Pseudo Relative Permeability Research Articles

Assisted Upscaling of Miscible CO2-Enhanced Oil Recovery Floods Using an Artificial Neural Network-Based Optimisation Algorithm

Due to the high computing cost of the fine-scale compositional simulations needed to effectively model miscible CO2 flooding, upscaling techniques are needed to approximate the behaviour of these fine-scale grids on more realistic coarse-scale models. The use of transport coefficients to better represent small-scale interactions, such as the time-dependent flux of the components within the hydrocarbon phases (molecular diffusion), and the pseudoisation of relative permeabilities to ensure the matching of large-scale effects, such as the volumetric fluxes of the phases, are two of these procedures. Most times, a mismatch between the phase fluxes of the integrated fine-scale and that of the coarse-scale is observed. By adjusting or calibrating some of the generated coarse-scale pseudo functions, such as the transport coefficients, absolute permeability, or relative permeability endpoints, the accuracy of the upscaling results can be improved. This procedure can be treated a reservoir history matching problem which is typically computationally expensive. In this study, we provide a framework for representing the dynamics of small-scale molecular diffusion and macro-scale heterogeneity-induced channelling related to miscible CO2 displacements on upscaled coarser grid reservoir models. The method used was based on the pseudoisation of relative permeability and transport coefficients and was applied to two benchmark reservoir models from the Society of Petroleum Engineers (SPE). Our results demonstrated that using effectively calibrated transport coefficients improved the upscaling results, so that the calculated pseudo-relative permeability functions can be ignored. We proposed a unique approach to upscaling miscible floods that utilised a genetic algorithm and a neural-network-based proxy model to minimise the associated computing cost. The data-driven approximation model considerably decreased the computing cost associated with the assisted tuning technique, and the optimisation algorithm was used to reduce the error between the predictions of the upscaled models. In conclusion, the methodology described in this study effectively captured the small- and large-scale behaviour related to the miscible displacements on upscaled coarse-scale reservoir models while reduced associated computational costs.

Upscaling Low-Salinity Benefit from Laboratory Scale to Field Scale: An Ensemble of Models with a Relative Permeability Uncertainty Range

Summary The distribution of low-salinity benefit for an ensemble of models is required to evaluate low-salinity enhanced oil recovery (OREC) projects. To enable this, low-salinity pseudorelative permeability curves are required to estimate the benefit of low-salinity waterflooding at the field level. We present how the low-salinity benefit can be propagated through an ensemble of full-field models in which each simulation case could have a set of distinctive high-salinity pseudos. A 0.5-ft vertical resolution sector and its 10-ft upscaled counterpart are used. Relative permeability curves and the low-salinity benefit from corefloods are used in the high-resolution sector to create profiles. Pseudohigh- and low-salinity curves are generated for the upscaled sector by history matching high-salinity and incremental low-salinity profiles. Low-salinity benefit is typically measured from corefloods and the same benefit is often assumed at the field scale. Our results show that generating low-salinity curves for high-salinity pseudos using low-salinity benefit from corefloods slightly underestimates the true low-salinity benefit at field scale estimated from high-resolution models. This conclusion is consistent for two extreme relative permeability scenarios tested (i.e., a high-total-mobility unfavorable fractional flow and low-total-mobility favorable fractional flow). Including capillary pressure in high-resolution models was crucial. We would have come to another conclusion if we had not used capillary pressure in fine-grid simulation as approximately one-third of the benefit of low-salinity waterflooding was attributable to more favorable capillary pressure under low-salinity injection. We demonstrate how a set of high-salinity relative permeability data obtained from corefloods, which encompasses a range for fractional flow and total mobility, can be included in ensemble modeling appropriately and how low-salinity benefit could be estimated for such an ensemble. It is adequate to generate low-salinity curves for bounding high-salinity sets of curves. The bounding low-salinity curves can then be used to estimate low-salinity curve for any interpolated high-salinity curve. This workflow significantly simplifies the process of generating the distribution of low-salinity benefit corresponding to an ensemble of models which may be calibrated to limited history.

