Issue 49

A. Kostina et alii, Frattura ed Integrità Strutturale, 49 (2019) 302-313; DOI: 10.3221/IGF-ESIS.49.30 304 conservation law, energy conservation law, Darcy’s law for oil, steam and water filtration. Water-vapor phase change is determined by the additional heat source proposed in [25]. Inelastic deformations of the reservoir induced by propagation of the thermal front are described by the phenomenological viscoplastic model. On the second step of the algorithm, the values of mechanical stresses near the top of the reservoir are determined. The last step is the assessment of the caprock failure according to Drucker-Prager criterion. The specific feature of this work is that two qualitatively different scenarios of porosity evolution is considered. The first scenario corresponds to the case of the pore compression which can be described by the model [10]. The second scenario demonstrates increase in porosity induced by the volumetric strains. This effect can be described by the model [11] which is widely used in SAGD simulation. M ATHEMATICAL MODEL he developed model of SAGD is based on the following assumptions. Fluid within the pore space consists of the three immiscible components (water, steam and oil). The flow of each component is slow and obeyed to Darcy’s law. Capillary pressure is negligible due to relatively high porosity. The change in the oil viscosity is the result of the change in the temperature only. The deformations of porous media are small. Elastic behavior of solid skeleton is described by Hook’s law. Effective stress concept is used to take into account the effect of pore pressure on the stress- strain state. Viscoplastic behavior of the reservoir is described by Perzyna’s theory and Drucker-Prager yield criterion [26- 27]. Therefore, the complete system of equations can be written as:             w w w w w n S q t v , (1)             s s s s s n S q t v , (2)             0 o o o o n S t v , (3)    1 w s o S S S , (4)         rw w w w Kk p v g , (5)         rs s s s Kk p v g , (6)         ro o o o Kk p v g , (7)                                             , , , , 1 r r i i i eff i i i i i w o s i w o s T n c n S c T S c nT Q t v , (8)      eff σ g 0 , (9)            0 : vp T B T T p σ C ε E ε E , (10) T