Hydro-mechanical coupling is imperative when the stress disturbances induced by production/injection processes affect the reservoir performance. However, the application of coupled hydro-mechanical models in actual fullfield studies is still limited, mainly because of the high computational cost. Despite the existence of simplified coupling strategies (one-way coupling and loose coupling) that reduce the computational cost, numerical simulations remain challenging because of the significant computing time required to simulate coupled processes in complex and heterogeneous reservoir models. With the appropriate extension, flow diagnostics could also be used to screen and assess the impact of hydro-mechanical processes on reservoir performance so as to select a smaller number of models for detailed, and computationally costly, fully coupled hydro-mechanical simulations. We hence present an approach that allows us to extend the existing flow diagnostics to account for geomechanical effects without increasing the computational overhead significantly. Flow diagnostics approximate the dynamic reservoir behaviour in seconds by computing the time of flight and steady-state tracer distributions directly on the reservoir grid. Hence, the extended flow diagnostics simulations complement full-physics simulations for estimating reservoir connectivity, fluid-fronts distributions, fluid displacement efficiency and well allocation factors under geomechanical effect. The acceleration of the proposed hydro-mechanical coupling is achieved by: 1) the representation of the dynamic behaviour through the use of flow diagnostics simulations (Møyner et al., 2014); 2) the formulation of the hydromechanical problem to account for steady-state conditions based on poro-elastic theory (Coussy, 1994, 2004); 3) a sequential stress-flow coupling using stress-dependent permeability as a coupling term. This coupling strategy ensures stability and fast convergence of the hydro-mechanical solution using a stress-fixed split strategy (Kim et al., 2011a, 2011b) and yields a significant reduction of the CPU time. Two cases studies were analysed based on the SPE 10 Model (Christie and Blunt, 2001) in which the effect of a 5-spot injection pattern subjected to a gravity load is studied, and the effect of mechanical heterogeneity is considered. These examples demonstrate the application of the proposed methodology to assess geomechanical impact in highly heterogeneous formations and the importance of not only account for petrophysical heterogeneities when assessing reservoir performance but also for the heterogeneity of mechanical properties as these alter the petrophysical properties when stress-sensitive reservoirs are produced. Geomechanically informed flow diagnostics account for coupled hydro-mechanical effects that can alter the performance of stress-sensitive reservoirs during production.@en

Accounting for poro-mechanical effects in full-field reservoir simulation studies and uncertainty quantification workflows using complex reservoir models is challenging, mainly because of the high computational cost. We hence introduce an alternative approach that couples hydrodynamics through existing flow diagnostics simulations with poro-mechanics to screen the impact of coupled poro-mechanical processes on reservoir performance without significantly increasing computational overheads. In flow diagnostics, time-of-flight distributions and influence regions can be used to characterise the flow field in the reservoir, which depends on the distribution of petrophysical properties that are altered due to production-induced changes in pore pressure and effective stress. These extended flow diagnostics calculations hence enable us to quickly screen how the dynamics in the reservoirs (e.g. reservoir connectivity, displacement efficiency, and well allocation factors) are affected by the complex interactions between poro-mechanics and hydrodynamics. Our poro-mechanically informed flow diagnostics account for steady-state and single-phase flow conditions based on the poro-elastic theory and assume that the reservoir does not contain fractures. Fluid flow and rock deformation calculations are coupled sequentially. The equations are discretised using a finite-volume method with two-point flux-approximation and the virtual element method, respectively. The solution of the coupled system considers stress-dependent permeabilities. Due to the steady-state nature of the calculations and the effective proposed coupling strategy, these calculations remain computationally efficient while providing first-order approximations of the interplay between poro-mechanics and hydrodynamics, as we demonstrate through a series of case studies. The extended flow diagnostic approach hence provides an efficient complement to traditional reservoir simulation and uncertainty quantification workflows and enable us to assess a broader range of reservoir uncertainties.@en