A novel flow-based geometrical upscaling method for representing fault zones with two-phase fault rock properties into a dynamic reservoir model

Faults are generally represented in conventional upscaled models as 2D planar surfaces with transmissibility multipliers used to represent single-phase fault properties. However, faults are structurally complex 3D zones in which both single-phase and two-phase fault rock properties can be significant. Ignoring this structural and petrophysical complexity within faults may impart considerable inaccuracy on the predictive performance of upscaled models. This study has developed a two-phase flow-based geometrical upscaling method capable of representing simultaneously the complex geometry and saturation-dependent two-phase flow properties of realistic fault zones. In this approach, high-resolution sector models are built of small portions of the fault zones and assigned appropriate single-phase and two-phase fault rock properties. Steady state two-phase flow simulations at different fractional flows of oil and water are used to determine the saturation dependent upscaled pseudo relative permeability functions which are incorporated into upscaled models. The method is applied to an example model containing two 3D fault zone components and tested by comparing the flow results of upscaled model with those of a high-resolution truth model. Results show that two-phase flow-based geometrical upscaling is a promising method for representing the effects of two-phase fault rock properties and complex 3D fault zone structure simultaneously.

Scaling Up Low-Salinity Waterflooding in Heterogenous Reservoirs

SummaryModeling the dynamic fluid behavior of low-salinity waterflooding (LSWF) at the reservoir scale is a challenge that requires a coarse-grid simulation to enable prediction in a feasible time scale. However, evidence shows that using low-resolution models will result in a considerable mismatch compared with an equivalent fine-scale model with the potential of strong, numerically induced pulses and other dispersion-related effects. This work examines two new upscaling methods that have been applied to improve the accuracy of predictions in a heterogeneous reservoir where viscous crossflow takes place.We apply two approaches to upscaling to bring the flow prediction closer to being exact. In the first method, we shift the effective-salinity range for the coarse model using algorithms that we have developed to correct for numerical dispersion and associated effects. The second upscaling method uses appropriately derived pseudorelative permeability curves. The shape of these new curves is designed using a modified fractional-flow analysis of LSWF that captures the relationship between dispersion and the waterfront velocities. This second approach removes the need for explicit simulation of salinity transport to model oil displacement. We applied these approaches in layered models and for permeability distributed as a correlated random field.Upscaling by shifting the effective-salinity range of the coarse-grid model gave a good match to the fine-scale scenario, while considerable mismatch was observed for upscaling of the absolute permeability alone. For highly coarsened models, this method of upscaling reduced the appearance of numerically induced pulses. On the other hand, upscaling by using a single (pseudo)relative permeability produced more robust results with a very promising match to the fine-scale scenario. These methods of upscaling showed promising results when they were used to scale up fully communicating and noncommunicating layers as well as models with randomly correlated permeability.Unlike documented methods in the literature, these newly derived methods take into account the substantial effects of numerical dispersion and effective concentration on fluid dynamics using mathematical tools. The methods could be applied for other models where the phase mobilities change as a result of an injected solute, such as surfactant flooding and alkaline flooding. Usually these models use two sets of relative permeability and switch from one to another as a function of the concentration of the solute.

An Analysis of Numerically Induced Pulses in Simulations of Low-Salinity Waterflooding and Their Reduction by Flow Upscaling

