Analysis of Interference Tests with Horizontal Wells
- Mohammed N. Al-Khamis (Saudi Aramco) | Erdal Ozkan (Colorado School of Mines) | Rajagopal S. Raghavan (ConocoPhillips Co.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- August 2005
- Document Type
- Journal Paper
- 337 - 347
- 2005. Society of Petroleum Engineers
- 4.1.2 Separation and Treating, 5.8.6 Naturally Fractured Reservoir, 5.3.1 Flow in Porous Media, 4.1.5 Processing Equipment, 5.6.4 Drillstem/Well Testing
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One of the common assumptions in horizontal-well interference-test analysisis to ignore fluid flow in and out of the horizontal observation well andrepresent it by a point. In some cases, the active well is also approximated bya vertical line source. Using a semianalytical model, this paper answers threefundamental questions:
• What is the critical distance between the wells to represent thehorizontal observation well by an observation point?
• Where should the observation point be placed along the horizontalwell?
• Under what conditions may the active well be approximated by a verticalline source and the exponential integral solution be used to analyzeobservation-well responses?
Two correlations are presented to simplify the analysis of horizontal-wellinterference tests. Example applications are presented, and error bounds aredocumented.
Analysis of horizontal-well interference tests is an extremely difficultproblem because the lengths, orientations, locations, and distances betweenwells need to be considered. One of the assumptions used to make thehorizontal-well interference-test analysis a tractable problem is to ignore theflow pattern that results because of the existence of the horizontal well andto treat the horizontal observation well as an observation point. It also hasbeen suggested that if the distance between the two wells were sufficientlylarge, then the active horizontal well could be replaced by a vertical well. Inthis case, the observation-well responses may be approximated by theexponential integral solution, and the analysis is reduced to the conventionalinterference-test analysis between vertical wells.
For the application of the approximate analytical techniques, two questionsneed to be answered. The first question is whether the distance between the twohorizontal wells is large enough for the geometry of the wells to be ignored.Malekzadeh investigated this question by considering the interference between ahorizontal active well and a vertical observation well in an isotropicreservoir. Because anisotropy has a major effect on the pressure-transientresponses of horizontal wells, the results of Malekzadeh have limitedapplicability. In addition, the influence of the geometry of the observationwell cannot be deduced from the model used by Malekzadeh.
The second question is, where should the equivalent observation point (EOP)be placed in the reservoir if the horizontal well were to be replaced by avertical well? This question has yet to be addressed in the literature. The EOPis defined as the location at which the pressure recorded at the heel of thehorizontal observation well would exist in the absence of the observation well.Because of the lack of theoretical guidance, the physical location of the heelor the center of the observation well is usually chosen as the observationpoint.1 But such an assumption ignores the fact that fluids enter and leave thehorizontal observation well although there is no surface production. Therefore,some disturbance of equipotential lines around the observation well should beexpected. Thus, if the horizontal well were to be removed from the system, wemay expect the pressure recorded at the heel of the horizontal well to exist ata different location. The location of the EOP would be a function of thevariables that determine pressure at the observation well.
This work uses a semianalytical model to answer the above questions. Themodel has been discussed in detail in Refs. 4 and 5 and is capable ofconsidering interference between two horizontal wells in a homogeneous butanisotropic reservoir. Based on the results of the semianalytical model, twocorrelations have been developed to significantly simplify the analysis ofhorizontal-well interference tests without sacrificing accuracy.
The first correlation provides the location of the EOP, which has not beenavailable in the literature. The second correlation provides information on thedistance under which both horizontal wells may be treated as vertical wells andthe exponential integral solution may be used to analyze the interference test.Compared with the correlation presented by Malekzadeh, the correlationpresented here is more comprehensive because it accounts for the effects ofanisotropy, location of the EOP, and relative position of the wells. To assessthe adequacy of the correlations, error bounds have been calculated and aredocumented in this paper.
The correlations enable us to analyze horizontal-well interference tests bythe single-horizontal-well solutions or by the exponential integral solution.The convenience of the single-horizontal-well models for the regressiontechniques used in well-test-analysis software becomes clear if thecomputational complexity of the rigorous horizontal-well interference-testmodels4,5 is noted (the increase in the speed of computations is usually morethan six-fold).
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