Naturally Fractured Reservoirs (NFR's) have received little attention as potential CO2 storage sites. Two main facts deter from storage projects in fractured reservoirs: (1) CO2 tends to be nonwetting in target formations and capillary forces will keep CO2 in the fractures, which typically have low pore volume; and (2) the high conductivity of the fractures may lead to increased spatial spreading of the CO2 plume. Numerical simulations are a powerful tool to understand the physics behind brine-CO2 flow in NFR's. Dual-porosity models are typically used to simulate multiphase flow in fractured formations. However, existing dual-porosity models are based on crude approximations of the matrix-fracture fluid transfer processes and often fail to capture the dynamics of fluid exchange accurately. Therefore, more accurate transfer functions are needed in order to evaluate the CO2 transfer to the matrix. This work presents an assessment of CO2 storage potential in NFR's using dual-porosity models. We investigate the impact of a system of fractures on storage in a saline aquifer, by analyzing the time scales of brine drainage by CO2 in the matrix blocks and the maximum CO2 that can be stored in the rock matrix. A new model to estimate drainage time scales is developed and used in a transfer function for dual-porosity simulations. We then analyze how injection rates should be limited in order to avoid early spill of CO2 (lost control of the plume) on a conceptual anticline model. Numerical simulations on the anticline show that naturally fractured reservoirs may be used to store CO2.@en

Spontaneous countercurrent imbibition into a finite porous medium is an important physical mechanism for many applications, included but not limited to irrigation, CO2 storage, and oil recovery. Symmetry considerations that are often valid in fractured porous media allow us to study the process in a one-dimensional domain. In 1-D, for incompressible fluids and homogeneous rocks, the onset of imbibition can be captured by self-similar solutions and the imbibed volume scales with √t. At later times, the imbibition rate decreases and the finite size of the medium has to be taken into account. This requires numerical solutions. Here we present a new approach to approximate the whole imbibition process semianalytically. The onset is captured by a semianalytical solution. We also provide an a priori estimate of the time until which the imbibed volume scales with √t. This time is significantly longer than the time it takes until the imbibition front reaches the model boundary. The remainder of the imbibition process is obtained from a self-similarity solution. We test our approach against numerical solutions that employ parametrizations relevant for oil recovery and CO2 sequestration. We show that this concept improves common first-order approaches that heavily underestimate early-time behavior and note that it can be readily included into dual-porosity models.@en

Relative permeabilities show significant dependence on the saturation path during CO2 enhanced oil recovery (EOR) and storage. This dependence (or hysteresis) is particularly important for water-alternating-gas (WAG) injection, a successful CO2 EOR and storage method for clastic and carbonate reservoirs. WAG injection is characterized by an alternating sequence of drainage and imbibition cycles. Hysteresis is hence common and results in residual trapping of the CO2 phase, which impacts the volume of CO2 stored and the incremental oil recovery. The competition between hysteresis and geological heterogeneity during CO2 EOR and storage, particularly in carbonate reservoirs, is not yet fully understood.In this study, we use a high-resolution simulation model of a Jurassic Carbonate ramp, which is an analogue for the highly prolific reservoirs of the Arab D formation in Qatar, to investigate the impact of hysteresis during CO2 EOR and storage in heterogeneous carbonate formations. We then compare the impact of residual trapping (due to hysteresis) on recovery to the impact of heterogeneity in wettability and reservoir structure. End-member wettability scenarios and multiple wettability distribution approaches are tested, while, effective fracture permeabilities are computed using discrete fracture networks (DFN), ranging from sparsely distributed background fractures to fracture networks where intensity varies with proximity to faults.The results enable us to analyze the efficiency of oil recovery and CO2 sequestration in carbonate reservoirs by comparing the impact of physical displacement processes (e.g., imbibition, drainage, residual trapping) and heterogeneous rock properties (e.g., wettability, faults, fractures, layering) that are typical in carbonate reservoirs. We show that although the fracture network properties have the greatest impact on the fluid flow, the effect of wettability and hysteresis is nontrivial. Our results emphasize the need for wettability to be accurately measured and appropriately distributed in a reservoir simulation model. Similarly, our results indicate that hysteresis effects in cyclic displacement processes must be accounted for in detail to ensure that simulation models give accurate predictions.@en

