Conventional Reservoir Simulation Research Articles

Hydromechanical simulation of a carbonate petroleum reservoir using pseudo-coupling

In the domain of petroleum reservoir management, numerical flow simulation stands as the primary tool for prediction and control. Traditionally, rock compressibility has been the key geomechanical parameter, often applied as a single, unchanging value across the entire reservoir model throughout the simulation. This study introduces a novel methodology that enhances reservoir simulation accuracy by incorporating rock mechanical behavior through a pseudo-coupling approach, without increasing computational costs. This approach empowers reservoir engineers to consider rock hydromechanical behavior in daily reservoir studies.The pseudo-coupling updates both porosity and permeability based on tables that correlate pore pressure to porosity and permeability multipliers, thereby replacing the conventional reliance on compressibility. It begins with reservoir-rock samples selection guided by lithological composition, followed by mechanical and hydromechanical laboratory tests, and numerical adjustments with ABAQUS stress analysis software. The resulting mechanical parameters serve for generating pseudo-coupling tables tailored to each facies.Validation experiments comparing pseudo-coupling simulations with conventional and fully coupled models reveal convergence in porosity and permeability variations with pore pressure between both coupled approaches. Extensive assessments further compare pseudo-coupling simulations against conventional reservoir simulations using a synthetic model based on a carbonate post-salt reservoir, denoted as Field B. The pseudo-coupling approach emerges as a more robust model capable of discerning preferential flow paths, all while maintaining computational efficiency. Moreover, these preferential flow paths were also predicted by the reservoir team responsible for the field development, but through a trial-and-error procedure to match production history, whilst the pseudo-coupling predicted it based on rock mechanical behavior.In this way, the proposed methodology enables an enhancement in the accuracy and efficiency of petroleum reservoir management by considering geomechanical effects, without incurring any additional computational costs when compared to conventional reservoir simulation.

Rapid Inference of Reservoir Permeability from Inversion of Traveltime Data Under a Fast Marching Method-Based Deep Learning Framework

Summary The fast marching method (FMM) is a highly efficient numerical algorithm used to solve the Eikonal equation. It calculates traveltime from the source point to different spatial locations and provides a geometric description of the advancing front in anisotropic and heterogeneous media. As the Eikonal solution, the diffusive time of flight (DTOF) can be used to formulate an asymptotic approximation to the pressure diffusivity equation to describe transient flow behavior in subsurface porous media. For the infinite-acting flow that occurs in porous media with smoothly varying heterogeneity, traveltime of the pressure front from the active production or injection well to the observation well can be directly estimated from the DTOF using the concept of radius (or depth) of investigation (ROI or DOI), which is defined as the moment when a maximum magnitude of the partial derivative of pressure to time occurs. Based on the ROI or DOI definition, we propose a deep neural network called the inversion neural network (INN) to inversely estimate heterogeneous reservoir permeability by inverting the traveltime data. The INN is trained by traveltime data created for a large data set of distinct permeability fields from FMM simulations, which can be two orders of magnitude faster than conventional reservoir simulators. A convolutional neural network (CNN), the U-Net architecture, is incorporated into the INN, which establishes a nonlinear mapping between the heterogeneous permeability fields and the traveltime data collected at sparse observation wells. The loss function used for the INN is defined as the root mean square error (RMSE) between the logarithm of the predicted permeability and the logarithm of the true permeability. The performance of the INN is tested on reservoir models with both smoothly varying heterogeneity and high-contrast media properties. For the 2D smoothly varying heterogeneous models with a grid size of 49×49, the permeability predicted by the INN has an average estimation error of 8.73% when a set of 7×7 uniformly distributed observation wells is used to collect “observational” traveltime data from the FMM simulation. For models with the same grid size and observation well density but with high-contrast media properties, the INN can still capture the general heterogeneity distribution, although with reduced prediction accuracy. Using a graphics processing unit (GPU) for training and prediction allows the entire inverse modeling process for a 2D 49×49 reservoir model to be completed within 7 minutes.

