Matlab Reservoir Simulation Toolbox Research Articles

Characterization of Low-Frequency Distributed Acoustic Sensing Signals in Hydraulic Fracturing Stimulation - A Coupled Flow-Geomechanical Simulation Approach

Low-frequency distributed acoustic sensing (LF-DAS) is one of the promising diagnostic techniques for detecting and characterizing hydraulic fractures. LF-DAS signals can capture fracture hits and the strain field around the hydraulic fracture. However, the interpretation of field LF-DAS data can be challenging due to the complexity of the underground conditions. This study develops a fracture propagation model to simulate the hydraulic fracturing process. The modelling results are analyzed to examine patterns and trends observed in interpreting field LF-DAS data.The fracture propagation model, coupled with the flow and geomechanical computations, is implemented in the MATLAB Reservoir Simulation Toolbox (MRST). The flow and geomechanical calculations are discretized by the finite volume and the virtual element methods, respectively. The hydraulic fracture is set to propagate along a prescribed path with a specific propagation or activation criterion. The accuracy of our model is validated against the KGD analytical solutions for the leak-off-viscosity, storage-viscosity and leak-off-toughness dominated regimes.The simulated stress and strain features are consistent with those interpreted from field LF-DAS signals. Several case studies and sensitivity analyses demonstrate the approach's utility and examine fracture interference, closure, and stress shadowing effects. The modelling work facilitates interpreting field measurement data by investigating characteristics of fracture hits from adjacent wells. The modelling method provides insights into fracture interference and its implications on optimal designs during hydraulic fracturing stimulation.

Upscaling relative permeability and capillary pressure from digital core analysis in Otway formation: Considering the order and size effects of facies

Digital Core Analysis (DCA) has emerged as a crucial instrument in reservoir characterization in recent times. With the advent of high-resolution micro-CT imaging, it is now possible to visualize the three-dimensional microstructures of in-situ pores and flow patterns within rocks. DCA offers several notable benefits over traditional techniques, such as a higher density of measurements, faster processing times, and the preservation of rock samples. It also demonstrates considerable flexibility with challenging core conditions and can derive numerous parameters from each individual sample. The objective of this work is to utilise DCA data from Otway formation to enhance reservoir characterisation and CO2 plume forecast. However, a critical challenge is that these data are obtained at a micro-scale, necessitating an upscaling of DCA properties from the micro-scale to core scale, and subsequently to the site and field scale, for compatibility with reservoir simulation and field studies. This study proposes an implicit and iterative method to upscale DCA properties and explore the impact of facies order and size on the upscaling process of relative permeability and capillary pressure. This method is implemented in an open-source simulator known as the Matlab Reservoir Simulation Toolbox (MRST). The findings indicate that relative permeability and capillary pressure outcomes from upscaling are influenced by order and portion of facies. This highlights the importance of considering both the size and arrangement of facies during the upscaling process, given their potential impact on fluid dynamics and the accuracy of reservoir simulation results.

Generalized functionals for qualification of geological carbon storage injection sites

Many nations have pledged to reach carbon neutrality by 2050. Embarking on the decarbonization journey, they posited geological carbon storage (GCS) as a pivotal technology within the carbon capture, utilization, and storage (CCUS) framework. The CCUS chain operates to reduce “hard-to-abate” emissions at key sectors by capturing carbon dioxide (CO2), reusing it, transporting it, or disposing of it via injection into underground geological formations for permanent storage. Despite the global success of GCS ventures, mainly driven by the oil and gas industry, GCS initiatives are still in their early stages in several developing countries. In Brazil, for instance, a full setup covering precise storage capacity databases, potential CCUS clusters, national regulatory structure, and auxiliary computer-aided engineering is underway. Intended to push the frontier in the latter subject, this paper introduces mathematical models for qualifying underground CO2 storage sites. Our research explores a family of multivariate functionals endowed with underlying reservoir features and distinct weighting functions, thus envisioning two primary objectives. Firstly, it clarifies non-linear interactions between rock and fluid properties using quality indicators. Secondly, it evaluates geographical regions considering structural traps/caprocks settings. Backed by the Matlab Reservoir Simulation Toolbox (MRST) capabilities, the methodology is a subsidiary resource for identifying suitable injection and storage sites. A case study using the UNISIM-I-D model generated dozens of volumetric quality maps that point to unique potential storage sites. Numerical simulation experiments of injection comparing legacy and novel wells reveal storage surpluses improved by up to 50%. The paper seeks to establish foundational knowledge in GCS efficiency for general underground settings. One expects that these outcomes leverage well-repurposing perspectives and stimulate field appraisal actions to scale up GCS projects both in Brazil and worldwide.

