Title: Analytical coupled axial-radial semi-steady state productivity model for horizontal wells in anisotropic medium

Authors: Thormod Ekely Johansen; Jie Cao; Lesley James

Addresses: Faculty of Engineering and Applied Science, Memorial University of Newfoundland, 230 Elizabeth Ave, St. John's, NL, A1B 3X9, Canada ' Faculty of Engineering and Applied Science, Memorial University of Newfoundland, 230 Elizabeth Ave, St. John's, NL, A1B 3X9, Canada ' Faculty of Engineering and Applied Science, Memorial University of Newfoundland, 230 Elizabeth Ave, St. John's, NL, A1B 3X9, Canada

Abstract: The classical productivity models are solutions to one-dimensional radial flow equations for vertical wells at different flow conditions. A new, fully analytical model for coupled radial well inflow and axial reservoir flow has been developed under the assumption of semi-steady state flow, i.e. the axial flow and the well inflow are solved simultaneously in closed form expressions. This coupled axial-radial flow model results in a quadratic pressure profile in the axial direction and a quadratic-logarithmic pressure profile in the radial direction. The new productivity equations are formulated by using either external pressure or average reservoir pressure in addition to flowing wellbore pressure. For the special case where axial flow or radial flow is zero, it is shown that the formulas coincide with the classical formulas for radial and linear flow, respectively. The new productivity model is also developed for an anisotropic medium by implementing a space transformation in the near-well region. The anisotropic productivity model highlights the flow in the near-well region and provides flexibility in choosing configuration of near-well simulation grid blocks. An algorithm for the simulation of the near-well flow and horizontal well productivity is presented.

Keywords: analytical productivity models; semi-steady state flow; horizontal wells; modelling; coupled axial-radial flow; anisotropic medium; radial well inflow; axial reservoir flow; external pressure; reservoir pressure; wellbore pressure; simulation; near-well flow; horizontal well productivity.

DOI: 10.1504/IJPE.2016.081789

International Journal of Petroleum Engineering, 2016 Vol.2 No.3, pp.225 - 245

Available online: 20 Jan 2017 *

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