Immiscible Viscous Fingering at the Field Scale: Numerical Simulation of the Captain Polymer Flood

Summary Immiscible fingering in reservoirs results from the displacement of a resident high-viscosity oil by a significantly less viscous immiscible fluid, usually water. During oil recovery processes, where water is often injected for sweep improvement and pressure support, the viscosity ratio between oil and water (μo/μw) can lead to poor oil recovery due to the formation of immiscible viscous fingers resulting in oil bypassing. Polymer flooding, where the injection water is viscosified by the addition of high-molecular-weight polymers, is designed to reduce the impact of viscous fingering by reducing the μ0/μw ratio. A considerable effort has been made in the past decade to improve the mechanistic understanding of polymer flooding as well as in developing the numerical simulation methodologies required to model it reliably. Two key developments have been (i) the understanding of the viscous crossflow mechanism by which polymer flooding operates in the displacement of viscous oil and (ii) the simulation methodology put forward by Sorbie et al. (2020), whereby immiscible fingering and viscous crossflow can be simply matched in conventional reservoir simulators. This publication extends the work of Beteta et al. (2022b) to conceptual models of a field case currently undergoing polymer flooding—the Captain field in the North Sea. The simulation methodology is essentially “upscaled” in a straightforward manner using some simple scaling assumptions. The effects of polymer viscosity and slug size are considered in a range of both 2D and 3D models designed to elucidate the role of polymer in systems both with and without “water slumping.” Slumping is governed by the density contrast between oil and water, the vertical communication of the reservoir and the fluid velocity, and, when it occurs, the injection of water channels along the bottom of the reservoir directly to the production well(s). It is shown that polymer flooding is very applicable to a wide range of reservoirs, with only modest injection viscosities and bank sizes returning significant volumes of incremental oil. Indeed, oil incremental recoveries (IRs) of between 29% and 89% are predicted in the simulations of the various 2D and 3D cases, depending on the slug design for both nonslumping and slumping cases. When strong water slumping is present, the performance of the polymer flood is significantly more sensitive to slug design, as alongside the viscous crossflow mechanism of recovery, a further role of the polymer is introduced—sweep of the “attic” oil by the viscous polymer flood, which is able to overcome the gravity-driven slumping, and we also identify this mechanism as a slightly different form of viscous crossflow. In slumping systems, it is critical to avoid disrupting the polymer bank before sweeping of the attic oil has been performed. However, as with the nonslumping system, modest injection viscosities and bank sizes still have a very significant impact on recovery. The conceptual models used here have been found to be qualitatively very similar to real field results. Our simulations indicate that there are few cases of viscous oil recovery where polymer flooding would not be of benefit.

A Study on the Production Performance of a Horizontal Shale Gas Well Using a Fully Coupled Flow and Geomechanics Modeling

Conventional petroleum reservoir simulators use constant rock compressibility to denote rock deformation. However, due to the stress-sensitive nature of the shale formations, using constant rock compressibility in reservoir simulators does not accurately capture the pressure diffusion in the reservoir, leading to a higher error margin in flow rate estimation. Fluid flow coupling with geomechanics is used to account for such a phenomenon numerically. Such an approach is important for shale numerical studies and any energy underground storage modeling (i.e., CO2 storage). Usually, when fluid flow coupling with geomechanics is studied for shale formations, the fluid, and the stimulated reservoir petrophysical properties are overlooked. This paper aims to present a study on the effect of the fluid and reservoir petrophysical properties on the performance of a gas-producing well. In addition, the results from the cases when geomechanics is coupled and decoupled with fluid flow in reservoir simulations are compared. The governing equations were discretized using the Finite Element Method. First, the model was validated against Terzaghi's consolidation theory analytical solution. After that, a history matching for the production flow rate was performed using field production data from Barnett Shale. Then a sensitivity analysis was carried out for the gas viscosity, Stimulated Reservoir Volume (SRV) porosity, and fracture conductivity. Next, the sensitivity analysis was conducted for the coupled and decoupled cases. Finally, the sensitivity analysis results were compared between the coupled and decoupled cases. The results show that lower gas viscosity, higher SRV porosity, and higher fracture conductivity improved horizontal well production performance. In addition, when the geomechanical effects were decoupled, the reservoir simulator overestimated the production flow rate and cumulative production.

