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Unformatted text preview: Semilog Analysis For Gas Wells 1 Semilog Analysis For Gas Wells 2 Upon completion of this section, the student should be able to: 1. Identify the range of validity of each of the following analysis variables: pressure, pressuresquared, pseudopressure, and adjusted pressure. 2. Estimate pressure drop due to nonDarcy flow. 3. Analyze flow and buildup tests for gas wells using semilog analysis and any of the following analysis variables: pressure, pressuresquared, pseudopressure, and adjusted pressure. Semilog Analysis For Gas Wells 3 Semilog Analysis For Gas Wells 4 The PDE describing flow of a slightly compressible liquid of constant viscosity in a homogeneous porous medium is the diffusivity equation. This equation is derived from 3 principles  the continuity equation, or conservation of mass, the equation of state for slightly compressible liquids, and Darcys law. Other PDEs must be developed to describe gas flow or multiphase flow. The diffusivity equation is a linear equation, allowing us to use superposition in both space and time to develop solutions for complex geometries and variable rate histories from simple single well solutions. Semilog Analysis For Gas Wells 5 Nomenclature p  absolute pressure, psi V  volume, ft 3 z  real gas deviation factor, dimensionless n  number of moles R  ideal gas constant, 10.72 (ft 3 )(lb)/(mole)(in 2 )( R) T  temperature, R Semilog Analysis For Gas Wells 6 Nomenclature p  absolute pressure, psi p p real gas pseudopressure, psi 2 /cp p base pressure, psi. Arbitrary; often taken to be 0 or atmospheric pressure z  real gas deviation factor, dimensionless  gas viscosity, cp Semilog Analysis For Gas Wells 7 The flow equation for gases has the same form as the diffusivity equation for slightly compressible liquids, with pressure replaced by the real gas pseudopressure p p . This PDE is exact , if the 3 assumptions used in its derivation are applicable. However, unlike the diffusivity equation for liquids, it is nonlinear , because the product c t is a strong function of pressure. Semilog Analysis For Gas Wells 8 If we assume that the term z is constant, then we can write the gas flow equation in a form similar to that of the diffusivity equation, with pressure replaced by pressuresquared. This PDE is approximate because of the assumption of constant z. It is also nonlinear , because the product c t is a strong function of pressure. Semilog Analysis For Gas Wells 9 This figure shows the behavior of the term z with pressure at 200 deg F, for different gas gravities. The term z is fairly constant at low pressures, less than approximately 2000 psi. Semilog Analysis For Gas Wells 10 If we assume that the term p/ z is constant, then we can write the gas flow equation in a form similar to that of the diffusivity equation using pressure as the dependent variable....
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 Spring '08
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