Developing a numerical model for microbial methanation in a depleted hydrocarbon reservoir

Biological methanation is a promising option for CO2 utilization and energy storage. While the underground condition is not appropriate for a methanation reaction, microorganisms act as a catalyst and make the reaction possible. This study investigates the performance of biological methanation in depleted gas reservoirs using numerical simulation. To do this, a one-dimensional synthetic homogeneous depleted gas reservoir is modeled with the two-phase flow comprising components H2, CO2, CH4, and H2O. Then, the simultaneous injection of CO2 and H2 into the reservoir is numerically simulated to evaluate the methane production rate in MATLAB Reservoir Simulation Toolbox (MRST) open-source software. Long-term results show propagating composition waves and pressure profiles. Sensitivity analysis reveals that methane production is positively correlated with the initial reservoir pressure and the number of methanogenic microorganisms, but negatively correlated with the temperature and the bacterial decay rate. The bacterial growth rate has an insignificant effect on methane production in this model. The bacterial population is the most critical parameter, as 1e7 methanogenic microorganisms per cubic meter of aqueous phase can produce 96% pure methane after 12 years. Overall, the work demonstrates harnessing in-situ bio-reactions to utilize CO2 and recover depleted gas reservoirs.

Compositional Simulation for Carbon Storage in Porous Media Using an Electrolyte Association Equation of State

Summary We present a new algorithm based on automatic differentiation that enables precise computation of the derivatives of the Z-factor, facilitating the utilization of Newton’s method or coupling with a robust flow solver. Leveraging a free open-source code [MATLAB Reservoir Simulation Toolbox (MRST)], we develop an electrolyte cubic plus association (e-CPA) equation of state (EoS) model to accurately represent the injection of carbon dioxide (CO2) in brine. By integrating flow and thermodynamics, we construct an advanced compositional simulator using MRST’s object-oriented, automatic differentiation framework and the newly developed e-CPA EoS model. This simulator offers flexibility through both overall-composition and natural-variable formulations, achieved by selecting different primary variables. The Péneloux volume translation technique is employed to modify the EoS model’s volume, ensuring accurate density calculation for the mixture. Additionally, we introduce a viscosity model, e-CPA-FV, which accurately predicts the viscosity of carbon capture and storage (CCS) fluids, surpassing the accuracy of the traditional Lohrenz-Bray-Clark (LBC) model. Our simulator demonstrates superior performance in predicting CO2-brine systems compared with the standard formulation based on the Peng-Robinson (PR) EoS and can handle brine with various salts. The self-contained source code necessary to reproduce all examples is available on the open-access Zenodo digital repository (doi: 10.5281/zenodo.10691505).

Development of 3D flow diagnostic numerical simulator and rock property modelling for a homogeneous faulted reservoir

