A novel steady-state productivity equation for horizontal wells in bottom water drive gas reservoirs

It is known that there is a discrepancy between field data and the results predicted from the previous equations derived by simplifying three-dimensional (3-D) flow into two-dimensions (2-D). This paper presents a new steady-state productivity equation for horizontal wells in bottom water drive gas reservoirs. Firstly, the fundamental solution to the 3-D steady-state Laplace equation is derived with the philosophy of source and the Green function for a horizontal well located at the center of the laterally infinite gas reservoir. Then, using the fundamental solution and the Simpson integral formula, the average pseudo-pressure equation and the steady-state productivity equation are achieved for the horizontal section. Two case-studies are given in the paper, the results calculated from the newly-derived formula are very close to the numerical simulation performed with the Canadian software CMG and the real production data, indicating that the new formula can be used to predict the steady-state productivity of such horizontal gas wells.

[1]  Michael L. Wiggins,et al.  Horizontal-Well Productivity and Wellbore-Pressure Behavior Incorporating Wellbore Hydraulics , 2005 .

[2]  Robert A. Wattenbarger,et al.  Simplified Productivity Equations for Horizontal Wells Producing at Constant Rate and Constant Pressure , 1998 .

[3]  F. M. Giger,et al.  Horizontal Wells Production Techniques in Heterogeneous Reservoirs , 1985 .

[4]  L. H. Reiss.  Production from horizontal wells after 5 years , 1987 .

[5]  D. Zwillinger,et al.  Standard Mathematical Tables and Formulae , 1997, The Mathematical Gazette.

[6]  S. D. Joshi,et al.  Augmentation of Well Productivity Using Slant and Horizontal Wells , 1986 .

[7]  L. H. Reiss,et al.  The Reservoir Engineering Aspects of Horizontal Drilling , 1984 .

[8]  D. K. Babu,et al.  Productivity of a horizontal well , 1989 .

[9]  S. D. Joshi,et al.  Augmentation of well productivity with slant and horizontal wells , 1988 .

[10]  L. Rosenhead.  Conduction of Heat in Solids , 1947, Nature.

[11]  H. J. Ramey,et al.  The Use of Source and Green's Functions in Solving Unsteady-Flow Problems in Reservoirs , 1973 .

[12]  Alfred Daniel Hill,et al.  A Comprehensive Model of Multilateral Well Deliverability , 2000 .

[13]  R. Rogers,et al.  A Supplemental Discussion of Productivity Formulae of Horizontal Wells , 2003 .

[14]  G. Renard,et al.  Formation damage effects on horizontal-well flow efficiency , 1991 .

[15]  J. Lu,et al.  A Mathematical Model of Horizontal Wells Pressure Drawdown and Buildup , 2002 .

[16]  Robert W. Chase,et al.  Dimensionless Inflow-Performance-Relationship Curve for Unfractured Horizontal Gas Wells , 2001 .

[17]  F. M. Giger,et al.  Some practical formulas to predict horizontal well behavior , 1986 .

[18]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[19]  J. Lu,et al.  New Productivity Formulae of Horizontal Wells , 2001 .

[20]  R. D. Carmichael,et al.  Mathematical tables and formulae , 1958 .

[21]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[22]  D. K. Babu,et al.  Productivity of a Horizontal Well Appendices A and B , 1988 .

[23]  Leif Larsen.  Productivity Computations for Multilateral, Branched and Other Generalized and Extended Well Concepts , 1996 .