Acta Geotechnica

, Volume 2, Issue 3, pp 139–153 | Cite as

A locally conservative finite element framework for the simulation of coupled flow and reservoir geomechanics

  • Birendra Jha
  • Ruben JuanesEmail author
Research Paper


In this paper, we present a computational framework for the simulation of coupled flow and reservoir geomechanics. The physical model is restricted to Biot’s theory of single-phase flow and linear poroelasticity, but is sufficiently general to be extended to multiphase flow problems and inelastic behavior. The distinctive technical aspects of our approach are: (1) the space discretization of the equations. The unknown variables are the pressure, the fluid velocity, and the rock displacements. We recognize that these variables are of very different nature, and need to be discretized differently. We propose a mixed finite element space discretization, which is stable, convergent, locally mass conservative, and employs a single computational grid. To ensure stability and robustness, we perform an implicit time integration of the fluid flow equations. (2) The strategies for the solution of the coupled system. We compare different solution strategies, including the fully coupled approach, the usual (conditionally stable) iteratively coupled approach, and a less common unconditionally stable sequential scheme. We show that the latter scheme corresponds to a modified block Jacobi method, which also enjoys improved convergence properties. This computational model has been implemented in an object-oriented reservoir simulator, whose modular design allows for further extensions and enhancements. We show several representative numerical simulations that illustrate the effectiveness of the approach.


Geomechanics Iteratively coupled Local mass conservation Mixed finite elements Oil and gas Poroelasticity Reservoir Unconditionally stable Undrained split 



The authors are thankful for financial support from the members of the affiliate program of the Stanford University Petroleum Research Institute for Reservoir Simulation (SUPRI-B). Partial support was also provided by Foundation CMG; this support is gratefully acknowledged.


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Occidental Oil and Gas CorporationLong BeachUSA
  2. 2.Department of Civil and Environmental EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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