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The SPE has split the former "Management & Information" technical discipline into two new technical discplines:
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Abstract The training speed is slow for the convolutional neural network (CNN)-based physics-informed neural network (PINN) in surrogate models and it is difficult to be applied to large-scale engineering problems. The Fourier Neural Operator (FNO) network can speed up 100 times faster than the PINN according to current literature. But the current FNO only handles the 3D (x, y, t) spatial-temporal domain. In this work, we developed a new framework to simulate the 4D (x, y, z, t) subsurface flow problems using the FNO network and the domain decomposition method. After numerical simulation runs, the obtained results of subsurface flow field distributions in 4D spatial-temporal domain (x, y, z, t) are decomposed into multiple 3D spatial-temporal domains (x, y, t) in the z dimension. Then, multiple FNO networks are used to train 3D spatial-temporal domain (x, y, t) in parallel to predict the distributions of the flow field in subsequent time steps. Finally, the predicted results of the 4D spatial-temporal solution in subsequent time steps are obtained by re-coupling the trained 3D (x, y, t) results in the z dimension. In this way, our new framework successfully extends FNO-network from 3D (x, y, t) to 4D (x, y, z, t) to predict field distributions in subsurface flow. The new framework was successfully applied to some very complex cases of CO2 injection for enhanced oil recovery (EOR) in compositional simulations. The predicted accuracy is enough for the method to be applied to simulate the complex CO2 EOR in fractured systems. The computational speed in 4D (x, y, z, t) can be as fast as it does in 3D (x, y, t) through parallel training. The tested results show that our new framework can efficiently simulate the EOR processes by injecting CO2 into complex fracture reservoirs. For the first time, we developed a new methodology that successfully extends the current FNO network from 3D (x, y, t) to 4D (x, y, z, t). Our framework paves way for the fast FNO network to solve the large-scale spatial-temporal domain of reservoir engineering systems.
Andrianov, Nikolai (Geological Survey of Denmark and Greenland, GEUS) | Amour, Frédéric (Technical University of Denmark) | Hajiabadi, Mohammad Reza (Technical University of Denmark) | Nick, Hamidreza M. (Technical University of Denmark) | Haspang, Martin Patrong (Gas Storage Denmark)
Abstract We develop a two-phase transient non-isothermal wellbore flow model, augmented with a radial heat conduction in the annulus, casing, and the reservoir. Using the available data for a saline aquifer in Denmark, we build a one-dimensional geomechanical well model and assess the stresses at the wellbore wall using the analytical Kirsch formula. Using the temperature at the wellbore wall, we calculate the corresponding thermal stresses. Furthermore, we assess the impact of the uncertainty in thermal expansion coefficients on the magnitudes of thermal stresses. For the cases considered, the magnitude of the changes in the critical pressure and in the fracture pressure with and without thermal stresses does not exceed 3%.
Abstract Long-term production of gas from the Groningen field has led to subsidence and seismicity in the region. Most of the prior Groningen modeling studies assumed elastic deformation of the reservoir due to the challenges in modeling poroplasticity in a reservoir with hundreds of faults and decades of production history. Here we quantify the role of inelastic deformation in production-induced subsidence and seismicity in the field via 3D high-resolution multiphysics modeling which couples multiphase flow and elastoplastic deformation in a complex geologic system made of claystone overburden, carboniferous underburden, and the gas-bearing sandstone reservoir compartmentalized with 100+ faults. We drive the model with four decades of historical production, spanning the period of induced seismicity, and two decades of future production under gas injection-enhanced recovery. We calibrate the model using the available pressure and subsidence data and analyze compartmentalized depletion and deformation due to spatially varying production and fault distribution. We analyze stress and strain in the caprock-reservoir depth interval to elucidate the role of inelasticity. We use the evolution in shear and normal tractions on seismogenic faults that hosted 1991-2012 seismicity to quantify the evolution in Coulomb stress and geomechanical stability of the faults.
Abstract Black-oil simulations with phase changes are challenging, because of the complex interactions between the different components and the equilibrium behavior of the phases. The common method for solving this type of nonlinear problem is to use a fully-implicit approach. However, the conventional black-oil model can lead to difficulties with converging using Newton's method. Discontinuities in discrete system can occur when a phase transition happens, which can lead to oscillations or even failure of the Newton iterations. The goal is to design a smoothing formulation that eliminates any sudden changes in properties or discontinuities that occur during phase transitions. We first employ a compositional formulation based on K-values to describe the standard black-oil model. Next, the coupled system is reformulated such that the discontinuities are carried over to the phase equilibrium model. In this manner, a single, succinct non-smooth equation is obtained, which allows for deriving a smoothing approximation. A mixed complementarity problem (MCP) for phase-equilibrium in the area of chemical process modeling served as the foundation for the reformulation. The new formulation is non-intrusive and simple to implement, requiring minor changes to current black-oil simulator frameworks. We analyze and demonstrate that phase changes lead to the changes of fluid-properties and discrete system, under the conventional black-oil formulation. By comparison, the newly proposed formulation uses a smoothing parameter to ensure smooth transitions of variables between the phase regimes. It also generates unique solutions that are valid for all three phases. Several complex heterogeneous problems are tested. The conventional black-oil model experiences many time-step cuttings and wasting nonlinear iterates. On the contrary, the smoothing model exhibits excellent convergence behaviors. Overall, the new formulation addresses the issues with convergence caused by phase-changes, while barely affecting solution results.
