Multi-segment Well Modeling in a Sequential Implicit Coupling Framework

Abstract

Accurate well modeling becomes essential in the reservoir simulation because more and more complex well operations are employed in the petroleum industry. The prevailed standard well model is proved to be computationally efficient, while it lacks the ability to capture the multiphase flow details within the wellbore. MultiSegment well (MSWell) model was then proposed to approximate the actual physical shape of the well and perform accurate simulation within the wellbore. However, the increasing complexity of the MSwell model also introduced additional difficulties in solving the coupled MSWell and reservoir flow problem. Several nonlinear solver and linear solver techniques were proposed to accelerate the convergence of the MSWell problem, while there isn't a systematic discussion about the convergence and the accuracy of the various proposed techniques. In this work, we discuss the convergence and the accuracy for different coupling strategies for coupled MSWell and reservoir flow problem. First, we introduce the numerical implementation of the MultiSegment well (MSWell) in an in-house simulation Automatic-Differentiation General Purpose Research Simulator (AD-GPRS) under the General Implicit Coupling Framework (GENIC). A consistent normalization technique for MSWell equations is discussed and carefully clarified. In addition, the component-based CFL number and the phase-based CFL number for MSWell equations are introduced, which are coherent with the CFL number defined in the reservoir block. After the clear illustration of the model details, we investigate three different coupling strategies for couple MSWell and reservoir flow problem, which are fully implicit method, sequential fully implicit method and fully implicit method with local facility solver. Numerical examples are constructed to validate the convergence and the accuracy of these three coupling strategies. Then a general discussion about the convergence and accuracy based on CFL number is conducted regarding different time step and grid size (segment length). The numerical results and the theoretical analysis show that the relative nonlinearity between the MSWell equations and the reservoir flow equations is the primary factor affecting the global convergence rate, while the time step will significantly influence the simulation accuracy of the wellbore flow. Thus, we proposed a possible solution to achieve both high accuracy for wellbore flow and global computational efficiency.