Oil Reservoir Simulation Research Articles

An insight into the effect of different parameters for optimizing parallel reservoir simulation performance

Parallel simulation significantly reduces runtime in oil reservoir simulations, enabling higher-resolution analysis and a better understanding of reservoir behavior. This study comprehensively evaluates how simulation time, hardware configuration, and various physical parameters impact the efficiency, scalability, and performance metrics such as run time reduction (RTR) and number of optimal cores (NOC) in parallel simulations. This study introduced the reduced simulation time (RST) concept, an innovative approach that enhances parallel simulation efficiency, and dynamic load balance. In this approach, simulations were performed using only 5% of the total simulation time. The findings reveal that in 80% of the models, switching to RST mode has no effect on NOC but significantly reduces overall execution time in most cases. In complex models, this time reduction can be as high as 60% compared to serial mode. In the remaining 20%, the number of cores in the total simulation time (TST) mode may be higher than in the RST mode, but this difference can be disregarded due to limited hardware resources and no change in RTR.

Field-split preconditioned active-set reduced-space algorithm for complex black oil reservoir simulation at large-scale

Accurate black oil reservoir simulation is important for the understanding of underground resources in hydrology and petroleum reservoir engineering. The success of fast prediction relies on a robust and scalable black oil simulator, which can handle the complex subsurface fluid dynamics with coupling several different physical processes, and meanwhile run efficiently on distributed memory parallel computers. In this work, we introduce a highly parallel simulator to accurately compute the reservoir flow coupling with wells, including some adaptive fully implicit schemes for the temporal discretization, the improved active-set reduced-space algorithm for the nonlinear algebraic system, and several types of field-split methods for preconditioning. This parallel simulator is applied on the domain decomposition framework, which is designed to overcome the computational issues of traditional simulators implemented for personal computers or small workstations. High-resolution reservoir simulation results on the Society of Petroleum Engineers (SPE) comparative solution project or real-field cases are obtained and analyzed, and the parallel performance of the algorithm is studied on a supercomputer with scaling up to 27440 processor cores. The numerical experiments indicate that the proposed black oil simulator is capable of accurately predicting the highly complex physical processes and interactions between wells and the reservoir for full field scale simulation.

Multiphase flow simulation of fractured karst oil reservoirs applying three-dimensional network models

The characteristics of karst reservoirs are extremely varied and anisotropic, exhibiting notable differences in porosity, permeability, and corresponding fluid flow pathways. Fractured karst petroleum reservoirs, such as distinct caverns and fractures, are an example of a typical discrete media type. The traditional reservoir modeling approach and discrete fracture-like local refinement models are unsuitable for field application of fractured karst oil reservoirs due to the needs of high fidelity geological description and huge computing efforts. Based directly on the spatial characteristics of seismic surveys, a numerical simulation model in three dimensions, akin to a node-like network, is presented here for cracked karst oil reserves. First, the watershed image processing technique and the automatic connection identification procedure are used to extract the three-dimensional node-network model. After that, automatic differentiation is used to build the numerical finite volume scheme, and the proper gradient-based adjoint approach is used to conduct the related historical matching rapidly. After validation by a synthetic model in a commercial simulator, this proposed three-dimensional network numerical model is used for a field reservoir block of deep formation in the Tarim basin to demonstrate its computational efficiency and viability for enormously comparable karst oil reservoirs.

