Abstract: The coupling between subsurface flow and reservoir geomechanics plays a critical role in obtaining accurate results for both environmental and petroleum engineering applications. Due to its physical nature, the geomechanics problem can cope with a coarse time step compared to the flow problem. Multirate coupling schemes exploit the different time scales for the mechanics and flow problems by taking multiple finer time steps for flow within one coarse mechanics time step. In this work, we first formulate multirate iterative and explicit coupling schemes for coupling flow with geomechanics in poro-elastic and fractured poro-elastic media. Second, we analyze convergence properties of the devised multirate coupling schemes in both homogeneous and heterogeneous poro-elastic media. For the iterative coupling schemes, our analysis is based on studying the equations satisfied by the difference of iterates, and is an extension of the work in [1,2]. By a Banach contraction argument, we prove that the corresponding iterative scheme is a fixed-point Banach contraction. In addition, the analysis provides the values of adjustable coefficients used in the proposed schemes. For the explicit coupling schemes, we consider stability rather than convergence, and we show that, for both single rate and multirate explicit coupling schemes, our computed solution remain well-behaved as long as the initial date and source terms are well-behaved. Third, we validate the accuracy and efficiency of the proposed multirate schemes numerically in IPARS (the Integrated Parallel Accurate Reservoir Simulator), in which the Multipoint Flux Mixed Finite Element Method (MfMFE) is used for flow discretization, and Conformal Galerkin is used for the linear elasticity problem.
 V. Girault, K. Kumar, and M. F. Wheeler. Convergence of iterative coupling of geomechanics with in a fractured poroelastic medium. Comput Geosci (2016) 20: 997. https://doi.org/10.1007/s10596-016-9573-4
 Andro Mikelic and Mary Wheeler. Convergence of iterative coupling for coupled flow and geomechanics. Computational Geosciences, 17:455-461, 2013.
Bio: Tameem Almani is a research scientist and the 4th Industrial Revolution Simulation Champion at EXPEC Advanced Research Center, Saudi Aramco. In December, 2016, he obtained his PhD degree in Computational Sciences, Engineering, and Mathematics from the University of Texas at Austin under the supervision of Prof. Mary F. Wheeler. In his PhD dissertation, he worked on the analysis and modeling of coupled multiphase flow and geomechanics problems in poro-elastic media, with emphasis on multirate couplings and linear and nonlinear solvers for the related discretized systems. Tameem has authored/submitted more than 10 publications, with 4 published in peer-reviewed journals. His research interests span the areas of numerical methods for coupling fluid flow with geomechanics in porous media, and solving the related linear and nonlinear discretized systems. Tameem holds a B.S. degree (2007) in Computer Sciences, with first honors, from King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia, an M.S. degree (2011) in Computational and Mathematical Engineering from Stanford University, and an M.S. (2014) and Ph.D. (2016) degrees in Computational Sciences, Engineering, and Mathematics from the University of Texas at Austin.