A comparison of adaptive time stepping methods for coupled flow and deformation modeling

Abstract

Many subsurface reservoirs compact or subside due to production-induced pressure changes. Numerical simulation of this compaction process is important for predicting and preventing well-failure in deforming hydrocarbon reservoirs. However, development of sophisticated numerical simulators for coupled fluid flow and mechanical deformation modeling requires a considerable manpower investment. This development time can be shortened by loosely coupling pre-existing flow and deformation codes via an interface. These codes have an additional advantage over fully-coupled simulators in that fewer flow and mechanics time steps need to be taken to achieve a desired solution accuracy. Specifically, the length of time before a mechanics step is taken can be adapted to the rate of change in output parameters (pressure or displacement) for the particular application problem being studied. Comparing two adaptive methods (the local error method-a variant of Runge-Kutta-Fehlberg for solving odeÕs-and the pore pressure method) to a constant step size scheme illustrates the considerable cost savings of adaptive time stepping for loose coupling. The methods are tested on a simple loosely-coupled simulator modeling single-phase flow and linear elastic deformation. For the Terzaghi consolidation problem, the local error method achieves similar accuracy to the constant step size solution with only one third as many mechanics solves. The pore pressure method is an inexpensive adaptive method whose behavior closely follows the physics of the problem. The local error method, while a more general technique and therefore more expensive per time step, is able to achieve excellent solution accuracy overall.

An unconditionally stable explicit and precise multiple timescale finite element modeling scheme for the fully coupled hydro-mechanical analysis of saturated poroelastic media

“…Consequently, considerable effort is required to reduce the fully coupled computational time. In this case, to estimate the local truncation error and control the time-step size, adaptive time-stepping methods have to be developed [21,[23][24][25][26]. However, the dilemma in selecting between a suitable time-step size and a high computation accuracy still exists.…”

An Adaptive Time-Stepping Scheme with Local Convergence Verification Using Support Vector Machines

“…In accordance with the flow computed by (8) and the enthalpy of the flow, the heat H is updated. Then, we separate liquid/vapor phases with certain velocities.…”

“…been placed on how to decide time-step size h in (1) [6]- [8]. The problem of selecting h can be divided into two parts: how to set tentative h to calculate y n+1 and how to accept or reject h after obtaining provisional y n+1 .…”

“…Also, absolute or relative changes of systems' states were used as criteria [8], [9]. These two approaches are preferred mostly by computer simulators that require fast calculation since these add only negligible computational cost in general.…”

Investigations on several numerical methods for the non-local Allen–Cahn equation

“…Future research will concern the extension of the Fourier spectral operator splitting method to temporal adaptive algorithm [9,23,24], as well as the simulation of the 3D Cahn-Hilliard equation [9,25].…”