Decoupling numerical method based on deep neural network for nonlinear degenerate interface problems

Many practical problems, including modeling composite materials, nuclear waste disposal, oil reservoir simulations, and flows in porous medium, commonly involve interface problems. However, the solution to interface problems with discontinuous coefficients of PDEs using fully decoupled numerical methods is challenging. The main objective is to solve the interface problems with fully decoupled numerical methods. This paper proposes an efficient decoupled numerical method for solving degenerate interface problems with double singularities. First, we divide the whole domain into singular and regular subdomains. Then, we use the Deep Neural Network (DNN) to find the solution on the singular subdomain and approximate the solution on the regular subdomain using the finite difference method. The scheme combines the solutions of singular and regular subdomains, which is an exciting idea. The key to the new approach is to split nonlinear degenerate partial differential equations with an interface into two independent boundary value problems based on deep learning. In this way, the expansion of the solution on the singular domain does not contain undetermined parameters, and two independent boundary value problems can be solved with any well-known traditional numerical methods. The main advantage of the proposed scheme is that we not only get the order of convergence of the degenerate interface problems on the whole domain, but we also can calculate VERY BIG jump ratio (such as 1012:1 or 1:1012) for the interface problems including degenerate and non-degenerate cases. Finally, with examples, we demonstrate the efficiency and accuracy of methods for 1 and 2D problems. It is also interesting that the proposed method is valid for the interface problems with degenerate and non-degenerate cases, we show it with some examples.

End-to-end dimensionality reduction and regression from 3D geological uncertainties to estimate oil reservoir simulations

Managing geological uncertainties in reservoir engineering involves significant challenges mainly due to the prohibitive computational costs of traditional simulation methods. These simulations, essential for generating geological models, often require extensive computational resources and can take days or weeks to complete. The computational load limits the number of viable models while the high dimensionality of properties compounds the challenge, and the abundance of producing wells, each associated with different objective functions, further complicates the problem. Current methodologies have focused on training an Artificial Neural Network (ANN) for each producer well to create a proxy model. Instead, we propose the development of a single ANN designed to simultaneously predict the behavior of multiple objective functions. This work proposes a novel end-to-end deep neural network that can handle 3D geological uncertainties and replicate the simulator’s response for several cumulative production curves. This approach leverages 3D convolutions to process spatial and depth dimensions within heterogeneous reservoirs, including diverse geostatistical realizations. The end-to-end solution was successfully implemented in a Brazilian offshore field and accurately replicated the simulator’s behavior and yielded results that outperformed state-of-the-art methods. The results indicate correlations that exceeded 0.95 between the proxy response and the numerical simulator. Additionally, our approach demonstrated robustness even when trained with a limited number of simulation models, and it notably reduced computational costs. The findings highlight our architecture’s capacity to integrate dimensional reduction and regression analysis within a unified framework, effectively predicting different fluid behaviors in the reservoir and showcasing robustness against high dimensionality and sparse data.

Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method

This paper studies a parameter estimation problem for the non-linear diffusion equation within multiphase porous media flow, which has important applications in the field of oil reservoir simulation. First, the given problem is transformed into an optimization problem by using optimal control framework and the constraints such as well logs, which can restrain noise and improve the quality of inversion, are introduced. Then we propose the widely convergent homotopy method, which makes natural use of constraints and incorporates Tikhonov regularization. The effectiveness of the proposed approach is demonstrated on illustrative examples.

Multiple machine learning models in estimating viscosity of crude oil: Comparisons and optimization for reservoir simulation

Development of predictive models for estimation of reservoir fluids properties as function of temperature, fluid composition, and pressure would be essential for simulation of oil reservoirs. The measurement of the viscosity of heavy crude oil is an essential part of petroleum science which can be done by experimental methods, however computational methods can be integrated to the experimental methods to reduce the effort and save time of measurements. For the purpose of predicting the heavy-oil viscosity, this work applies a number of different models to the dataset that is currently available for correlating viscosity to input parameters. The Gradient Boosting Regression Tree (GBR), the Support Vector Machine (SVM), and the Stochastic Gradient Decent (SGD) are the models that have been utilized in this investigation, and the genetic algorithm (GA) has been applied in order to optimize the hyper-parameters of these models. The RMSE error rates for the completed versions of the GBR, SGD, and SVM models are, in descending order, 26.6, 29.8, and 30.5. For the purposes of this research, the GBR model was determined to be the most suitable option among those available for estimation of crude oil viscosity.

