13th International Conference on Fracture June 16–21, 2013, Beijing, China -6temperatures in excess of 200 oC, at depth of burial ranging between 3000m and 7000m [19]. We examine the sensitivity of crack propagation to variations of initial depth of burial in the range of 3500-5000m. The initial temperature is assumed as T0 = 150 oC. We also assume that Δp 0 = Δpth and the stress intensity factor equals the threshold value KIth due to the excess oil pressure at the initial state. Other physical and geometrical parameters used in our simulation are summarized in Table 1[14, 16-19]. Table 1 Physical and geometrical parameters used in the numerical simulation Symbols Definition Value(unit) Rock Matrix E ν ρs KIth A n a0 H0 T0 G S Oil ρoil Methane m Tc Pc Kinetics B EA R Young’s modulus Poison’s ratio Average sediment density Threshold stress intensity factor Subcritical crack growth constant Subcritical crack growth index Initial half crack length Initial depth of burial Initial temperature Geothermal gradient Burial rate Oil density Molar mass Critical temperature Critical pressure Pre-exponential constant Activation energy Universal gas constant 2.0 GPa 0.4 2350 kg/m3 0.06 MPa-m1/2 107 m/s/(MPa-m1/2)10 10 50 μm 4000 m 150 oC 30 oC/km 0.1 km/M.y. 850 kg/m3 16 g/mol 191.1 K 4.64 MPa 1.744×1013 sec-1 217.6 kJ/mol 8.314 J/mole/K 3.1 Single crack case When b/a0→∞ the crack interaction disappears and the problem reduces to the single crack case. Figures 2 shows crack propagation distance versus time corresponding to three different values of H0 for a single crack. The corresponding excess pressure profiles are shown in Figure 3. Similar to the kerogen conversion to oil case [4], subcritical crack propagation rate is much faster than the oil-gas conversion rate, so the crack propagation duration is governed by the oil-gas transformation kinetics. The excess pressure decreases monotonically as crack propagation distance increases with time, which is indicated by Eq. (10). It is seen from Figure 2 that the final crack length increases with decreasing initial depth of burial. It can be explained by considering the gas compressibility in Eq. (8). Gas density increases monotonically with increasing depth of burial, so the density difference between the transformation precursor and end product becomes smaller. Therefore, the crack propagation distance becomes smaller at greater depth of burial. From Figure 3 we can see that at a given time, the excess pressure within the crack is lower at a shallower depth of burial because longer cracks require smaller overpressure to grow as suggested by Eq. (10).
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