Issue 49

A. Kostina et alii, Frattura ed Integrità Strutturale, 49 (2019) 302-313; DOI: 10.3221/IGF-ESIS.49.30 303 leads to the formation of a high-temperature steam chamber. Increase in the temperature reduces oil viscosity and enhances oil mobility. Oil together with the pore water and the condensed steam flow downwards into the production wells under the gravity. Optimization of SAGD requires formulation of mathematical models which takes into account multiphase flow, filtration, phase change processes and alteration of the stress-strain state due to the thermal and mechanical loading of the reservoir. Injection of the hot steam under the high pressure leads to the various geomechanical phenomena. For example, dilation and fracture significantly increase the porosity whereas compaction of soil grains and its thermal expansion reduces it [2]. Moreover, excessive stresses in the reservoir can break the integrity of the steam chamber. Loss of the caprock integrity is a serious problem for human safety and the environment which leads to the water and air pollution. Usually, numerical models of SAGD include momentum, mass and energy conservation laws which are supplemented by state and constitutive equations [3-6]. To describe the effect of fluid flow on a stress-strain state of porous media poroelastic Biot’s theory is used. To provide a full coupling between fluid flow and the stress-strain state of the reservoir it is necessary to include a constitutive equation for porosity evolution into the model. The porous media is a complicated system which deformational behavior and properties are strongly depend on the level of the applied load, initial heterogeneity, anisotropy and many other factors. Therefore, there is a wide variety in the choice of relations for the description of the porosity evolution. In the simplest case, the porosity can be related to the pore pressure using the pore compressibility coefficient [7-8]. In [9-10] the incremental relation between the porosity and the mean stress with the coefficient which is linearly dependent on the current porosity value has been obtained. In case of the low compressibility, the porosity can be associated with the mean effective stresses using the composition of the linear fractional function and the exponent [11]. Another exponential dependence of the porosity on the mean effective stresses has been obtained in [12]. The incremental equation relating porosity to the linear combination of the volumetric strains and pore pressure has been proposed in [13-14]. In case of the low compressibility the dependence between the porosity and volumetric strains is also expressed as the exponential function [15-16]. At the same time, a linear fractional dependence of the porosity on volumetric strains has been proposed in [17-19]. As regards to the viscous oil production, the main mechanisms affecting the value of porosity is the shear dilation. In [1] it has been mentioned that propagation of the thermal front within the reservoir leads to the rise in the horizontal compressive stresses and substantial reduction of the vertical stresses. Such changes cause a significant shear dilation which enhances permeability and increases porosity of the soil. This effect can be described by the models which relate porosity to volumetric strains [4], [15-19]. However, when the effective confining pressures are high the shear dilation can be suppressed. In this case, the pore compression leads to the squeezing of the oil out of the pore space which can be described by relating of the porosity to the effective stresses [9-12]. Alteration of porosity during thermal oil production can significantly affect mechanical state of the reservoir near the caprock. Analysis of the existing works have shown that only few works are devoted to the study of the caprock integrity during SAGD. Rahmati et al. [20] investigated effect of the intrinsic anisotropy of caprock on maximum operating pressure of SAGD. For this purpose, they combined anisotropic Mohr-Coloumb failure criterion with transversely isotropic elastic model. They have shown that isotropic model gives a little bit higher values of maximum operating pressure than anisotropic. McLellan et al. [21] took into account statistical distribution of the natural fractures in caprock. Khan et al. [22] proposed an integrated geomechanics approach to evaluate caprock integrity which is based on the construction of the real three-dimensional formation taking into account petrophysical properties of the reservoir, strength parameters of the caprock and the results of mini-frac or leak-off tests. The obtained geological model is integrated with the coupled reservoir simulator which allows one to obtain stress-strain state of the considered formation. These results can be used for estimation of the caprock failure on the base of Mohr-Coulomb fracture criterion. Walters et al. [23] confirmed that the key factors determining maximum operating pressure in SAGD are the knowledge of the initial stress-strain state of the reservoir and its material properties. They have conducted analytical and numerical analysis of the stress change during SAGD. Analytical method was based on the theory of poro-thermo-elasticity and the Mohr-Circle analysis for evaluation of the shear failure. Numerical assessment included a coupled reservoir and geomechanical simulator. Tensile and shear stress ratios were used as failure indicators. Uwiera-Gartner et al. [24] have analyzed caprock integrity of SAGD project in northeast Alberta (Canada) using geological and geomechanical parameters. The drawback of this method is existence of the uncertainties in geomechanical parameters of the caprock. The key uncertainties affecting the analysis are heterogeneity, anisotropy, delamination and large fractures, which can reduce rock strength. This work is devoted to the investigation of SAGD operating parameters (the temperature and the pressure of the injected steam) on the caprock integrity near its base. The following algorithm has been used in order to estimate the integrity. Firstly, the coupled thermo-hydro-mechanical problem is solved to obtain mechanical state of the reservoir. An originally proposed model is applied to this purpose. According to the model, the process of steam injection is governed by mass