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Characterizing natural fractures has a decisive effect on production forecasts in fractured oil and gas reservoirs. Discrete Fracture Networks (DFN) constitutes the main modeling framework for fractured geosystems. However, myriads of uncertainties are enclosed prior modeling representative stochastic or deterministic DFN ensembles. This paper presents a novel methodology for DFN calibration and an efficacious field application, which incorporates Well-testing interpretation, Embedded Discrete Fracture Model (EDFM) framework, and numerical reservoir simulation. The proposed workflow starts with the DFN generation from seismic data, imaging logging data and core data. After multiple DFNs are modeled, well-test analysis is employed to calibrate the intrinsic properties of fractures at different locations. Then, these fracture networks are characterized dynamically by EDFM, which promotes capturing the optimal fracture model quickly screened. Finally, pressure and production history match are reached for the DFN realization that honors the optimal fracture model.

Depletion-induced stress change causes the redistribution of stress field in reservoirs, which can lead to the reorientation of principal stresses. Stress reorientation has a direct impact on fracture propagation of infill wells. To understand the effect of stress reorientation on the propagation of infill well's fractures, an integrated simulation workflow that combines the reservoir flow calculation and the infill well hydraulic fracturing modeling is adopted. The reservoir simulation is computed to examine the relationship between the extent of stress reversal region and reservoir properties. Then, the hydraulic fracturing model considering the altered stress field for production is built to characterize the stress evolution of secondary fracturing. Numerical simulations show that stress reorientation may occur due to the decreasing of the horizontal stresses in an elliptical region around the parent well. Also, the initial stress difference is the driving factor for stress reorientation. However, the bottom hole pressure, permeability and other properties connected with fluid flow control timing of the stress reorientation. The decrease of the horizontal stresses around the parent well lead to asymmetrical propagation of a hydraulic fracture of the infill well. The study provides insights on understanding the influence of stress reorientation to the infill well fracturing treatment and interference between parent and infill wells.

Volume rendering techniques are essential to inspect volume data. In this work, we consider volume rendering for unstructured meshes. We focus on the visualization of black oil reservoir simulation models, represented by irregular hexahedral meshes with geometry distortions and discontinuities. We conduct an experimental study comparing three different strategies to compute the volume integration. The first strategy resamples the model in a regular grid; the second linearizes the model geometry and the variation of the scalar field within a hexahedron cell; the third uses an accurate evaluation of the scalar field at each sample. We compare performance and image quality delivered by each strategy by running a set of experiments with different models. We also investigate the gain in perception applying directional ambient occlusion shading effects. All strategies were entirely implemented on the graphics card.

Reservoir simulator is widely known in the petroleum industry for analysing and predicting the fluid flow behaviour through porous media. Conventional mathematical approach, which is the mostly used approach in reservoir simulation, assumes several unrealistic assumptions. Introducing the memory formalism with classical mathematical approach can eliminate this shortcoming. Because, the assumptions of fundamental laws (e.g., mass conservation, equation of state, and constitutive equation) used in reservoir simulation are reduced through incorporation of memory formalism. Memory-based flow model accounts the time varying nature of rock-fluid properties. To date, flow models do not yet exist where all the possible reservoir properties are considered as a function of time and space. The present study shows a comprehensive workflow in developing a memory-based reservoir simulator. The fundamentals of memory formalism and fractional calculus along with the use of fractional order derivative to formulate memory formalism are summarized. The proposed memory approach is validated using an application. A comparison of memory approach and multi-continuum approach is shown to depict the significance of the memory formulation for anomalous diffusion. This research is expected to open a door for introducing non-linear solvers in reservoir simulation study where cloud points solutions will be obtained instead of a single point solution. The outcome of this study will help engineers and researchers to develop more transparent simulator instead of creating a black box.

Viscosity is defined as the resistance of the fluid to flow. It plays a very significant role in most oil and gas engineering applications. The measured viscosity for any crude oil at surface condition is called by the dead oil viscosity, where the dead oil viscosity is a function in any correlation to calculate the viscosity of the crude oil. Thus, the dead oil viscosity is important in most applications related to the petroleum engineering. Accordingly, a new mathematical and artificial neural network (ANN) dead oil viscosity correlations were developed for Libyan crudes and compared with renowned dead oil viscosity correlations using 104 samples from different reservoirs. The evaluation in this study has been done by statistical and graphical error analysis. The results shown that the ANN model has proven to be a useful tool for predicting where the ANN model has given the best result with low error AAD was 14.40509 % and R^2 was 95.91%. The ANN model and mathematical model gave the lowest error when they compared with different empirical correlations.

In this work, a flowing material balance equation (FMBE) is established for undersaturated coalbed methane (CBM) reservoirs, which considers immobile free gas expansion effect at the dewatering stage. Based on the established FMBE, five straight-line methods are proposed to determine the control area, initial water reserve, initial free gas reserve, initial adsorbed gas reserve, original gas in place, as well as permeability at the same time. Subsequently, the proposed FMBE methods for undersaturated CBM reservoirs are validated against a reservoir simulation software with and without considering free gas expansion. Finally, the proposed methods are applied in a field case when considering free gas expansion effect. Validation cases show that the straight-line relationships for the proposed five FMBE methods are excellent, and good agreements are obtained among the actual reserves and permeabilities and those evaluated by the proposed five FMBE methods, indicating the proposed five FMBE methods are effective and rational for CBM reservoirs. Results show that a small amount of free gas will result in a great deviation in reserve evaluation; hence, the immobile free gas expansion effect should be considered when establishing the material balance equation of undersaturated CBM reservoirs at the dewatering stage.

The numerical simulation of multicomponent compressible flow in porous media is an important research topic in reservoir modeling. Traditional semi-implicit methods for such problems are usually conditionally stable, suffer from large splitting errors, and may accompany with violations of the boundedness requirement of the numerical solution. In this study we reformulate the original multicomponent equations into a nonlinear complementarity problem and discretize it using a fully implicit finite element method. We solve the resultant nonsmooth nonlinear system of equations arising at each time step by a parallel, scalable, and nonlinearly preconditioned semismooth Newton algorithm, which is able to preserve the boundedness of the solution and meanwhile treats the possibly imbalanced nonlinearity of the system. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm on the Tianhe-2 supercomputer for both standard benchmarks as well as realistic problems in highly heterogeneous media.

The India National Gas Hydrate Program Expedition 02 (NGHP-02) discovered gas hydrate at high saturation in sand reservoirs at several sites in the deepwater Bay of Bengal. To assess the potential response of those deposits to scientific depressurization experiments, comprehensive geologic models were constructed to enable numerical simulation for two sites. Both sites (NGHP-02-09 and NGHP-02-16) feature thick sequences of thinly-interbedded reservoir and non-reservoir facies at sub-seafloor depths less than 300 m and sub-sea depths of 2400 m or more. These settings pose significant challenges to current modeling capabilities. First, the thinly-interbedded reservoir architecture complicates the determination of basic reservoir parameters from both log and core data due to measurement resolution issues. Secondly, the fine scale variation in sediment properties imparts great contrasts in key parameters over very short distances, creating high gradients at multiple scales and varying orientations that necessitate careful design of high-definition simulation grids. Thirdly, the deposits include internal sources of water, as well as a range of complex boundary conditions, including variable permeability within the overlying mud-rich “seals,” that complicate reservoir depressurization. Lastly, because of the unique combination of great water depth and relatively shallow sub-seafloor depth: models designed to maximize the dissociation rate impose large pressure drawdowns on relatively low-strength sediments. This condition renders the proper evaluation and integration of the geomechanical response to hydrate dissociation critical. In this report, we review the history of gas hydrate reservoir simulation, discuss methods for creating geologic input models, and summarize the key findings and implications of the collaborative NGHP-02 numerical simulation effort. Together, the studies confirm the viability of the modeled accumulations for scientific testing and identify key challenges related to the selection of specific test sites and the design of test wells.

