Issue 49

A. Kostina et alii, Frattura ed Integrità Strutturale, 49 (2019) 302-313; DOI: 10.3221/IGF-ESIS.49.30 309 (a) (b) Figure 1 : (a) Schematic representation of the simulated domain (  1 is the boundary of the injection well,  2 is the boundary of the production well,  3 is the left boundary,  4 is the right boundary,  5 is the upper boundary,  6 is the lower boundary). All sizes are in mm. (b) Dependence of the dynamic oil viscosity on the temperature [30]. (a) (b) Figure 2 : Steam chamber distribution after 100 days of heating: (a) p b =2.5 MPa, T b =213 K; (b) p b =3.5 MPa, T b =220K. The effect of volumetric strains and effective stresses on the porosity evolution is shown in fig. 3. It can be seen that the considered models (17) and (18) give a qualitatively and quantitatively different distribution of the porosity. The porosity Eqn. (17) describes compression of the soil in the process of SAGD (fig. 3(a)). Pore compression leads to the decrease in pore pressure and increase in effective compressive stresses in such a way that all domain is in the compressive state. The highest contraction is observed within the area which corresponds to the spreading steam chamber. By contrast, the model (18) demonstrates pore expansion due to the influence of the pore pressure and temperature. According to this model, the porosity changes only in the heating zone and does not affect the rest of the domain. Thus, the first model is more sensitive to the applied mechanical and thermal loading than the second one. To choose the more appropriate model of the porosity for the specific reservoir it is necessary to determine the prevailing mechanism of its evolution because the obtained results can significantly affect the oil production rate. The effect of porosity evolution on the oil production rate is studied using the Kozeny-Carman model which is widely applied to the problems of petroleum engineering. The model relates absolute permeability to the porosity and can be written in the following form [31]:        2 3 0 2 3 0 0 1 1 n n K K n n , (33) where 0 K is the initial value of an absolute permeability; 0 n is the initial value of porosity. Fig. 4 shows specific oil production rate obtained by the proposed SAGD model after the establishment of the interwell communication using models (17)-(18) and two abovementioned sets of operational parameters. The first case of the operational parameters gives an upward trend of the production rate while the second case shows a stable production rate corresponding to the spreading phase of the steam chamber. As the one would expect, the highest value of the production