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18) gives ρ φcf + φ o cR ∂p =∇· ∂t ρ k (∇p − ρ℘∇z) + q. µ Defining the total compressibility ct = cf + we see that φρct ∂p =∇· ∂t φo cR , φ ρ k (∇p − ρ℘∇z) + q, µ which is a parabolic equation in p (cf. 12). 4 Chapter 2. Flow and Transport Equations Equations for gas flow For gas flow, the compressibility cg of gas is usually not assumed to be constant. 21) ∂ρ dφ +ρ . 22) ZRT where W is the molecular weight, Z is the gas compressibility factor, and R is the universal gas constant. 057. For a pure gas reservoir, the gravitational constant is usually small and neglected.

2 Horizontal Wells .................................................. 3 Treatment of Faults ............................................. 4 Corner Point Techniques ..................................... 5 Mixed Finite Element Methods ......................................... 1 Rectangular Mixed Spaces ................................. 2 Triangular Mixed Spaces ..................................... 6 Well Constraints ................................................................ 7 The Seventh SPE Project: Horizontal Well Modeling .......

The development of single phase flow in deformable and fractured porous media is applicable to two-phase flow. We do not pursue this similar development. 37). 24 Chapter 2. Flow and Transport Equations Formulation in phase pressures Assume that the capillary pressure pc has a unique inverse function: Sw = pc−1 (po − pw ). We use pw and po as the main unknowns. 37) that ∇· ρw ∂(φρw pc−1 ) kw (∇pw − ρw ℘∇z) = − qw , µw ∂t ∇· ∂ φρo (1 − pc−1 ) ρo ko (∇po − ρo ℘∇z) = − qo . , 1959). The equations in this system are strongly nonlinear and coupled.