Research has shown that faults, especially sealing faults, have become a barrier to flow. Flow diagnostics, on the other hand, are straightforward and controlled numerical flow experiments that are performed to examine a reservoir model, build links and offer rudimentary volume estimates as well as to quickly produce a qualitative representation of the reservoir’s flow patterns. To evaluate, assess, and validate reservoir models and production scenarios, the ’diagnostics’ module in the Matlab Reservoir Simulation Toolbox (MRST) provides a computationally less expensive alternative to running fully featured multiphase simulations. This is done to determine qualitatively regions for well placement to maximize hydrocarbon recovery. Monitoring flow fields, timelines, and tracers—neutral particles in the fluid that flow with the fluid—are all part of flow diagnostics. These techniques are used to determine volumetric communication between a pair of injector-producer wells, as well as flow patterns between injection-production wells and the arrival time between them. To create the grid, the simulation schedule, the wells, upscaling, arrival time computation, and flow diagnostics (drainage and sweep regions) were all done using the Matlab reservoir simulation toolbox (MRST) package by “Makemodel 3” on the data obtained from “SPE 10th comparative solution project” on the MRST package. This was done for a homogeneous anisotropic faulted porous medium. The simulation runs for about 473,739 milliseconds on a fine grid having 20040 active cells while in the coarse model with faster computational time of about 200 seconds, 112 milliseconds. At the early stages of the reservoir bottom-hole pressure for injector I1(about 7000psia) and three producers P1, P2 and P3 remains constant over time (about 3600psia) thanks to pressure support by I1. The extent of residence time after 10 years for the fine, coarse and more coarser model is that fluid element find it easier to transverse through the fault line from I1 to P1, P2 then P3 which takes lesser time than crossing across two intersecting faults, It can also be seen that the sweep efficiency of the fine grid is more effective than the coarse grid. Finally, it has been seen clearly that the fine grid model gives more accurate details but slower computational time while the coarse model which is less accurate but with faster computational time.

A multi-mechanism numerical simulation model for CO2-EOR and storage in fractured shale oil reservoirs

Under the policy background and advocacy of carbon capture, utilization, and storage (CCUS), CO2-EOR has become a promising direction in the shale oil reservoir industry. The multi-scale pore structure distribution and fracture structure lead to complex multiphase flow, comprehensively considering multiple mechanisms is crucial for development and CO2 storage in fractured shale reservoirs. In this paper, a multi-mechanism coupled model is developed by MATLAB. Compared to the traditional Eclipse 300 and MATLAB Reservoir Simulation Toolbox (MRST), this model considers the impact of pore structure on fluid phase behavior by the modified Peng–Robinson equation of state (PR-EOS), and the effect simultaneously radiate to Maxwell–Stefan (M–S) diffusion, stress sensitivity, the nano-confinement (N-C) effect. Moreover, a modified embedded discrete fracture model (EDFM) is used to model the complex fractures, which optimizes connection types and half-transmissibility calculation approaches between non-neighboring connections (NNCs). The full implicit equation adopts the finite volume method (FVM) and Newton–Raphson iteration for discretization and solution. The model verification with the Eclipse 300 and MRST is satisfactory. The results show that the interaction between the mechanisms significantly affects the production performance and storage characteristics. The effect of molecular diffusion may be overestimated in oil-dominated (liquid-dominated) shale reservoirs. The well spacing and injection gas rate are the most crucial factors affecting the production by sensitivity analysis. Moreover, the potential gas invasion risk is mentioned. This model provides a reliable theoretical basis for CO2-EOR and sequestration in shale oil reservoirs.

A numerical pressure transient model of fractured well with complex fractures of tight gas reservoirs considering gas-water two phase by EDFM

Tight gas reservoirs considering gas-water two phase is common and show obvious permeability stress sensitivity and non-Darcy seepage characteristic. However, conventional analytical and semi-analytical solving method cannot simulate wellbore pressure response of tight gas reservoirs considering gas-water two phase. Numerical model can overcome the disadvantage of analytical and semi-analytical method and achieve wellbore pressure response simulation of fractured well with complex fracture. Therefore, a gas-water two phase mathematical model of the fractured well is established and solved by embedded discrete-fracture method (EDFM) and finite volume method. Transmissibility corrections is improved on the basis of the framework of Matlab Reservoir Simulation Toolbox (MRST). Result shows that the seven flow regimes can be found according to the pressure drop derivative curves characteristic. When permeability stress sensitivity and non-Darcy is considered, pressure and derivative curve of middle-late stage shows obvious ‘upwarp’ and non-Darcy make reservoirs pressure uneven distribution. Induced fractures parameters have obvious influence on pressure and derivative curves during early and middle flow regime. In addition, fracture intersection and neighbor well production style has obvious influence on pressure curve.