Carbon dioxide (CO2) flooding has been widely applied to enhance oil recovery. In low temperature reservoirs, CO2 injection may result in the formation of three hydrocarbon phases at thermodynamic equilibrium. In addition, an aqueous phase is always present in the reservoir. The aqueous phase can coexist with three hydrocarbon phases to form a four-phase equilibrium system. To evaluate CO2 utilization and storage in these low temperature petroleum reservoirs, a robust and efficient four-phase equilibrium calculation framework involving water is necessary for a compositional reservoir simulator. This is challenging not only because the number of variables increases but also because stability analysis becomes much complicated as the number of phases increases. In this research a novel four-phase equilibrium calculation framework is proposed for compositional reservoir simulation. A reduced variables method is used to solve four-phase flash problems efficiently and robustly. Multiphase flash calculations using reduced variables (RV) can converge to the equilibrium solution faster than formulations using conventional variables (Petitfrere and Nichita, 2015). Secondly, RV does not suffer from numerical problems in the Newton iterations when trace components are present in the aqueous phase. In addition to the implementation of the RV formulation, a systematic procedure consisting of stability analysis and flash calculations is proposed without any prior knowledge of initial K-values. Sets of different initial K-values are appropriately tested in each stability analysis. We performed comprehensive testing using characterized fluids found in the literature in order to validate the robustness of the proposed procedure. The four-phase regions in pressure-composition (Px) space could be accurately identified using our procedure. On the other hand, in some instances mixtures were incorrectly evaluated as three-phase when using existing approaches such as Li and Firoozabadi (2012). Our approach proposed in this paper is a promising four-phase equilibrium calculation framework for compositional reservoir simulation. The procedure achieved excellent robustness and efficiency with minimal modification to the conventional two or three-phase equilibrium calculation framework.

Exploitation of gas from deep-sea methane hydrate-bearing layers might lead to some geological disasters, including marine landslides and excessive settlement of marine ground. The first offshore gas production tests for methane hydrate-bearing sediments were carried out in eastern Nankai Trough. However, knowledge on mechanical behavior of gas hydrate reservoirs with similar gradation and minerology component to the marine sediment is still insufficient. Consequently, proper modeling of geomechanical properties of methane hydrate-bearing sediments is crucial for reservoir simulation and deep ocean ground stability analysis for long-term gas production in the future. This study conducted a series of triaxial shear tests to examine the shear response of methane hydrate-bearing sediments with a similar grading curve and minerology components to the hydrate-rich sediments in Nankai Trough. The test results demonstrated that the presence of hydrate mass between sand grains altered the stress-strain pattern from strain-hardening to postpeak strain-softening. A simple constitutive model based on several empirical relationships of granular materials is proposed to describe the stress-strain relationship of methane hydrate-bearing sediments under triaxial stress condition. This model can reproduce the enhancement of shear strength, initial stiffness, and dilation behavior of methane hydrate-bearing sediments containing different amounts of fines content with a rise in the methane hydrate saturation at a wide range of effective confining pressures. The numerical results indicate that the parameter A associated with initial stiffness of stress-strain curve and the parameter α related with dilation properties are jointly governed by the confining pressure, fines content, and hydrate saturation.

The Multiscale Robin Coupled Method (MRCM) is a recent multiscale numerical method based on a non-overlapping domain decomposition procedure. One of its hallmarks is that the MRCM allows for the independent definition of interface spaces for pressure and flux over the skeleton of the decomposition. The accuracy of the MRCM depends on the choice of these interface spaces, as well as on an algorithmic parameter β in the Robin interface conditions imposed at the subdomain boundaries. This work presents an extensive numerical assessment of the MRCM in both of these aspects. Two types of interface spaces are implemented: usual piecewise polynomial spaces and informed spaces, the latter obtained from sets of snapshots by dimensionality reduction. Different distributions of the unknowns between pressure and flux are explored. Two non-dimensionalizations of β are tested. The assessment is conducted on realistic, high contrast, channelized permeability fields from a SPE benchmark database. The results show that β , suitably non-dimensionalized, can be fixed to unity to avoid any indeterminacy in the method. Further, with both types of spaces it is observed that a balanced distribution of the interface unknowns between pressure and flux renders the MRCM quite attractive both in accuracy and in computational cost, competitive with other multiscale methods from the literature

The National Gas Hydrate Program 01 Expedition (2006) and the National Gas Hydrate Program 02 Expedition (2015) have established the presence of large deposits of gas hydrates in deep-water areas offshore India. This paper presents the results of a techno-economic study carried out for the development of a hypothetical gas hydrate field in the Krishna-Godavari (KG) Basin located along the eastern margin of India. Standard industry approaches have been used to carry out capital cost and operational cost estimates. Based on initial reservoir simulation modelling results, three cases have been considered to encompass the possible range of reservoir production responses. In the first case, 18 MMSCMD of gas is envisaged to be produced from 120 wells for a production period of 10 years. In the second case, 12 MMSCMD of gas is envisaged to be produced from the 120 wells for 16 years. In the third case, 6 MMSCMD of gas is envisaged to be produced from the 120 wells for 30 years. The production rates assumed in Case 3 best represents what is believed to be the most reasonable production rates as modeled for a gas hydrate accumulation (NGHP-02 Area B; Site NGHP-02-16) drilled during NGHP-02. For Case 1, an initial determination is that field development is economically viable for prevailing gas price of USD 7.67/MMBTU with NPV of 1921 MMUSD and IRR of 27.87% with a cost of production of USD 4.74/MMBTU. For Case 2, the study indicates that field development is viable with NPV of USD 986 MMUSD and IRR of 20.27% and cost of production of USD 5.8/MMBTU. For Case 3, the cost of production is USD 9/MMBTU. No production data is available for the gas hydrate accumulations discovered during NGHP-02 in the offshore of India; therefore, these techno-economic results generated in this study can only be validated after matching the results from future pilot production testing under actual field conditions.

Modeling reservoir permeability is one of the crucial tasks in reservoir simulation studies. Traditionally, it is done by kriging-based methods. More rigorous modeling of the permeability results in more reliable outputs of the reservoir models. Recently, a new category of geostatistical methods has been used for this purpose, namely multiple point statistics (MPS). By this new category of permeability modeling methods, one is able to predict the heterogeneity of the reservoir permeability as a continuous variable. These methods consider the direction of property variation in addition to the distances of known locations of the property. In this study, the reservoir performance of a modified version of the SPE 10 solution project as a pioneer case is used for investigating the efficiency of these methods and paralleling them with the kriging-based one. In this way, the permeability texture concept is introduced by applying some MPS methods. This study is accomplished in the conditions of real reservoir dimensions and velocities for the whole reservoir life. A continuous training image is used as the input of calculation for the permeability modeling. The results show that the detailed permeability of the reservoir as a continuous variable makes the reservoir simulation show the same fluid front movement and flooding behavior of the reservoir similar to the reference case with the same permeability heterogeneity. Some MPS methods enable the reservoir simulation to reproduce the fluid flow complexities such as bypassing and oil trapping during water flooding similar to the reference case. Accordingly, total oil production is predicted with higher accuracy and lower uncertainty. All studied cases are identical except for the permeability texture. Even histograms and variograms of permeabilities for the studied reservoir are quite similar, but the performance of the reservoir shows that kriging-based method results have slightly less accuracy than some MPS methods. Meanwhile, it results in lower uncertainty in outputs for this water flooding case performance.

The analysis of numerical dispersion in reservoir simulation usually focuses on its impacts on liquid saturation and component concentration profiles. However, the production of coalbed methane (CBM) reservoirs is highly sensitive to the pressure diffusion owing to its unique gas storage and flow mechanism. The effect of numerical dispersion on pressure diffusion during gas production has not been studied yet. In this work, the numerical dispersion term of pressure diffusion equation is derived using finite difference scheme to determine the influence of numerical dispersion on pressure diffusion. Simulation examples are then performed to evaluate the effect of numerical dispersion on pressure diffusion and gas production in CBM reservoirs. Finally, a field case is presented to study numerical dispersion impacts on gas rate, using the production history of two wells in Ordos Basin, China. The numerical dispersion term of pressure diffusion equation, derived in this paper, illustrates that the numerical dispersion is controlled by pressure diffusivity, grid size, time step and finite difference scheme. The simulation results indicate that both coarse grid and low permeability contribute to dramatic numerical dispersion and significant errors in simulation. Once the permeability is lower than 200 mD, there is a dramatic effect of grid size on numerical dispersion. A slight deviation of pressure still results in an unacceptable error in CBM production simulation. The simulation results and field example show that the numerical dispersion of pressure may overestimate the dewatering efficiency and gas production rate. An effective way to diminish the numerical dispersion in CBM reservoir simulation is to apply the fine grid system.