SummaryNumerical fidelity is required when using simulations to predict enhanced-oil-recovery (EOR) processes. In this paper, we investigate the conditions that lead to numerical errors when simulating low-salinity (LS) waterflooding (LSWF). We also examine how to achieve more accurate simulation results by scaling up the flow behavior in an effective manner.An implicit finite-difference numerical solver was used to simulate LSWF. The accuracy of the numerical solution has been examined as a function of changing the length of the grid cell and the timestep. Previously we have shown that numerical dispersion induces a physical retardation such that the LS front slows down while the formation water front speeds up. We also report for the first time that pulses can be generated as numerical artifacts in coarsely gridded simulations of LSWF. These effects reflect the interaction of dispersion, the effective-salinity range, and the use of upstream weighting during calculation, and can corrupt predictions of flow behavior.The effect of the size of the timestep was analyzed with respect to the Courant condition, traditionally related to explicit numerical schemes and also numerical stability conditions. We also investigated some of the nonlinear elements of the simulation model, such as the differences between the concentrations of connate water salinity and the injected brine, effective-salinity-concentration range, and the net mobility change on fluids through changing the salinity. We report that to avoid pulses it is necessary, but not sufficient, to meet the Courant condition relating timestep size to cell size. We have also developed two approaches that can be used to scale up simulations of LSWF and tackle the numerical problems. The first method is dependent on a mathematical relationship between the fractional flow, effective-salinity range, and the Péclet number and treats the effective-salinity range as a pseudofunction. The second method establishes an unconventional proxy method equivalent to pseudorelative permeabilities. A single table of pseudorelative permeability data can be used for a waterflood instead of two tables, as is usual for LSWF. This is a novel approach that removes the need for relative permeability interpolation during the simulation.Overall, by avoiding numerical errors, we help engineers to more efficiently and accurately assess the potential for improving oil recovery using LSWF and thus optimize field development. We also avoid the numerical pulses inherent in the traditional LSWF model.

Pseudorelative Permeabilities for Simulation of Unstable Viscous Oil Displacement

Summary Relative permeabilities are well understood for light oils involving stable displacement. However, conflicting arguments have been presented in the literature regarding relative permeabilities for viscous oils. Most nonthermal viscous oil displacements are unstable. Depending on the magnitude of mobility ratio, displacement is influenced by varying degrees of viscous instability, often referred to as fingering. For viscous oils (>500 cp), even a polymer flood must be designed at partially stable conditions (mobility ratio > 1) to maintain an economical processing rate [% pore volume (PV) injected (PVI) per year]. Typically, viscous fingering is difficult to model in full-field simulation because of the large grid sizes used. To design and optimize a partially stable polymer or waterflood, it is critical to correctly upscale the laboratory-generated relative-permeability curves for reservoir simulation. In recent years, such models have been published in the Society of Petroleum Engineers literature. Unfortunately, most of these models require multiple fitting parameters (at least three). In this work, we present a simplified technique that requires systematic change in only one parameter to generate upscaled relative permeability curve for a given viscosity ratio. Using fine-grid simulations, we show that the flow at high-viscosity ratio is channelized even in a core perceived to be homogeneous at laboratory scale. This happens because of small-scale heterogeneities that are present in every rock. Upscaling averages these fine variations in heterogeneities, causing the grids to be overswept, thus overpredicting recovery. To compensate for this shortcoming, it is recommended to upscale the relative-permeability curves in the simulation model.

Multi-model hybrid compositional simulator with application to segregated flow

In cases with significant density difference between the injection mixture and the reservoir fluids, segregation can take place on short temporal scales relative to the typical time-step lengths of the simulation. A fully resolved 3D description is computationally demanding and is often difficult to achieve with buoyancy segregated flow. Vertical equilibrium (VE) is one possible technique for effective upscaling in regions of gravity segregation and has been widely considered for CO2 storage applications. VE has connections to pseudo-relative permeability models for gas injection. In this work, we use a general pseudo-relative permeability model to couple conventional 3D and upscaled models, including VE formulations with support for compositional simulations. This gives a flexible framework where different choices of coarsening and pseudoization can be used locally throughout the domain, allowing for an optimal trade-off between runtime and accuracy. The new approach is demonstrated within the framework of a fully implicit compositional flow simulator with nonlinear equation-of-state, which provides a robust and stable base for inclusion of additional physical effects. Moreover, we discuss the limitations of different possible approximations for the phase equilibrium of the compositional VE regions, and which cases they may be useful for. Possible applications for this methodology include gas injection for enhanced oil recovery, CO2 storage in aquifers, or other gas-storage scenarios. We demonstrate the approach for gas injection and migration on both conceptual unstructured grids as well as corner-point models taken from real fields and saline aquifers from the Norwegian Continental Shelf.

