir. Gas-flood recovery was on par with water-flood recovery for this cross-section.

Modelling of Solid Precipitation From Reservoir Fluid

Abstract A solid precipitation model is proposed for liquid-solid equilibrium based on the Flory-Huggins polymer solution theory along with a modification to account for the colloidal suspension effect of partial soluble solid compounds in the fluid mixture. The colloidal effect is dependent on the estimation of the critical resins concentration. A linear variation of free volume is assumed in terms of the component molecular weight for the evaluation of volume fraction in the polymer solution formulation. The binary interaction energy coefficient is introduced to allow for positive or negative deviation from the ideal solution. The effect of heat capacity difference between the liquid and solid phases and the effect of pressure correction are included in the model. New correlations have also been developed for the model. A multimodel multiphase flash algorithm is formulated using an equation of state for vapour-liquid equilibrium and the proposed model for liquid-solid equilibrium. A detailed discussion of the model performance and the effect of the model parameters on the fitting to experimental results are also presented. Introduction Solid precipitation from reservoir crudes has been a serious problem in the oil industry. In reservoir engineering, the original reservoir fluid is well-stabilized after it has formed and migrated geologically to the reserve area where it is found. The production of the reservoir fluid alters the storage conditions which may cause solid deposition. These deposits can cause formation damage and in situ plugging which result in the loss of reservoir permeability and degradation of the porous media. The deposition of the heterocompounds on the surface of the media may reverse its wettability and decrease the transmissivity(9). In miscible gas flooding, solvents are injected into the reservoir in order to reduce the interfacial tension of the reservoir fluids and to recover more crude oil from the formation. This process can significantly change the fluid phase behaviour and result in asphaltenes, or other solid components, instability in the solution, thus increasing the potential for solid deposition in the reservoir. The solid problem is frequently observed in the wellbore and well tubing. It may plug wells, increasing the fluid pressure gradient which can result in significant reduction in well productivity. It can also cause operation problems in the subsurface and surface equipment. In these cases, costly well workovers or other production treatments may be required. Review Many investigators have done considerable research on the nature of heavy organic compounds and the mechanisms of the solid deposition(10,14,27,28,31,32,34). The complexity of the solid compounds has impeded progress toward accurate prediction and efficient treatment of solid deposition during oil recovery. The precipitated solid usually constitutes the heavy organic compounds of waxes, asphaltenes and resins. Waxes-are defined as normal paraffins and other molecules containing long chain alkyl groups usually ranging from C18 to about C60. Upon cooling below their cloud point temperature, the solid waxes crystallize and precipitate. Waxes can dissolve in many kinds of hydrocarbon solvents to form a homogeneous solution.

El Furrial Field Miscible Gas and Water Injection Enhanced Oil Recovery Project: ABSTRACT

El Furrial Field Miscible Gas and Water Injection Enhanced Oil Recovery Project: ABSTRACT

5515919 Enhanced oil recovery process including the simultaneous injection of a miscible gas and water: Stevens Chris; McPherson Steven; Larson John R; Robie Donnell R; Wackowski Ronald, Orchard Point, CO, Singapore assigned to Chevron USA Inc

5515919 Enhanced oil recovery process including the simultaneous injection of a miscible gas and water: Stevens Chris; McPherson Steven; Larson John R; Robie Donnell R; Wackowski Ronald, Orchard Point, CO, Singapore assigned to Chevron USA Inc

Theory of Multicomponent Gas/Oil Displacements

Chromatographic separations that occur during two-phase flow in a porous medium are analyzed for one-dimensional, dispersion-free displacement of a liquid hydrocarbon mixture (oil) by a vapor phase mixture (gas). The authors show that displacement behavior is controlled by a set of key equilibrium the lines, all of which are determined by geometric constructions in composition space: two of the key tie lines are those that extend through the initial oil and injection gas compositions, and the remainder are tie lines that are located at intersections of ruled surfaces of tie lines. Very efficient displacement of oil by gas results if any of the key tie lines is a critical tie line. That high displacement efficiency is the basis of so-called miscible gas injection processes for enhanced oil recovery.