History-Matching and Forecasting Production Rate and Bottomhole Pressure Data Using an Enhanced Physics-Based Data-Driven Simulator

Summary In this study, we present a novel application of our newly developed physics-based data-driven interwell numerical simulator (INSIM) referred to as INSIM-BHP to history match highly variable real-life (oscillatory) oil rate and bottomhole pressure (BHP) data acquired daily in multiperforated wells produced from an oil reservoir with bottomwater drive mechanism. INSIM-BHP provides rapid and accurate computation of well rates and BHPs for history matching, forecasting, and production optimization purposes. It delivers precise BHP calculations under the influence of a limited aquifer drive mechanism. Our new version represents the physics of two-phase oil-water flow more authentically by incorporating a harmonic-mean transmissibility computation protocol and including an arithmetic-mean gravity term in the pressure equation. As the specific data set considered in this study contains a sequence of highly variable oil rate and BHP data, the data density requires INSIM-BHP to take smaller than usual timesteps and places a strain on the ensemble-smoother multiple data assimilation (ES-MDA) history-matching algorithm, which utilizes INSIM-BHP as the forward model. Another new feature of our simulator is the use of time-variant well indices and skin factors within the simulator’s well model to account for the effects of well events on reservoir responses such as scaling, sand production, and matrix acidizing. Another novel modification has been made to the wellhead term calculation to better mimic the physics of flow in the wellbore when the production rate is low, or the well(s) is(are) shut in. We compare the accuracy of the history-matched oil rate and BHP data and forecasted results as well as computational efficiency for history matching and future prediction by INSIM-BHP with those from a high-fidelity commercial reservoir simulator. Results show that INSIM-BHP yields accurate forecasting of wells' oil rates and BHPs on a daily level even under the influence of oscillatory rate schedules and changing operational conditions reflected as skin effects at the wells. Besides, it can help diagnose abnormal BHP measurements within simulation runs. Computational costs incurred by INSIM-BHP and a high-fidelity commercial simulator are evaluated for the real data set investigated in this paper. It has been observed that our physics-based, data-driven simulator is about two orders of magnitude faster than a conventional high-fidelity reservoir simulator for a single forward simulation. The specific field application results demonstrate that INSIM-BHP has great potential to be a rapid approximate capability for history matching and forecasting workflow in the investigated limited-volume aquifer-driven development.

Three-Way Coupled Modeling Evaluates CO2 Sequestration in Depleted Reservoir

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 206156, “Importance of Three-Way Coupled Modeling for Carbon-Dioxide Sequestration in a Depleted Reservoir,” by Prasanna Chidambaram, SPE, Pankaj K. Tiwari, SPE, and Parimal A. Patil, SPE, Petronas, et al. The paper has not been peer reviewed. _ Three major depleted gas reservoirs in the Central Luconia field offshore Sarawak, Malaysia, are being evaluated for future carbon-dioxide (CO2) storage. A three-way coupled modeling approach that integrates dynamic, geochemistry, and geomechanics models is used to obtain the cumulative effect of all three changes. This integrated model provides a more-accurate estimate of CO2 storage capacity, caprock-integrity evaluation, CO2-plume migration path, and volume of CO2 stored through different mechanisms. Background The CO2 storage sites being evaluated are depleted gas reservoirs that have been in production for a few decades. At the end of their producing life, they have the potential to be converted into CO2 storage sites. The Central Luconia sedimentary basin is in a seismic-free zone with limited faults and consists of shale interbedded with high-sand-content sediment, making it ideal for CO2 storage. These reservoirs provide the required geological characteristics and volume needed to ensure long-term CO2 storage in a safe and economical way. The depleted gas reservoirs have an in-place volume of approximately 1.5–3 Tscf. Their thickness ranges from 100 to 150 m, with a porosity of 15–32% and permeability of 10–1600 md. These fields are believed to be supported by a regional aquifer several thousand feet thick. Large seafloor subsidence has been observed in these reservoirs. Storage-Capacity Estimation Storage capacity of a depleted hydrocarbon reservoir is affected by several factors including voidage created; aquifer influx and efflux during the production and CO2-injection phases, respectively; maximum injection pressure; rock compressibility; and geochemical effects. Depending on which of these factors are prominent in the storage reservoir, CO2-storage capacity may be estimated using a simple material-balance model or may require a more-complex approach to capture these effects. Use of the Three-Way Coupled Model Injected CO2 is anticipated to react with reservoir rock, leading to either dissolution of reservoir rock or precipitation of solids that are products of the geochemical reactions, causing a net change in porosity and permeability. With regard to geomechanical effects, uplift is anticipated to occur during CO2 injection. The degree to which subsidence is reversed depends on whether compaction of the reservoir is fully elastic or if plastic deformation has occurred. During production, reduction in porosity and permeability has occurred because of subsidence. Conventional or stand-alone reservoir simulation does not capture geochemical and geomechanical effects. Hence, it is critical to use an integrated model that captures the effects of dynamic, geochemical, and geomechanical changes caused by CO2 injection in order to evaluate suitability of the reservoir for long-term CO2 storage. A three-way coupled modeling approach that integrates dynamic, geochemistry, and geomechanics models provides a more-accurate estimate of CO2 storage capacity, along with estimation of subsidence. In three-way coupled modeling, the dynamic model is at the center, which passes input parameters to the geochemical and geomechanical models. Once it receives updated porosity and permeability values back from the geochemical and geomechanical models, the dynamic model incorporates these changes before proceeding to the next simulation timestep.

