Low-Pressure Gases (approximate) ( β units are psia 2-md-ft-D/Mscf, kPa 2 High-Pressure Gases (approximate) ( β units are psi-md-ft Real Gases ( β units are psi 2-md-ft-D/Mscf/cp, kPa 2 Liquids ( β units are psi-md-ft-D/STB, kPa-m 2-m-d/std m 3). The first line of each equation is in fundamental units, the second in oilfield units, and the third in SI units. Where β is given by the following expressions, which include the unit conversions necessary to apply Eq. First, a "generic" potential difference, Δ ψ, can be expressed for each of the fluid cases according to Table 1.Ī general radial-flow equation can then be expressed for all cases as So that one simplified set of equations can be used throughout the remainder of the chapter, some additional parameters will be defined. Note that the conversion between the real-gas potential in oilfield vs. 4 – Example graph showing that the product μ gB g is approximately constant for gases at pressures greater than approximately 2,000 psia. Also, although it is not readily apparent from the plot, at low pressures the product μz is approximately constant.įig. Note that at high pressures, p/ μz is approximately constant. Twice the area under the curve between any two pressures represents the real-gas potential difference. Where the real-gas potential Δ m is defined byįig. The exact pressure at which the oil formation volume factor and viscosity are evaluated is not critical because the product of is approximately constant.īecause this approximation is not generally valid for gases, the steady-state radial gas-flow equation is written as Where Δ p = p 2 - p 1 and is evaluated at some average pressure between p 1 and p 2. Steady-state radial horizontal liquid flowįor liquids, the product of B o μ o is approximately constant over a fairly wide pressure range so that for practical purposes, Eq. Liquid (small and constant compressibility).When multiple-line equations are presented, the first will be in fundamental units, the second in oilfield units, and the third in SI units.įour different fluid representations are considered: In the resulting equations, presented next, flow rate is taken as being positive in the direction opposite to the pressure gradient, thus dropping the minus sign from Darcy’s law. The different forms of the equations are based on appropriate equations of state (i.e., density as a function of pressure) for a particular fluid. However, different forms of Darcy’s law arise for different fluids when flow rates are measured at standard conditions. The basis for all well-performance relationships is Darcy’s law, which in its fundamental differential form applies to any fluid-gas or liquid. 7 Using gas-well deliverability relationships.6.1 Pressure-transient testing of gas wells.1.2 Steady-state radial horizontal gas flow.1.1 Steady-state radial horizontal liquid flow.
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