Rami M. Younis

A sharp analytical bound on the spatiotemporal locality in general two-phase flow and transport phenomena

Abstract The objective is to understand, for any two-phase flow situation, the instantaneous spatiotemporal nature of the domain-of- dependence. The focal setting is generally nonlinear and heterogeneous, compressible two-phase flow and transport in porous media. The analytical approach develops a sequence of approximations that ultimately recast the general conservation equa- tions into an infinite-dimensional Newton process. Within this process, the spatiotemporal evolution is dictated by linear dif- ferential equations that are easily analyzed. We develop sharp conservative estimates for the support of instantaneous changes to flow and transport variables. Several computational examples are used to illustrate the analytical results.

A Fully Coupled XFEM-EDFM Model for Multiphase Flow and Geomechanics in Fractured Tight Gas Reservoirs

Unconventional reservoirs are typically comprised of a multicontinuum stimulated formation, with complex fracture networks that have a wide range of length scales and geometries. A timely topic in the simulation of unconventional petroleum resources is in coupling the geomechanics of the fractured media to multiphase fluid flow and transport.We propose a XFEM-EDFM method which couples geomechanics with multiphase flow in fractured tight gas reservoirs. A proppant model is developed to simulate propped hydraulic fractures. The method is verified by analytical solutions. A simulation example with the configuration of two multiple-fractured horizontal wells is investigated. The influence of stress-dependent fracture permeability on cumulative production is analyzed.

Localized Computation of Newton Updates in Fully-implicit Two-phase Flow Simulation☆

Abstract Fully-Implicit (FI) Methods are often employed in the numerical simulation of large-scale subsurface flows in porous media. At each implicit time step, a Newton-like method is used to solve the FI discrete nonlinear algebraic system. The linear solution process for the Newton updates is the computational workhorse of FI simulations. Empirical observations suggest that the computed Newton updates during FI simulations of multiphase flow are often sparse. Moreover, the level of sparsity observed can vary dramatically from iteration to the next, and across time steps. In several large scale applications, it was reported that the level of sparsity in the Newton update can be as large as 99%. This work develops a localization algorithm that conservatively predetermines the sparsity pattern of the Newton update. Subsequently, only the flagged nonzero components of the system need be solved. The localization algorithm is developed for general FI models of two phase flow. Large scale simulation results of benchmark reservoir models show a 10 to 100 fold reduction in computational cost for homogeneous problems, and a 4 to 10 fold reduction for strongly heterogeneous problems.