PSI - Issue 37

A. Kostina et al. / Procedia Structural Integrity 37 (2022) 431–438 A.Kostina/ Structural Integrity Procedia 00 (2019) 000 – 000

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addition, strong dilation can substantially enhance reservoir properties and improve the oil recovery rate (Shafei and Dusseault (2013)). In a large number of SAGD models geomechanical effects are often neglected ( Mozaffari et al. (2013), Dianatnasab et al.(2016), Huang et al. (2018), Liu et al. (2018), Zhang et al. (2020) ). Early works consider injection of hot water into thermo-elastic reservoir ( Aktan and Farouq Ali (1978) ). However, even in this case, it has been shown that thermal stresses play a more significant role than gravitational forces. Gao and Chen (2020) used an extended Drucker-Prager model with cap plasticity to describe geomechanical effects during the pre-heating stage in Karamay oil sands. They obtained that the plastic zone has a shape of a circle and starts in the near-well area. Lin et al. (2017) also applied the extended Drucker-Prager model with cap plasticity to study strain-dependent permeability evolution during water injection in horizontal well-pairs located at Karamay oil field. They obtained that dilative zones are dependent on temperature of the injected water. However, plastic strains didn’t occur in field conditions and the dilation was induced by poroelastic strains. Rahmati et al. (2017) used Mohr-Coulomb criterion with variable values of cohesion and friction angle to analyze caprock integrity taking into account its intrinsic anisotropy. They have shown that an isotopic fracture criterion of caprock integrity gives 7% percent higher values of maximum operating pressure in comparison with anisotropic. Yin and Liu (2015) have studied creep of the stratum induced by thermal oil recovery at Jin.25 Block in Liaohe Oilfield. They obtained that injection pressure significantly affect the creep process and should not exceed 14MPa. As regards the hydraulic conductivity, the creep strains should be taken into consideration when the value of this parameter is above 1 × 10 − 9 m/s. The presented brief literature review has shown that geomechanics cannot be neglected in order to reproduce real rock behavior and coupled thermo-hydro-mechanical models should be developed. In this work, we propose a SAGD model which takes into account such key effects of this method as oil viscosity reduction, gravity-based drainage, phase change and evolution of stress-strain state leading to a change in porosity and permeability of the reservoir. We have applied this model to study shear dilation effect on oil recovery rate and evolution of reservoir properties as it is one of the possible reasons why SAGD has become more efficient in practice than it has been predicted by early simulation results (Shafei and Dusseault (2013)) . 2. Coupled thermo-hydro-mechanical model of SAGD The governing equations of the model includes momentum, mass, energy balance laws which are supplemented by constitutive equations and state laws. It is assumed that pore space is occupied by three immiscible phases (steam, oil and water). Filtration of each phase is described by Darcy’s law. Effect of pore fluid on stress -strain state of the reservoir is described within Biot theory. The reservoir is assumed to be isotropic and the strains are assumed to be small. Hook’s law is applied to evaluate elastic strains. Plastic strains are estimated by associated flow rule with Drucker-Prager yield criterion. The soil behavior is assumed to be perfectly plastic. Heat release due to steam condensation near the phase change front is determined by the additional heat source . 2.1. Three-phase flow The model considers flow of pore fluid which consists of steam, water and oil. To describe this flow, we have applied mass balance equations and Darcy’s laws of filtration. Conservation of mass for each phase is expressed as: ( ) ( ) i i i i i n ρ S ρ q t  +  =  v , (1) where n is the porosity of the reservoir, i ρ is the density of steam ( i s = ), water ( i w = ) and oil ( i o = ), i S ( , , i s w o = ) is the saturation of each phase, t is the time,  is the divergence operator, i v is the phase velocity, i q ( , i s w = ) is the mass source induced by phase transition. For oil phase i q is equal to zero, because no phase transition is assumed in hydrocarbon component. Dar cy’s velocity i v is written in the following form: