Formulation and sequential numerical algorithms of coupled fluid/heat flow and geomechanics for multiple porosity materials

Formulation and sequential numerical algorithms of coupled fluid/heat flow and geomechanics for multiple porosity materials J. Kim ∗ , E. Sonnenthal, and J. Rutqvist Earth Sciences Division, Lawrence Berkeley National Laboratory. 1 Cyclotron Road 90R1116, Berkeley, CA 94720, USA SUMMARY We generalized constitutive relations of coupled flow and geomechanics for the isothermal elastic double porosity model in the previous study to those for the non-isothermal elastic/elastoplastic multiple porosity model, finding coupling coefficients and constraints of the multiple porosity model, and determining the upscaled elastic/elastoplastic moduli as well as relations between the local strains of all materials within a gridblock and the global strain of the gridblock. Furthermore, the coupling equations and relations between local and global variables provide well-posed problems, implying that they honor the dissipative mechanism of coupled flow and geomechanics. For numerical implementation, we modified the fixed-stress sequential method for the multiple porosity model. From the a priori stability estimate, the sequential method provides numerical stability when an implicit time stepping algorithm is used. This sequential scheme can easily be implemented by using a modified porosity function and its porosity correction. In numerical examples, we observe clear differences among the single, double, and multiple porosity systems, and the multiple porosity model can reflect high heterogeneity that exists within a gridblock. We also identify considerably complicated physics in coupled flow and geomechanics of the multiple porosity systems, which cannot accurately be detected in the uncoupled flow simulation. KEY WORDS: double porosity, multiple porosity, poromechanics, multiple interacting continua (MINC), fractured reservoirs, fixed-stress split 1. INTRODUCTION Coupled fluid, heat, and mechanical processes are important in many engineering fileds. In mechanical engineering, coupled heat and mechanics (e.g., thermoelasticity, thermoplasticity) are considered to analyze interactions between deformation of a material body and thermal stress [1, 2]. Rapid movement of the body such as vibration can be a source in heat flow, and heat induces additional stress in mechanics, which can expand the body. In turn, the expanded body affects accumulation in heat flow because of the change in material volume. Coupled fluid, heat, and mechanical processes are also critically important in geo-engineering [3]. In geotechnical engineering, an increase (or decrease) of pore pressure causes dilation (or shrinkage) of porous media, which changes strain and stress fields [4, 5, 6, 7, 8]. These changes also affect pore-volume, resulting in variation of pore-pressure, again. In petroleum engineering, changes in permeability as well as porosity induced by geomechanics are critical issues in order to predict fluid flow and production accurately, for example, in hydraulic fracturing, reservoir compaction, and gas-hydrate recovery [9, 10, 11, 12, 13, 14]. In geological carbon storage, the effect of large scale injection ∗ Correspondence to: J. Kim, Earth Sciences Division, Lawrence Berkeley National Laboratory. 1 Cyclotron Road 90R1116, Berkeley, CA 94720, USA. Email: JihoonKim@lbl.gov