New Insights into Hybrid Low-Salinity Polymer Flooding through a Coupled Geochemical-Based Modeling Approach

Summary Low-salinity polymer (LSP) flooding is a synergic emergent enhanced oil recovery (EOR) technique. Previous laboratory experiments showed noticeable improvements in displacement efficiency, polymer rheology, injectivity, and viscoelasticity. Nevertheless, when it comes to modeling LSP flooding, it is still challenging to develop a mechanistic predictive model that captures polymer-brine-rock (PBR) interactions. Therefore, this study uses a coupled MATLAB reservoir simulation toolbox (MRST)-IPhreeqc simulator to investigate the effect of water chemistry on PBR interactions during LSP flooding through varying overall salinity and the concentrations of divalent and monovalent ions. For describing the related geochemistry, the presence of polymer in the aqueous phase was considered by introducing novel solution species (Poly) to the Phreeqc database. The developed model’s parameters were validated and history matched with experimental data reported in the literature. Moreover, different injection schemes were analyzed, including low-salinity (LS) water, LSP injection (1 × LSP), and 5-times spiked LSP injection (5 × LSP) with their related effects on polymer viscosity. Results showed that polymer viscosity during LSP flooding is affected directly by Ca2+ and Mg2+ and indirectly by SO42− owing to PBR interactions on a dolomite rock-forming mineral. Monovalent ions (viz. Na+ and K+) have minor effects on polymer viscosity. Ca2+ and Mg2+ ions discharged from dolomite dissolution create polymer complexes (acrylic acid, C3H4O2) to reduce polymer viscosity significantly. The increased SO42− concentration in the injected LSP solution affects the interactions between the polymer and positively charged aqueous species, leading to minimized polymer viscosity loss. For LSP flood derisking measures, the cation’s effect was related to the charge ratio (CR). Thus, it is key to obtain an optimal CR where viscosity loss is minimal. This paper is among the few to detail the mechanistic geochemical modeling of the LSP flooding technique. The validated MRST-IPhreeqc simulator evaluates the previously overlooked effects of water chemistry on polymer viscosity during the LSP process. Using this coupled simulator, several other geochemical reactions and parameters can be assessed, including rock and injected-water compositions, injection schemes, and other polymer characteristics.

Multiphase flow behavior of diesel in bog, fen, and swamp peats

Hydrocarbon fate and transport in various categories of peatlands is complicated by the botanical origin, and thus variations in the hydraulic structures and surface chemistry of its peat soils. There has been no systematic evaluation of the role of different peat types on hydrocarbon migration. Thus, two-phase, and three-phase flow experiments were performed for living and partially decomposed peat cores from bog, fen, and swamp peatlands. Numerical simulations of water drainage were performed using HYDRUS-1D, diesel-water and diesel-water-air flow using MATLAB Reservoir Simulation Toolbox (MRST). Five water table (WT) fluctuations were imposed to explore its potential to reduce residual diesel saturation in peat columns. Our results demonstrate a good match of the relative water permeability (krw) – saturation (S) relations estimated using the unsaturated hydraulic conductivity-S relation derived from HYDRUS-1D modeling of two-phase flow, and krw – S from MRST for three-phase flow, for all tested peat columns. Thus, we recommended using two-phase system based krw – S predictions if multiphase data are unavailable for peatland sites' spill management plans. We found the discharge of water and diesel both increase with increasing hydraulic conductivity, while residual water and diesel were within the range of 0.42–0.52 and of 0.04–0.11, respectively. High diesel discharge rates suggest that quick spill-response is required to manage its spread in peatlands. Up to 29% of residual diesel saturation was yielded by the five WT fluctuations, and thus we strongly recommend WT manipulation as a first step towards diesel decontamination progression in peatlands.

