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.It is concluded that the presented model showed improved efficiency in interpreting the step-drawdown test results by considering the contribution of the time-varying well loss under transient pumping conditions. Estimation of well efficiency under different pumping rate conditions suggests that the contribution of well loss to the total drawdown varies from 82 to 98% for well D8 and 95.5 to 99.93% for well D10, depending on the pumping rates and the applied models. The discrepancies between the estimated RMSEs of different models tend to increase under higher pumping rates, indicating that transient well-loss hydraulics could be important to estimate the well efficiency, particularly for high-capacity wells. Comparisons between the analysis results of different models showed that this model yielded the smallest root mean square errors (RMSEs) between the observed and simulated drawdowns. The suggested method was validated through comparisons with previous models and applied to two public-supply pumping wells (wells D8 and D10) in an agricultural region of South Korea. An equation to represent time-varying well loss is suggested and formulated to develop a model for the transient step-drawdown test analysis. A method is proposed for analyzing transient step-drawdown test data by considering potential transient well-loss hydraulics. A step-drawdown test is one of the most widely used aquifer tests to estimate the groundwater well yield and the well performance.
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