This paper examines the transient pressure response from slug tests in wells completed in multiple, hydraulically fractured coal seams. We developed a model for stimulated wells producing from commingled reservoirs, i.e., reservoirs in which the layers communicate only at the wellbore and not in the fracture or reservoir. With this model, we have investigated the effects of various reservoir properties on the slug test pressure behavior and have found that the characteristic pressure response depends more on the contrast between layer properties than their absolute values. We also present a method for correlating the slug test pressures from multi-layer and single-layer reservoirs, thus allowing us to use single-layer type curves to analyze slug tests.
Conventional slug test type curves and analysis techniques are based on single-layer, radial-flow models. Since coal seams are relatively thin compared to conventional natural gas reservoirs, economically viable coalbed methane wells often must be completed in multiple seams. In addition, the typical range of permeabilities observed in coal requires that wells be hydraulically permeabilities observed in coal requires that wells be hydraulically fractured, especially for the critical dewatering phase early in a well's productive life. Therefore, these conventional slug test analysis techniques are not valid for either evaluating wells completed in multiple coal seams or assessing the post-fracture potential of hydraulically fractured coalbed methane wells. potential of hydraulically fractured coalbed methane wells. Karsaki, et al examined the pressure behavior during slug tests in wells intersecting infinite-conductivity, vertical fractures. Similarly, Rushing, et al. investigated slug testing in wells with finite-conductivity, vertical fractures. Both studies, however, were limited to single-layer cases. Karaski, et al. also studied the slug test pressure response in unstimulated layered reservoirs, but their study only considered homogeneous, two-layer formations.
The purpose of this paper is to investigate the transient pressure behavior during slug tests in wells completed in multiple. hydraulically fractured coal seams We developed a model for stimulated wells completed in commingled reservoirs, i.e., reservoirs in which the layers communicate only at the wellbore and not in the fractures or reservoir. Under these conditions, our model is applicable either for wells in which the layers have been stimulated with separate fracture treatments but are produced through a common wellbore, or for wells completed in multiple layers intersected by a single fracture in which negligible gravity effects and low vertical fracture permeabilities limit vertical flow.
DEFINITIONS AND MODEL DEVELOPMENT
Following the work of Spath, et al. and Johnston and Lee, we model a commingled reservoir having multiple, hydraulically fractured layers. The model considers a reservoir in which each layer can have distinct reservoir and fracture properties; however, each layer is an isotropic, homogeneous, infinite, horizontal medium with a uniform thickness, permeability, and porosity. In addition, each layer is assumed to contain a slightly compressible fluid with viscosity and compressibility that are independent of pressure. Finally, we assume the initial pressures in all layers are pressure. Finally, we assume the initial pressures in all layers are equal and single-phase flow exists at all times. Under these conditions, the Laplace transform of the total, dimensionless pressure response for the layered system is pressure response for the layered system is 1pfD(u, nkj hj 1k h pfDj(u)j=1
where u is the Laplace space variable, n is the number of layers, and j is the layer index. The dimensionless pressure, pfDj(u), in the jth layer is computed with Cinco-Ley, et al. model which considers a well intersected by a fully-penetrating. finite-conductivity, vertical fracture. The fracture is modeled as a homogeneous, uniform slab. Because the fracture width is assumed to he much smaller than the fracture length and height, the model assumes flow in the fracture is linear and fluid influx at the fracture tips is negligible. In addition, the model assumes fluid production from the reservoir to the wellbore occurs only through the fracture.