Abstract The objective is to use future simulated well behavior to optimize well management within a complex reservoir simulation model. This can be used to increase simulated plateau life and reserves. Traditional well management systems often rely on instantaneous well potential to choose guide rates to determine the well allocation within a group of wells. This has proved to be a very effective strategy. However, for the problem of plateau optimization, one can observe the high instantaneous potential of many wells after the plateau is exhausted; this is because the traditional well management system has no knowledge of future behavior. In this work, the future behavior of all the wells and groups with a large and complex giant reservoir simulation model is determined by spawning a coarsened "Look-Ahead model" (LAM). This is performed concurrently, while the main model is still running. After a pre-determined simulation time the LAM model is harvested by the main model, and approximate future behavior is integrated into the well management system of the main model. One simple yet effective technique is to evaluate the current potential of the well to be an average of the current instantaneous potential and the future potential, in, for example, 10 years ahead of the current simulations time. Thus wells whose future performance is inhibited because of high GOR or high water cuts will get there current allocation reduced, and wells with future high potential will get allocated more rate. The use of LAM models is demonstrated in a water flood problem to increase plateau time of a large and complex reservoir model. The LAM model is automatically constructed by collapsing the grid, maintaining some resolution of the current wells and future wells, and coarsening heavily the areas of the grid with spent wells. By doing so a 10x improvement in elapse time of the LAM model, which enables the frequent spawning of LAM models from the main model, and a subsequently the most up-to-date LAM model is integrated into the main well management system. The use of LAM to approximate future behavior of wells, and integrated this behavior into the well management of the reservoir simulator is a novel and practical approach to further optimize the well management system of a reservoir simulator.
Abstract Salt precipitation is a major issue in gas fields as it may reduce production significantly. Salt precipitation can be triggered through evaporation of the brine into the gas leading to an increased brine salt concentration and - if reaching its solubility - precipitation will occur reducing the rock porosity and, consequently, the permeability. In this work, the open-source fully implicit black-oil reservoir simulator OPM-flow is extended to allow for salt precipitation and water evaporation modeling. In comparison to compositional approaches, the proposed formulation simplifies the model set-up and calculation procedure. An existing black oil simulation may easily be converted to include water vaporization and salt precipitation functionality. This facilitates the modeling of fields that suffer from salt precipitation and their incorporation in history matching and optimization workflows. The black-oil formulation was modified to allow the gas to contain vaporized water in addition to vaporized oil. The salt transport equation is modified to account for a solid salt precipitate, and the permeability reduction is dealt with through a mobility multiplier that depends on the change in porosity. Together, a novel fully implicit formulation was developed for salt precipitation/dissolution and water evaporation for a three-phase black-oil simulator and implemented in OPM-flow. This implementation enables simulation of salt precipitation for gas-condensate production wells in addition to gas production wells.
Fraces, Cedric G. (Department of Energy Resources Engineering, Stanford University, Stanford, CA) | Tchelepi, Hamdi (Department of Energy Resources Engineering, Stanford University, Stanford, CA)
Abstract We present a Parametrization of the Physics Informed Neural Network (P-PINN) approach to tackle the problem of uncertainty quantification in reservoir engineering problems. We demonstrate the approach with the immiscible two phase flow displacement (Buckley-Leverett problem) in heterogeneous porous medium. The reservoir properties (porosity, permeability) are treated as random variables. The distribution of these properties can affect dynamic properties such as the fluids saturation, front propagation speed or breakthrough time. We explore and use to our advantage the ability of networks to interpolate complex high dimensional functions. We observe that the additional dimensions resulting from a stochastic treatment of the partial differential equations tend to produce smoother solutions on quantities of interest (distributions parameters) which is shown to improve the performance of PINNS. We show that provided a proper parameterization of the uncertainty space, PINN can produce solutions that match closely both the ensemble realizations and the stochastic moments. We demonstrate applications for both homogeneous and heterogeneous fields of properties. We are able to solve problems that can be challenging for classical methods. This approach gives rise to trained models that are both more robust to variations in the input space and can compete in performance with traditional stochastic sampling methods.
