Pseudo Relative Permeability Research Articles

Factors affecting pseudo relative permeability curves

A large number of grid cells are needed to simulate very large field reservoirs such as those in the Middle East. Pseudo relative permeability curves are used to reduce the dimensionality of reservoir simulation models and also to account for intra-cell rock property variations. Identifying the parameters affecting pseudo relative permeability curves is very important so that the model cells can be grouped in different categories in which appropriate pseudo relative permeabilities are generated for each group. The objective of this study is to identify the factors affecting pseudo relative permeability curves. Different reservoir rock and fluid properties were studied for an homogeneous 2D reservoir model. Validation of some curves is also done. The most pronounced effect on pseudo relative permeability curves was found to be caused by the reservoir dip angle. Layer thickness and PVT properties have some effect. Production rate and vertical to horizontal permeability ratio have no significant effect within the parameter ranges studied. While absolute permeability on low dip angle cases has no effect, absolute permeability effects on high dip angle cases needs consideration.

Use of Higher Moments for the Description of Upscaled, Process Independent Relative Permeabilities

Summary Traditional approaches for the scale up of highly detailed reservoir descriptions to the coarser scales more appropriate for reservoir simulation often rely on the use of pseudo relative permeabilities. Two of the major limitations in the use of pseudo relative permeabilities are the process dependency inherent in the resulting curves and the need for a different set of curves in each coarse scale grid block. In this paper, these limitations are illustrated and quantified through numerical simulations of viscous dominated displacements in fine scale, heterogeneous, two dimensional systems. It is concluded that the functional form of traditional pseudo relative permeability descriptions is too limited to capture a wide variety of flow behavior and that an ‘extended description,’ in which the upscaled relative permeabilities depend on variables in addition to the phase saturations, is required. The additional variables we propose are higher moments of the fine scale variables, specifically the variance of saturation, the variance of pressure and the velocity-saturation covariance. It is then shown that these new variables are capable of accurately correlating upscaled relative permeabilities for a variety of displacements in a process independent manner; i.e., the extended description can account for varying inlet conditions and permeability realizations. The practical use of this methodology in an actual reservoir simulation will, however, require the derivation and solution of coarse scale evolution equations for the moments.

A Critical Review of the Use of Pseudorelative Permeabilities for Upscaling

SummaryThe properties and limitations of different dynamic pseudorelative permeability methods are summarized. Severe difficulties common to all methods are discussed: choosing the number and locations of the coarse-grid rock types, defining the simulations from which the pseudos are generated, and the dependence of the pseudos on well rates and positions. It is concluded that, in practice, pseudos cannot be used reliably to scale up from a "fine-grid" geological model to a "coarse-grid" fluid-flow model except for cases where capillary or gravity equilibrium can be assumed at the coarse-gridblock scale. Scaling up from the core scale to the geological model is more likely to be possible because capillary forces are more important at smaller scales. A practical approach to the dynamic upscaling problem is outlined, but one should not expect that the effects of the detail in the geological model will be captured more than qualitatively.

The Scaleup of Two-Phase Flow in Porous Media Using Phase Permeability Tensors

Abstract The effects of different levels of geological heterogeneity on a fluid displacement process may be captured at a larger scale using scaleup techniques. In the context of reservoir simulation, these are algorithms which should reproduce the results of fine grid calculations on a coarser grid. These techniques are referred to as pseudo-isation, the main objective being to produce pseudo-functions which can be used on the coarse grid. When carried out successfully, the pseudo-functions (e.g. pseudo relative permeabilities) incorporate the interaction between the fluid mechanics and the heterogeneity as well as correcting for numerical dispersion. These pseudo-functions also depend on the viscous/capillary and viscous/gravity ratios and are valid for the boundary conditions relevant to the particular flows. For single phase flow, the scaleup problem involves the derivation of effective permeability which, in general, is a tensor quantity. Multi-phase flow is more complex since scaled-up dynamic transport quantities must be calculated which depend on phase saturation, flow rate etc. In this paper, we present a method which extends the idea of tensor (absolute) permeability to tensor effective phase permeabilities. They are extensions of conventional functions which also include the off-diagonal phase crossflow terms which may be important in certain systems. Two phase tensor methods are presented which are valid (a) in the capillary equilibrium limit and (b) for arbitrary values of viscous/capillary and viscous/gravity ratios. Numerical examples of the application of these methods are presented for ripple-bedded systems where the two phase crossflow effects are significant, and where oil trapping within the lamina structure may occur under certain conditions. The results show that it is important to use phase tensors in upscaling where gravity effects are significant, in order to generate the correct vertical flows.

