13th International Conference on Fracture June 16–21, 2013, Beijing, China -42h is the crack spacing. Initially the crack is subjected to uniform oil pressure on the crack surface. The initial excess pressure is denoted by Δp0 which is the oil pressure beyond the overburden pressure. The excess pressure increases as oil to gas conversion proceeds. At time t, the excess pressure can be obtained as follows ( ) 0 ( ) ( ) gas s gas s p P gz P g H St ρ ρ ρ ρ Δ = − = − + (9) where ρs is the average sediment density, g = 9.8 m/s 2 is gravitational acceleration, and P(ρ gas ) is the gas pressure given by Eq. (8). The stress intensity factor (SIF) at the crack tips is given by 2 tan 2 I a K p b b π ⎛ ⎞ =Δ ⎜ ⎟ ⎝ ⎠ (10) where b = a + h. The volume per unit thickness in the y direction of the crack is ( ) 2 2 16 1 ln sec 2 t crack b p a V E b ν π π Δ − ⎡ ⎤ ⎛ ⎞ = ⎢ ⎜ ⎟⎥ ⎣ ⎝ ⎠⎦ (11) where E and ν are Young’s modulus and Poisson’s ratio of the source rock, respectively. Since the crack is fully saturated with oil and gas, the volume of the crack must equal the sum of oil and gas volumes, that is, oil gas t t t crack V V V + = (12) From Eq. (11), we can get the initial mass of oil within the crack ( ) 2 2 0 0 0 16 1 ln sec 2 oil b p a M E b ρ ν π π Δ − ⎡ ⎤ ⎛ ⎞ = ⎢ ⎜ ⎟⎥ ⎣ ⎝ ⎠⎦ (13) where a0 is the half initial crack length. Clearly the SIF increases with the increasing excess pressure. Subcritical crack propagation will be initiated once the SIF reaches a threshold value KIth, but less than the rock fracture toughness KIc. Generally, the subcritical crack growth can be described by the Charles power law [17] [ ] ( ) n I da v A K a dt = = (14) where v is the subcritical propagation velocity, n is the subcritical crack growth index and A is a material constant. It follows from Eq. (10) that the excess fluid pressure corresponding to the onset of subcritical crack growth is 0 / 2 tan 2 th th a p K b b π Ι ⎛ ⎞ Δ = ⎜ ⎟ ⎝ ⎠ (15) The corresponding crack volume is ( ) 2 2 0 0 0 16 1 ln sec 2 2 tan 2 th crack b K a V b a E b b ν π π π Ι − ⎡ ⎤ ⎛ ⎞ = ⎢ ⎜ ⎟⎥ ⎣ ⎝ ⎠⎦ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (16) The time needed for the excess pressure to reach thpΔ from the start of oil-gas transformation, denoted by t0, can be determined by solving the following two equations ( ) 0 0 0 ( ) / 2 tan 2 th gas s th a P g H St K b b π ρ ρ Ι ⎛ ⎞ − + = ⎜ ⎟ ⎝ ⎠ (17)
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