... properly for the coupled systems by taking appropriate stabilization terms for stability and convergence with energy analyses. Specifically, an apparent fracture stiffness is used for for numerical stabilization. Because this fracture stiffness depends on the fracture length, the stabilization term needs...

... function OPC stability Injection Rate candidate solution base solution long-term opc case study Artificial Intelligence constraint optimization workflow Optimization Opportunity optimal solution water production reservoir Scenario Introduction As volatility in oil prices is a new...

... general behavior of irreversibility. Focusing on immiscible two-phase flow, we mainly investigate mathematical analysis of stability, and find that the method based on the plasticity can provide well-posedness (thermodynamic stability) and algorithmic stability (B-stability). Then, the numerical scheme...

... & Simulation pore compressibility reservoir geomechanics coupling step Upstream Oil & Gas variation Reservoir Characterization reservoir simulation convergence adaptive scheme posteriori error tolerance Artificial Intelligence compressibility error tolerance porosity time step stability...

..., and the extended fixed-stress split. We perform new stability and convergence analysis for the undrained-adiabatic and extended fixed-stress split methods, introducing a new extended norm for nonlinear stability analysis, which can cover all-way coupled thermoporomechanical problems. In this study we show...

... Abstract Von Neumann analysis is the most commonly used method for determining stability of an explicit-in-time finite difference method. Watts and Ramé (1999) describe a different approach based on the error growth matrix for the finite difference method. In this approach, called herein...

... that for systems with multiple fluid phases, the ‘equivalent’ pore-pressure, p E , defined as p ¯ minus the interfacial energy is the appropriate quantity. We investigate the accuracy and stability of the fully implicit method (FIM) for multiphase flow and mechanical deformation based on p...

... of the reservoir. The fluid and solid phases coexist, yielding a high nonlinearity for flow and mechanics, so the coupled problem for hydrates is exceptionally complicated. In previous study, the stability of hydrate-bearing sediments was assessed by one-way coupled analysis, where the change of fluid properties...

... attempts to reduce the CPU overhead associated with the fully implicit scheme, without sacrificing the benefits from FIM's signature unconditional stability. A few representative approaches are summarized as follows: Adaptive Implicit Method (AIM): More explicit schemes, e.g., IMPES or SI...

... Abstract We perform detailed stability and convergence analyses of iteratively coupled solution methods for coupled fluid flow and reservoir geomechanics. We analyse four different operator-split strategies: two schemes in which the mechanical problem is solved first (drained and undrained...

... to effectively reduce numerical cross-wind diffusion effects, leading to improved resolution of concentration and saturation fronts. Artificial Intelligence Fluid Dynamics Saturation profile stability Upstream Oil & Gas approximation contribution reservoir simulation upwind scheme information...

... Abstract Coupled geomechanical-fluid flow models are needed to account for rock deformation resulting from flow-induced pressure changes in stress sensitive reservoirs. There are, however, issues of numerical stability that must be addressed before these coupled models can be used reliably...

... forces are included, while tensor considerations are neglected. The flow equations are discretized in space and time, with explicit composition and mobility used in the interblock flow terms (the Impes case). Published stability analyses for this flow in a less general framework indicate that the CFL...

... method newton iteration gridblock equation cfl condition upstream oil & gas preconditioner saturation submatrice implicit matrix equation stability inflow neighbor Introduction As use of unstructured grids and multicomponent fluid representations becomes more common, the adaptive...

... with less implicitness. We find that in most cases the greatest efficiency occurs when only a small number of blocks (less than 5 percent) are treated implicitly. In many cases the most efficient method is IMPES with time steps selected using the numerical stability calculations of AIM, Smaller time steps...

... ABSTRACT A stability criterion for determining the degree of implicitness in adaptive-implicit compositional reservoir simulation is derived and discussed. The criterion is based on the Courant-Friedrichs-Lewy (CFL) condition for the stability of explicit discretizations of hyperbolic systems...

... ) govern flow. We easily see that ( 35 ) is necessary for stability; if s i , j n = 0 and s n is 1 in all cells upstream to ( i, j ), then s i , j n + 1 is the left-hand side of ( 35 ). In three dimensions, let the velocity vector be ( u, v, w ), with velocities...

... indicate that the Petrov-Galerkin method does significantly reduce numerical-diffusion errors, while it retains the stability of the first-order, upwind methods. It is also relatively simple to implement. Both the upwind, and Petrov-Galerkin, finite element methods demonstrate little sensitivity to grid...

... ABSTRACT The adaptive implicit method enables a reservoir simulator to choose the degree of implicitness in a grid block to guarantee stability. At any moment different grid blocks can have different degrees of implicitness. As a calculation proceeds these shift in space and time depending...