The Problem of Stability of Gas-Condensate Mixture at Pore-Scale: The Study by Density Functional Hydrodynamics

The method of the density functional hydrodynamics (DFH) is used to model compositional gas-condensate systems in natural cores at pore-scale. In previous publications, it has been demonstrated by the authors that DFH covers many diverse multiphase pore-scale phenomena, including fluid transport in RCA and SCAL measurements and complex EOR processes. The pore-scale modeling of multiphase flow scenarios is performed by means of the direct hydrodynamic (DHD) simulator, which is a numerical implementation of the DFH. In the present work, we consider the problem of pore-scale numerical modeling of three-phase system: residual water, hydrocarbon gas and hydrocarbon liquid with phase transitions between the two latter phases. Such situations happen in case of gas-condensate or volatile oil deposits, in oil deposits with gas caps or in EOR methods with gas injection. The corresponding field development modeling by the conventional reservoir simulators rely on phase permeabilities and capillary pressures, which are provided by laboratory core analysis experiments. But the problem with gas-liquid hydrocarbon mixtures is that in laboratory procedures it may be difficult or even impossible to achieve full thermodynamic equilibrium between phases as it must be under the reservoir conditions of the initial reservoir state. However, reaching the said equilibrium is quite possible in numerical simulation. In this work, the gas-liquid mixture, after being injected into core sample, would slowly undergo the rearrangement of the phases and chemical components in pores converging to the minimum of the Helmholtz energy functional. This process is adequately described by DFH with consequent impact on phase permeabilities and capillary pressure. We give pore-scale numerical examples of the described phenomena in a micro-CT porous rock model for a realistic gas-condensate mixture with quantitative characterization of phase transition kinetic effects.

An optimized neuro-fuzzy system using advance nature-inspired Aquila and Salp swarm algorithms for smart predictive residual and solubility carbon trapping efficiency in underground storage formations

Carbon dioxide (CO2) emission is an emergency issue in terms of environmental pollution. Estimation of carbon capture, utilization, and storage (CCUS) is a necessary task that received wide attention. Due to this fact, numerous studies proposed underground carbon storage to reduce CO2 emissions in the atmosphere. However, there are some drawbacks about estimation accuracy trapping efficiency in deep saline aquifers. Also, the time computation of conventional reservoir simulators requires weeks or months to complete the simulation tasks. Hence, a new approach about accuracy and a fast predictive model needs to propose for promoting the application of carbon capture and storage projects. Therefore, this paper proposes an optimized Adaptive Neuro fuzzy inference system (ANFIS) to predict two indices of the CO2 Trapping in deep saline aquifers, namely, solubility trapping index (STI) residual trapping index (RTI), using 6810 simulation samples, 8 input features of subsurface information from 33 fields of ten previous studies. We utilize the recently developed optimization algorithms, called Aquila optimizer (AO) and Salp Swarm Algorithm (SSA), to train the ANFIS model and to optimize its parameters to boost the prediction performance of the traditional ANFIS. The search mechanism of the SSA is used instead of the original one of the AO algorithm, which enhances the exploration process of the traditional AO. The proposed AOSSA-ANFIS is outperformed to seven optimized ANFIS models.Futhermore, AOSSA-ANFIS schemes achieves overall Mean Relative Absolute Error (MRAE) of 0.69495 and 0.36304, Mean Absolute Error (MAE) of 0.09771 and 0.04594, Root Mean Square Error (RMSE) of 0.15001 and 0.06904, and Mean Square Error (MSE) of 0.02269 and 0.00484 for RTI and STI, respectively. Additionally, the developed AOSSA-ANFIS demonstrated the superiority to existing study that used SVR, ANN, Liner regression and MLP. Due to this latter, the findings of this study provide a better understanding of the role of optimized hybrid ANFIS for CCUS as well as other subsurface disciplines. Finally, this study consider as template is easy to adapt to the similar effort of fast computational modeling.