Various fracture-propagation models have been used to capture complex hydraulic fracture (HF) geometry. However, they cannot obtain the production performance. Besides, many researchers developed reservoir simulators to obtain production performance with given fracture geometry. However, these geometries are easy to deviate from the reality of a certain reservoir. To fill this gap, there is an urgent demand to integrate the simulation of fracturing and production processes. In this work, we present an integrated workflow for fracture-propagation and reservoir simulation for tight oil. First, we employ cohesive zone model (CZM) to simulate fracture propagation. In comparison with previous studies, our CZM can simulate complex fractures. Then, we apply the complex fracture geometry to embedded discrete fracture model (EDFM). In this reservoir simulator, nonlinear flow in the tight matrix, complex HF geometry, and pressure-dependent fracture permeability (stress sensitivity effect) are considered simultaneously. Finally, we obtain production performance of this fractured well. To verify the reliability of our models, we compare the results of laboratory experiment and commercial simulator with CZM and EDFM, respectively. Using this workflow, we studied the effect of geological factor (i.e. natural fracture distribution) and fracturing schedule (i.e. injection rate) on production performance. Results reveal that the cumulative oil production in the case with regular natural fracture (NF) is 1.67% higher than that with staggered NF, and 14.6% higher than that without NF. There is an optimal injection rate to maximum production performance. In this case, medium injection rate increases cumulative oil production by 2.42% than higher injection rate, and 1.1% than lower injection. Most importantly, the continuous simulation of fracturing and production processes is implemented in our proposed simulation workflow. In this way, this workflow can be used to optimize both fracturing and production schedule to maximize production performance and/or economic benefit for tight oil in our future work. Furthermore, our method can be further extended to the simulation of multi-stage fractured horizontal well (MFHW) in tight oil or other unconventional oil and gas resources.

Carbonate reservoirs usually contain multi-scale fractures with a wide range of lengths and various levels of connectivities, which causes great challenges in reservoir simulation. To accurately characterize multi-scale fractures without dramatically increasing the number of simulation grids and computing time, a connectivity-based hierarchical model is proposed integrating different numerical models according to the geometrical size and fracture connectivity for different types of fractures. In this study, three types of fractures are defined. Large-scale fractures, which are usually characterized by seismic interpretations, are referred to as Type I fractures. They dominate the flow pattern globally due to their large geometrical and petrophysical properties. Thus, Type I fractures are modeled by discrete fracture model (DFM) in unstructured grids. For smaller fractures, we propose a methodology of fracture type classification to identify them as Type II and Type III fractures based on the level of connectivity to neighboring fractures. The resulting Type II fractures with relatively strong communications are characterized by a dual porosity/dual permeability model (DP). Type III fractures with weak communications contribute to an equivalent matrix system with enhanced porosity and permeability should be simulated by the enhanced matrix medium model (EMM). For integrating these three numerical models, the global flow-based upscaling method is applied to obtain transmissibilities. In order to test the accuracy and applicability, the proposed model is applied to a conceptual case of complicated fracture system and a field case of highly fractured carbonate reservoir in South China Sea, respectively. In the conceptual case, the simulation results of the proposed hierarchical model are compared with different classic models. The control group experiment demonstrates that the simulation results of the proposed hierarchical model are more accurate, compared to the classic models. A field case of four production wells are analyzed and discussed, which are drilled in the offshore carbonate reservoir with strong aquifer in South China Sea. Especially, water cuts increased rapidly within a short period in that reservoir. The simulation results show that our proposed model is capable of capturing such drastic flow accurately. As a result, the connectivity-based hierarchical model has great potential in characterizing multi-scale fracture system more precisely for reservoir simulation.

Traditionally, production optimization is performed based on repeatedly running a full-scale reservoir simulation model, which is quite time-consuming. Recently, we developed a computationally efficient data-driven model, which is referred to as interwell-numerical-simulation model (INSIM), for history matching, characterizing interwell connectivity, monitoring, and optimization for a waterflood. In this research, we develop a new workflow for fast optimization of waterflooding performance which only requires one single INSIM forward run. Specifically, the optimized well injection rate and production rate are determined with the help of the new INSIM-derived injection efficiency and the existing injector-centered allocation factor. The basic idea of the proposed optimization workflow is to recover more oil by injecting more water to those injector-producer pairs that have more remaining oil left; whereas decrease water injection for those connections without much oil left. The major criterion to tune the injection rate is based on the injection efficiency calculated with INSIM, a value to measure the effectiveness of injected water from an injector. The larger the injection efficiency is, the more oil can be produced by injecting a unit amount of water. The advantage of this method is that the well controls are optimized based on the reservoir-engineering point of view which is easy to understand and visualize. Also, the new workflow is very easy to implement and is much more computationally efficient than the traditional optimization workflow. We test the proposed workflow with two examples including a large-scale field example. The computational results indicate that, by using the proposed workflow, the field oil production is increased with less producing water.

Efficient simulation of multiphysics problems is a challenging task. This is often due to the multiscale nature of the physics and nonlinear coupling between the different processes. One approach to this problem is to solve the entire multiphysics problem simultaneously in a fully coupled manner. However, due to the strong coupling and multiphysics interactions, it is difficult to design and analyze fully coupled solvers, which often entail the construction and solution of global fully coupled Jacobian systems. Another approach is the sequential-implicit method, whereby the full multiphysics problem is split into different subproblems. Each subproblem is constructed and solved separately; then the solutions of the subproblems are stitched together in a specific sequence. Isolation of each subproblem allows for the design of specialized solvers that tackle the complexity of the particular subproblem efficiently. The sequential-implicit approach offers wide flexibility and extensibility. However, these advantages are often offset by slow convergence rates when there is strong coupling between the subproblems. This slow convergence rate of the overall coupled system is directly linked to the use of a fixed-point outer-loop iteration in sequential-implicit methods. We present a Sequential Implicit Newton (SIN) approach, whereby the sequence of implicit subproblems is wrapped with an outer full Newton scheme. We demonstrate that the SIN formulation improves the overall convergence rate from linear to quadratic. The SIN method uses the same sequential-implicit scheme as the fixed-point method, but after each sequential iteration a Newton update is computed. Wrapping a Newton loop around the traditional sequential-implicit scheme leads to significant improvements in the convergence rate. The SIN method allows for the ability to split a multiphysics problem into individual subproblems while taking advantage of the quadratic convergence rate of the Newton method. We demonstrate the effectiveness of SIN using two different multiphysics porous-media problems: flow-thermal in geothermal reservoir simulation and flow-mechanics in geomechanics reservoir simulation. Just as with the fixed-point iteration version of the sequential-implicit method, SIN benefits from careful design of the constraints used to stitch the sequence of the subproblems. Our numerical experiments show that the SIN approach improves the overall convergence rate for all the nonlinear multiphysics problems considered. For specific cases where there is strong nonlinear coupling between the subproblems, we see up to two orders of magnitude decrease in the number of sequential iterations when using SIN compared with the fixed-iteration scheme.

In reservoir engineering, history matching is the technique of conditioning a reservoir simulation model to the available production data. The reservoir properties have uncertainties which lead to discrepancies between the observed data and the reservoir simulator response, making history matching an indispensable tool in the petroleum industry. The standard Ensemble Smoother with Multiple Data Assimilation (ES-MDA) application has become popular in history matching problems. However, in the standard methodology, the number of iterations must be previously defined by the user, what makes it a determinant parameter in the ES-MDA results. One way to solve this problem is to perform adaptive algorithms: these algorithms keep iterating until they reach desirable matchings with the real data. Furthermore, to apply this method in large-scale reservoirs, it is necessary to use some localization technique to prevent spurious updates and high uncertainty reduction after the ES-MDA is applied. This work evaluates the influence of the distance-based Kalman Gain localization in an adaptive Ensemble Smoother, by applying the mentioned methodology in a large-scale synthetic reservoir model. The experiments showed a connection between the localization parameters and the number of iterations required by the adaptive algorithm. Moreover, the results presented significant reduction in the production data mismatch, regardless the localization, being the mismatch of the prior and posterior models an important parameter to determine the history matching quality.