Stability of Displacement Fronts in WAG Operations

Abstract This paper presents an analytical and numerical study of the stability of gas-oil-water displacement fronts in two spatial dimensions. The flow equations are simplified by averaging in the dip-normal direction assuming vertical equilibrium to give analytical expressions for three-phase pseudo relative permeabilities and capillary pressures for a stratified reservoir. A similarity transform results in a set of two coupled, ordinary differential equations and a simple technique is presented to identify the traveling-wave solution when certain conditions are met, and the shape of the front is calculated. The technique is based on an analysis of initial and boundary conditions and is verified by numerical simulation. Dietz's classical stability theory for two-phase displacement fronts has recently been extended to layered reservoirs. To our knowledge, the present paper is the first to treat three-phase flow. It is shown that stable water-oil-gas fronts occur only for a limited number of the injection gas-water ratio, if at all.

Full-Field Reservoir Modeling of Central Oman Gas-Condensate Fields

Summary Gas reserves sufficient for a major export scheme have been found in Central Oman. To support appraisal and development planning of the gas and condensate fields, a dedicated, multidisciplinary study team comprising both surface and subsurface engineers was assembled. The team fostered a high level of awareness of cross-disciplinary needs and challenges, resulting in timely data acquisition and a good fit between the various work activities. A field-development plan was completed in March 1994. The foundation of the subsurface contributions was a suite of advanced full-field reservoir models that were used to do the following. Provide production and well requirement forecasts. Quantify the impact of uncertainties on field performance and project costs. Support the appraisal campaign. Optimize the field-development plan. Derive recovery factor ranges for reserves estimates. The models were constructed early during the study, initially with general data with large uncertainty ranges and gradually refined with new appraisal data. This ultimately resulted in more than 20 full scenarios, quantifying and ranking the remaining uncertainty ranges. Geological/petrophysical uncertainties were quantified by use of newly developed, 3D probabilistic modeling tools. An efficient computing environment allowed a large number of sensitivities to be run in a timely, cost-effective manner. The models also investigated a key concern in gas-condensate fields, well impairment caused by near-well condensate precipitation. Its impact was assessed by use of measured, capillary-number-dependent, relative permeability curves. Well-performance ranges were established on the basis of equation-of-state (EOS) single-well simulations and translated into the volatile-oil full-field models with pseudorelative permeability curves for the wells. The models used the sparse available data in an optimal way and, as part of the field-development plan, sustained confidence in the reserves estimates and the project, which is currently in the project specification phase.

Draugen Field development; the role of gravity drainage and horizontal wells

The Draugen Field is an elongate, low relief, anticline containing mainly multi-Darcy sandstones. Oil initially in-place (STOOIP) is 182 x 10 6 Sm 3 . The 1987 Plan for Development and Operation (PDO) assumed a central cluster of 6 deviated production wells and 3 subsea water injectors at each end of the field. In addition two subsea wells would provide early production. Unsteady state relative permeability data indicate a residual oil saturation of 35%. In the full field simulation model this was increased to 40% to account for small-scale heterogeneity. The model yielded a recovery of some 67 x 10 6 Sm 3 . Modern steady state and centrifuge techniques have since demonstrated a long tail of very low oil relative permeability before reaching a residual oil saturation of some 15%. Fine grid simulations translated this into a gravity segregation process behind the displacement front. Other fine grid models reveal that horizontal wells will yield a slower build up of water cut than vertical wells. The increased productivity of the horizontal wells reduced the required number of platform producers from 6 to 5. Pseudo-relative permeabilities were developed to represent fine grid model performance in a new sophisticated full field model. This model predicted an ultimate recovery of 94 x 10 6 Sm 3 (40% increase). The additional predicted recovery is attributed to a reduction of the effective residual saturation and delayed water production associated with horizontal wells. In October 1993 Draugen started production from one horizontal subsea well, which has since demonstrated a better than expected coning performance. Production from platform wells was initiated in June 1994 with initial well rates up to 8000 Sm 3 per day, confirming the expected high productivity of horizontal wells. Optimization and tuning of facilities has since allowed the peak production rate for the field to be increased from the planned 17 500 Sm 3 per day to a present actual level of 24 600 Sm 3 per day. Further de-bottlenecking is ongoing with the aim of increasing process capacity.

