Christian Wolfsteiner

Well Modeling in the Multiscale Finite Volume Method for Subsurface Flow Simulation

A multiscale method for effective handling of wells (source/sink terms) in the simulation of multiphase flow and transport processes in heterogeneous porous media is developed. The approach extends the multiscale finite volume (MSFV) framework. Our multiscale well model allows for accurate reconstruction of the fine‐scale pressure and velocity fields in the vicinity of wells. Accurate and computationally efficient modeling of complex wells is a prerequisite for field applications, and the ability to model wells within the MSFV framework makes it possible to solve large‐scale heterogeneous problems of practical interest. Our approach consists of removal of the well singularity from the multiscale solution via a local change of variables and the computation of a smoothly varying background field instead. The well effects are computed using a separate basis function, which is superposed on the background solution to yield accurate representation of the flow field. The multiscale well treatment accounts for b...

Calculation of well index for nonconventional wells on arbitrary grids

Wells are seldom modeled explicitly in large scale finite difference reservoir simulations. Instead, the well is coupled to the reservoir through the use of a well index, which relates wellbore flow rate and pressure to grid block quantities. The use of an accurate well index is essential for the detailed modeling of nonconventional wells; i.e., wells with an arbitrary trajectory or multiple branches. The determination of a well index for such problems is complicated, particularly when the simulation grid is irregular or unstructured. In this work, a general framework for the calculation of accurate well indices for general nonconventional wells on arbitrary grids is presented and applied. The method entails the use of an accurate semianalytical well model based on Greens functions as a reference single phase flow solution. This result is coupled with a finite difference calculation to provide an accurate well index for each grid block containing a well segment. The method is demonstrated on a number of homogeneous example cases involving deviated, horizontal and multilateral wells oriented skew to the grid. Both Cartesian and globally unstructured multiblock grids are considered. In all these cases, the method is shown to provide results that are considerably more accurate compared to results using standard procedures. The method is also applied to heterogeneous problems involving horizontal wells, where it is shown to be capable of approximating the effects of subgrid heterogeneity in coarse finite difference models.

An Adaptive Multiphase Multiscale Finite Volume Simulator for Heterogeneous Reservoirs

We developed an adaptive reservoir simulator for accurate modeling of multiphase flow and transport in large scale heterogeneous reservoirs. The simulator is based on a multiscale finite volume (MSFV) method. We describe both IMPES and sequential implicit formulations. The algorithms are sensitive to the specific characteristics of flow (i.e., pressure and total velocity) and transport (i.e., saturation). To obtain the fine scale (i.e., fine grid) flow field, two sets of basis functions - dual and primal - are constructed. The dual basis functions, which are associated with the dual coarse grid, are used to calculate the coarse scale transmissibilities. The fine scale pressure field is computed from the coarse grid pressure via superposition of the dual basis functions. Having a locally conservative fine scale velocity field is essential for accurate solution of the saturation equations (i.e., transport). The primal basis functions, which are associated with the primal coarse grid, are constructed for that purpose. The dual basis functions serve as boundary conditions to the primal basis functions. To resolve the fine scale flow field in and around wells, a special well basis function is devised. As with the other basis functions, we ensure that the support for the well basis is local. Our MSFV simulator is designed for adaptive computation of both flow and transport in the course of a simulation run. Adaptive computation of the flow field is based on the time change of the total mobility field and triggers selective updates of basis functions. The key to achieving scalable (efficient for large problems) adaptive computation of flow and transport is the use of high fidelity basis functions with local support. We demonstrate the robustness and computational efficiency of the MSFV simulator using a variety of large heterogeneous reservoir models, including the SPE 10 comparative solution problem.

black oil formulation for the multiscale finite volume method

until now, the multiscale finite volume (msfv) method has shown great promise in petroleum subsurface flow simulation when applied to large and highly heterogeneous reservoirs. recently, the method was extended from incompressible multiphase flow to a standard black oil formulation, i.e., compressible rock/fluid system with gravity and solution gas. the new formulation requires modified basis functions and handles upstream consistently in pressure and transport calculations. in our approach we split the governing operator is into an incompressible, a compressible and a gravity contribution to handle the physics correctly on fine and coarse scale. we detail the formulation and assess the accuracy of the new method with numerical examples relative to detailed fine grid simulations. keywords multiscale, finite volume, subsurface, black oil