This article considers upscaling of polymer adsorption. Input to adsorption values employed in reservoir simulation models are typically obtained from core plug measurements. There are several orders of magnitude in scale difference between core plugs and grid cells in reservoir simulation models, which foster a need for upscaling of the adsorption values. Polymer concentration distribution on the lithofacies scale is investigated in this article. The effect of diffusion on concentration distribution is investigated analytically. The slow diffusion of polymer molecules retards mixing even at the lithofacies scale. We introduce a formula to estimate the redistribution of polymer due to capillary forces in a layered model, and this formula is validated through numerical simulations. From our considerations we conclude that it is questionable to assume a constant polymer concentration in lithofacies models. This impedes applying steady-state upscaling techniques. Such upscaling techniques will over-predict polymer adsorption. Different methods for upscaling adsorption are presented in this paper, and applied to a simplified layered model and to more realistic fine-scale numerical models based on the SPE10 model. These numerical models were populated with adsorption values obtained from published experiments conducted on samples from the Brent sequence modeled in SPE10. Simulations of tertiary polymer flooding on the upscaled models were compared to simulations of the same flooding sequences on the original fine scale models. The tested upscaling methods include a volume averaging technique employed by other authors, and a method were we distribute the adsorption values by the same functional relationship as in the fine scale model. In addition we introduce upscaling methods were we assign zero adsorption to fine scale grid cells with permeability below a given cut-off value. The cut-off value is obtained from a single phase simulation on the fine scale model. In our models the cut-off value methods yield the best match between the coarse scale and fine scale simulation results. The volume averaging technique over-predict the polymer adsorption. Results from both the lithofacies and geomodel scale indicate a tendency to over-predict polymer adsorption, which could lead to conservative estimates for the effect of polymer flooding.

Near-well flow analysis is an important tool for gaining detailed insight of the flow behaviour and for improving well design and production optimization of real reservoirs. One challenge of accurate numerical modelling of the flow field in the vicinity of the well is related to the scale disparity factor in space and time. The numerical scale gap between the reservoir and the wellbore justifies the representation of a well as a point or line sink/source term in traditional reservoir models. However, standard numerical techniques for reservoir simulation are incapable of resolving the near-singular character of the pressure field in the vicinity of the well. Under the assumption that all length scales have impact on flow patterns, we present a proof-of-concept study aimed at improving the quality of the numerical simulation by considering the geometry and fluid flow near the wellbore in a fully connected system, thus accounting for the fine scale phenomena by means of a hybrid Navier-Stokes/Darcy wellbore model coupled with a full scale reservoir model. A weak coupling method based on fixed-point iterations, that preserves the mass flux transport across the coupled interface, while adjusting productivity indices, is demonstrated via numerical experiments. Several different numerical experiments are performed to demonstrate the versatility and the improved well performance insight that the coupled method offers, including horizontal well inflow profile, influence of formation damage and optimal well configuration.

Well placement optimization is a decisive task for the reliable design of field development plans. The use of optimization routines coupled to reservoir simulation models as an automatic tool is a popular practice, which could improve the decision-making process on well placement problems. However, despite the various automatic techniques developed, there is still a lack of robust computer-added optimization tool, which can solve the well placement problem with high accuracy in reasonable time while handling the technical constraints properly. In this paper, a hybrid intelligent system is proposed to deal with a real well placement problem with arbitrary well trajectories, complex model grids, and linear and nonlinear constraints. In this intelligent approach, a Genetic Algorithm (GA) combined with a hybrid constraint-handling strategy is applied in conjunction with a constrained space-filling sampling design, Gaussian Process (GP) surrogate model, and one proposed adaptive sampling routine. This self-adaptive framework allows to consecutively augment the quality of surrogate, enhance the accuracy of the process, and thus guide the optimization rapidly into the optimal solution. To demonstrate the efficiency of the developed method, a full-field reservoir case is considered. This case covers a real well placement project in a fractured unconventional reservoir of El Gassi, which is a mature field located in Hassi-Massoud, Algeria. The obtained results highlighted the effectiveness of the proposed approach for solving the real well placement problem with high accuracy in reasonable CPU-time. These auspicious features make it a reliable tool to be used on other real optimization projects.

In order to improve the current recovery factor of unconventional reservoirs and take it to the next level (10–20%), gas Huff and Puff is a very promising enhanced oil recovery technology used currently. Many laboratory works and field pilot tests have been conducted recently. However, most of the research work is based on CO2 as an injected gas. Few of them were built upon the more realistic lean gas Huff and Puff process. From the feedback of lean gas Huff and Puff pilot in Eagle Ford, the field response is always beyond analysis and reservoir simulation forecast. Methane, the main component of lean gas, and its adsorption and desorption effects on the unconventional resources are pronounced due to nanopore confinement effects and a much larger surface area than conventional reservoirs. On the other hand, the minimum miscibility pressure of lean gas in Eagle Ford is high (>4000 psi), which makes gas phase and liquid phase still separate in a long period of Huff and Puff process before reservoir pressure is elevated high enough to developing the supercritical state. Therefore, relative permeability hysteresis – gas trapping effect in nature, should be also very significant on gas EOR performance for unconventional resources. To our best knowledge, there are no such studies about the lean gas adsorption and gas trapping for Huff and Puff process of unconventional reservoir reported so far. In this study, these two mechanisms are systematically analyzed and quantified in a compositional reservoir simulation study. The gas EOR dependence on permeability is also studied and the resulting gas injectivity problem is answered, trying to explore the real problem encountered in the pilot practice.

One characteristic of unconventional shale rock is the abundance of nanoscale pores and pore throats. For many shale reservoirs, these are the dominant factors controlling the total reserve, production rate, and overall production. Accordingly, many new phenomenon related to nanopore physics need to be considered for shale reservoir. A key mechanism controlling hydrocarbon gas transport from pores to fractures in shale reservoirs is molecular diffusion. As a result, the diffusion coefficient of light hydrocarbon becomes an important parameter in reservoir simulation to estimate production rate, especially for the long-term or late time production. The diffusion coefficient is also a key parameter in nuclear magnetic resonance (NMR) logging for fluid typing in determining hydrocarbon-in-place. Diffusion in nanopore systems is complicated by two important factors. First, the gas molecules collide more with pore surfaces than with each other; therefore, simple diffusion theory based on gas molecule collision is not applicable. Second, the occurrence of capillary condensation in small pores or pore throats and the adsorption to the pore surface makes the hydrocarbon transport a mixed process of liquid diffusion and gas diffusion in the reservoir. We derived a theoretical model for mixed phase diffusion under fast exchange for shale gas reservoirs. We obtained that the effective diffusion coefficient of mixed fluid is a fractional average of the liquid and gas diffusivity. We verified this model using NMR to measure n-hexane diffusion in a well-characterized hierarchical carbon with both nanometer pores and micrometer pores so that both gas and liquid can be prepared to exist in the sample simultaneously. We found that the diffusion coefficient of hexane in these hydrophobic nanopores is approximately one magnitude of order larger than the bulk liquid value. The effective diffusion coefficient in this study can be used in reservoir simulation and interpretation of NMR logs for shale gas reservoirs.

Capillary pressure heterogeneity causes local capillary trapping of CO2 in saline aquifers. However, quantifying local capillary trapping using conventional reservoir simulation is computationally intensive. This work employs a geologic criterion (GC) to rapidly estimate the volume capacity of local capillary traps in static geologic models. The criterion refers to the ‘critical capillary entry pressure’ that is used to indicate flow barriers and flow paths during buoyant flow. A previous study (Saadatpoor, 2012) found that issues exist in the criterion method: unknown physical critical capillary entry pressures and boundary barriers. This work addresses the two issues. It is shown that the criterion method gives a close upper bound estimation of local capillary trap volume capacities. Several fine-scale geostatistical realizations of capillary entry pressure fields are considered, and the effects of reservoir heterogeneity, system sizes, aspect ratios, and boundary types are examined. The results from the GC are also strictly interpreted through invoking a simple counting argument. The overall work enhances our mechanistic understanding of the geological controls of local capillary traps.

Corner-point is an industry-standard type grid for application in reservoir simulation. The flexible gridding in corner-point grids provides several advantages over Cartesian grids for the representation of complex geological features. In this work, an embedded discrete fracture model (EDFM) is extended to corner-point grids with a full-permeability-tensor formulation to simulate complex fractures in this type of grids. The developed model is implemented in an IMPEC, compositional reservoir simulator. We first describe the formulations of the full-permeability-tensor implementation together with the modified governing equations for EDFM simulations. Then, we present methodologies for computing matrix-fracture intersections and fracture-fracture connections in the EDFM considering the various block geometries in corner-point grids. Subsequently, case studies are presented to verify the developed model, where the impacts of grid distortion and cross derivatives on simulation results are discussed. Three-dimensional case studies are also shown to illustrate the influence of natural fractures on secondary recovery. The results of this study demonstrate the reliability of the developed model, and they also show the compatibility of the EDFM with different types of numerical solution schemes in existing simulators.