Fractures can have variable effects on fluid flow in a porous rock. Moderately conductive fractures may enhance the rock's overall effective permeability, while highly conductive fractures may completely dominate fluid transport. Fluid flow modeling is important to quantify the impact of fractures on the performance of a reservoir. However, simulating fluid flow is computationally intensive due to the heterogeneities introduced by the fracture network. In this work, complex fracture patterns are simplified using hybrid implicit-explicit representations to yield a computationally tractable model. Hybrid modeling requires the selection of a partitioning size to group fractures by size. Small fractures are upscaled with the rock matrix; large fractures are explicitly represented. Our study shows that, given a naturally fractured reservoir, an upper limit exists for the partitioning size and that this threshold partitioning size can be determined without trial and error. Using artificial and realistic fracture patterns, we created hybrid models using different partitioning sizes and subjected them to pressure drawdowns. Simulated production rates were compared against reference results obtained from simulations on the original fracture patterns. Beyond a threshold partitioning size unique to each fracture pattern, hybrid model results deviate significantly from reference solutions. The threshold is identified from the relationship between upscaled permeabilities and partitioning sizes and corresponds to the point where the effective permeability of small fractures begins to increase rapidly. The permeability-size relationship is obtained using numerical flow-based upscaling. For uniformly distributed fractures with no abutment relationships, the effective medium theory is shown to generate accurate permeability-size relationships.@en

Flow modelling challenges in fractured reservoirs have led to the development of many simulation methods. It is often unclear which method should be employed. High-resolution discrete fracture and matrix (DFM) studies on small-scale representative models allow us to identify dominant physical processes influencing flow. We propose a workflow that utilizes DFM studies to characterize subsurface flow dynamics. The improved understanding facilitates the selection of an appropriate method for large-scale simulations. Validation of the workflow was performed via application on a gas reservoir represented using an embedded discrete fracture model, followed by the comparison of results obtained from hybrid and dual-porosity representations against fully explicit simulations. The comparisons ascertain that the high-resolution small-scale DFM studies lead to a more accurate upscaled model for full field simulations. Additionally, we find that hybrid implicit–explicit representations of fractures generally outperform pure continuum-based models.@en

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.@en

Water-Alternating-Gas (WAG) injection could be an efficient way to improve recovery factors in fractured carbonate reservoirs. However, there are many geological uncertainties and engineering designs that influence the efficiency of the WAG process. In this study, we explore the challenges of combining polynomial chaos expansion (PCE)-based proxy modelling with multi-objective optimization using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to optimize the design of a WAG injection method under pseudo-miscible conditions for a fractured carbonate reservoir that is an analogue for the Arab D formation. A range of realistic geological uncertainties and engineering parameters are considered. Our results show that the order of the PCE-based proxy model needs to be carefully established for each geological scenario in a fractured reservoir. Likewise, the iterative enrichment of the proxy-model is non-monotonic, and each geological scenario requires its own evaluation of the proxy model during iterative enrichment. The convergence of the proxy is independent of the degree at which the reservoir is fractured but depends on the dimensions of the parameter space. The more engineering controls are considered, the more iterations are needed. Without a continuous and careful evaluation of the proxy model, the resulting simulation estimates may deviate significantly from full-physics simulations.@en

Fractures are often implicitly represented in models used to simulate flow in fractured porous media. This simplification results in smaller models that are computationally tractable. As computational power continues to increase, there has been growing interest in simulation methods that explicitly represent fractures. The embedded discrete fracture model (EDFM) is one such method. In EDFM, fracture and matrix grids are constructed independently. The grids are then coupled to each other via source/sink relations. This modeling approach makes EDFM versatile and easy to use. EDFM has been shown to be able to handle complex fracture networks. The grid construction process is also straightforward and requires minimal fine-tuning. Within academia and industry, EDFM has been used to study geothermal energy production, unconventional gas production, multiphase flow in fractured reservoirs, and enhanced oil recovery processes. In this chapter, the mathematical formulation of EDFM is introduced. We then demonstrate the usage of EDFM via three examples. The first example involves a simple fracture network containing only three fractures. The second involves upscaling a stochastically generated fracture network. Finally, a well test will be simulated in a publicly available data set sourced from the Jandaira carbonate formation in Brazil.@en