Scaleup of Reservoir-Model Relative Permeability With a Global Method

Summary Geoscientists and engineers commonly build geologic or geostatis-tical reservoir models that contain more than 106 grid cells. For flow simulation, the number of grid cells must be reduced by a factor of 10 or more. Such scaling up necessarily involves a loss of information that must be restored through the use of effective or pseudorelative permeabilities. This paper describes an approach to generate such functions that, when combined with global absolute permeability scaleup,1 offers a significant improvement over existing "dynamic pseudo" methods that require extensive fine-grid simulation and that are very sensitive to flow conditions.1 The method builds on previous work to scale up absolute permeability through a global technique that minimizes the loss of permeability variance and the spatial correlation in an unequally sized grid system. This paper shows that, when the residual permeability following global absolute permeability scaleup is spatially uncorrected, the velocity of a fluid-displacement shock front correlates with a well-defined universal heterogeneity number that is related to the permeability distribution. The paper presents an analytic computation of the pseudo as a superposition of the shock velocities for the residual field, found from a table look-up, and the fine-grid field when the fine-grid relative permeabilities (usually based on measured relative permeabilities) have the same normalized form. The method is then generalized to multiple functional forms of fine-grid-cell relative permeabilities with new relative permeability and capillary pressure averaging methods. The procedure eliminates the need for fine-scale simulation and is equally applicable to geologic deterministic or stochastic models. The paper describes the technique in detail and demonstrates the procedure with one two-dimensional (2D) and one three-dimensional (3D) reservoir model waterflood simulation. In the latter case, the number of cells is reduced from 23,600 (fine scale) to 4,000 (coarse scale) with very little change in the water breakthrough and water-cut behavior.

Integration of Geology, Geostatistics, Well Logs and Pressure Data to Model a Heterogeneous Supergiant Field in Iran: ABSTRACT

The geological reservoir study of the supergiant Ahwaz field significantly improved the history matching process in many aspects, particularly the development of a geostatistical model which allowed a sound basis for changes and by delivering much needed accurate estimates of grid block vertical permeabilities. The geostatistical reservoir evaluation was facilitated by using the Heresim package and litho-stratigraphic zonations for the entire field. For each of the geological zones, 3-dimensional electrolithofacies and petrophysical property distributions (realizations) were treated which captured the heterogeneities which significantly affected fluid flow. However, as this level of heterogeneity was at a significantly smaller scale than the flow simulation grid blocks, a scaling up effort was needed to derive the effective flow properties of the blocks (porosity, horizontal and vertical permeability, and water saturation). The properties relating to the static reservoir description were accurately derived by using stream tube techniques developed in-house whereas, the relative permeabilities of the grid block were derived by dynamic pseudo relative permeability techniques. The prediction of vertical and lateral communication and water encroachment was facilitated by a close integration of pressure, saturation data, geostatistical modelling and sedimentological studies of the depositional environments and paleocurrents. The nature of reservoir barriers and baffles variedmore » both vertically and laterally in this heterogeneous reservoir. Maps showing differences in pressure between zones after years of production served as a guide to integrating the static geological studies to the dynamic behaviour of each of the 16 reservoir zones. The use of deep wells being drilled to a deeper reservoir provided data to better understand the sweep efficiency and the continuity of barriers and baffles.« less

Comparison of 2D and 3D Fractal Distributions in Reservoir Simulations

Summary Fractal geostatistics can be used to generate distributions of such reservoir properties as porosity and permeability. We compare three different methods that use these distributions in reservoir simulations. The first method is a hybrid finite-difference/stream-tube method that starts with 2D vertical cross sections with relatively fine grids, the second uses pseudo-relative permeabilities and also is based on 2D cross sections, and the third uses 3D distributions. A mature waterflood in a carbonate reservoir serves as a field test case.