Field development optimisation is a critical task in the modern reservoir management processes. The optimum setting provides the best exploitation strategy and financial returns. However, finding such a setting is difficult due to the non-linearity between the reservoir response and the development strategy parameters. Therefore, growing attention is being paid to computer-assisted optimisation algorithms, due to their capabilities in handling optimisation problems with such complexities. In this paper, the performance of ( μ + λ ) Evolution Strategy (ES) Algorithm is compared to Genetic Algorithm (GA), Particle Swarm Optimisation (PSO) and ( μ , λ ) Covariance Matrix Adaptation Evolution Strategy (CMA-ES) using five different optimisation cases. The 1st and 2nd cases are well placement and trajectory optimisation, respectively, which have rough objective function surfaces and a small number of dimensions. The 3rd Case is well control optimisation with a small number of dimensions, while the 4th case is a high-dimensional control optimisation. Lastly, the 5th case is joint optimisation that includes the number of wells, type, trajectory, and control, which has a high dimensional rugged surface. The results show that the use of ES as the optimisation algorithm delivers promising results in all cases, except case 3. It converged to a higher NPV compared to the other algorithms with the same computational budget. The obtained solutions also outperformed the ones delivered by reservoir engineering judgments.

We study the impact of explicitly including hysteresis effects (HEs) for relative permeabilities in numerical simulations of enhanced oil recovery approaches grounded on the application of Water Alternate Gas (WAG) injection protocols. Our work explores the significance of hysteresis exhibited by the relative permeability of the non-wetting and/or intermediate wetting phases on the results of reservoir simulations performed within a black-oil modeling approach. We consider four diverse strategies that can be employed to model relative permeabilities of fluid phases under WAG scenarios implemented in a water-wet system following primary waterflooding. The effects of all these modeling strategies are assessed in terms of field oil efficiency (FOE) and gas oil ratio (FGOR) evaluated at the total production lifetime of the reservoir, as compared against a base case where only waterflooding is applied to promote oil recovery. Two of these strategies are implemented and used in typical commercial black-oil reservoir simulators and either neglect hysteresis or consider it only for the gas phase. We then examine a procedure where only hysteresis for relative permeability of the oil phase is considered. Finally, we explicitly consider hysteresis of both non- and intermediate-wetting phases. Our results generally show that including HEs yields an increased FOE and a decreased FGOR. This is consistent with the observation that when injection well controls are set at an optimum value, a non-negligible portion of the domain is associated with saturation paths corresponding to three-phase flow conditions, where saturation history can play a significant role. As compared against a base case where waterflooding is considered as the sole strategy for oil recovery, including hysteresis on three-phase relative permeabilities in the numerical simulations of WAG promotes an increased net present value. We also analyze the impact on reservoir simulation responses of the main WAG injection parameters, i.e., (i) injection rate of gas and water, and duration of (ii) WAG cycles, and (iii) primary waterflooding.

The pressure pulse-decay permeability (PDP) measurement is a well-established technique to measure the permeability of tight rock samples such as shale. The conventional applications of the PDP measurement almost exclusively treat shale samples as a single-continuum system, even though the gas flow in some shale samples may be more accurately characterized by a dual-continuum, which is due to the large range of pore size distribution and chemical/mineralogical difference between organic and inorganic matters. However, studies about measurements of flow parameters for dual-continuum shale rock samples are very limited in literature. Liu et al. (2016) proposed a new analytical technique to characterize the dual-continuum behavior of a test sample using the PDP measurement with the same upstream and downstream reservoir volumes. In this study, a more general analytical technique is proposed and allows for using different upstream and downstream reservoir volumes in the PDP setup. With this new technique, all the existing PDP systems in laboratories can be conducted to characterize the dual-continuum behavior of a test sample without the need of modifying the upstream and downstream reservoir volumes, and the measured flow parameters of samples can be used as input parameters in the reservoir simulation of the dual-continuum system. The validity and practical usefulness of the new technique is demonstrated by the successful identification and characterization of the dual continuum behavior of test samples in laboratory.

Future optimal rule curves are required for operating reservoir under uncertainty situation. This study applied the genetic algorithm (GA) connected a reservoir simulation model with smoothing function and adjusting of expert participation to search for future optimal reservoir rule curves for the Ubolrat Reservoir, which is located in the Northeast of Thailand, in period 2015–2064. The future optimal rule curves considered the impact of climate change with the PRECIS model under two emission scenarios, A2 and B2, and future land use maps using the CA Markov model. The future streamflow into the reservoir was determined using the Soil and Water Assessment Tool (SWAT) model. The results showed that the average future streamflow for the A2 and B2 were increased in comparison to the baseline year (1997–2014) due to the increase of average rainfall and temperatures, including widest land use change from rice and forest area to the sugarcane. The smoothing function applied to be the constraint can reduce the fluctuation of the upper and lower obtained rule curves from the GA. Further, the future rule curves can mitigate the frequency of water shortage situations and the releases of excess water during the increasing streamflow impacted by both climate scenarios and land use changes situation more than the existing and historic rule curves. Moreover, adjusted future rule curves with the expert participation were acceptable to operate the reservoir.

When localization methods used in reservoir history matching were introduced from outside the oil and gas industry, the differences between data assimilation for other industries and reservoir history matching were not considered. However, these differences can be extremely important when considering the validity of these methods. This problem is discussed within the context of the roles of covariance localization in detail in this paper. This paper starts with discussion of relations between two significant problems, ill-posedness and spurious correlations, and their solution methods. This analysis leads to a conclusion about two appropriate roles of the covariance localization method. This conclusion is used to validate the cross-covariance localization methods used in reservoir simulation. In addition, for the cross-covariance localization in reservoir history matching, there are many different processes, especially different correlation functions, proposed by different authors. This makes it difficult to choose a proper method when solving history matching or data assimilation problems. The performance of different cross-covariance localization correlation functions is also analyzed theoretically and experimentally in this paper.

Recent core-lab study of Marcellus Shale illustrated that effect of gas slippage and matrix compaction are significant on gas production because of substantial reservoir pressure depletion, especially during the late time of gas production. However, the impact of gas slippage and matrix compaction on gas recovery evaluation and hydraulic fracturing design is still not clearly understood and systematically investigated. Additionally, such impact varies with production time and completion/production circumstances. Therefore, it is critical to develop a laboratory-modeling based approach that properly characterizes the two permeability effects and evaluates their impact on well production evaluation and hydraulic fracturing design. In this study, a comprehensive parametric study is conducted by running reservoir simulations using empirical permeability correlations developed from core-lab tests under different confining stress and pore pressure conditions. Simulations of different case scenarios are run in two contrast groups. One group considers the effect of gas slippage and matrix compaction on gas production and the other group ignores the two effects. By comparing the simulated gas production, critical conductivity, and proppant pumping amount/cost of the two contrast groups, a better understanding of the effect of gas slippage and geomechanics on shale gas well performance and hydraulic fracturing design can be developed for operators. The results show that ignoring the two permeability effect in reservoir simulation leads to an overestimation of gas production evaluation, which is up to 11% for Marcellus Shale. It also leads to an over-design of proppant pumping amount, resulting in early staging, screening-out, and excessive pumping cost. Calculations further show that, an average of over 2 million dollars can be wasted for fracturing a single horizontal well in Marcellus Shale if excluding the two effect from a fracturing design. The two effects are more significant for lower BHP, longer hydraulic fracture, and larger stage spacing conditions.

Accurate apparent permeability (AP) model for oil transport in shale must consider natural fractures and micro/nano-pores within organic matter and inorganic matrix. Furthermore, the effect of pore geometry, tortuosity, pore size distribution (PSD), the spatial distribution of different pores, total organic content (TOC), and liquid slip should also be taken into account. However, all of the aforementioned factors are not simultaneously considered in one AP model. In this work, we develop an AP model in 3D for shale oil to overcome this drawback. We first validate our model by comparing with the published data. Then sensitivity analysis for some parameters is investigated. After that, shale oil APs are used in a macro-scale reservoir simulation model. In this way, the effect of some micro-scale factors on production performance can be quantitatively evaluated. Notably, on the basis of embedded discrete fracture model (EDFM), our reservoir simulation model considers non-linear flow in shale matrix, complex hydraulic fracture geometry, and pressure-dependent permeability of hydraulic fractures. Results show that natural fractures contribute the most to AP, followed by organic pores and inorganic pores. In general, the AP in the horizontal direction is approximately twice that in the vertical direction in shale. Furthermore, the maximum error caused by the pore type on shale oil production is ∼31%, followed by tortuosity (∼25%), pore shape (∼13%) and slip effect (∼4.8%). In conclusion, it is necessary to simultaneously incorporate the influences of the aforementioned factors. Our stochastic permeability model can serve as an efficient tool to determine shale oil AP.