Simulation of multiphase flow in fractured reservoirs still poses a challenge due to the different timescales of fluid flow in fractures and matrix. Common approaches to modeling fractures in reservoir simulators include the discrete fracture and matrix (DFM) method, where the fractures are explicitly represented as lower-dimensional elements in the computational mesh, and multicontinuum approaches (e.g., dual-porosity and dual-permeability models) where the behavior of the fractures and matrix are integrated and treated as distinct continua. The latter requires models (bespoke “transfer functions”) that upscale the multiphase transfer between fracture and matrix. There are several formulations for transfer functions available in the literature, and they are often application dependent. Here, we propose a unified framework for simulation of flow in fractured media. The framework makes no distinction between dual-continuum and DFM methods, treating fractures and one or more matrix domains as flowing domains and virtual domains. Transfer functions are reinterpreted as fluxes between cells of different domains. This enables us to create an abstraction that encompasses both methods and makes it easy to build hybridized models including different regions with different matrix/fracture interaction concepts. We present a series of cases to illustrate the main differences between both modeling approaches and the benefit of a flexible implementation that enables the development of a fit-for-purpose simulator for fractured reservoirs.@en

Naturally fractured reservoirs are currently being considered as potential candidates for geological storage of CO2. Simulations of fractured reservoirs are notoriously challenging. Dual-porosity models are a cost-effective way of representing fractured reservoirs whose fundamental ingredient are transfer functions that represent fracture-matrix interaction in an up-scaled manner. In order to develop accurate transfer functions, it is essential to capture the underlying physics of the fluid transfer. Material properties and dominant processes in CO2 storage differ from the ones in conventional production environments. In this contribution we develop a novel transfer function that accounts for these differences. We first analyse the simplifying hypotheses that are commonly made in the current existing transfer functions. Those simplifications lead to inaccurate results in the context of CO2 storage. We then develop a transfer function for buoyancy displacement based on the timescale of the one-dimensional equation for immiscible two-phase flow in porous media. We analyse how the newly developed transfer functions improve over the current existing ones in simple matrix-block geometries. The results are evaluated against high-resolution numerical simulations of matrix blocks considering realistic physical properties of CO2/Brine systems and fractured rocks. Our results show that the developed transfer functions are able to represent accurately the basic physics of the process, and improve over other existing transfer functions in the literature. The transfer functions are also implemented in a dual-porosity simulator and different CO2 injection scenarios are tested. We show that a careful design of the injection schedule may increase the mass of CO2 that is stored in the matrix block.@en

Naturally Fractured Reservoirs usually exhibit power law length distributions which do not possess any characteristic length scale, rendering the use of continuum methods difficult. This necessitates the adoption of hybrid models that represent a subset of the fractures as continua and the remainder as discrete fractures. However, the appropriate partitioning of fractures into these two subsets is an unresolved issue. In this regard, we propose a workflow which utilizes the Effective Medium Theory (EMT) by Sævik et al. (2013) as both an upscaling tool and a partitioning guide for single porosity hybrid modelling. EMT is used to find the largest nonpercolating subset of small fractures which will be upscaled into a single porosity background. The remaining fractures will be represented explicitly. This workflow allows reservoir engineers to systematically design an appropriate partitioning strategy for hybrid modelling. The paper explores this workflow via a two-part study. Part one validates the accuracy of EMT. Part two compares simulation results generated from different partitioning choices. The results show that the output of EMT matches that of numerical upscaling and that the workflow proposed leads to a hybrid model that is fit-for-purpose with a reduction in computational costs.@en

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 analyse how poro-mechanics could impact reservoir dynamics in naturally fractured reservoirs without significantly increasing computational overhead. Our new poro-mechanical informed dual-porosity flow diagnostics account for steady-state and singlephase flow conditions in the fractured medium while the fracture-matrix fluid exchange is approximated using a physics-based transfer rate constant which models two-phase flow using an analytical solution for spontaneous imbibition or gravity drainage. The deformation of the system is described by the dualporosity 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 discretised using a finite volume method with two-point flux-approximation while the governing equations for poro-mechanics are discretised 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 analogue 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, 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 impact reservoir dynamics. Due to the steady-state nature of the calculations and the effective coupling strategy, these calculations do not incur significant computational overheads. They hence provide an efficient complement to traditional reservoir simulation and uncertainty quantification workflows as they enable us to assess a broader range of reservoir uncertainties (e.g. geological, petrophysical and hydro-mechanical 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.@en