Study on seepage model of Multiple Horizontal wells with complex fracture networks in tight Reservoir Based on boundary element method

Horizontal well and volume fracturing technology are the key technologies to develop unconventional reservoirs. Tight reservoir is belonging to multi-scale seepage mediaafter fracturing, and theflow of fluid in it is extremely complicated. In this paper, based on the boundary element method (BEM), the seepage model of horizontal wells with complex fracture networks in irregular boundary reservoir is established for the first time. The model takes into account the influence of irregular reservoir boundary, dual media, complex fracture network and interference of multiple wells on horizontal well seepage. Using this model, the sensitivity analysis of wellbore storage coefficient, skin factor, fracture permeability and interporosity transfer coefficient is carried out. The model expands the application scope of BEM in the field of seepage simulation of unconventional oil and gas reservoirs and provides theoretical guidance for the development of tight oil reservoirs.

A Comprehensive Review of the Oil Flow Mechanism and Numerical Simulations in Shale Oil Reservoirs

The pore structure of shale oil reservoirs is complex, and the microscale and nanoscale effect is obvious in the development of shale oil reservoirs. Understanding the oil flow mechanism in shale reservoirs is essential for optimizing the development plan and enhancing the recovery rate of shale oil reservoirs. In this review, we briefly introduce the occurrence status of shale oil and shale oil flow in the inorganic matrix and the organic matrix (including the shrinkage of kerogen, oil diffusion in kerogen, oil transport in the organic pore channels, coupling of diffusion, and fluid transport in the organic matrix). Then, the shale oil microflow simulation and a coupling model of double-porous media for microflow and macroflow in the production process of shale oil are discussed. Finally, we summarize the main conclusions and perspectives on the oil flow mechanism and numerical simulations in shale oil reservoirs. An accurate description of shale oil occurrence status and shale oil flow in the inorganic and organic matrices is crucial for the numerical simulation of shale oil reservoirs. It can provide a basis and reference for the future directions of shale oil flow and numerical simulations during the development of shale oil reservoirs.

UNCERTAINTY QUANTIFICATION OF WATERFLOODING IN OIL RESERVOIRS COMPUTATIONAL SIMULATIONS USING A PROBABILISTIC LEARNING APPROACH

In the present paper, we propose an approach based on probabilistic learning for uncertainty quantification of the water-flooding processes in oil reservoir simulations, considering geological and economic uncertainties and multiple quantities of interest (QoIs). We employ the probabilistic learning on manifolds (PLoM) method, which has achieved success in many different applications. This methodology enables the construction of surrogate models to cope with expensive computational costs using high-fidelity simulators. It also allows the incorporation of unavoidable uncertainties, like in the porosity and permeability fields, resulting from difficulties in the characterization of the heterogenous subsurface media, or arising from economic instabilities. We are particularly interested in computing high-order statistics of the system response, which combines oil operational production and economic aspects, to evaluate risk losses. In this paper, we assess the efficacy of the PLoM stochastic surrogate through two numerical examples contemplating the above uncertainties and typical reservoir configurations.

Numerical Simulation of Low Salinity Water and Alkaline Surfactant-Polymer Flooding with Optimal Injection Pattern

Combined Low Salinity Water (LSW) and Alkaline-Surfactant-Polymer (ASP) flooding is a new enhanced oil recovery method that aids oil recovery from reservoirs following the traditional recovery methods. Experimental studies on combined LSW and ASP flooding show additional oil recovery potential. This paper used numerical simulation to investigate different flooding patterns with LSW and ASP combined. A homogenous reservoir was saturated with oil and water to obtain the required modelled factors. Oil reservoir simulations of 11 flooding patterns were created and run using ECLIPSE 100. These patterns were used in the field's development for five years. The results showed the normal 7-spot pattern to provide the best recovery, while the direct line drive provided the worst. The high salinity, low salinity, and combined LSW and ASP flooding recorded oil recoveries of 30%, 55%, and 93%, respectively. An economic analysis was also done to analyse the project’s economic viability which proved to be economical with a profit margin of 40.7%. Furthermore, it was discovered that normal flood patterns outperformed their inverted counterparts. It was thus concluded that the normal 7-spot pattern provides the highest profits from a purely technical standpoint.