One of the important mechanisms involved in solvent-aided thermal recovery processes is interphase-mass transfer phenomenon. However, in current reservoir simulation models a local equilibrium is commonly assumed such that a simulation grid block is at instantaneous equilibrium. The assumption of local equilibrium often fails at larger scales or in situations where flow velocities are considerable compared to that of mass or heat transfer which results in significant discrepancies between reservoir simulation predictions and field scale observations. In this work, solvent-aided gravity drainage of bitumen was simulated with propane as a solvent. The effect of non-equilibrium mass transfer was included in the model to simulate the process using a kinetic approach. The results show that the assumption of the local instantaneous equilibrium results in lower oil recovery for the typical field scale simulation models. The analysis shows that this mismatch can be mitigated fairly through the inclusion of the non-equilibrium interphase mass transfer. Correlations for the non-equilibrium interphase mass transfer coefficients for propane/bitumen mixture were developed which can be used as guidelines for field scale modeling of solvent-aided thermal recovery processes.

The purpose of this study is to present the numerical evaluation of the upscaling of secondary and tertiary CO2 flooding at reservoir pressure and temperature. In all simulation cases, CO2 is injected from the top of the fracture in a fracture-matrix block system and displaces oil toward the bottom of the block. Our numerical models provide comprehensive sensitivity analyses that are proved to be important for the upscaling of CO2 injection from lab to reservoir scale. In addition, we address the scale dependency of the diffusion mechanism in a large matrix-fracture domain. In our earlier studies, we have conducted a significant number of reservoir-condition CO2 flood experiments by employing fractured core systems and North Sea reservoir oil. Our experimental and numerical studies are proved to be useful to investigate the complex physical phenomena affecting the efficiency of CO2 injection in oil recovery from a fracture reservoir. The height of the core plugs used in our experiments varies from 7 to 28 cm while the fracture spacing varies between ∼4 cm and 12 cm. In all cases, we find the important role of diffusion mechanism in increasing oil recovery in a fracture-matrix system at the lab scale. However, the field matrix block size is often 1-to-2 orders of magnitude larger than that in the lab scale. Recovery mechanisms are significantly affected by the matrix dimension. For instance, the impact of diffusion mechanism on oil recovery may alter with the size of the matrix block and the fracture spacing. This highlights the importance of upscaling from lab to the field scale that is addressed in this study. We employ a compositional reservoir simulation with a developed equation of state (EOS) to model CO2 injection in a fracture-matrix system at reservoir conditions. In all the numerical simulations, the single-porosity (SP) model consists of a single axial fracture with a typical fracture aperture of 1 mm. The SP model also contains a single matrix block that feeds the producer through fracture next to it. The dimension of the fracture-matrix block varies in the SP models to account for the scale dependency of the results. In our modeling framework, we assume a network of open fractures that are homogenously distributed in the reservoir and links the oil in the matrix to the production wells. We initialize the matrix with the North-Sea-Chalk-Field (NSCF) live oil and the fracture with the injected gas (CO2). The whole displacement process is operated at the constant reservoir conditions of 3750 psia and 110 °C, representing typical NSCF reservoir conditions. Prior to conducting simulations, we successfully tune EOS parameters against the extensive PVT data, sampled from a specific fractured NSCF reservoir. The tuned EOS model assures the proper estimation of the complex phase and volumetric properties for CO2 and oil mixtures at reservoir conditions. In addition, the multi-component diffusion coefficients that are tuned using experimental data are employed as input parameters for the compositional simulations. We study the effect of several key parameters on oil recovery; e.g. matrix block size, fracture spacing, CO2 injection rate, density difference, vaporization and the diffusion. The results show that the mass transport is mainly dominated by diffusion in the lab scale which is not the case for the large matrix block size. Finally, we test the accuracy of the dual-porosity (DP) model against the SP model at various displacement conditions. Results show that when diffusion and vaporization are significant the DP model fails to predict the results of the SP reservoir model. Our findings are an important step towards modeling the tertiary-CO2 flooding in an actual fracture-chalk system. We also provide some important inputs that are necessary for upscaling tertiary-CF from a lab-scale into a field-scale reservoir model.

Optimum subsurface well spacing is key to developing unconventional reservoirs. From a field application perspective, this paper presents our systematic study on subsurface well spacing in the Permian Basin for unconventional reservoirs which consisted of four main components, i.e., numerical modeling, well interference quantification through simulation and regression, field pilot analogs, and economic evaluation. In this paper, field pilot wells are actual wells in the field to test different well spacing and completion designs. To capture upsized and downsized completions, a wide range of fracture designs in combination with different well spacing scenarios are conducted for both hydraulic fracture modeling and reservoir simulation. At the section level (1 mile by 1 mile, 640 acres), multiple wells are simulated to better capture well interactions and reservoir property variations. A complex fracture network is generated by considering interactions between natural fracture and hydraulic fracture. Well interference, which is determined by estimating ultimate recovery (EUR) difference between a single well and a middle well from multiple wells, is analyzed for general trend regressions and validated through field test results. At the section level, economics is done to evaluate capital efficiency of various scenarios. Results from both modeling work and pilots indicate that larger hydraulic fracture size without an increase in subsurface well spacing does not necessarily improve section EUR and there is a point of diminishing returns. Larger subsurface well spacing with bigger fracture size is thereby a preferable combination.

For situations where reservoir management based on developing and running a full-scale reservoir simulation model is not plausible, data-driven models may provide an attractive alternative. Recently, we developed a simple data-driven model, INSIM-FT for reservoir flow and transport as a replacement for a reservoir simulator. However, INSIM-FT only considers two-dimensional flow in a reservoir that contains only vertical wells. In this work, we develop a new data-driven model that extends the interwell numerical simulation model with front-tracking (INSIM-FT) from single-layer reservoirs to full three-dimensional (3D) multi-layer reservoirs. The new model, which is referred to as INSIM-FT-3D, can be used for history matching and reservoir performance predictions for a three-dimensional reservoir under waterflooding. The novelty of the new approach includes: (1) INSIM-FT-3D replaces the original Riemann solver in INSIM-FT by a new Riemann solver based on a convex-hull method that enables the solution of the Buckley–Leverett problem with gravity; (2) unlike the original INSIM-FT model, which assumes all wells are vertical, the INSIM-FT-3D model allows for the inclusion of wells with arbitrary trajectories with multiple perforations; (3) INSIM-FT-3D applies Mitchell's best-candidate algorithm to automatically generate the imaginary wells that are evenly distributed in the reservoir given a set of prefixed actual well nodes and (4) INSIM-FT-3D utilizes our own modification of Delaunay triangulation to build the 3D connection map necessary to use the general INSIM-FT-3D formulation. History matching of the INSIM-FT-3D model parameters is performed using the ensemble-smoother with multiple data assimilations. The model parameters for history matching include the connection-based parameters, the parameters defining the power-law relative permeabilities and the parameters defining the well indices for the perforated zones of a well with multiple perforated well segments. The reliability of the analytical water-saturation solution obtained with INSIM-FT-3D is validated by comparison with corresponding results from an Eclipse [47] model with very fine grids and small time steps. After illustrating the utility and reliability of the method for a three-dimensional synthetic problem, the method is shown to give reasonable history-matching and prediction results for a field example. At last, the proposed method is tested for Brugge field, a field-scale synthetic reservoir simulation model.

Shale gas is one of the world’s strategic energy reserves. The microscopic pores and the fracture structure of the shale rocks play an important role in shale gas flow. An effective reservoir simulation must account for the heterogeneity and anisotropy of the microscopic pore structure as well as the dynamics between the gas flow and the gas diffusion processes. In this study, the time lag effect, the dynamic coupling of gas flow and diffusion as well as the heterogeneity and anisotropy of the pores are taken into account in order to properly model shale gas production on a large scale. The effect of these variables on the temporal scale analysis of the wellbore gas pressure is presented, as the reliable estimate of wellbore pressure would allow better prediction of the duration of well shut-in periods. Gas production under the intermittent operation scheme at different temporal scales is discussed. The results showed that the well startup is composed of five stages, while the well shut-in is composed of only three stages. The crossflow stage is prolonged by the dynamic coupling. The heterogeneity, anisotropy and dynamic coupling phenomena are accurately presented on the temporal scale diagram. Moreover, the impact of time lag on the gas pressure is better captured by the dynamic coupling between the gas flow and the gas diffusion. The proposed model better simulates actual shale reservoirs and, hence, would be helpful in selecting suitable production rates.

