A novel procedure is proposed for a quick and accurate evaluation of bottomhole wellbore pressure. The procedure has led to simple correlations for both horizontal and vertical wells which can be applied to calculate the bottomhole wellbore pressure and productivity index for the entire producing period. The correlations proposed here provide an excellent approximation of the semi-analytical solution at a much reduced computational time. Successful validation of the equations for different well locations and different reservoir geometries has also been achieved.
Bottomhole wellbore pressure and productivity index are two important quantities for both horizontal and vertical wells. For a horizontal or vertical well in a homogeneous but anisotropic reservoir, analytical equations can be obtained for bottomhole wellbore pressure drawdown once pseudo-steady state is reached. Practically, simple equations to evaluate the bottomhole wellbore pressure drawdown in early and transient time are as important as those for late time when the pseudo-steady state flow occurs. Although either the integral transformations (IT) (such as Laplace and Fourier) and separation of variables (SOV) method or the instantaneous point source/sink superposition and the Newman's product method may be used to determine the wellbore pressure drawdown, they take nontrivial (and usually long) computational time to get results, as a consequence they are impractical for routine reservoir engineering applications, such as well performance modeling. Therefore, a novel procedure is proposed here to develop simple yet accurate correlations to evaluate bottomhole wellbore pressure and well productivity index. The idea is very simple and the procedure consists of the following three steps:
Step 1. Use the instantaneous point source/sink solution (IPSS) approach to compute wellbore pressure drawdown at different times;
Step 2. Design appropriate functional forms which reflect characteristics of the wellbore pressure variation with time;
Step 3. Apply a nonlinear regression method to determine the relevant correlation coefficients.
Correlations for Horizontal Wells. Two functional forms of the wellbore pressure drawdown of horizontal wells, which are valid for the entire time period (from early time to transient and then to late-time long after pseudo-steady state is reached) have been tried for correlating the wellbore pressure drawdown data for different horizontal wells:
Form I:
(1)
Form II:
(2)
where
(3)
The values of correlation coefficients, a, b, A and B, for different horizontal wellbore lengths, well locations and reservoir dimension ratios are given in Ref. 2. It was found that both functional forms can provide accurate predictions of the wellbore pressure for the entire time range.
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