13th International Conference on Fracture June 16–21, 2013, Beijing, China -2readily create overpressure in excess of lithostatic pressure and cause microfracturing in an effectively sealed reservoir. As a result, microfractures driven by the overpressure may grow and coalesce to form interconnected fracture networks, which may facilitate further migration of hydrocarbons [2, 7]. Convincing evidence from field observations has been presented to support the concept that microfractures induced by overpressure from hydrocarbon generation serve as migration conduits for hydrocarbons. Examples include the Bakken shale in Williston Basin [8], La Luna source rocks in the Maracaibo Basin [9], Woodford Formation in Oklahoma and Arkansas [10], fractured source rocks from the Oligocene Frio Formation, Texas [11], mature shales in the Hils area in Germany [12] and Alberta Basin in Canada [13]. Detailed observations by Lash and Engelder [14] showed that layer parallel microcracks filled with bitumen in organic-rich Dunkirk shale of Catskill delta, New York resulted from hydrocarbon generation. Common features of these microfractures in overpressured source rocks are summarized as follows: (1) the microcracks are of opening mode, i.e. mode I; (2) the preferred orientation of microfractures is parallel or sub-parallel to bedding plane; (3) most microcracks contain bitumen or calcite, showing the characteristic of petroleum generation; and (4) microfractures are found in organic-rich source rocks at high maturity level. More recently, Jin et al. [4] developed a model of primary migration of oil by collinear microcrack coalescing during the main stage of oil generation and found that microfractures propagate subcritically since excess pressure resulted from kerogen conversion to oil is not high enough to drive critical crack growth. In the present paper we extend our previous work to investigate subcritical growth of a series of periodically spaced subhorizontal collinear microfractures driven by excess fluid pressure due to thermal cracking of oil to gas. As a special case, the propagation of a single crack is also studied. We focus on the effects of gas compressibility and crack spacing on the crack propagation behavior including crack propagation distance and duration, as well as excess pressure evolution. 2. Formulation of theoretical model of crack propagation during gas generation 2.1. Thermal cracking of oil to gas Transformation of oil to gas satisfies the following first order differential equation [15] ( ) exp A E dM BM dt RT t ⎡ ⎤ =− ⎢− ⎥ ⎣ ⎦ (1) where M is the mass of convertible oil at time t, B is a pre-exponential constant, EA is the activation energy of the transformation, R is the universal gas constant, and T is the absolute temperature. We assume a constant burial rate S and a constant geothermal gradient G so that the depth of burial z and time-varying temperature T can be written as ( ) 0 z t H St = + , ( ) ( ) 0 0 0 Tt T GzH T GSt = + − = + (2) where H0 is the initial burial depth at which the oil-filled cracks are located, T0 is the corresponding temperature at H0. By integrating Eq. (1) with Eq. (2) and using mass conservation, Fan et al. [7] obtained the volumes of oil and gas at time t as follows ( ) 0 exp t oil oil V M t ρ = ⎡⎣ −Φ ⎤⎦ , ( ) { } 0 1 exp t gas gas V M t ρ = − ⎡−Φ ⎤ ⎣ ⎦ (3) where M0 is the initial mass of oil, ρoil is the density of oil, ρgas is the gas density which is a function of pressure and temperature determined by the equation of state (EOS), and Ф(t) is given by
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