The selection of an optimal model from a set of multiple realizations for dynamic reservoir modelling and production forecasts has been a persistent issue for reservoir modelers and decision makers. Current evidence has shown that many presumably good reservoir models which originally matched the true historic data did not always perform well in predicting the future of the reservoir as a result of uncertainties. In this paper, a new method for optimal model selection using Signal Detection Principle (SDP) approach is presented. In principle, SDP approach models the dissimilarity between various realizations as a cross-function of spatial distance, statistical correlation and the inherent noise level in the model; while the existing methods estimate the dissimilarity between parameter values of different realizations as a function of distance (statistical or spatial distance) or quality factor. SDP approach fills the model divergence gap by way of classifying the information-bearing patterns in a model as signals, and identifying random patterns which bears no information as noise. Thus, it quantifies the mismatch uncertainty and the inherent fudge in every realization as a measure of the model's reliability. The SDP approach has been validated with historical data, and the results show that the reliability factor of the best model has a value of one. Thus, if the strongest reservoir model has a reliability factor of one, then that model will make approximately the closest and best predictions as the true system in every forecast; whereas if the reliability factor of the model is less than or greater than one, its predictions will always disperse from historical data and is unsuitable for reservoir forecasts. Two examples based on real field data are used to demonstrate the application of SDP approach. In these case examples SDP was used to analyse the difference between the reservoir models in a set of multiple realizations. The target variable in this study was STOIIP (Stock Tank Oil Initially in Place). The results show that the models with a lower reliability factor made similar predictions as the real reservoir data in almost all the forecasts. Similarly, the models with higher reliability factors made dissimilar and more unreliable predictions in most of the forecasts.

Current US unconventional resource revolution has more than doubled US oil production and made US the largest oil production country in the world recently. Although the industry is trying all means including screening sweet spots, conducting infill drillings and optimizing the well spacing to improve recovery factor (RF) from primary production, unconventional reservoirs will encounter what the past conventional reservoir production experienced: difficult to explore new giant resource, run out of ‘easy oil’ (sweet spot), production comes to a plateau and declines. Therefore, it is time to implement enhanced oil recovery for unconventional resources. The goal of this work is to improve oil recovery by implementing and optimizing gas Huff and Puff method for one of the US major tight oil reservoirs-Bakken formation. Pressure dependent permeability and porosity are implemented into the compositional reservoir simulation to represent geomechanics effects. Gas diffusion effects is systematically analyzed to quantify the importance comparing with the natural fracture system in tight oil fractured reservoirs. Alternative gas composition instead of using CO2 in the Huff and Puff process is investigated and the recovered oil components is analyzed. The complex natural fracture structure and natural fracture permeability proved to be important affecting factors to oil production of Bakken reservoirs.

In this study, we present an embedded discrete fracture model (EDFM) for an in-house reservoir simulator that incorporates the effect of each fracture with arbitrary orientations, lengths and fracture conductivities. Instead of using the linear flow approximation for the EDFM, the interflows between local matrix grids and fracture elements are derived using boundary element method, which considers the effect of local grid geometry and boundary pressure on the flow into the fracture. The implementation is generally compatible with existing finite-difference reservoir simulators, and the accuracy of the EDFM is validated by comparing the results of analytical/semi-analytical models for fracture flow, LGR modules for fracture flow in commercial reservoir simulators and complex fracture flow in discrete fracture network using finite element method. A grid-sensitivity study is conducted to show the convergence of the new method. Moreover, the cases of multiple bi-wing fractures and complex fracture systems are presented to demonstrate the robustness, applicability and computational convenience of the novice approach for simulating the fracture flow in anisotropic reservoir.

The large computational requirements associated with subsurface flow simulation limit the use of realistic models for demanding applications such as optimization and uncertainty quantification. This has motivated the development of reduced-order models, in particular those based on proper orthogonal decomposition (POD). In this study, we implement a POD-based Gauss–Newton with approximated tensors (GNAT) method for oil–water reservoir simulation. Our formulation, which is described in detail, incorporates promising features from previous implementations involving GNAT and discrete empirical interpolation method (DEIM) procedures. A theoretical analysis of the computational cost of GNAT for our problem, and the speedup it may provide relative to the full-order simulation, suggests a complex dependency of speedup on GNAT parameters and solver implementation. Systematic assessments, involving several comprehensive numerical experiments, are then presented. These include a detailed evaluation of GNAT performance on a 2D model, in which 576 different GNAT parameter combinations are considered, which allows us to elucidate the impact of parameter values on error. Detailed comparisons with an existing reduced-order modeling procedure based on trajectory piecewise linearization, POD-TPWL, are also presented. Around 1500 test cases, with varying levels of perturbation relative to training cases, are considered. We show that GNAT is only slightly more accurate than POD-TPWL for cases with small perturbation, but its accuracy advantage increases for larger perturbations. We also demonstrate the successful application of GNAT to a more realistic 3D model.

Carbonate formations are usually highly fractured. The fractures exist at all length scales ranging from microscopic fissures to kilometer-size structures. Consequently, it is vitally important to rigorously characterize the multi-scale fracture system and to accurately model the fluid flow in such highly fractured porous media. In this paper, we will present an integrated workflow for characterization of natural fracture system and accurate numerical modeling of fluid flow in fractured rocks. The fracture characterization usually involves the integration of multiple data sources including core analysis, image logs and seismic interpretations etc., at different scales. The fracture mappings are thus required to perform at different length scales and resolutions. In this study, we present a systematic approach that characterizes the actual fracture distribution with seismic and log interpretations. Firstly, the small-scale fractures are interpreted using image logs and seismic anisotropy analysis with a co-Kriging and stochastic modeling approach. The small-scale fractures are initially constructed in an explicit fashion, and are then incorporated in the matrix medium using a flow-based upscaling procedure. Secondly, the large-scale fractures are mapped out from post-stack seismic data with ant-tracking and maximum curvature analysis. The reservoir is then gridded into unstructured tetrahedral or prism meshes to fully resolve these large fractures. This discrete fracture model (DFM) is employed in a reservoir simulation study based on such grid system. We applied the procedure for simulation study and history match on a portion of a carbonate gas reservoir in Longwangmiao formation in Southwest China. Currently, there are 7 horizontal and 2 vertical wells in operation. Due to the connection of some large-scale fractures to edge water, early water breakthrough and drastic water invasion were observed. We partitioned the reservoir block into 0.6 million cells, in which 153 large-scale and thousands of small-scale fractures are fully resolved. The simulation study was performed and automated history match was successfully achieved using our extended Ensemble Karman Filter algorithm based on a parameterized description of the fractures that are explicitly represented in DFM. This proposed overall procedure is able to efficiently capture such extreme flow dynamics and achieve significantly better history match results.

One of the most crucial tasks in hydrocarbon field development, it is an optimal wells placement. Simulation-based well placement optimization can be intricate to implement or computationally expensive. In this paper, a novel approach for the reduction of computational challenges by combining population-base optimization algorithm with self-adapt reservoir clusterization method to determine initial well placement position for the similar producing zones is presented. The developed methodology supported initial well placement location and allowed to shrink search space area. As a result, the computational time was decreased by 18% for particle swarm optimization and by 21% for genetic algorithm. Additionally, the project profitability was increased by 0.24% in case of genetic algorithm utilization and 0.59% for particle swarm optimization, what confirms the necessity for precise well placement localization. The average convergence factor for the employed algorithms increased from 18.43% to 60.78% for genetic algorithm and from 41.71% to 46.96% for particle swarm algorithm. An additional advantage of the developed clustering method is a notable reduction in time to reach high solution diversity in particle swarm algorithm. Increasing SOM training time for the large data set is negligible in comparison with full reservoir simulation run. The proposed methodology is based on the typical numerical model without requirement of additional dataset or streamline and can be easily transferred from field to field. The power and the workflow utility are demonstrated by the results of significant improvement for the algorithm's convergence rate and time.

Characterization of rock properties in shale gas reservoirs is vitally important for production forecasting and reserve estimation of natural gas in an efficiently and economically viable fashion. Because of nano-scale pore spaces in organic-rich shale formations, the mechanisms of gas transport in shales are far more complex than those in conventional reservoirs such as sandstone formations. Numerical characterization of shale permeability on multiscale digital rocks has become a powerful tool that greatly complements to lab measurements by combing advanced imaging techniques with numerical simulations. One of the key challenges in unconventional reservoir simulation is how to preserve fine-scale information in coarse-scale reservoir simulation for reliable production forecasting and reserve estimation. Accurate prediction of shale permeability using numerical tools requires well understanding of transport mechanisms at the nano-scale, as well as the upscaling from nano-scale to larger scale simulations. In this work, we present the coupling of MD with LBM on multiple-scale digital rocks, and we develop an upscaling workflow that integrates simulations at nanometer-scale, micrometer-scale, and centimeter-scale. The present approach allows calculating macro-scale transport properties with minimum amount of loss of critical nano/micro-scale information.