Analytical modification of EDFM for transient flow in tight rocks

The commercial development of unconventional resources with multiply fractured horizontal wells has been in the spotlight over the last ten years because of the significant contribution of unconventional oil and gas (UOG) reservoirs to the total US oil and gas production. UOG reservoirs contain multiscale fractures with heterogeneous properties, so the focus has been on efficient and accurate models that can account for these fractures individually. One of such models is the embedded discrete fracture model (EDFM), which has been applied to various types of fractured reservoirs. This work shows that the application of EDFM in fractured tight rocks yields significant errors because it cannot account for the expected transient flow between the matrix and fractures. To address the limitation when EDFM is used in tight rocks with structured Cartesian grids, we modified the matrix/fracture non-neighboring connection (NNC) flux in EDFM by multiplying it with a transient factor. We obtained this factor as in the transient matrix/fracture transfer term for dual-continuum models and implemented it in in our open-source shale simulator. We simulated a single vertical fracture in the middle of a tight reservoir with and without this EDFM modification and show the importance of the proposed modification. We also simulated cyclic gas enhanced oil recovery (CGEOR) in a fractured Bakken shale oil well and analyzed the model results using standard rate-transient analysis plots to evaluate the significance of the proposed modification. The results show that the standard EDFM underestimates oil and gas production by up to 73% at early times. This work presents the first analytical modification of EDFM to account for the nonlinear pressure drop expected near fracture surfaces. Comparing the modified and standard EDFM model results to a reference solution shows that the modified EDFM matches it. In contrast, the standard EDFM cannot match the reference solution when we use structured Cartesian grids with linear spacing. Additionally, by timing the simulation of a representative Bakken shale oil reservoir with 256 fractures, we show that the analytical modification proposed is only 1.5% slower than the standard EDFM.

Technology transition from traditional oil and gas reservoir simulation to the next generation energy development

Energy transition has been a focus in both scientific research and social concerns in the past decade, thanks to the urgent need of reducing carbon emissions, slowing down the abnormal speed of global climate and achieving a balance between environmental protection and economic development. Although the global energy sector is shifting from the fossil-based energy systems, including oil and gas, to the renewable energy resources like hydrogen, the necessity of conventional energy development has received increasing attentions with regard to the stable supply and maturely developed technologies. The long-history simulation techniques developed for oil and gas reservoir investigations have enabled the deeper explorations into reservoir properties and enhanced significantly the resource recovery. As a main direction in energy transition, the development of hydrogen energy is profoundly influencing the long-term reconstruction of the world’s energy supply and application system, and is accelerating the transition and generational evolution in the fields of transportation, power generation, chemicals, and housing. In this paper, three research directions are proposed as the potential focus of technology transition, where traditional oil and gas reservoir simulation technologies can be adjusted and improved to be used to benefit the development of hydrogen energy. Cited as: Zhang, T., Liu, J., Sun, S. Technology transition from traditional oil and gas reservoir simulation to the next generation energy development. Advances in Geo-Energy Research, 2023, 7(1): 69-70. https://doi.org/10.46690/ager.2023.01.08

Deviation from Darcy Law in Porous Media Due to Reverse Osmosis: Pore-Scale Approach

