By Boresi and Schmidt

ISBN-10: 0471271799

ISBN-13: 9780471271796

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**Example text**

108) k=1 The compressibility of the flooding phase and rock requires introducing the following definitions: 1 ∂ρk A CA = , (109) ρA ∂ pA at a fixed temperature, for the acqueous phase, and CR = 1 dφ , φ dp A (110) for the rock. Assuming that the fluid and rock compressibilities are constant over a certain range of pressures, the above equations can be readily integrated to give ρ A ≈ ρ0 + ρ0 C A ( p A − p0 ) , (111) φ ≈ φ 0 + φ0 C R ( p A − p 0 ) , (112) where we have used Taylor series expansions to approximate the exact solutions of Eqs.

2007). Irregular and stochastic distributions of small ( f ) and large fractures (F) can also be handled using a triple-continuum model. For example, experimental observations show that in typical fractured rocks there may be many more small fractures than large ones (Liu et al. 2000). Therefore, in a triple-continuum model the fracturematrix system can be conceptualized as consisting of a single porous rock matrix and two types of fractures: large globally connected fractures and small fractures that are locally connected to the large fractures and the rock matrix.

108), using relations (106) and (107), and replacing ρ A v A by Darcy’s law written in the form ρ A v A = −λk · ∇ p A − λα k · (∇ pcα A − ρα g∇z) , (113) α where λα is the phase mobility defined as λα = kr α μα n ρk ckα , k=1 (114) Compositional Flow in Fractured Porous Media … 27 and pcα A is the capillary pressure function pcα A = pα − p A , (115) which is used to evaluate all other phase pressures, we obtain the pressure equation φC m ∂ pA − ∇ · (λk · ∇ p A ) = ∇ · ∂t λα k · (∇ pcα A − ρα g∇z) + α L k , (116) k=1 where C is the total compressibility defined as C = φ0 φ m ρk0 ck (Ck A + C R ) .

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