Numerical simulation study on the bottom-water invasion in the carbonate gas reservoir with high angle fractures and high permeability zones

Numerical simulation of carbonate gas reservoir with bottom-water is still a challenging issue, due to the presence of nature conductive fractures. When the water invades into the gas well, the permeability of gas phase decreases sharply. The high angle fractures and high permeability zones have a serious impact on the production performance of the gas wells. The characteristic of the water invasion was unpredictable in conventional dynamic analysis.In fractured carbonate reservoir, the geometric shapes of the angled fracture are difficult to be described using commercial numerical simulation software. The method that calculating the pseudo relative permeability of the grid block containing high angle fracture was utilized in this paper. Through this method, the rapid water advancement in the conductive fracture was accurately tracked without modifying the grid geometry, and the influence of the conductive fracture to the water breakthrough phenomenon was studied by using the IMEX module in CMG. The results show that the water invasion intensity depends on the conductivity of fracture, and the higher the conductivity is, the shorter the water breakthrough time is. The breakthrough time of water is affected by the angle of the fracture, the relative horizontal distance, the length of the fracture, the production rate and the type of water invasion. According to the characteristic curve, the type of water invasion can be quickly distinguished, which provides a basis for further study on the enhanced recovery of the fractured carbonate gas reservoir with water.

On the prediction of pseudo relative permeability curves: meta-heuristics versus Quasi-Monte Carlo

This article reports the first application of the Quasi-Monte Carlo (QMC) method for estimation of the pseudo relative permeability curves. In this regards, the performance of several meta-heuristics algorithms have also been compared versus QMC, including the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and the Artificial Bee Colony (ABC). The mechanism of minimizing the objective-function has been studied, for each method. The QMC has outperformed its counterparts in terms of accuracy and efficiently sweeping the entire search domain. Nevertheless, its computational time requirement is obtained in excess to the meta-heuristics algorithms.

An improved procedure for generating pseudorelative permeabilities for water flooding in stratified reservoirs

This paper presents an improved procedure for generating pseudorelative permeability curves for stratified water flooding using either constant pressures or constant flux at the reservoir/grid block boundaries. The concept of pseudorelative permeability reflects the generation of a relative permeability curve that can be used to represent the entire reservoir thickness, rather than a specific layer during reservoir simulation, thus saving computational time. In this paper, fractional flow theory is applied to the generation of pseudorelative permeability curves for (1) constant flow rate and (2) constant pressure boundary conditions. Previously, pseudorelative permeability curves were generated for constant flow rate only, since the analytical solutions for constant pressure boundaries were non-existant. In this paper, this restriction has been removed based on novel analytical solutions for constant pressure boundaries. The method within this paper also differs from previous methodologies and studies, which are all based on an approximation using piston-like displacement for water flooding. Instead, this new model uses fractional flow theory to its fullest extent to generate pseudorelative permeability curves that are physically more realistic. The solution is extended to generate pseudorelative permeability curves for waterflooding of a reservoir under the assumption of constant pressure boundaries which is an equally realistic assumption in comparison to constant flow rate. The generated pseudorelative permeability curves are used in a 2D areal reservoir model in a standard reservoir simulator to predict the behavior of the fully layered 3D reservoir model. It is found that there is considerably better agreement between the results obtained with this new method and the fully layered reservoir model compared to previous methods.