Reservoir simulations for petroleum fields and seismic imaging are known as the most demanding workloads for high-performance computing (HPC) in the oil and gas (O&G) industry. The optimization of the simulator numerical parameters plays a vital role as it could save considerable computational efforts. State-of-the-art optimization techniques are based on running numerous simulations, specific for that purpose, to find good parameter candidates. However, using such an approach is highly costly in terms of time and computing resources. This work presents TunaOil, a new methodology to enhance the search for optimal numerical parameters of reservoir flow simulations using a performance model. In the O&G industry, it is common to use ensembles of models in different workflows to reduce the uncertainty associated with forecasting O&G production. We leverage the runs of those ensembles in such workflows to extract information from each simulation and optimize the numerical parameters in their subsequent runs. To validate the methodology, we implemented it in a history matching (HM) process that uses a Kalman filter algorithm to adjust an ensemble of reservoir models to match the observed data from the real field. We mine past execution logs from many simulations with different numerical configurations and build a machine learning model based on extracted features from the data. These features include properties of the reservoir models themselves, such as the number of active cells, to statistics of the simulation's behavior, such as the number of iterations of the linear solver. A sampling technique is used to query the oracle to find the numerical parameters that can reduce the elapsed time without significantly impacting the quality of the results. Our experiments show that the predictions can improve the overall HM workflow runtime on average by 31%., 21 pages, 9 figures. Preprint submitted to Journal of Computational Science

Unlike sedimentary formations, flood basalts have the potential for relatively rapid mineral trapping when used as an injection target for CO2 storage. While CO2 storage in basalt and its underlying geochemistry have been studied in various ways, including two successful small-scale pilot projects, there are still open questions surrounding the viability of large-scale CO2 storage in basalt, including how the properties of the target formation will be altered after decades of geochemical activity. Field-scale numerical models can play a part in answering these questions. In this work, we present an overview and initial results of our recent development of a flexible, computationally efficient reactive transport model for CO2 mineral trapping in basalt (Postma et al., 2021). The model combines a fully customizable geochemistry solver with a vertically integrated description of two-phase flow in porous media. It provides a platform for extensive field-scale numerical modeling studies of large-scale CO2 storage in basalt, which in turn can help address some of the current barriers to its implementation in the field.

This paper summarizes a reservoir simulation study to evaluate the potential storage of 675 million metric tons of CO2 over 30 years at the Project ECO2S storage site—a 12,000-hectare storage complex adjacent to Mississippi Power Company’s (MPC) Plant Ratcliffe facility in Kemper County, Mississippi, USA. The project team studied the storage capacity of the target formations, estimated the CO2 plume size, performed a sensitivity analysis to examine the influence of reservoir and fluid properties, and tested the impact of active plume management—a process that includes extracting water from down-dip water production wells and re-injecting it through up-dip water injection wells within the storage formation—on CO2 plume migration and its extent. The ECO2S site appears to be capable of storing captured CO2 emissions from multiple Southern Company operated power sources, which together emit 22.5 million metric tons per year (675 million metric tons over 30 years). To investigate field development strategies for large volume CO2 injection and storage at ECO2S, the project team developed a base model using the latest geological interpretation. Thirty years of CO2 injection is simulated through seven injection pads with each pad hosting three injection wells, positioned in the center of the potential storage site, followed by 30 years of CO2 plume monitoring. The simulation results show that the 675 million metric tons of CO2 can be injected into the storage formations, safely and securely. The largest CO2 plume, which occurs in the shallowest reservoir, covers a 202-square kilometer area. Active plume management shows a small impact on controlling the plume size and its migration due to extremely high vertical permeability minimizing the impact of the water curtain. Project ECO2S is part of the CarbonSAFE Program and is financially supported by the USDOE-NETL and Mississippi Power Company. The project is managed by the Southern States Energy Board. Technical Support is provided by Southern Company Research and Development.

CO2 injection into geological reservoirs is considered as a promising technology to improve oil recovery from oil reservoirs and to reduce greenhouse gas emissions. However, due to the density difference between the injected CO2 and formation brine, the injected CO2 tends to move vertically towards the surface. The risk of this vertical CO2 movement can be prevented by four different trapping mechanisms (i.e. structural, residual, dissolution, and mineral trapping). From the dissolution of CO2 in the aquifer brine, carbonic acid will be formed. Then, this carbonic acid will be reacted with rock minerals and resulted in mineral dissolution and precipitation. However, the effect of these mineral interactions on the porosity-permeability evolution during the CO2 storage process in the sandstone reservoir has not been addressed effectively. Thus, here, we developed a 3D reservoir simulation model to investigate the effect of mineral interactions on the reservoir porosity and permeability during CO2 injection and storage processes in a sandstone reservoir. The multicomponent, chemically reactive, non-isothermal and multiphase flow numerical simulation program TOUGHREACT has been used. The model length was 1000 m, model width was 1000 m and the model thickness was 1000 m (ranging from top depth of 1000 m and bottom depth of 2000 m) with a regularly spaced grid of 15 × 15 × 48 grid (10800 gridblocks). The developed reservoir simulation model consists of two main regions which are reservoir rock region (sandstone) and cap rock region (shale). The simulated sandstone formation consists of quartz, kaolinite, chlorite, and illite. Our results show that CO2 injection leads to significant mineral reactionس (dissolution and precipitation) in the sandstone reservoir. Furthermore, the results indicate that these mineral reactions lead to increase in the sandstone porosity and permeability during the storage period. Thus, we conclude that the mineral reactions (dissolution and precipitation) due to CO2 injection in the sandstone reservoir affect the sandstone porosity and permeability, and hence, affect the CO2 geological storage capacity.

A preliminary study for Carbon Capture Utilization and Storage (CCUS) pilot project in an East Java oil and gas field Indonesia has been conducted. CCUS projects have dual purposes: providing a means for increasing production in declined oil fields and reducing greenhouse gas emissions from oil and gas sector by injecting the separated CO2 into the declined oil and gas reservoir. CCUS will be attractive in Indonesia since it could offer additional income for the country from the incremental oil and gas productions and the implementation could use the existing regulations that valid for oil and gas sector. The study of a CCUS pilot project plan has been conducted in order to make sure that the reservoir is suitable for CO2 EOR storage. The CCUS pilot project plan is situated in an oil onshore field in East Java province, Indonesia, which was discovered in 2001. It is situated in the Tuban block, and has nearly 308 million STB of oil in place and more than 100 million barrels of oil in cumulative production. The chosen oil field for has been in production decline for several years and yet the efforts to increase recovery, such as water injection, have been ongoing. Suitability for a CO2-EOR operation is dependent on the petrophysical properties of the reservoir, such as porosity, permeability, and fluid saturation, as well as in-situ reservoir fluid properties such as oil density and viscosity. Reservoir depth is also a key parameter in making a decision as it will impact the miscibility and interaction between CO2 and oil phases. This CO2 EOR pilot project consists of a total of five wells – four production wells at the four corners of a square with an injection well in the middle. The preliminary design for a pilot scale is based on the available CO2 from the field itself, which currently produces 4.4 million SCF (240 tones) of CO2 per day. This pilot-scale test is aimed at examining the performance and viability of a gravity stable CO2 flood. The proposed CO2 injection volumes at the pilot scale are 5 million SCFD respectively, which are estimated to correspond to a production increase of 400 BOPD. For a gravity (gas cap) drive EOR system, the gas (in this case CO2) will be injected into the gas cap above the producing zone. This will help in driving the oil down to the production zones and into the production wells. When injecting into the gas cap, the wellbore integrity in the gas zone and just above the gas zone in the sealing layer must be evaluated. This is to ensure that the CO2 does not escape up the wellbore outside the casing and enter a higher layer. It is essential to include well integrity in the baseline monitoring program to evaluate periodic changes in the well integrity with injection. Monitoring is crucial for the success of a subsurface CO2 injection operation. CO2 injection monitoring is used to verify and compare the injection behaviour with reservoir simulation predictions as well as monitor for potential CO2 leakage through faults or wellbore and avoid any CO2 migration to and accumulation at the surface.