![]() ![]() The pressure change and pressure derivative curves leave the unit slope line at relatively early times and take a relatively long time to reach the MTR.ĭifferences in drawdown and buildup test type curves When the skin factor is negative, the pressure derivative approaches a horizontal line from below. The pressure change and pressure derivative are separated by approximately one log cycle when WBS ends. When the skin is near zero, the pressure derivative rises to a maximum and then falls only slightly before flattening for the MTR. 5 – Shape of the type curves provides a qualitative estimate of skin factor. The shapes of the derivative stems are much more distinctive than those for the pressure-change type curve.įig. Note the unit slope lines at earliest times and the horizontal derivative at later times. 2 shows the derivatives, including those times. t D/ C D will coincide and will have slopes of unity.įor values of t D( ∂p D/ ∂t D) between the end of complete wellbore storage distortion and the start of infinite-acting radial flow, no simple solutions are available to guide us, but Fig. 9 is that, on logarithmic coordinates, graphs of p D and t D( ∂p D/ ∂t D) vs. In terms of dimensionless variables, the derivative becomes The derivative, t∂Δ p/ ∂t, is qBt/24 C, the same as the pressure change itself. When wellbore storage completely dominates the pressure response (all produced fluid comes from the wellbore, none from the formation), Thus, when the distorting effects of wellbore storage have disappeared, the pressure derivative will become constant in an infinite-acting reservoir, and, in terms of dimensionless variables, will have a value of 0.5. 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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