Modeling reactive multi-component multi-phase flow for Geological Carbon Sequestration (GCS) with Matlab

We present a reactive multi-component multi-phase flow program for simulating Geological Carbon Sequestration (GCS), an approach that reduces carbon emissions by storing CO2 in deep subsurface formations. The program, called MRST_CO2, is implemented in the library Matlab Reservoir Simulation Toolbox (MRST). It can simulate multi-phase flow and transport of species undergoing chemical reactions and mass exchanges among gas, liquid and solid phases. Equations for flow, mass transport and chemical reactions are solved with a sequential iteration approach. The program was tested with a 1D benchmark. It has also been applied to heterogeneous 2D and 3D cases with a structured or unstructured grid.

Numerical simulation of fractured horizontal well considering threshold pressure gradient, non‐Darcy flow, and stress sensitivity

AbstractConventional numerical simulators cannot accurately predict the production of fractured horizontal wells in tight sandstone gas reservoirs due to the threshold pressure gradient (TPG) and stress sensitivity. Additionally, non‐Darcy flow in hydraulic fractures further complicates the prediction. Therefore, a numerical simulation model was developed to accurately predict the production of fractured horizontal wells that considers the TPG, non‐Darcy flow, and stress sensitivity using the embedded discrete fracture model. The model was solved using the automatic differentiation framework of MATLAB Reservoir Simulation Toolbox. The numerical simulation demonstrated that the Darcy flow model provided an optimistic prediction of the productivity of fractured gas wells in tight reservoirs. The TPG, non‐Darcy flow, and stress‐sensitive phenomena reduced the productivity of gas wells to varying degrees and severely affected the production of gas wells. The TPG effect, non‐Darcy effect, and stress sensitivity phenomenon reduced the gas well production by 1.66%, 12.9%, and 42.42%, respectively, compared with that of the Darcy flow. In contrast to the conventional Darcy flow model, the model established in this study can accurately predict the production of gas wells in production history matching.

Analysis of fracture interference – Coupling of flow and geomechanical computations with discrete fracture modeling using MRST

A new discrete fracture model (DFM) is implemented in the MATLAB Reservoir Simulation Toolbox (MRST) – an open-source reservoir simulation software – to couple flow and geomechanical computations. Unstructured meshing is used to discretize the gridding domain. The matrix-to-matrix, fracture-to-fracture, and fracture-to-matrix fluxes are computed explicitly in the computational domain following the control volume formulation. The flow calculations and the geomechanical computations are solved sequentially: the governing equations for poroelasticity are incorporated, and the fixed stress splitting coupling methodology is employed. The results are compared with an uncoupled model, where the geomechanical effects are ignored.Several case studies demonstrate the utility of the proposed coupling strategy for analyzing production performance and stress evolution in hydraulically fracturing formations. This model considers the effects of poroelasticity and stress or strain variation in the fractured domains, and factors influencing the behaviour of fracture interference are examined. Finally, an analysis of the computational costs is also presented.This simulation approach can more accurately capture the dynamic behaviour of stress evolution and fracture interference in hydraulically fractured wells. This flexible framework can incorporate more functional modules, including fracture propagation, in future works. The results illustrate the significance of incorporating geomechanical effects in the flow simulation process. Insights pertinent to the operational strategies are also highlighted based on the simulation results.

An Extended Unified Viscoelastic Model for Predicting Polymer Apparent Viscosity at Different Shear Rates

