Single-Phase Inflow Performance Relationship for Horizontal, Pinnate-Branch Horizontal, and Radial-Branch Wells

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Summary Horizontal and multibranch wells are likely to become the major means of modern exploitation strategies; inflow performances for these wells are needed. Because this paper considers the finite conductivity of a horizontal well, it establishes the inflow performance relationships (IPRs) for different branch configurations of horizontal wells. We find that the IPR of a horizontal well presents nonlinear characteristics and is similar to Vogel's equation, which has been used extensively and successfully for analyzing the IPR of a vertical well in a solution-gas-drive reservoir. Instead of the effect of a two-phase (oil and gas) flow in a reservoir described by Vogel's equation, the nonlinear characteristics of horizontal wells are mainly the result of pressure drops caused by friction, acceleration, and gravity along the horizontal wellbore. The nonlinearity coefficient presents the pressure drop along the major branch, and it is a function of major-wellbore length, major-wellbore diameter, oil viscosity, and relative roughness. Then, the horizontal-well IPR is used to study the performance of the pinnate-branch horizontal well and the radial-branch (horizontal lateral) well. The branch number, branch length, major-wellbore length, major-wellbore diameter, oil viscosity, and relative roughness are combined into grouped parameters to present the effect on the deliverability incremental ratio JH and the nonlinearity coefficient ratio Rv of the pinnate-branch horizontal well to the conventional horizontal well, which show regression relationships with the grouped parameters for pinnate-branch horizontal wells. In addition, another binomial relationship between the deliverability incremental ratio JV and the grouped parameter combined by branch number, branch length, and equivalent oil drainage diameter is obtained for radial-branch (horizontal lateral) wells. The new IPR also covers conventional horizontal wells and vertical wells (with no branch) because the deliverability incremental ratios JH and JV in both cases are unity. The IPR is very valuable for calculating the productivity of horizontal wells, pinnate-branch horizontal wells, and radial-branch wells.