Pseudorelative Permeabilities from Fractal Distributions

ABSTRACT Fractal distributions of porosity and permeability in two-dimensional vertical cross sections can be used to represent reservoir heterogeneity. We compare a hybrid finite-difference/streamtube method and pseudo-relative permeabilities as two methods of using these distributions in reservoir simulations. We simulate waterflood displacements in a field case study and some additional sensitivity cases. In all the cases studied, predicted cumulative oil production values agree within 5 percent between the two methods.

A Laboratory Investigation of the Pseudo Relative Permeability Characteristics of Unstable Immiscible Displacements

Abstract Enhanced oil recovery operations often involve immiscible displacement of the more viscous oil by a less viscous fluid. This often leads to an unstable and inefficient displacement process because of fingering of the more mobile displacing fluid through the more viscous oil. Although, with application of reported stability theories, it is possible to roughly predict whether or not a field displacement is likely to be unstable, rigorous mathematical models to predict the recovery performance of such unstable displacements are not available. The usual practice has been to employ a Buckley-Leverett type analysis, which is based on the assumption of a stable and stabilized displacement, and to account for the presence of instabilities by using empirical sweep efficiency corrections. The relative permeabilities used in this type of analysis are usually obtained from laboratory tests which pay little or no attention to possible viscous instabilities. A more direct approach to account for the presence of viscous instabilities in immiscible displacements would be to use pseudo-relative permeabilities which are modified true relative permeability curves (modified to account for the instabilities). However, before development of such an approach is attempted, one needs to examine whether or not the conventional Buckley-Leverett model, with modified relative permeability curves, can be used to describe the recovery and pressure drop performance of unstable displacements. This was the main objective of this study. Several unstable immiscible displacement experiments were carried out in a rectangular model. The effects of different parameters on the oil recovery were examined and pseudo-relative permeability curves were generated for each set of conditions. The dependence of these pseudo-relative permeability curves on displacement rate, viscosity ratio, gravity, and the presence or absence of initial water saturation were examined. The performance of current stability theories in predicting the breakthrough recovery was tested against the results of these displacements. It was found that the "wettability number" proposed by Peters and Flock was not a constant for a given rock fluid system but rather a function of the flood velocity. Introduction Recovery of oil by waterflooding is an efficient process, provided the water advances as a stable front and sweeps the reservoir uniformly. This occurs when the oil is more mobile than the displacing water and the reservoir is not too heterogeneous. However, when the oil mobility is low as would be the case in medium gravity and heavy oils, the displacing water has a tendency to finger through the oil and this leads to poor recovery efficiency. The factors which control this type of flow instability include the displacement velocity, oil/water viscosity ratio, relative permeability characteristics and the interfacial tension between oil and water. Although, with application of reported stability theories, it is possible to roughly predict whether or not a field displacement is likely to be unstable, rigorous mathematical models to predict the recovery performance of such unstable displacements are not available. The usual practice has been to employ a Buckley-Leverett type analysis(1,2). The Buckley-Leverett theory applies to a linear displacement process involving two immiscible fluids with no mass transfer taking place between them.