Performance Analysis and Optimization of the Prudhoe Bay Miscible-Gas Project

Summary Because EOR oil response at Prudhoe Bay has been difficult to measure directly, a number of different types of field measurements have been made to evaluate the miscible-flood displacement efficiency. These measurements include water- and solvent-injection profiles, logging data from an observation well, and single-well tracer test (SWTT) data. Despite ambiguity in these data, the measurements support the simulation and laboratory data and generally indicate that the Prudhoe Bay Miscible Gas Project (PBMGP) is performing well. The most useful EOR surveillance data have been the separator-gas-sample database, with ≈4,000 compositional analyses. Separator flash analysis and allocation programs use this database to infer EOR performance on the basis of produced solvent. Reservoir mechanisms that adversely affect the EOR process efficiency have been identified. The project has exceeded initial expectations in terms of solvent retained within the reservoir, which has favorable implications for solvent sweep efficiency. Procedures have been developed to use the field and simulation data to determine how the solvent should be allocated to the existing patterns and when the project should be expanded into new areas. These procedures are designed to maximize the value of the PBMGP.

Analytical Software For Pool-wide Performance Prediction of EOR Processes

Abstract In order to facilitate management of large scale gas miscible EOR projects, a software package called FAME (Forecast Analyser for Miscible EOR) has been developed based on an analytical approach. The primary role of the software is to provide pool-wide performance predictions from mechanistic displacement characteristics determined either by part-pattern numerical simulations, Of by preliminary history matching of field data. The notable features incorporated into the software are that:important flood parameters, such as pattern allocation factors, solvent distribution and sweep, are dependent on pool-wide fluid movement and pattern interactions, which in turn are dependent on the injection/production sequence of historical and planned flood operations,crucial physical mechanisms associated with the gas miscible EOR, such as gravity override, solvent and chase gas miscibility with reservoir oil, and miscible and immiscible displacement processes are adequately represented, andresults of mechanistic numerical simulations or history-matching past field data can be mimicked through variations of a small number of parameters. The software has impacted the management of the Judy Creek hydrocarbon miscible projects with the achievement of a successful history match and the provision of useful information related to flood performance. Introduction During the operation of large-scale oil recovery projects, especially in enhanced oil recovery projects such as hydrocarbon miscible floods, it is highly desirable to be able to assess the project performance. Factors of interest include pool-wide fluid movements, local fluid distribution, sweep efficiency and displacement characteristics, as well as the prediction of future performance under different operating scenarios. Numerical simulation is a powerful method to assess the compound effects of numerous crucial mechanisms involved in various enhanced oil recovery processes. However, numerical simulation models for enhanced oil recovery processes require a large number of simulation grid blocks and small rime steps in order to adequately represent the critical mechanisms. A typical example of such a mechanism is the gravity override of injected solvent in gas miscible processes which causes low sweep efficiencies of solvent as described by H. Stone(1). The solid curve in Figure 1 is the theoretical relationship between the vertical sweep efficiency and water to solvent injection ratio (WAG ratio) at the fixed total fluid rate based on the Jenkins' analytical Expression(2) derived from the Stone's vertical conformance theory. The triangles and circles are corresponding outputs of the Todd-Longstaff type numerical simulations(3) using the horizontal and vertical numbers of grids of 10 × 3 and 15 × 13, respectively. In these numerical simulations, the sweep efficiencies were determined from values of tertiary oil recovery normalized by the tertiary oil potential at the two pore volumes of solvent injection. It is apparent in Figure 1 that the number of grids of 10 × 3 is not enough and overestimating the sweep efficiency, whereas the 15 × 13 is sufficient for representing the mechanism of gravity override. In three-dimensional models, several thousand grid blocks typically are necessary for part-pattern (such as a quarter five-spot pattern) simulations, even with a uniform geology description.