Numerical effects on the simulation of surfactant flooding for enhanced oil recovery

Numerical simulation of surfactant flooding using conventional reservoir simulation models can lead to unreliable forecasts and bad decisions due to the appearance of numerical effects. The simulations give approximate solutions to systems of nonlinear partial differential equations describing the physical behavior of surfactant flooding by combining multiphase flow in porous media with surfactant transport. The approximations are made by discretization of time and space which can lead to spurious pulses or deviations in the model outcome. In this work, the black oil model was simulated using the decoupled implicit method for various conditions of reservoir scale models to investigate behavior in comparison with the analytical solution obtained from fractional flow theory. We investigated changes to cell size and time step as well as the properties of the surfactant and how it affects miscibility and flow. The main aim of this study was to understand pulse like behavior in the water bank, which we report for the first time, Our aim was to identify their cause and associated conditions. The pulses are induced by a sharp change in relative permeability as the interfacial tension changes. Pulses are diminished when adsorption is modeled, and ranged from 0.0002 kg/kg to 0.0005 kg/kg. The pulses are absent for high-resolution model of 5000 cells in x direction with a typical cell size as used in well-scale models. The growth or dampening of these pulses may vary from case to case but in this instance was a result of the combined impact of relative mobility, numerical dispersion, interfacial tension and miscibility. Oil recovery under the numerical problems reduced the performance of the flood, due to large amounts of pulses produced. Thus, it is important to improve existing models and use appropriate guidelines to stop oscillations and remove errors.

A coupled geomechanics and reservoir simulator with a staggered grid finite difference method

For a stress-sensitive reservoir, the constant rock compressibility term used in a conventional reservoir simulator (CRS), does not account for change of porosity and permeability. This paper develops a coupled geomechanics and reservoir simulator (CGRS) which accounts for changes in porosity and permeability related to deformation.

Complete Equation of State Thermal Formulation for Simulation of CO2 Storage

Summary Storage of carbon dioxide (CO2) in depleted gas reservoirs or large aquifers is one of the available solutions to reduce anthropogenic greenhouse gas emissions. Numerical modeling of these processes requires the use of large geological models with several orders of magnitude of variations in the porous media properties. Moreover, modeling the injection of highly concentrated and cold CO2 in large reservoirs with the correct physics introduces numerical challenges that conventional reservoir simulators cannot handle. We propose a thermal formulation based on a full equation of state (EoS) formalism to model pure CO2 and CO2 mixtures with the residual gas of depleted reservoirs. Most of the reservoir simulators model the phase equilibriums with a pressure-temperature-based formulation. With this usual framework, it is not possible to exhibit two phases with pure CO2 contents. Moreover, in this classical framework, the crossing of the phase envelope is associated with a large discontinuity in the enthalpy computation, which can prevent the convergence of the energy conservation equation. In this work, accurate and continuous phase properties are obtained, basing our formulation on enthalpy as a primary variable. We first implement a new phase-split algorithm with input variables as pressure and enthalpy instead of the usual pressure and temperature, and we validate it on several test cases. This algorithm can model situations in which the mixture can change rapidly from one phase to the other at constant pressure and temperature. Then, treating enthalpy instead of temperature as a primary variable in both the reservoir and the well modeling algorithms, our reservoir simulator can model situations with pure or near pure components, as well as crossing of the phase envelope that usual formulations implemented in reservoir simulators cannot handle. We first validate our new formulation against the usual formulation on a problem in which both formulations can correctly represent the physics. Then, we show situations in which the usual formulations fail to represent the correct physics and that are simulated well with our new formulation. Finally, we apply our new model for the simulation of pure and cold CO2 injection in a real depleted gas reservoir from the Netherlands.

Simulating Core Floods in Heterogeneous Sandstone and Carbonate Rocks

AbstractThe characterization of multiphase flow properties is essential for predicting large‐scale fluid behavior in the subsurface. Insufficient representation of small‐scale heterogeneities has been identified as a major gap in conventional reservoir simulation workflows. We systematically evaluated the workflow developed by Jackson et al. (2018), https://doi.org/10.1029/2017wr022282 for use on rocks with complex porosity and capillary heterogeneities. The workflow characterizes capillary heterogeneity at the millimeter scale. The method is a numerical history match of a coreflood experiment with the 3D saturation distribution as a matching target and the capillary pressure characteristics as a fitting parameter. Coreflood experimental datasets of five rock cores with distinct heterogeneities were analyzed: two sandstones and three carbonates. The sandstones exhibit laminar heterogeneities. The carbonates have isotropic heterogeneities at a range of length scales. We found that the success of the workflow is primarily governed by the extent to which heterogeneous structures are resolved in the X‐ray imagery. The performance of the characterization workflow systematically improved with increasing characteristic length scales of heterogeneities. Using the validated models, we investigated the flow rate dependency of the upscaled relative permeability. The findings showed that the isotropic heterogeneity in the carbonate sample resulted in non‐monotonic behavior; initially the relative permeability increased, and then subsequently decreased with increasing flow rate. The work underscores the importance of capturing small‐scale heterogeneities in characterizing subsurface fluid flows, as well as the challenges in doing so.