Flow Simulation Using Local Grid Refinements to Model Laminated Reservoirs

Super-giant carbonate fields, such as Ghawar, in Saudi Arabia, and Lula, at the Brazilian pre-salt, show highly heterogeneous behavior that is linked to high permeability intervals in thin layers. This article applies Local Grid Refinements (LGR) integrated with upscaling procedures to improve the representation of highly laminated reservoirs in flow simulation by preserving the static properties and dynamic trends from geological model. This work was developed in five main steps: (1) define a conventional coarse grid, (2) define LGR in the conventional coarse grid according to super-k and well locations, (3) apply an upscaling procedure for all scenarios, (4) define LGR directly in the simulation model, without integrate geological trends in LGR and (5) compare the dynamic response for all cases. To check results and compare upscaling matches, was used the benchmark model UNISIM-II-R, a refined model based on a combination of Brazilian Pre-salt and Ghawar field information. The main results show that the upscaling of geological models for coarse grid with LGR in highly permeable thin layers provides a close dynamic representation of geological characterization compared to conventional coarse grid and LGR only near-wells. Pseudo-relative permeability curves should be considered for (a) conventional coarse grid or (b) LGR scenarios under dual-medium flow simulations as the upscaling of discrete fracture networks and dual-medium flow models presents several limitations. The conventional approach of LGR directly in simulation model, presents worse results than LGR integrated with upscaling procedures as the extrapolation of dynamic properties to the coarse block mismatch the dynamic behavior from geological characterization. This work suggests further improvements for results for upscaling procedures that mask the flow behavior in highly laminated reservoirs.

An upscaling approach using adaptive multi-resolution upgridding and automated relative permeability adjustment

The upscaling process of a high-resolution geostatistical reservoir model to a dynamic simulation grid model plays an important role in a reservoir study. Several upscaling methods have been proposed in order to create balance between the result accuracy and computation speed. Usually, a high-resolution grid model is upscaled according to the heterogeneities assuming single phase flow. However, during injection processes, the relative permeability adjustment is required. The so-called pseudo-relative permeability curves are accepted, if their corresponding coarse model is a good representation of the fine-grid model. In this study, an upscaling method based on discrete wavelet transform (WT) is developed for single-phase upscaling based on the multi-resolution analysis (MRA) concepts. Afterwards, an automated optimization method is used in which evolutionary genetic algorithm is applied to estimate the pseudo-relative permeability curves described with B-spline formulation. In this regard, the formulation of B-spline is modified in order to describe the relative permeability curves. The proposed procedure is evaluated in the gas injection case study from the SPE 10th comparative solution project’s data set which provides a benchmark for upscaling problems [1]. The comparisons of the wavelet-based upscaled model to the high-resolution model and uniformly coarsened model show considerable speedup relative to the fine-grid model and better accuracy relative to the uniformly coarsened model. In addition, the run time of the wavelet-based coarsened model is comparable with the run time of the uniformly upscaled model. The optimized coarse models increase the speed of simulation up to 90% while presenting similar results as fine-grid models. Besides, using two different production/injection scenarios, the superiority of WT upscaling plus relative permeability adjustment over uniform upscaling and relative permeability adjustment is presented. This study demonstrates the proposed upscaling workflow as an effective tool for a reservoir simulation study to reduce the required computational time.

Unstable Immiscible Displacements in Oil-Wet Rocks

Displacement of a viscous fluid by a lower viscosity immiscible fluid (such as waterflood of a viscous oil) in a porous medium is unstable. The displacement front generates viscous fingers which lead to low oil recovery efficiency. These fingers are much smaller in width than typical reservoir simulation grid blocks, and capturing their effect in reservoir simulation is important. A dimensionless scaling group (viscous finger number) had been suggested in the past, which has a power-law relationship with the breakthrough recovery and cumulative recovery in unstable core floods. The relative permeability used in large grid block simulations had been modified to so-called pseudo-relative permeability on the basis of the dimensionless group, thus incorporating the effect of fingers in waterflood predictions. However, the previous proposed models were constructed from experiments in only water-wet rocks. This paper extends the recent viscous fingering models to oil-wet systems. Sandstone cores were treated to alter the wettability to oil-wet. Adverse viscosity water floods were performed in oil-wet cores. Viscosity ratio, velocity and diameter were varied. It is shown that the previously developed viscous finger number does not work for the oil-wet experiments. The correlating dimensionless number is modified for oil-wet systems; it is also different from the dimensionless group identified by Peters and Flock (Soc Petroleum Eng, 1981. doi: 10.2118/8371-PA ) for oil-wet cores. A pseudo-relative permeability model has been developed for oil-wet cores. Corefloods have been matched by the new pseudo-relative permeability model to determine the model parameters. This pseudo-relative permeability model can be used in reservoir simulations of water and polymer floods in viscous oil-wet reservoirs.