Summary Polymer flooding is one of the most commonly used chemical enhanced oil recovery (EOR) methods. Conventionally, this technique was believed to improve macroscopic sweep efficiency by sweeping only bypassed oil. Nevertheless, recently it has been found that polymers exhibiting viscoelastic behavior in the porous medium can also improve microscopic displacement efficiency resulting in higher additional oil recovery. Therefore, an accurate prediction of the complex rheological response of polymers in porous media is crucial to obtain a proper estimation of incremental oil to polymer flooding. In this paper, a novel viscoelastic model is proposed to comprehensively analyze the polymer rheological behavior in porous media. This proposed model was developed and validated using 30 coreflooding tests obtained from the literature and further verified against a few existing viscoelastic models. The proposed viscoelastic model is considered an extension of the unified apparent viscosity model provided in the literature and is termed as extended unified viscoelastic model (E-UVM). The main advantage of the proposed model is its ability to capture the polymer mechanical degradation at ultimate shear rates primarily observed near wellbores. Moreover, the fitting parameters used in the model were correlated to rock and polymer properties using machine learning technique, significantly reducing the need for time-consuming coreflooding tests for future polymer screening works. Furthermore, the E-UVM was implemented in MATLAB Reservoir Simulation Toolbox (MRST) and verified against the original shear model existing in the simulator. It is worth mentioning that the irreversible viscosity drop for mechanical degradation regime was captured during implementing our model in the simulator. It was found that implementing the E-UVM in MRST for polymer non-Newtonian behavior might be more practical than the original method. In addition, the comparison between various viscosity models proposed earlier and E-UVM in the reservoir simulator showed that the latter model could yield more reliable oil recovery predictions as the apparent viscosity is modeled properly in the mechanical degradation regime, unlike UVM or Carreau models. This study presents a novel viscoelastic model that is more comprehensive and representative as opposed to other models in the literature. Furthermore, the need to conduct an extensive coreflooding experiment can be reduced by virtue of developed correlations that may be used to estimate model fitting parameters accounting for shear-thickening and mechanical degradation.

A Numerical Multistage Fractured Horizontal Well Model Concerning Hilly-Terrain Well Trajectory in Shale Reservoirs with Natural Fractures

Multistage hydraulic fracturing is one of the most prevalent approaches for shale reservoir development. Due to the complexity of constructing reservoir environments for experiments, numerical simulation is a vital method to study flow behavior under reservoir conditions. In this paper, we propose a numerical model that considers a multistage fractured horizontal well with a hilly-terrain trajectory in a shale reservoir with the presence of natural fractures. The model was constructed based on the MATLAB Reservoir Simulation Toolbox and used the Embedded Discrete Fractured Model (EDFM) to describe the interrelationship between the matrix, fractures, and wellbore. The model was then applied to an actual condensate gas well producing from a shale reservoir, and the effects of reservoir parameters on the simulation data were studied based on this well case. The simulation results were highly consistent with the actual production data, which validates the accuracy of this model and proves its potential for predicting future production trends. We extended the discussion to two examples with extreme well trajectories by reviewing the inflow contribution of each hydraulic fracture with respect to fracture pressure, and the changes in static pressure with time. In conclusion, the proposed model is capable of providing simulation results close to reality and thus guiding field design and operation in the fracturing and drilling process.

Mechanistic modeling of hybrid low salinity polymer flooding: Role of geochemistry

Low salinity polymer (LSP) based enhanced oil recovery (EOR) technique is getting more attention due to its potential of improving both displacement and sweep efficiencies. Modeling LSP flooding is challenging due to the complicated physical processes and the sensitivity of polymers to brine salinity. In this study, a coupled numerical model has been implemented to allow investigating the polymer-brine-rock geochemical interactions associated with LSP flooding along with the flow dynamics. MATLAB Reservoir Simulation Toolbox (MRST) was coupled with the geochemical software IPhreeqc, which is the interface module of Phreeqc (i.e., pH-Redox-Equilibrium in C programming language). The effects of polymer were captured by considering Todd–Longstaff mixing model, inaccessible pore volume, permeability reduction, polymer adsorption as well as salinity and shear rate effects on polymer viscosity. Regarding geochemistry, the presence of polymer in the aqueous phase was considered by adding a new solution specie and related chemical reactions to Phreeqc database files. Thus, allowing for modeling the geochemical interactions related to the presence of polymer. Coupling the two simulators was successfully performed, verified, and validated through several case studies. The coupled MRST–IPhreeqc simulator allows for modeling a wide variety of geochemical reactions including aqueous, mineral precipitation/dissolution, and ion exchange reactions. Capturing these reactions allows for real time tracking of the aqueous phase salinity and its effect on polymer rheological properties. The coupled simulator was verified against Phreeqc for a realistic reactive transport scenario. Furthermore, the coupled simulator was validated through history matching a single-phase LSP coreflood from the literature. This paper provides an insight into the geochemical interactions between partially hydrolyzed polyacrylamide (HPAM) and aqueous solution chemistry (salinity and hardness), and their related effect on polymer viscosity. This work is also considered as a base for future two-phase polymer solution and oil interactions, and their related effect on oil recovery.