Evaluating geomechanical effects related to the production of a Brazilian reservoir

This paper presents a coupled finite element approach for modeling geomechanical effects induced by production/injection processes in petroleum reservoirs. The module developed employs coupled- reservoir analysis using CMG IMEX® as the flow simulator and a finite element program in MATLAB® as the stress–strain simulator, in a two-way explicit partial coupling scheme. The flow and mechanical problems are coupled by the change of effective stress due to the change in pore pressure and by varying stress-dependent reservoir properties, such as pore compressibility, absolute permeability, and porosity. The coupling procedure was applied to the Namorado Field (Campos Basin, Brazil) to quantify the impact of the rock deformation on fluid recovery. Based on the cases studied, the coupled analyses predicted higher oil recovery than the conventional reservoir simulations. The results showed that the reservoir deformation can affect its performance and must be taken into account in reservoir-engineering studies depending on production strategy and reservoir stiffness. Besides, the geomechanical calculations were performed only in the coupling timesteps, reducing the computational effort and making this coupling method feasible on a field scale.

Shale Poroelastic Effects on Well Performance Analysis of Shale Gas Reservoirs

The effect of poroelastic properties of the shale matrix on gas storage and transport mechanisms has gained significant attention, especially during history-matching and hydrocarbon production forecasting in unconventional reservoirs. The common oil and gas industry practice in unconventional reservoir simulation is the extension of conventional reservoir simulation that ignores the dynamic behavior of matrix porosity and permeability as a function of reservoir effective net stress. This approach ignores the significant impact of the poroelastic characteristics of the shale matrix on hydrocarbon production. The poroelastic characteristics of the shale matrix highly relate to the shale matrix geomechanical properties, such as the Young’s Modulus, Poisson’s ratio, bulk modulus, sorption behavior, total organic content (TOC), mineralogy and presence of natural fractures in the multi-scale shale structure. In this study, in order to quantify the effect of the poroelasticity of the shale matrix on gas production, a multi-continuum approach was employed in which the shale matrix was divided into organic materials, inorganic materials and natural fractures. The governing equations for gas transport and storage in shale were developed from the basic fundamentals of mass and momentum conservation equations. In this case, gas transport in organics was assumed to be diffusive, while gas transport in inorganics was governed by convection. Finally, a fracture system was added to the multi-scale shale gas matrix, and the poroelastic effect of the shale matrix on transport and storage was investigated. A modified Palmer and Mansoori model (1998) was used to include the pore compression, matrix swelling/shrinkage and desorption-induced deformation of shale organic matter on the overall pore compressibility of the shale matrix. For the inorganic part of the matrix, relations between rock mechanical properties and the pore compressibility were obtained. A dual Langmuir–Henry isotherm was also used to describe the sorption behavior of shale organic materials. The coupled governing equations of gas storage and transport in the shale matrix were then solved using the implicit finite difference approach using MATLAB. For this purpose, rock and fluid properties were obtained using actual well logging and core analysis of the Marcellus gas well. The results showed the importance of the poroelastic effect on the pressure response and rate of gas recovery from the shale matrix. The effect was found to be mainly due to desorption-induced matrix deformation at an early stage. Coupling the shale matrix gas production including the poroelastic effect in history-matching the gas production from unconventional reservoirs will significantly improve engineering completion design optimization of the unconventional reservoirs by providing more accurate and robust production forecasts for each hydraulic fracture stage.