Estimation of pseudo-relative permeability curves through an analytical approach for steam assisted gravity drainage (SAGD) and solvent aided-steam assisted gravity drainage

Fluid flow through the reservoir is defined on the basis of the relative permeability which essentially captures the preferential flow of any specific fluid. Utilization of steam assisted gravity drainage (SAGD) presents challenges to the conventional understanding of relative permeability due to the introduction of heat to the reservoir. The presence of three distinct fluid phases (steam, water, and oil) in conjunction with a temperature dependency has many implications for the modelling of complex fluid dynamics. However, effective characterization of relative permeability curves is integral to successful simulation and so a model capable of representing three-phase flow is required. By implementing a simplified fractional flow analysis, this study is able to regress three-phase flow in the laboratory to a pseudo two-phase relative permeability. Modifications of conventional fractional flow theory allow for the extension of the analysis to the SAGD and solvent aided-SAGD (S-SAGD) process. Overall displacement is defined on the basis of both a microscopic component represented by modified capillary number and a macroscopic component represented by mobility ratio. Negation of the liquid-gas interaction through the assumption of waterflooding enables the generation of pseudo two-phase relative permeability curves that result in comparable performance to lab scale experiments. Because the experimentally obtained SAGD and S-SAGD results are used to construct the pseudo-relative permeability curves, our model includes the many complex fundamental changes occur in viscosity and relative permeability during SAGD and S-SAGD in the newly constructed relative permeability curves. Thus, our results offer a simplistic way to ease the compositional simulation of SAGD and S-SAGD through waterflooding approach.

Viscous-Fingering Function for Unstable Immiscible Flows

Summary Displacement of viscous oils often involves unstable immiscible flow. Viscous instability and its influence on relative permeability were studied in this work at different viscosity ratios, injection rates, and domain widths. Micromodels and pore-scale models were used to visually inspect the interplay of viscous and capillary forces in the viscous-dominated regime. A new dimensionless scaling parameter, NI=(vwμwσow)(μoμw)2(D2/K), was developed that is useful in predicting the recoveries of unstable displacements at various viscosity ratios and injection rates. The scaling parameter showed excellent fit with experimental data of 68 corefloods. A lumped finger model was developed to modify multiphase flow equations and to yield pseudorelative permeability functions that account for viscous fingering. The parameters of the lumped model can be estimated from the new dimensionless number, NI. This pseudorelative permeability function could be applied at each gridblock on the basis of the local NI to simulate large-scale unstable floods in water-wet porous media.

Estimation of pseudo relative permeability curves for a heterogeneous reservoir with a new automatic history matching algorithm

Abstract Reliable relative permeability curves are important for successful reservoir simulation and modeling. These curves may be available on fine scale models. However, detailed descriptions demand a huge amount of memory and processing time. Therefore, it is needed to upscale core-size relative permeability curves measured by laboratory experiments to a scale suitable for the various types of simulation. This upscaling is accomplished with pseudo functions. In this work, a new automatic history matching algorithm based on B-spline representation was applied to estimate pseudo relative permeability curves. The performance of the generated pseudo curves were compared with four dynamic pseudo functions for a 3D heterogeneous water-flooding case. In addition, the effect of the pseudo function estimation uncertainty on the cumulative oil production was investigated after 10 years of production. Results revealed that relative permeability curves obtained from history matching gives the best performance among other pseudos and this methodology can be used for reservoir simulation over periods beyond that of the original match.

Axi-Symmetric Two-Phase Suspension-Colloidal Flow in Porous Media during Water Injection

Injection of colloids and suspensions in natural reservoirs with particle capture results in well injectivity decline. However, some initial improvement in injectivity was observed during waterflooding of oilfields and explained by increasing mobility of two-phase fluid during the displacement of more viscous oil by water. We derive an analytical model for axi-symmetric two-phase flow with simultaneous deep bed filtration of injected particles, formation of external filter cake, and its stabilization due to particle dislodgement. The explicit formula for dimensionless pressure drawdown (impedance) yields the type curve for impedance history. It is shown that the initial injectivity increase, induced by varying two-phase mobility, adds three degrees of freedom to one-phase impedance growth model. This additional information is used for tuning the models with the Corey relative permeability and the pseudo-relative permeability under the viscous-dominant displacement. Treatment of the data from three synthet...