Yu, Xiangyu (Colorado School of Mines) | Yan, Xia (China University of Petroleum, East China) | Wang, Cong (Saudi Aramco) | Wang, Shihao (Chevron N America Upstream) | Wu, Yu-Shu (Colorado School of Mines)
Abstract The long-term fluid circulation of Enhanced Geothermal Systems (EGS) involves complex coupled Thermal-Hydrological-Mechanical (THM) processes dominated by hydraulic and induced natural fractures. The hydraulic fracture of arbitrary shape in response to pressure changes and thermal strains can be handled by the three-dimensional (3D) eXtended Finite Element Method (XFEM). The induced/natural fractures are incorporated into the model and treated as one continuum of the Multiple INteracting Continua (MINC) for the investigation of their impacts. A TOUGH-code-based program, TOUGH2-EGS, is utilized to simulate the Thermal-Hydrological processes. The 3D Embedded Discrete Fracture Method (EDFM), compatible with the 3D XFEM, is adopted to model the hydraulic fracture. TOUGH2-EGS is then coupled with an XFEM simulator by the sequentially coupled fixed-stress split approach. The convergence performance of this coupling scheme is firstly analyzed by introducing the fracture stiffness coefficient into a single-fracture model. Sensitivity analyses are performed for this model in terms of injection temperature and thermal expansivity. The hybrid EDFM and MINC model is established and analyzed for an EGS with both hydraulic and induced/natural fractures. The convergence performance of the single-fracture model shows that an appropriate stiffness coefficient is essential for this model and different choices of the coefficient value result in distinct performances. The sensitivity analyses for injection temperatures and thermal expansivity are conducted by comparing effective stresses, pressure, temperature, and porosity/permeability distributions, as well as dynamic production temperature, outflow rate, and injection fracture permeability. The results illustrate that the fracture aperture is opened by the cold fluid injection and the reservoir is dominated by the thermal stress/strain. The temperature and pressure distribution are both affected by the thermal-hydrological-mechanical processes through the dynamic porosity, permeability, stress/strain, and fluid viscosity. The thermal breakthrough curves reflect that the conduction contributes the most to heating the fluid while the outflow rates demonstrate the mass loss due to the porosity/permeability altered by thermo-poro-elasticity. In the hybrid model, the enhancement of the natural fracture permeability notably delays the thermal breakthrough by allowing injected fluid to contact more hot reservoirs. Natural fracture spacing, MINC partition numbers are also varied to investigate their influence on the production behavior: the increased spacing delays the thermal breakthrough and needs more MINC partitions for modeling accuracy. Traditional coupled THM models are only applicable under the assumption of infinitesimal strains which does not hold in hydraulically fractured EGS reservoirs. The introduction of fracture stiffness stabilizes the numerical solution. The combined 3D XFEM and EDFM is capable of handling arbitrary fracture shapes in a 3D EGS model. Moreover, the hybrid hydraulic and induced/natural fracture model enables us to establish the stimulated reservoir volume of the EGS and investigate the operational and geological parameters.
Abstract Accurate simulation of the thermoporoelasticity problems is beneficial for the exploitation activities of aquifers, geothermal, and hydrocarbon reservoirs. Simulating such problems using a finite-element Continuous Galerkin scheme (CG) lacks local energy/mass conservation. Despite being a conservative scheme, Discontinuous Galerkin (DG) is computationally expensive with much higher degrees of freedom (DoFs). This paper presents the Enriched Galerkin scheme (EG) implementation for thermoporoelasticity problems to ensure local energy/mass conservation with fewer DoFs.
Wheeler, Mary (The University of Texas at Austin) | Girault, Vivette (Sorbonne Université) | Li, Hanyu (The University of Texas at Austin)
Abstract Flow coupled with geomechanics problems has gathered increased research interest due to its resemblance to engineering applications, such as unconventional reservoir development, by incorporating multiple physics. Computations for the system of such a multiphysics model is often costly. In this paper, we introduce a posteriori error estimators to guide dynamic mesh adaptivity and to determine a novel stopping criterion for the fixed-stress split algorithm to improve computational efficiency. Previous studies for flow coupled with geomechanics have shown that local mass conservation for the flow equation is critical to the solution accuracy of multiphase flow and reactive transport models, making mixed finite element method an attractive option. Such a discretization maintains local mass conservation by enforcing the constitutive equation in strong form and can be readily incorporated into existing finite volume schemes, that are standard in the reservoir simulation community. Here, we introduced a posteriori error estimators derived for the coupled system with the flow and mechanics solved by mixed method and continuous Galerkin respectively. The estimators are utilized to guide the dynamic mesh adaptivity. We demonstrate the effectiveness of the estimators on computational improvement by a fractured reservoir example. The adaptive method only requires 20% of the degrees of freedom as compared to fine scale simulation to obtain an accurate solution. To avoid solving enormous linear systems from the monolithic approach, a fixed-stress split algorithm is often adopted where the flow equation is resolved first assuming a constant total mean stress, followed by the mechanics equation. The implementation of such a decoupled scheme often involves fine tuning the convergence criterion that is case sensitive. Previous work regarding error estimators with the flow equation solved by Enriched Galerkin proposed a novel stopping criterion that balances the algorithmic error with the discretization error. The new stopping criterion does not require fine tuning and avoids over iteration. In this paper, we extend such a criterion to the flow solved by mixed method and further confirm its validity.