The Effect of Shear Failure on the Cyclic Steam Process and New Pseudo Functions for Reservoir Simulation

Abstract The steam stimulation process is a proven, commercially viable recoveryprocess in oil sand reservoirs. However, an understanding of the recoverymechanism is far from complete. Recent studies of the geotechnical aspects oftar sands point to the importance of shear failure created by pore pressureincrease on fluid flow in the reservoir during steam injection. The changes inmass and heat transport properties in the heterogeneously deformed failure zonehave been shown to be important factors for the recovery mechanism. This paperdescribes the theoretical and practical aspects of representing the shearfailure zone in reservoir simulation, by the means of pseudo relativepermeability functions. Relative permeability hysteresis is commonly used in the simulation of thesteam stimulation process, but its mechanism is not clear. The paper reviewsthe existing methods for treating hysteresis and gives the theory for thepseudo relative permeabilities caused by heterogeneously failed media. The newfunctions are derived by considering the shear failure phenomenon. A new set ofstress-dependent pseudo relative permeabilities is proposed and a practicalmethod for the use of the pseudo functions (including hysteresis) in areservoir simulator is given. The method applies to injection as well asproduction cycles. Its effect on simulating the cyclic steam process is givenin examples and shows that the hysteresis should be stress-dependent ratherthan saturation-dependent. Introduction When the same set of water-oil relative permeability data is used tosimulate the injection and production periods of a cyclic steam stimulationprocess in tar sands or a heavy oil reservoir, the simulated water-oil ratiosare usually much greater than those observed in the field. To achieve a bettermatch of field data in the reservoir simulator, a higher relative permeabilityto water is used during the injection period than that used during theproduction period. The use of this technique in simulating a cyclic steamstimulation process is reported in a number of papers. It is based on theresults of laboratory studies on the hysteresis phenomenon of relativepermeability which will be briefly reviewed.

Renormalization calculations of immiscible flow

Oil reservoir properties can vary over a wide range of length scales. Reservoir simulation of the fluid flow uses numerical grid blocks have typical lengths of hundreds of metres. We need to specify meaningful values to put into reservoir engineering calculations given the large number of heterogeneities that they have to encompass. This process of rescaling data results in the calculation of ‘effective’ or ‘pseudo’ rock properties. That is a property for use on the large scale incorporating the many heterogeneities measured on smaller scales. For single phase flow, a variety of techniques have been tried in the past. These range from very simple statistical estimates to detailed numerical simulation. Unfortunately, the simple estimates tend to be inaccurate in real applications and the numerical simulation can be computationally expensive if not impossible for very fine grid representations of the reservoir. Likewise, pseudorelative permeabilities are time consuming to generate and often inaccurate. Real-space renormalization is an alternative technique which has been found to be computationally efficient and accurate when applied to single-phase flow. This approach solves the problem regionally rather than trying to solve the whole problem in one simulation. The effective properties of small regions are first calculated and then placed on a coarse grid. The grid is further coarsened and the process repeated until a single effective property has been calculated. This has enabled calculation of effective permeability of extremely large grids to be performed, up to 540 million grid blocks in one application. This paper extends the renormalization technique to two-phase fluid flow and shows that the method is at least 100 times faster than conventional pseudoization techniques. We compare the results with high resolution numerical simulation and conventional pseudoization methods for three different permeability models. We show that renormalization is as accurate as the conventional methods when used to predict oil recovery from heterogeneous systems.

Two Phase Flow in Nodular Systems: Laboratory Experiments

Heterogeneity effects within the grid block of a reservoir numerical model are generally taken into account by using pseudo-relative permeability and capillary pressure curves. Some insight into the physics of these pseudo-functions can be obtained from multiple scale analysis such as largescale averaging. Previous theoretical results have shown specific behaviour associated with nodular systems. Laboratory scale experiments were performed that emphasize the difference in behaviour of nodular systems when the properties of the different regions are interchanged. Sandstone nodules embedded in a more permeable continuous region made of sand showed a quasi-static behaviour under experimental conditions while the reverse situation, i. e. sand nodules in a sandstone continuous region, exhibited a totally different behaviour in terms of final saturation and recovery curves. These results are discussed with respect to the large-scale averaging objective.

