PSI - Issue 28

A. Kostina et al. / Procedia Structural Integrity 28 (2020) 675–683 Author name / Structural Integrity Procedia 00 (2019) 000–000

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soil can significantly increase porosity and permeability of the reservoir and thereby magnify recovery factors. In this work we propose damage model which describes this effect in steam-assisted gravity drainage (SAGD) method of heavy oil recovery. Continuum damage mechanics (CDM) is an effective tool for the description of the dispersed randomly oriented microcracks which affect material compliance in terms of the one or several internal variables. The pioneering work of Kachanov (1958) has laid a foundation to the application of such models to various mechanical problems. Recent advances in employment of CDM to geomechanics are focused on implementation of such models to practical problems of rock mining. Shojaei and Shao (2017) applied CDM to simulation of hydraulic fracturing. They combined CDM with Biot’s theory of consolidation and tracked crack path according to the von Mises stress distribution and pore pressure distribution. Yi et al. (2019) proposed coupled damage-flow model for simulation of hydraulic fracture which takes into account dependence of rock permeability on damage value. They have shown that damaged area increases with the rise in the injection pressure and fluid viscosity as well as with the drop in minimum in-situ stresses. Mobasher et al. (2017) developed numerical algorithm for non-local damage transport model based on displacement pressure permeability mixed finite element formulation which could be applied to the problems of hydraulic fracture and damage-enhanced consolidation. Sahara et al. (2017) demonstrated applicability of CDM to the analysis of borehole breakout in sandstone reservoirs. They could successfully describe such effects as localized crack distribution near the borehole wall and shear fracturing. Eremin at al. (2020) applied CDM to the problem of underground coal extraction. The developed model allows them to propose the explanation of roof cavings as the progressive increase of the rock volume where rotation of maximum principal stresses takes place. Wu et al. (2020) formulated damage evolution model with regard to volumetric strain and applied it to the problem of stability of the four diversion tunnels. The proposed model can describe dilatancy in the presence of negative volumetric strains during tunneling. In this work we consider application of the modified damage model originally proposed by Naimark (2003) to SAGD. We restrict ourselves to the symmetric damage tensor and consider the case of randomly distributed defects in the reservoir. To describe oil recovery by SAGD, we have developed coupled thermo-hydro-mechanical model which takes into account main mechanisms of SAGD which are reduction of the oil viscosity and gravity-based drainage. The reservoir is considered as a multiphase system, which includes solid skeleton, pore water, oil and the steam. Flow of all pore fluids is described by Darcy’s law. Temperature evolution is described by heat transfer equation with includes such effects as convection and phase transition. Structural damage defined by internal damage-variable simulates additional contribution to strain induced by the growth of the volumetric-type defects (microcracks) due to the increase in the shear-type defects (microshears). In turn, increase in volumetric strains provides evolution of porosity and permeability of the reservoir as well as leads to the surface heave. Specific feature of the simulation is accounting for the non-uniform steam distribution along the horizontal wellbore which strongly affects the shape of the steam chamber. As reported by Huang et al. (2018) non-uniformity could be induced by various reasons such as wellbore flow resistance, steam injection rate, pressure drop and steam characteristics. In general, simulation of the steam chamber suggests consideration of the 2D profile. In opposite to this, we have made an attempt to describe not only coupled processes accompanying SAGD but also to predict the steam chamber shape more accurately and closer to the form observed in field conditions. To investigate this effect on SAGD efficiency we have carried out a comparative analysis of oil recovery rates and values of the vertical heave for the three following cases: uniform distribution of the steam chamber along the horizontal wellbore with account for the structural damage, non-uniform distribution of the steam chamber without structural damage (only thermo-elastic strains were considered) and non uniform steam distribution with structural changes. 2. Coupled thermo-hydro-mechanical model of SAGD Generally, coupled thermo-hydro-mechanical models include conservation laws which are supplemented by state laws and constitutive equations. In our SAGD model we have coupled fluid filtration with mechanical problem by Biot’s theory of effective stresses and utilized porosity and permeability models which depend on volumetric strains. Thermal and mechanical problems have been related by the contribution of thermal strains to total strain tensor. Fluid filtration and thermal problem have been coupled by accounting for the convective heat transfer and dependence of oil viscosity on temperature.