Water-Alternating-Gas injection could be an efficient way to improve recovery factors in fractured carbonate reservoirs. However, the complex geology of fractured carbonate reservoirs and the complexity of the WAG process itself create uncertainties when predicting the efficiency of WAG. It is hence challenging to identify engineering controls that allow us to optimize recovery during WAG while accounting for geological uncertainties. To overcome this challenge, we use Latin Hypercube and Box-Behnken experimental designs to set up multiple screened simulations of WAG injection in a fractured carbonate reservoir model that contains multiple geological uncertainties. From these simulations we construct surrogate response surfaces using polynomial chaos expansion. The response surface allow us to predict recovery factor, gas cumulative production, water cumulative production and NPV for different geological scenarios and engineering controls. Finally, we run the Non-dominated Sorting Genetic Algorithm-II on the response surface to obtain an optimal engineering design that not only accounts for geological uncertainties but also competing objectives. Our results show that only such a comprehensive simulation approach, which nevertheless can still be carried out on modern desktop PCs, is capably of analysing the complex interactions between geological and physical uncertainties and engineering controls to identify the most suitable WAG implementation.@en

Multi-scale fractured reservoirs can be modelled effectively using hybrid methods that partition fractures into two subsets: one where fractures are upscaled and another one where fractures are represented explicitly. Existing partitioning methods are qualitative or empirical. In this paper, we present a novel and quantitative partitioning approach based on a single-porosity hybrid modelling workflow that uses numerical (Embedded Discrete Fracture Methods - EDFM) and semi-analytical (Effective Medium Theory - EMT) methods for fracture subset upscaling. We demonstrate this workflow using synthetic fracture data and realistic data sourced from outcrops of the Jandaira Carbonate Formation in the Potiguar Basin, Brazil. Fracture subset upscaling with EDFM and EMT using three datasets (two real, one synthetic) shows that the smallest, most numerous fractures are poorly connected. The ability of fracture subset upscaling to identify these fractures is essential to the hybrid modelling workflow. EDFM and EMT methods give nearly identical results, but EMT enables us to greatly accelerate the calculations. To validate our workflow, hybrid models were created with different partitioning sizes and compared against EDFM simulations where all fractures are represented explicitly. A single-phase pressure drawdown was used a test problem. The simulation results show that once the upscaled fractures begin to connect, deviations in flow response start to grow because single-porosity representations are inadequate to capture the separation of timescales between flow in a well-connected fracture subset and flow in the matrix. In some cases, the flow regime in the model were observed to change entirely. Overall, the results justify the proposed workflow as a means for systematic and quantitative construction of hybrid models.@en

Naturally fractured reservoirs hold significant reserves but are highly heterogeneous and are challenging to simulate flow in. Dual Porosity (DP) methods, although widely used, require fine tuning using production data and thus lack predictive capability in green field applications. The Embedded Discrete Fracture Model (EDFM), which explicitly represents complex fracture network geometries at the cost of computational efficiency, is an excellent tool that can complement the DP method. Using EDFM, we study water coning phenomena in a green fractured Latin American gas field. We do this by simulating gas flow in a stochastically generated sector model representative of the field. EDFM simulations performed using different well rates revealed three possible flow regimes that the field may experience: stable flooding at low flow rates, coning with matrix production at moderate flow rates, and coning without matrix production at high flow rates. These results have implications in field development plans and can also be used for validating any DP models that may be used for full field simulations in the future. Through this study, we demonstrated how EDFM can be used, before any field production, to gain insights into the flow behaviour in a green field.@en

Fractured reservoirs often exhibit multiple length scales and are best modelled using hybrid methods that partition fractures into a subset to be upscaled and another to be represented explicitly. To address the open question of how partitioning can be done, we propose a single porosity hybrid modelling workflow that makes use of fracture subset upscaling to identify poorly connected small fractures for upscaling. Fracture subset upscaling was performed numerically on three datasets (two real, one synthetic); results showed that the smallest, most numerous fractures are the least connected. Semi-analytical fracture subset upscaling was also performed for the synthetic dataset, showing that this process can be accelerated with the aid of analytical upscaling tools. To test the proposed workflow, hybrid models were created with different partitioning sizes and compared against full Discrete Fracture Networks (DFN) using single phase pressure drawdown as a test problem. It is observed that as the upscaled small fractures begin to connect, deviations in flow response will start to grow. In some cases, the flow regime in the model will change entirely. Overall, the results justify the proposed workflow as a promising means for systematic construction of hybrid models with minimal guesswork.@en