![]() In terms of dimensionless variables, t D( ∂p D/ ∂t D) = 0.5. ![]() The derivative of ( p i – p wf) with respect to ln( t), expressed more simply as t∂Δ p/ ∂t, is 70.6 qBμ/ kh, a constant. This portion of the test is described by the logarithmic approximation to Ei-function solution, Eq. First, consider that part of a test response where the distorting effects of wellbore storage have vanished. Two limiting forms of this solution help illustrate the nature of the derivative type curve. The "derivative" referred to in this type curve is the logarithmic derivative of the solution to the radial diffusivity equation presented on the Gringarten type curve. eliminates the ambiguity in the Gringarten type curve. The derivative type curve proposed by Bourdet et al. However, adjacent pairs of curves can be quite similar, and this fact can cause uncertainty when trying to match test data to the "uniquely correct" curve.įig. Each different value of C D e 2 s describes a pressure response with a shape different (in theory) from the responses for other values of the parameter. the time function t D/ C D, with a parameter C D e 2 s ( Fig. In the Gringarten type curve, p D is plotted vs. The type curve is also useful to analyze pressure buildup tests and for gas wells. These assumptions indicate that the type curve was developed specifically for drawdown tests in undersaturated oil reservoirs. It is based on a solution to the radial diffusivity equation and the following assumptions: vertical well with constant production rate infinite-acting, homogeneous-acting reservoir single-phase, slightly compressible liquid flowing infinitesimal skin factor (thin "membrane" at production face) and constant wellbore-storage coefficient. presented a type curve, commonly called the Gringarten type curve, that achieved widespread use. Solutions to the diffusivity equation for more realistic reservoir models also include the dimensionless skin factor, s, and wellbore storage coefficient, C D, where This leads to much simpler graphical or tabular presentation of the solution than would direct use of Eq. 1 has the advantage that this solution, p D, to the diffusivity equation can be expressed in terms of a single variable, t D, and single parameter, r D. 2, the definitions of the dimensionless variables are (Variables that when the parameters are expressed in terms of the fundamental units of mass, length, and time, have no dimensions are sometimes said to have dimensions of zero.) 1 can be rewritten in terms of conventional definitions of dimensionless variables. 1, presented in terms of dimensional variables:Įq. To review dimensionless variables, consider the Ei-function solution to the flow equation, Eq. The solutions plotted on type curves are usually presented in terms of dimensionless variables. 4 Differences in drawdown and buildup test type curves.
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