Convergence of iterative coupling for coupled flow and geomechanics

In this paper, we study solving iteratively the coupling of flow and mechanics. We demonstrate the stability and convergence of two widely used schemes: the undrained split method and the fixed stress split method. To our knowledge, this is the first time that such results have been rigorously obtained and published in the scientific literature. In addition, we propose a new stress split method, with faster convergence rate than known schemes. These results are specially important today due to the interest in hydraulic fracturing (Dean and Schmidt SPE J. 14:707-714, 2009; Ji et al. SPE J. 14:423-430, 2009; Samier and De Gennaro 2007; Settari and Maurits SPE J. 3:219-226, 1998), in oil and gas shale reservoirs.