Waterflood simulation of stratified sandstone reservoirs using dynamic pseudo curves

Many studies have shown that pseudo relative permeability curves can be used in one-dimensional (1-D) linear models to successfully match simulation performance of two-dimensional (2-D) cross-sectional models. Additional studies have shown that pseudo relative permeability curves can be used in 2-D areal models to match 3-D model performance. The techniques, however, used in the latter studies were laborious and complex and often required multiple sets of pseudo relative permeability curves. This study shows that a 2-D areal model that uses only one set of pseudo relative permeability curves (generated from a cross-sectional model) allows accurate simulation of waterflood performance for highly stratified reservoirs that would otherwise require 3-D simulation or 2-D simulation with multiple sets of curves. The cases examined are waterfloods in reservoirs with repeating 5-spot patterns for several sandstone stratifications from beach, fluvial channel, and delta margin environments of deposition. Reservoir simulation in this study makes use of lab-derived capillary pressure curves and the method of Jacks et al. to compute pseudo relative permeability curves. Gravity numbers were developed to characterize cross-sectional and 5-spot (areal) displacements. These gravity numbers were correlated for several geological stratifications to minimize the need for iterative simulations of each particular cross-sectional model to obtain pseudo relative permeability curves. Two of these correlations were applied to field cases to demonstrate their utility.

Novel Relations for Drainage and Imbibition Relative Permeabilities

Abstract Exponential four- and five-parameter equations are proposed for gas/oil drainage and water/oil imbibition relative permeability curves. These equations match the experimentally determined curves, in particular at and near their initial points and endpoints, better than standard Corey et al.1 and polynomial approximations. Some of these parameters have a physical meaning; the others can be determined by nonlinear regression on the experimental data points, and can be adjusted to represent pseudorelative permeability curves. The proposed equations are particularly suitable to describe gas percolation in numerical model simulation of dissolved-gas-drive reservoirs.

Application of pseudo relative permeability curves to the simulation of stratified waterflooding.

This paper presents a discussion on the validity of approximating a two-dimensional cross sectional reservoir model by a one-dimensional linear model using two kinds of pseudo relative permeability curves. The study assumes the negligibility of gravity and capillary effects as compared with the viscous force effect. Also investigated are effects of (1) injection rate and (2) the size of a reservoir on the degree of the agreement among the calculated results. Producing water cut performance versus cumulative oil production, which are calculated by the one-dimensional simulation using pseudo functions, are compared with those computed by the two-dimensional simulation. Consequently, some insights are obtained as to the relation between the size of a reservoir and the degree of crossflow. The validity of approximating cross sectional reservoir simulation by one-dimensional simulation suggests possible manipulation of three-dimensional simulation by using a two-dimensional areal simulation model, which could reduce data preparation time and computation cost. Finally, the present method applied to a real reservoir demonstrates that a one-dimensional linear model using dynamic pseudo relative permeability curves can well approximate the water cut performance of the two-dimensional cross sectional simulation.