Evaluation of Low Salinity Water Injection Improved Oil Recovery in Liquid-Rich Unconventional Reservoirs

Since the shale matrix has a very low permeability, the flow in the matrix is often transient flow. Hence, conventional reservoir simulators often do not accurately estimate the mass exchange between matrix and fractures. To evaluate the effect of water injection on oil recovery realistically, reservoir simulators need to incorporate the mass transport in the reservoir at different scales. These issues have motivated us to evaluate the contribution of water injection on oil recovery in liquid-rich unconventional reservoirs accounting the effects of salinity, fluid type, shale swelling, and wettability alteration. In this research, a new mass transport model is used to compute the mass transfer mass exchange between the rock matrix and the fractures. A geomechanical model is also used to account for the effect of fluid–rock interaction on the permeability and porosity. The coupled model is solved for every matrix block within the reservoir-scale model to evaluate the overall effect of salt concentration, shale swelling, and wettability alteration on the mass exchange between the fractures and the shale matrix. The reservoir-scale simulation helps to determine the phase pressure, saturation, solute concentration, and liquid production. A computer code was developed to solve the transport and geomechanical equations simultaneously, and the code is validated with the benchmark problems as shown in the Appendix. The results show that osmosis significantly contributes to the recovery of oil from very low permeability shale matrix over a long time period. Shale matrix swelling also significantly reduces the permeability of the shale matrix and fractures, reducing overall oil recovery. Therefore, water injection is not recommended for formations with swelling potential. The modified-zipper pattern is recommended for enhanced oil recovery operations. The simulation results also suggested that oil recovery can be improved by increasing the density of hydraulic fractures.

Simulation Study of Fluid Flow and Estimation of a Heterogeneous Porous Media Properties Using Lattice Gas Automata Method

Most models used in reservoir simulation studies are on the scale of meters to hundreds of meters. However, increasing resolution in geological measurements results in finer geological models. Simulations study of particle movements provide an alternative to conventional reservoir simulation by allowing the study of microscopic and/or macroscopic fluid flow, which is close to the scale of geological models. In this paper, the FHP-II (Frisch, Hasslacher and Pomeau - FHP) model of lattice gas automata were developed to study fluid flow in order to estimate the properties of heterogeneous porous media. Heterogeneity simulated by placing solid obstacles randomly in a two-dimensional test volume. Properties of the heterogeneous porous media were estimated by the shape, size, number of the obstacles and by the distribution of the obstacles within the volume. Results of the effects of grain sizes and shapes, and its distribution in the porous media on the tortuosity, effective porosity, permeability and displacement efficiency were obtained. An investigation of fluid flow and comparison with laboratory experiment were also presented. Reasonably good agreement between the lattice gas automata simulation and laboratory experiment results were achieved.

A numerical characterization workflow for assessing the strength and failure modes of heterogeneous oil sands

Understanding the strength and failure modes of overburdens and reservoirs is a critical component in safety assessments for oil sands surface mining and in situ thermal recovery operations. Currently, assumptions of homogeneity are often made for the geomechanical properties of oil sands in conventional slope stability analyses and reservoir simulation. The purpose of this work is to propose a numerical characterization workflow that helps predict the failure mode and shear strength of heterogeneous oil sands interbedded with shale beddings during thermal recovery. Heterogeneous models are generated through sequential indicator simulation with a calibrated constitutive model and geomechanical parameters for each lithology. Numerical simulations with boundary conditions reflecting in situ stress changes are conducted to study the impact of shale beddings on stress–strain response, failure modes, and shear strength of the sheared zone. The results show that shear failures of the weaker shale beddings play a significant role in the elastoplastic behavior and reduced shear strength of heterogeneous oil sands. The shear band and weak plane failures are found to be closely related to the volume fraction, variogram range ratio, and inclinations of shale beddings. The proposed numerical workflow allows for quantitative investigations of geomechanical response for rock mass with complex lithological heterogeneities.