Shale and tight hydrocarbons are vital to global energy dynamics. The fluid flow in sub-micron pores of tight oil reservoirs varies from bulk fluid flow. The Darcy law is widely accepted to model creeping flow in petroleum reservoirs. However, traditional reservoir modeling approaches fail to account for the sub-micron mechanisms that govern fluid flow. The accuracy of tight oil reservoir simulators has been improved by incorporating the influence of sub-micron effects. However, there are still factors that affect sub-micron fluid mobility that need investigation. The influence of a chemical potential gradient on fluid flow in sub-micron pores was modeled by solving Darcy and the transport and diluted species equations. The findings indicate that when a chemical potential gradient acts in the opposite direction of a hydraulic pressure gradient (reverse osmosis), there exists a limiting pressure threshold below which a non-linear flow pattern deviating from the Darcy equation is observed. Furthermore, the simulation based on tight reservoir pore parameters shows that when the effect of a chemical potential gradient is added, the resultant flux is 8–49% less. Hence, including the effect of the chemical potential gradient will improve the accuracy of sub-micron pressure dynamics and flow velocity.

A hybrid GBPSO algorithm for permeability estimation using particle size distribution and porosity

Particle size distribution measurements can be used for permeability estimation, and it is widely accepted that there exhibits a certain degree of correlation between permeability and porosity. In this paper, an efficient, low-cost, and reliable approach is used to develop an empirical correlation for estimating permeability based on particle size distribution characteristics and porosity in two modes: mode #1 includes 5% (D5), 10% (D10) and 60% (D60) of the cumulative passing particle size distribution curve and porosity for situations where porosity is known, and mode #2 where porosity is unknown. To optimize the coefficient of the proposed relationships, genetic-binary particle swarm optimization algorithm is used. A database consisting of 50 samples collected from four wells drilled in two neighboring pads in Western Canada were used, and their permeability values were predicted successfully. A validation based on a reference study and an application of sand completion design based on the finding of this study are also discussed. The novelties of the proposed approach are examining the effect of fines content, investigating the full range of particle size distribution curve, and using a hybrid intelligent method to optimize the coefficients of the correlations. In addition to sand completion deigns purposes, the proposed method can be used in enhanced oil recovery studies, reservoir management, and reservoir simulation applications.

Research Status of and Trends in 3D Geological Property Modeling Methods: A Review

Three-dimensional (3D) geological property modeling is used to quantitatively characterize various geological attributes in 3D space based on geostatistics with the help of computer visualization technology, and the results are often stored in grid data. The 3D geological property modeling includes two main components, grid model generation and property interpolation. In this review article, the existing grid generation methods are systematically investigated, and both traditional and multiple-point geostatistical algorithms involved in interpolation methods are comprehensively analyzed. It is shown that considering the numerical simulation of oil reservoirs, the orthogonal hexahedral grid remains the most suitable grid model for simulations in petroleum exploration and development. For the interpolation methods aspect, most geological phenomena are nonstationary, to simulate various types of reservoirs; the main development trends are increasing geological constraints and reducing the limitation of stationarity. Both methods have certain constraints, and the multiscale problem of multiple-point geostatistics poses a main challenge to the field. In addition, the deep-learning based method is a new trend in geological property modeling.

Production Simulation of Oil Reservoirs with Complex Fracture Network Using Numerical Simulation

This paper established a numerical simulation model to analyze the pressure transient and rate transient behaviors in reservoir with complex fracture network. Firstly, the fractures are introduced into the coordinate system through the position, angle, and length. Secondly, a mathematical model is established by using unstable seepage model. Thirdly, the central difference method was used to solve the model and local grid refinement method is introduced to describe the network fractures. Finally, we compared the results obtained from this paper’s model with the production data. The results show acceptable and reasonable matches for typical well. Meanwhile, the sensitivity of two properties is discussed. The model solution is verified with an analytical method thoroughly. The novelty of this paper is to introduce each fracture in fracture network into the coordinate system. Then, the grid refinement is achieved according to the fracture information. The presented new model simplifies the analysis of the pressure transient and rate transient of the reservoir with complex fracture network, and it is more efficient than the conventional numerical method. Compared with the analytical methods, the new model describes the fractures system in more detail. However, the new model treats fractures as reservoirs with higher permeability in the central difference method, which is simpler and rougher than traditional numerical methods.

