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Start with the material balance equation: (A-1) Differentiating partially with respect to real time, t, we get (A-2) Rearranging: (A-3) where (A-4) Define pseudo-pressure as (A-5) Similarly from partially differentiating Equation (A-5) with respect to p, we get (A-6) For the gas compressibility is defined as (A-7) We also can recognize that (A-8) Substituting the values from Equations (A-4), (A-6) and (A8) in Equation (A-3), it follows (A-9) At this point, it is appropriate to introduce the definition of material balance pseudo-time for gas. (A-10) So the integer form of Equation (A-9) is (A-11).
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