PSI - Issue 13

4

A. Kostina et al. / Procedia Structural Integrity 13 (2018) 1159–1164 Author name / Structural Integrity Procedia 00 (2018) 000–000

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Fig. 1. Experimental and numerical stress-strain curves for the triaxial compression of the sandstone specimen ( σ  - the difference between maximum and minimal principal stresses, 0 σ - mean stress, points denote experimental data published in (Browning et al., 2017)) According to the experiment, a small preload (4MPa) was given to the sample. After that, the maximum principal stress was continuously increasing while the other principal stresses remains constant and equal to 4MPa. As it has been pointed out in (Browning et al., 2017), the dilatant cracking commences around 40 MPa. However, experimental stress-strain curves show that the sandstone specimen demonstrates the nonlinear behavior from the very beginning of the experiment. To describe this effect, the following nonlinear approximation for functions 1 0 ( ) f p , 2 ( ) f p has been used:     3 1 0 0 ( ) tan tan( ) f p a bp c c    , (15)     2 Arctan f p m n p  , where 5.5 a  , 1600 b  , 4.54 c   , 0.0051 m  , 4 10 n  - parameters of approximation. Results of the numerical simulation for volumetric, lateral and axial strains have shown a qualitative and quantitative agreement with the experimental data. Function (15) together with the equations (3)-(6), (9), (11)-(14) have been used for a three-dimensional numerical simulation of volumetric damage evolution in the reservoir. An initial distribution of 0 p is assumed to be heterogeneous near the wellbore due to technological operations such as drilling, Fig. 2(a). After 700 days of a continuous heating, the volumetric structural strain increases and inhomogeneity becomes more pronounced, Fig. 2(b). Vertical permeability k and volumetric strain 0 ε is related by (Rahmati et al., 2017):     0 0 0 ln / / k k β n ε  , where 0 k - initial permeability, 0 n - initial porosity, 0 11 22 33 ε ε ε ε    - volumetric strain, 5 β  - parameter of vertical permeability. Fig. 3 presents evolution of vertical permeability along the straight vertical line drawn from the upper boundary of the reservoir to the wellbore boundary, which has been obtained for two cases: the absence of volumetric structural strain (solution to thermo-elastic problem) (Fig. 3(a)) and the presence of volumetric structural strain (solution to thermo-inelastic problem). An analysis of data presented in figure 3 shows that the solution to thermo-inelastic problem gives smaller values of a vertical permeability. Therefore, an interaction between structural changes and thermal strains leads to the compaction of the soil and impedes oil mobility.