Analysis of Interference Tests With Horizontal Wells

Abstract

Summary One of the common assumptions in horizontal-well interference-test analysis is to ignore fluid flow in and out of the horizontal observation well and represent it by a point. In some cases, the active well is also approximated by a vertical line source. Using a semianalytical model, this paper answers three fundamental questions:• What is the critical distance between the wells to represent the horizontal observation well by an observation point?• Where should the observation point be placed along the horizontal well?• Under what conditions may the active well be approximated by a vertical line source and the exponential integral solution be used to analyze observation-well responses? Two correlations are presented to simplify the analysis of horizontal-well interference tests. Example applications are presented, and error bounds are documented. Introduction Analysis of horizontal-well interference tests is an extremely difficult problem because the lengths, orientations, locations, and distances between wells need to be considered. One of the assumptions used to make the horizontal-well interference-test analysis a tractable problem is to ignore the flow pattern that results because of the existence of the horizontal well and to treat the horizontal observation well as an observation point. It also has been suggested that if the distance between the two wells were sufficiently large, then the active horizontal well could be replaced by a vertical well. In this case, the observation-well responses may be approximated by the exponential integral solution, and the analysis is reduced to the conventional interference-test analysis between vertical wells. For the application of the approximate analytical techniques, two questions need to be answered. The first question is whether the distance between the two horizontal wells is large enough for the geometry of the wells to be ignored. Malekzadeh investigated this question by considering the interference between a horizontal active well and a vertical observation well in an isotropic reservoir. Because anisotropy has a major effect on the pressure-transient responses of horizontal wells, the results of Malekzadeh have limited applicability. In addition, the influence of the geometry of the observation well 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 a vertical well? This question has yet to be addressed in the literature. The EOP is defined as the location at which the pressure recorded at the heel of the horizontal observation well would exist in the absence of the observation well. Because of the lack of theoretical guidance, the physical location of the heel or the center of the observation well is usually chosen as the observation point.1 But such an assumption ignores the fact that fluids enter and leave the horizontal observation well although there is no surface production. Therefore, some disturbance of equipotential lines around the observation well should be expected. Thus, if the horizontal well were to be removed from the system, we may expect the pressure recorded at the heel of the horizontal well to exist at a different location. The location of the EOP would be a function of the variables that determine pressure at the observation well. This work uses a semianalytical model to answer the above questions. The model has been discussed in detail in Refs. 4 and 5 and is capable of considering interference between two horizontal wells in a homogeneous but anisotropic reservoir. Based on the results of the semianalytical model, two correlations have been developed to significantly simplify the analysis of horizontal-well interference tests without sacrificing accuracy. The first correlation provides the location of the EOP, which has not been available in the literature. The second correlation provides information on the distance under which both horizontal wells may be treated as vertical wells and the exponential integral solution may be used to analyze the interference test. Compared with the correlation presented by Malekzadeh, the correlation presented here is more comprehensive because it accounts for the effects of anisotropy, location of the EOP, and relative position of the wells. To assess the adequacy of the correlations, error bounds have been calculated and are documented in this paper. The correlations enable us to analyze horizontal-well interference tests by the single-horizontal-well solutions or by the exponential integral solution. The convenience of the single-horizontal-well models for the regression techniques used in well-test-analysis software becomes clear if the computational complexity of the rigorous horizontal-well interference-test models4,5 is noted (the increase in the speed of computations is usually more than six-fold).

Prediction of immiscible gas flooding performance: a modified capacitance–resistance model and sensitivity analysis

“…This parameter can be determined using CRM or other direct and indirect methods. Direct methods such as 4D seismic (Huang and Ling 2006;Huseby et al 2008;Yin et al 2015Yin et al , 2016, pulse testing (Dinges and Ogbe 1988;Fokker et al 2012), interference (Al-Khamis et al 2005;Ogbe and Brigham 1989;Stewart and Gupta 1984) well tests and tracer tests (Du and Guan 2005;Dugstad et al 1999;Huseby et al 2008;Lichtenberger 1991;Refunjol and Lake 1999) are operationally implemented in the field. Although indirect methods are data-driven models and are based on input-output signals which are developed mathematically or statistically, they include artificial neural networks (ANN) (Demiryurek et al 2008;Panda and Chopra 1998;Artun 2017), wavelet analysis (Jansen and Kelkar 1997), Spearman rank correlation (Heffer et al 1997;Fedenczuk and Hoffmann 1998;Refunjol and Lake 1999), extended Kalman filter (Liu et al 2009), pressure-based method (Dinh and Tiab 2008), multiwell productivity method (Valko et al 2000;Kaviani and Valkó 2010), network model (Gherabati et al 2017a, b), and streamline simulation (SS) (Batycky et al 1997(Batycky et al , 2005Thiele et al 2010;Thiele and Batycky 2006;Baker 2001).…”

On determination of interwell connectivity under immiscible gas injection process: Modified capacitance‐resistance model

“…Direct methods are based on a test performed in a reservoir such as tracer testing, multiple well testing, and 4D seismic surveying . Although direct methods are accurate, they are expensive and time‐consuming.…”