Issue 49

A. Kostina et alii, Frattura ed Integrità Strutturale, 49 (2019) 302-313; DOI: 10.3221/IGF-ESIS.49.30 307 where 0 p is the initial pressure; 0 w S is the initial water saturation;  1 denotes the boundary of the injection well; b p is the injection pressure;  2 denotes the boundary of the production well; w p is the pressure in the production well; n is the unit normal vector; ' q is the heat flux vector;  3 ,  4 denote left and right boundaries of the rectangular domain;  5 ,  6 denote upper and lower boundary of the rectangular domain. R ESULTS AND DISCUSSIONS he system of Eqns. (1)-(18) together with the initial and boundary conditions (19)-(32) was solved numerically using finite-element software Comsol Multiphysics®. For this purpose, the following algorithm has been proposed. Firstly, Eqns. (1)-(7) were reformulated using the total velocity of the three-phase flow. After this, the obtained equations were represented in the weak form. Each of the equations was multiplied by the test function. Then, the integration by parts was applied to reduce the order of differentiation. In the considered equations, the convective term prevails over the diffusive one. To smooth the oscillations caused by the convective terms the artificial diffusion was added to each equation. The resulting equations were implemented to Comsol Multiphysics® by Weak Form PDE interface. To solve the Eqns. (8)-(12) Heat Transfer and Structural Mechanics modules were used. The more detailed description of the algorithm can be found in [29]. The developed numerical algorithm has been applied to the three-dimensional numerical simulation of the rectangular reservoir containing two horizontal wells (injection and production). Schematic representation of the simulated domain is given in fig. 1 (a). The thickness of the considered area is 1 m. Dimensions in the X and Z directions are equal to 30 m and 24 m. The wells have diameter of 0.178 m. The production well is located at a distance of 10 m from the bottom of the reservoir. The distance between the wells is 5 m. The considered area has been discretized by triangular prismatic finite elements with the minimal element size of 0.03 m (near the wells) and the maximum element size of 1 m (near the boundary of the simulated domain). The reservoir and oil properties correspond to Yarega oil deposit (Russian crude oil deposit in Komi Republic). Physical and mechanical properties of water, steam, oil and reservoir are given in Tabs. 1-2. Fig. 1 (b) describes the temperature dependence of oil dynamic viscosity used in simulation. The main focus of this work is the assessment of the caprock integrity during oil production by SAGD with two sets of operational parameters: p b =2.5 MPa, T b =213 K and p b =3.5 MPa, T b =220 K. Values of other initial and boundary conditions are given in Tab. 3. The loads acting on a caprock are fully determined by the stress-strain state of the reservoir which depends on the structural changes induced by propagation of the steam chamber. Property Value Unit Young’s modulus 3·10 9 Pa Poisson’s ratio 0.25 Thermal expansion coefficient 5·10 -6 1/K Biot coefficient 0.44 Material parameter a 0.19 Material parameter b 475725 Pa Table 1 : Mechanical properties of reservoir. Fig. 2 shows the form of the steam chamber after 100 days of the heating with two different regimes. Steam injection with operational parameters p b =2.5 MPa, T b =213 K results in the vertical growth of the steam chamber while operational parameters p b =3.5 MPa, T b =220 K give a completely different shape with substantial sideway growth. It is noticeable that fig. 2(a) corresponds to the early stage of the steam chamber growth whereas fig. 2(b) illustrates the spreading phase. Therefore, the second regime of the heating is characterized by the very high values of the steam propagation within the reservoir. T