Multiscale Integration for Karst-Reservoir Flow-Simulation Models

Summary The significant oil reserves related to karst reservoirs in a Brazilian presalt field add new frontiers to the development of upscaling procedures to reduce time for numerical simulations. This work aims to represent karst reservoirs in reservoir simulators using special connections between matrix medium and karst medium, each modeled in different grid domains of a single-porosity flow model. This representation intends to provide a good relationship between accuracy and simulation time. The concept follows the embedded discrete-fracture model (EDFM) developed by Li and Lee (2008) and later extended by Moinfar et al. (2014); however, this work extends the approach for karst reservoirs [embedded discrete-karst model (EDKM)] by adding a representative volume through gridblocks to represent karst geometries and porosity. For the extension of the EDFM approach in a karst reservoir, we adapt the methodology to four stages: construction of a single-porosity model with two grid domains; geomodeling of karst and matrix properties, each for the corresponding grid domain; application of special connections through the conventional reservoir simulator to represent the transmissibility between the matrix and the karst medium; and calculation of transmissibility between the matrix and the karst medium. For a proper verification, we applied the EDKM methodology in a carbonate reservoir with megakarst structures, which consists of nonwell-connected enlarged conduits and greater than 300 mm of aperture. The reference model was a refined grid with karst features explicitly combined with matrix facies, including coquinas interbedded with mudstones and shales. The gridblock of the reference model measures approximately 10 × 10 × 1 m. For the simulation model, the matrix-grid domain has a gridblock size of approximately 100 × 100 × 5 m. The karst-grid domain had the same block size as the refined grid. Flow in the individual karst-grid domain or matrix-grid domain is governed by Darcy's equation, implicitly solved by a simulator. However, the transmissibility for the special connections between karst and matrix blocks is calculated as a function of open area to flow, matrix permeability, and block-center distance. The matrix properties were scaled up through conventional analytical methods. The results show that EDKM had a considerable performance regarding a dynamic matching response with the reference model, within a reduced simulation time, while maintaining a higher dynamic resolution in the karst-grid domain without using an unconstructed grid. This work aims to contribute to the extension of the EDFM approach for karst reservoirs, which can be applied to commercial finite-difference reservoir simulators. This could be a solution to reduce simulation time without disregarding the explicit representation of karst features in structured grids.

Development of a special connection fracture model for reservoir simulation of fractured reservoirs

The significant world oil and gas reserves related to naturally fractured carbonate reservoirs adds new frontiers to the development of upscaling and numerical simulation procedures for reducing simulation time. This work aims to accurately represent fractured reservoirs in reservoir simulators within a shorter simulation time when compared to dual porosity models, based on special connections between matrix and fracture mediums, both modeled in different grid domains of a single porosity flow model.For the definition of special connection fracture model (SCFM), four stages are necessary: (a) construction of a single porosity model with two symmetric structural grids, (b) geomodelling of fracture and matrix properties for the corresponding grid domain, (c) application of special connections through the conventional reservoir simulator to represent the fluid transfer between matrix and fracture medium, (d) calculation of the fracture-matrix fluid-transfer. For a proper validation, we apply our methodology in a fractured reservoir type II (tight matrix with flow controlled by fractures) and consider a probabilistic framework regarding geological and dynamic uncertainties.The probabilistic approach of SCFM under several static uncertainties revealed a good dynamic matching with DP. Under three rock-wettability scenarios (water-wet, oil-wet and intermediate-wet) the dynamic matching with DP is preserved. Furthermore, SCFM did not present convergence issues, considering all probabilistic realizations.The results revealed that the new method can be applied to commercial flow simulators in fractured reservoirs and it presents itself as a solution to reduce simulation time without disregarding the upscaling and dynamic representation of dual porosity flow models.

Modeling Dynamic Behaviors of Complex Fractures in Conventional Reservoir Simulators

Summary Field data have shown the decline of fracture conductivity during reservoir depletion. In addition, refracturing and infill drilling have recently gained much attention as efficient methods to enhance recovery in shale reservoirs. However, current approaches present difficulties in efficiently and accurately simulating such processes, especially for large-scale cases with complex hydraulic and natural fractures. In this study, a general numerical method compatible with existing simulators is developed to model dynamic behaviors of complex fractures. The method is an extension of an embedded discrete-fracture model (EDFM). With a new set of EDFM formulations, the nonneighboring connections (NNCs) in the EDFM are treated as regular connections in traditional simulators, and the NNC transmissibility factors are linked with gridblock permeabilities. Hence, manipulating block permeabilities in simulators can conveniently control the fluid flow through fractures. Complex dynamic behaviors of hydraulic fractures and natural fractures can be investigated using this method. The proposed methodology is implemented in a commercial reservoir simulator in a nonintrusive manner. We first present one synthetic case study in a shale-oil reservoir to verify the model accuracy and then combine the new model with field data to demonstrate its field applicability. Subsequently, four field-scale case studies with complex fractures in two and three dimensions are presented to illustrate the applicability of the method. These studies involve vertical- and horizontal-well refracturing in tight reservoirs, infill drilling, and fracture activation in a naturally fractured reservoir. The proposed approach is combined with empirical correlations and geomechanical criteria to model stress-dependent fracture conductivity and natural-fracture activation. It also shows convenience in dynamically adding new fractures or extending existing fractures during simulation. Results of these studies further confirm the significance of dynamic fracture behaviors and fracture complexity in the analysis and optimization of well performance.