Fast Screening Tool for Assessing the Impact of Poro-Mechanics on Fractured Reservoirs Using Dual-Porosity Flow Diagnostics

Summary Accounting for poro-mechanical effects in full-field reservoir simulation studies and uncertainty quantification workflows is still limited, mainly because of their high computational cost. We introduce a new approach that couples hydrodynamics and poro-mechanics with dual-porosity flow diagnostics to analyze how poro-mechanics could affect reservoir dynamics in naturally fractured reservoirs without significantly increasing computational overhead. Our new poro-mechanically informed dual-porosity flow diagnostics account for steady-state and single-phase flow conditions in the fractured medium while the fracture-matrix fluid exchange is approximated using a physics-based transfer rate coefficient, which models two-phase flow using an analytical solution for spontaneous imbibition or gravity drainage. The deformation of the system is described by the dual-porosity poro-elastic theory, which is based on mixture theory and micromechanics to compute the effective stresses and strains of the rock matrix and fractures. The solutions to the fluid flow and rock deformation equations are coupled sequentially. The governing equations for fluid flow are discretized using a finite-volume method with two-point flux-approximation while the governing equations for poro-mechanics are discretized using the virtual element method. The solution of the coupled system considers stress-dependent permeabilities for fractures and matrix. Our framework is implemented in the open-source MATLAB Reservoir Simulation Toolbox (MRST). We present a case study using a fractured carbonate reservoir analog to illustrate the integration of poro-mechanics within the dual-porosity flow diagnostics framework. The extended flow diagnostics calculations enable us to quickly screen how the dynamics in fractured reservoirs (e.g., reservoir connectivity, sweep efficiency, and fracture-matrix transfer rates) are affected by the complex interactions between poro-mechanics and fluid flow where changes in pore pressure and effective stress modify petrophysical properties and hence affect reservoir dynamics. Because of the steady-state nature of the calculations and the effective coupling strategy, these calculations do not incur significant computational overheads. They provide an efficient complement to traditional reservoir simulation and uncertainty quantification workflows because they enable us to assess a broader range of reservoir uncertainties (e.g., geological, petrophysical, and hydromechanical uncertainties). The capability of studying a much broader range of uncertainties allows the comparison and ranking from a large ensemble of reservoir models and select individual candidates for more detailed full-physics reservoir simulation studies without compromising on assessing the range of uncertainties inherent to fractured reservoirs.

Automatic Calibration of a Geomechanical Model from Sparse Data for Estimating Stress in Deep Geological Formations

Summary In this study, we demonstrate geomechanical modeling with fully automatic parameter calibration to estimate the full geomechanical stress fields of a prospective US carbon dioxide (CO2) storage site, based on sparse measurement data. The goal is to compute full stress tensor field estimates (principal stresses and orientations) that are maximally compatible with observations within the constraints of the model assumptions, thereby extending pointwise, incomplete partial stress measurement to a simulated full formation stress field, as well as a rough assessment of the associated error. We use the Perch site, located in Otsego County, Michigan, USA, as our case study. The input data consist of partial stress tensor information inferred from in-situ borehole tests, geophysical well logs, and processing of seismic data. A static earth model (SEM) of the site was developed, and geomechanical simulation functionality of the open-source MATLAB Reservoir Simulation Toolbox (MRST) was used to model the stress field. Adjoint-based nonlinear optimization was used to adjust boundary conditions and material properties to calibrate simulated results of observations. Results were interpreted through a Bayesian framework. The focus of this paper is to demonstrate how the fully automatic calibration procedure works and discuss the results obtained; it does not attempt a detailed analysis of the stress field in the context of the proposed CO2 storage initiatives. Our work is part of a larger effort to noninvasively determine in-situ stresses in deep formations considered for CO2 storage. Guided by previously published research on geomechanical model calibration, our work presents a novel calibration approach supporting a potentially large number of linear or nonlinear calibration parameters to produce results optimally agreeing with available measurements and thus extend partial pointwise estimates to full tensor fields compatible with the physics of the site.