Numerical Simulation Of The North Ricinus Cardium A Reservoir

Abstract The North Ricinus Cardium A Pool is a beach barrier system located on the edge of the disturbed belt, approximately 130, km northwest of Calgary, Alberta. The current operating mode for the pool involves a cycling scheme in the retrograde gas cap with the oil leg on primary depletion. A standard 3D-3 phase black oil model, modified with several specialized subroutines, was used to simulate the cycling scheme in the history match and prediction modes. Pseudo-relative permeability curves were used to describe displacement of rich gas by lean gas in the gas cap, while two sets of relative permeability curves were required to match oil production. The model was subsequently utilized to establish reserves and to optimize natural gas liquid recovery by infill drilling in the gas cap. Introduction The Ricinus Cardium A Pool, discovered in January 1969, is located approximately 130 kilometres northwest of Calgary, FIGURE 1. Location map. (Available in full paper) FIGURE 2. North Ricinus geology.(Available in full paper) Alberta (Fig. 1). The pool initially was considered to be a large retrograde condensate gas cap in association with a relatively small oil leg containing a high shrinkage oil. An application in June 1971(1) to concurrently produce the gas and oil based on good production practice was refused by the ERCB. In July 1972 a scheme to cycle the gas cap was subsequently approved with the provision that the operator show cause after one year of production why a VRR of unity need not be maintained(2). Gas cap cycling commenced in April 1973 and a performance review submitted in July 1974(3) indicated that a VRR of between 0.85 and 1.00 had no appreciable effect on gas cap liquid recoveries and the ERCB did not impose a full voidage replacement ratio at that time. Subsequent step out drilling to the north indicated that the oil leg was much larger than previously estimated; and in May 1979, the ERCB(4) requested a study to determine the effect of VRR on the oil recovery and also an updated estimate of original reservoir volumes. A black oil reservoir simulation study, incorporating special modifications, was initiated in June 1979 to address the ERCB's concerns. The model was subsequently utilized to establish pool reserves and to investigate optimization of natural gas liquid recovery by infill drilling. Geology The Ricinus Cardium Pools occur in the Cardium A Sand of Upper Cretaceous age. The reservoir is a beach barrier system trending 20 km in a northwesterly direction and averaging 3 – 5 km in width at a mean depth of 1325 m ss (Fig. 2). The reservoirs are complex structural traps occurring at the edge of the disturbed belt. The Cardium A Pool consists of a retrograde gas cap condensate overlying a volatile oil pool in a weakly folded synclinal structure that plunges gently to the northwest with the gas oil contact occurring at 1463 m ss. A major under thrust forms a pressure barrier to the Cardium K pool to the southwest with porosity pinchouts forming the reservoir boundaries in other directions (Fig. 2).

G-2 and G-3 Reservoirs, Delta South Field, Nigeria: Part 1-An Engineering Study

Summary This paper describes a two-dimensional, three-phase, black-oil simulation of the G-2 and G-3 reservoirs in the Delta South field offshore Nigeria. The purpose of these studies was to investigate, from an engineering standpoint, various operating schemes for optimizing the oil recovery from each of these highly gravity-segregated reservoirs. Introduction The G-2 and G-3 sands are two major reservoirs in the Delta South field. The field is offshore Nigeria in approximately 10 to 16 ft of water (Fig. 1). Production from these reservoirs began in March 1968. By the end of March 1978, about 61.3 MMSTB of oil and more than 64 Bscf of gas were produced from the G-2 reservoir, and about 92 MMSTB of oil and more than 75 Bscf of gas were produced from the G-3 reservoir. These productions represent about 2 1% of the original oil in place (OOIP) for G-2 and 29% of OOIP for G-3. During this period, the average reservoir pressures for G-2 and G-3 declined from 3,936 to 2,665 psig and 3,829 to 2,343 psig, respectively. The G-2 reservoir is at an average depth of 8,920 ft subsea. It is underlain by the G-3 reservoir, but the two are separated by a shale barrier. The two reservoirs are similar in structure and in rock and fluid properties. The drive mechanism for these reservoirs is primarily gravity segregation. These reservoirs are characterized as massive, clean sands with high porosity (about 28% for G-2 and 26.5% for G-3) and high horizontal and vertical permeabilities (kh=2,000 md and kv=1,000 md). This paper presents the results of the current G-2 and G-3 reservoir studies, which are extensions of previous work. First, a history match of 10 years of production performance was made. Later, several prediction cases were run under a variety of operating conditions. This study was undertaken to update the previous match, including the past performance data through March 1978. We believe that, by including more history match data, we have obtained a better reservoir characterization. Although about 20 prediction cases were run for each study, only four pertinent cases for G-2 and five for G-3 are included. Gulf's two-dimensional, black-oil model in an areal mode has been used for this study. The use of this areal model is believed sufficient in describing the reservoir and fluid flow behavior and is justified since the fluids will be segregated because of the high kv/kh ratio (about 0.5:1 were kh=2,000 md). In this cases, gravity/capillary equilibrium exists throughout the thickness. However, there are some limitations in using an areal model for this study:the well coning effects are represented by well pseudo relative permeability curves and not with grid blocks in the vertical direction,the well completions are represented by modifying the well relative permeability curves, andany well coning effect matched using pseudo relative permeability curves may not be strictly valid for future predictions. These limitations, however, do not seem to be very important for the G-2 and G-3 reservoirs.