Inflow Performance of Partially Open Horizontal Wells
Authors: Goode P.A. , Wilkinson D.J. 
Published: December 2007

Summary
When a horizontal well is selectively completed, the productive length maynot be the entire drilled length of the horizontal section. The productivity ofthe well will be affected by the total length and productivity of the well willbe affected by the total length and distribution of the open intervals. Thispaper presents a method to calculate the inflow performance of a horizontalwell that is selectively completed.

Introduction
Completion of horizontal wells as open holes or with slotted (Figs. 1a and 1b) leaves operators with little or no opportunity to perform diagnostic orremedial work. perform diagnostic or remedial work. Many horizontal wells thathave been producing for several years are now producing for several years arenow experiencing production problems that can be attributed to the lack ofcompletion control. This is particularly true in areas where the targets arethin and coning n a potential problem. It is inevitable that certain portionsproblem. It is inevitable that certain portions of the well will be closer tothe fluid/fluid contact than others and that hydraulic isolation of thoseportions would significantly improve long-term performance. Also, when drillingcontrol or sufficient geological knowledge is absent, portions of the well maynot even lie within the reservoir. Considerable knowledge has been developed onhow to complete horizontal wells successfully; what is missing is a method forpredicting the performance of different completion strategies. It may be thatit is not practical or cost effective to open the entire practical or costeffective to open the entire length of the well within the reservoir. Figs. 1c and 1d are schematics of a selectively completed well. The well in Fig. 1c was completed with external casing packers (ECP's) that had alternate slotted andunslotted sections. Fig. 1d shows that the same effective completion wasachieved with a cemented liner that was subsequently perforated. For thepurpose of inflow perforated. For the purpose of inflow calculations, thesecompletions are identical. As horizontal well technology has developed, severalinflow performance formulas for horizontal wells have been discussed in theliterature. In this paper, we expand the work of Goode and Kuchuk to includethe effects of having only a portion of the well open. They present a solutionfor the inflow performance of a horizontal well producing from a reservoir ofuniform producing from a reservoir of uniform thickness within a closed, rectangular drainage region. The well can be placed arbitrarily within thedrainage volume, provided that the distance from any part of the well (open toflow) to a lateral boundary is large compared with the scaled of the reservoir. In practice this is not an unduly restrictive assumption, unless the verticalpermeability is extremely low. It is much less permeability is extremely low. It is much less restrictive than the geometry required by Giger el al. and Karcher el al, where the well must be short enough, compared with the boundedregion, to permit the development of radial flow before the effect of thelateral boundaries is felt. The formulas presented by Babu and Odeh and Goodeand Kuchuk are for a well placed inside a drainage volume with no flux crossingany external boundary, while the formulas presented in Refs. 3 through 5 assumea constant pressure at the external lateral boundaries and no-flux conditionsat the top and bottom. The no-flux condition on all external boundaries is themost relevant for practical purposes and is the boundary condition used in thiswork.

Mathematical Model
We consider a horizontal well of length 2L 1/2 centered at (x w, y w, z w)and producing from a rectangular region of dimensions Lx and Ly, through n popen intervals, with Segment i of length 2L i centered at x i (Fig. 2). Thedistribution and number of open interviews is arbitrary, as is the position ofthe well within the drainage area, provided that the distance from any openinterval to a lateral is large compared will the scaled reservoir thickness h(kx/k z) 1/2. With this restriction, the pressure will be vertically equilibratedbefore the influence of any lateral boundaries is felt, and we may derive theinflow formula by writing the pressure drop as a sum of two terms. We firstpressure drop as a sum of two terms. We first consider a 2D fracture problemthat is analogous to the horizontal well problem at long times. We then accountfor the pressure drop in the third dimension, z, by including a pseudoskin, SzD, determined by solution of pseudoskin, S zD, determined by solution of a 3Dproblem (not 2D as in Refs. 3 through 5) that excludes the lateral boundaries. The inflow performance of a well is related to the long-time behavior of theconstant-rate pressure. At long times, when no flux is permitted to cross theexternal boundaries, the difference between the average pressure in thereservoir and wellbore pressure pressure in the reservoir and wellbore pressureapproaches a constant value that we call the inflow pressure.
JPT
P. 983