A Double-Scale method for near-well flow in reservoir simulation

Simulation of near-well flow around a single well in reservoirs is normally studied using radial logarithmic grids. A promising method for more complicated, multi-well cases is a combined approach of using a Cartesian and a radial grid. In this paper, a new method of overlapping grids is introduced in which a radial grid is overlapped on a coarse Cartesian grid in the area around a well. Connectivity between the two grids is established using an appropriate boundary condition. Five different algorithms of grids connectivity with internal boundary conditions are presented in which the data are transferred between the grids by interpolation pressure and saturations in each grid. This method is implemented in the open-source Matlab Reservoir Simulation Toolbox (MRST) using the modified black-oil model. The proposed approach is validated by simulation of a reference fine radial grid model on a gas-condensate reservoir. Comparing the results with the reference model indicates that the proposed Double-Scale method using a 21 × 21 coarse Cartesian grid is as accurate as a 1001 × 1001 simple Cartesian fine grid model. Then, a double-layer numerical problem with two production wells was simulated and sensitivity analysis was conducted to investigate the effect of critical condensate saturation and vertical permeability. Finally, the second SPE comparative solution project was simulated to compare the performance of the proposed method with the use of the perpendicular bisector (PEBI) grids around the well. Results showed that the accuracy of the PEBI grid and Double-Scale method are comparable. However, the proposed Double-Scale method is almost 2 times faster in this specific problem. • The new Double-Scale method is implemented in MRST toolbox. • The accuracy of results highly increases by using the Double-Scale method. • This method reduces the CPU time of simulation significantly. • The gravity drainage can be seen by monitoring vertical permeability variation. • The second SPE comparative solution project was simulated by the Double-Scale method.

Digital Image-Based Stress\u2013Permeability Relationships of Rough Fractures Using Numerical Contact Mechanics and Stokes Equation

Flow in fractures is sensitive to their geometrical surface characteristics. The surface can undergo deformation if there is a change in stress. Natural fractures have complex geometries and rough surfaces which complicates the modelling of deformation and fluid flow. In this paper, we present a computational model that takes a digital image of a rough fracture surface and provides a stress–permeability relationship. The model is based on a first-principle contact mechanics approach at the continuum scale. Using this first principle approach, we investigate numerically the effect of fracture surface roughness and shifting of surfaces on the permeability evolution under applied stress and compare the results with laboratory experiments. A mudrock core fracture surface was digitalized using an optical microscope, and 2D cross sections through fracture surface profiles were taken for the modelling. Mechanical deformation is simulated with the contact mechanics based Virtual Element Method solver that we developed within the MATLAB Reservoir Simulation Toolbox platform. The permeability perpendicular to the fracture cross section is determined by solving the Stokes equation using the Finite Volume Method. A source of uncertainty in reproducing laboratory results is that the exact anchoring of the two opposite surfaces is difficult to determine while the stress–permeability relationship is sensitive to the exact positioning. We, therefore, investigate the sensitivity to a mismatch in two scenarios: First, we assess the stress–permeability of a fracture created using two opposing matched surfaces from the rock sample, consequently applying relative shear. Second, we assess the stress–permeability of fractures created by randomly selecting opposing surfaces from that sample. We find that a larger shift leads to a smaller drop in permeability due to applied stress, which is in line with a previous laboratory study. We also find that permeability tends to be higher in fractures with higher roughness within the investigated stress range. Finally, we provide empirical stress–permeability relationships for various relative shears and roughnesses for use in hydro-mechanical studies of fractured geological formations.