An exploration of the IGA method for efficient reservoir simulation

Novel numerical methods present exciting opportunities to improve the efficiency of reservoir simulators. Because potentially significant gains to computational speed and accuracy may be obtained, it is worthwhile explore alternative computational algorithms for both general and case-by-case application to the discretization of the equations of porous media flow, fluid-structure interaction, and/or production. In the present work, the fairly new concept of isogeometric analysis (IGA) is evaluated for its suitability to reservoir simulation via direct comparison with the industry standard finite difference (FD) method and 1st order standard finite element method (SFEM). To this end, two main studies are carried out to observe IGA’s performance with regards to geometrical modeling and ability to capture steep saturation fronts. The first study explores IGA’s ability to model complex reservoir geometries, observing L2 error convergence rates under a variety of refinement schemes. The numerical experimental setup includes an 'S' shaped line sink of varying curvature from which water is produced in a 2D homogenous domain. The accompanying study simplifies the domain to 1D, but adds in multiphase physics that traditionally introduce difficulties associated with modeling of a moving saturation front. Results overall demonstrate promise for the IGA method to be a particularly effective tool in handling geometrically difficult features while also managing typically challenging numerical phenomena.Petroleum and Geosystems Engineerin

Hydro-mechanical modeling of two-phase fluid flow in deforming, partially saturated porous media with propagating cohesive cracks using the extended finite element method

In the present paper, a fully coupled numerical model is developed for the hydromechanical analysis of deforming, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non-wetting pore fluids. The governing equations involving the coupled two-phase fluid flow and deformation processes in partially saturated porous media containing cohesive cracks are derived within the framework of the generalized Biot theory. The displacement of the solid phase, the pressure of the wetting phase and the capillary pressure are taken as the primary unknowns of the three-phase formulation. A softening cohesive law is employed to describe the nonlinear behavior of the material in the fracture process zone. In order to account for the flux of the two fluid phases through the fracture faces, the mass balance equation for each flowing fluid inside the fully damaged zone and the cohesive zone is averaged over its cross section. The resulting equations provide mass couplings to the standard equations of the multiphase system. The effect of cracking and therefore change of porosity on the permeability of the damaged zone is also taken into account. To arrive at the discrete equations, the extended finite element method (XFEM) is utilized to discretize the weak form of the balance equations of mass and linear momentum in spatial domain along with the Generalized Newmark scheme for time domain discretization. By exploiting the partition of unity property of finite element shape functions, the evolving cohesive crack is simulated independently of the underlying finite element mesh and without continuous remeshing of the domain as the crack grows by adding enriched degrees of freedom to nodes whose support is bisected by the crack. For the numerical solution, the unconditionally stable direct time-stepping procedure is applied to solve the resulting system of strongly coupled non-linear algebraic equations using a Newton-Raphson iterative procedure. Finally, numerical simulations are presented to demonstrate the capability of the proposed method and the significant influence of the hydro-mechanical coupling between the continuum porous medium and the discontinuity on the results

Data-Driven Modeling of an Unsaturated Bentonite Buffer Model Test Under High Temperatures Using an Enhanced Axisymmetric Reproducing Kernel Particle Method

In deep geological repositories for high level nuclear waste with close canister spacings, bentonite buffers can experience temperatures higher than 100 {\deg}C. In this range of extreme temperatures, phenomenological constitutive laws face limitations in capturing the thermo-hydro-mechanical (THM) behavior of the bentonite, since the pre-defined functional constitutive laws often lack generality and flexibility to capture a wide range of complex coupling phenomena as well as the effects of stress state and path dependency. In this work, a deep neural network (DNN)-based soil-water retention curve (SWRC) of bentonite is introduced and integrated into a Reproducing Kernel Particle Method (RKPM) for conducting THM simulations of the bentonite buffer. The DNN-SWRC model incorporates temperature as an additional input variable, allowing it to learn the relationship between suction and degree of saturation under the general non-isothermal condition, which is difficult to represent using a phenomenological SWRC. For effective modeling of the tank-scale test, new axisymmetric Reproducing Kernel basis functions enriched with singular Dirichlet enforcement representing heater placement and an effective convective heat transfer coefficient representing thin-layer composite tank construction are developed. The proposed method is demonstrated through the modeling of a tank-scale experiment involving a cylindrical layer of MX-80 bentonite exposed to central heating.Comment: 51 pages, 19 figure