Reservoir production prediction with optimized artificial neural network and time series approaches

Numerical simulation of oil reservoirs is one of the most commonly used methods for reservoir production prediction, but its accuracy is based on accurate geological modeling and high-quality history matching. Therefore, numerical simulation is time-consuming and costly and requires extensive information. Traditional back-propagation neural networks and their improved algorithms are widely used for production prediction, but they are not suitable for time-series prediction problems. Based on variations in oil production, this study proposes a reservoir production prediction model based on a combined convolutional neural network (CNN) and a long short-term memory (LSTM) neural network model optimized by the particle swarm optimization (PSO) algorithm. First, the model extracts important temporal data features through the upper CNN, which is next imported to the lower LSTM network to further extract correlation features in the time dimension; then, it iteratively optimizes the key hyperparameters in the CNN-LSTM model through the PSO algorithm; finally, it uses the trained model for reservoir prediction. Compared with the training results of the LSTM neural network and CNN model, the PSO–CNN-LSTM model has higher prediction accuracy in time-series production prediction. Our proposed hybrid model is a data-driven method and is based on routinely available production data. Quick and accurate production prediction can lead to better informed operational decisions and optimization of recovery and economics.

A statistical thermodynamics-based equation of state and phase equilibrium calculation for confined hydrocarbons in shale reservoirs

The phase behavior of confined fluid in nanopores of shale reservoirs deviates significantly from that of bulk fluid. Confined fluid refers to fluid whose thermal motion is affected by nanopores, since nanopores have a comparative size to the mean free path of fluid molecules. To describe deviated phase behavior in nanopores, Travalloni et al. proposed PR-C EOS by introducing empirical modifications to the canonical partition function. The modifications consider the two main mechanisms that cause nanopore phase behavior to deviate: the finite volume effect and the fluid-pore wall interaction effect. However, in addition to its weakness on a theoretical basis, PR-C EOS possesses imperfections when applied to predict nanopore phase behaviors. In this work, we propose a new EOS derived from statistical thermodynamics for slit-like nanopores, named PR-X EOS. The PR-X EOS has an extra term to represent the fluid-pore wall interaction effect and a modification to the cubic EOS parameter to represent the finite volume effect. PR-C EOS and PR-X EOS are non-cubic, and each has some new parameters. The new parameters can be determined by fitting adsorption isotherms. When pore size approaches infinity, PR-C EOS and PR-X EOS both degenerate into classic PR EOS. To apply these two non-cubic EOS in reservoir simulators, we improve gas-oil phase equilibrium calculation methods. The improved simulator can model chemical potential equilibrium between the nanopore grid and the bulk grid, with chemical potentials of the two grids calculated using the modified EOS and conventional EOS, respectively, so that bulk grid pressure can be obtained. As a consequence, we can plot the adsorption isotherm or phase diagram under bulk pressure, which is practically measurable pressure. Therefore, we can validate the modified EOS with experimental or molecular simulation data. Validations demonstrate that PR-X EOS can match type I and type IV adsorption isotherms; whereas, PR-C EOS fails to match the type IV adsorption isotherm. Moreover, the phase diagrams calculated using PR-X EOS consistently shrink as pore size decreases, while PR-C EOS cannot guarantee this consistency. These two facts show that PR-X EOS is superior to PR-C EOS in modeling phase behavior of confined hydrocarbons. Furthermore, shale oil reservoir simulation shows that considering the confinement effect would lead to lower GOR.

Production simulation of tight oil reservoirs with coupled mathematical model

This paper constructed a coupled mathematical model with two flow directions (matrix inside fracture network) to analyse the rate transient behaviours in oil reservoirs. Firstly, we formulate the 1-D flow solutions for each region, and then couple them by imposing flux and pressure continuity across the boundaries between regions. Secondly, we solve the model with the linear flow model and using Laplace transform and Stehfest algorithm comprehensively. Thirdly, the corresponding algorithm is designed and the code is written for calculation. Finally, the model solution is verified with one flow direction model thoroughly.