Upscaling of Relative Permeability Using Pseudo Functions

Approximately all of the petroleum reservoirs are heterogeneous, and this heterogeneity exists on all levels from pores to simulation models. Since reservoir data are available on different scales and each property does not measure at the individual level, scale-up must be used for acquiring properties of coarse grid models. One of the most important reservoir properties in multiphase upscaling is relative permeability. Pseudo functions are the main methods for upscaling of relative permeability. Kyte and Berry and transmissibility weighted pseudos are two kinds of dynamic pseudo functions. The Kyte and Berry method is based on Darcy's law and the transmissibility weighted pseudos concentrate on saturation effects rather than pressure effects and uses a transmissibility weighted average for calculation of pseudo relative permeabilities. In this work, the effects of directional inter-block pseudos and well pseudos were first investigated. Then the results of coarse grid simulation with directional transmissibility weighted pseudos and Kyte and Berry pseudos were compared with the reference fine grid results.

A method for evaluation of water flooding performance in fractured reservoirs

A mathematical model is developed for evaluation of water flooding performance in a highly fractured reservoir. The model transforms a dual-porosity medium into an equivalent single porosity medium by using a pseudo relative permeability method to normalize the relative permeability. This approach allows both fractures and matrix to have permeability, porosity, endpoint saturation, and endpoint relative permeability by themselves. Imbibition is also taken into account by modifying Chen׳s equation. Some effects, including imbibition and recovery rates are investigated. The investigation shows that imbibition can determine the potential of a fractured reservoir and a low recovery rate can improve the water flooding situation in terms of retarding water breakthrough and controlling the rise of water cut. A new chart composed by water cut vs. recovery curves is protracted to estimate the ultimate water-flooding recovery rate. The water flooding performance of two reservoirs is evaluated. Compared with numerical simulation method, the error of these two cases are not more than 2%, which proved that this method is reliable. Both lab test data and field data are applied to a further discussion of the characteristics of water flooding performance in fractured reservoirs. On comparison with the classical method, such as Tong׳s method and the X-plot method, the reason why the new method is more suitable to fractured reservoirs is addressed by a theoretical analysis. An appropriate application of this method can help the reservoir engineer to optimize the reservoir management with low costs and high efficiency.

The impact of fine-scale turbidite channel architecture on deep-water reservoir performance

This article concentrates on the question, Which parameters govern recovery factor (RF) behavior in channelized turbidite reservoirs? The objective is to provide guidelines for the static and dynamic modeling of coarse reservoir-scale models by providing a ranking of the investigated geologic and reservoir engineering parameters based on their relative impact on RF. Once high-importance (H) parameters are understood, then one can incorporate them into static and dynamic models by placing them explicitly into the geologic model. Alternatively, one can choose to represent their effects using effective properties (e.g., pseudorelative permeabilities). More than 1700 flow simulations were performed on geologically realistic three-dimensional sector models at outcrop-scale resolution. Waterflooding, gas injection, and depletion scenarios were simulated for each geologic realization. Geologic and reservoir engineering parameters are grouped based on their impact on RF into H, intermediate-importance (M), and low-importance (L) categories. The results show that, in turbidite channel reservoirs, dynamic performance is governed by architectural parameters such as channel width, net-to-gross, and degree of amalgamation, and parameters that describe the distribution of shale drapes, particularly along the base of channel elements. The conclusions of our study are restricted to light oils and relatively high-permeability channelized turbidite reservoirs. The knowledge developed in our extensive simulation study enables the development of a geologically consistent and efficient dynamic modeling approach. We briefly describe a methodology for generating effective properties at multiple geologic scales, incorporating the effect of channel architecture and reservoir connectivity into fast simulation models.