Published techniques for after-closure analysis of fracturing data usually assume the presence of a vertical fracture intersecting a vertical well. In addition, these published techniques usually assume that the formation is homogeneous. When the formation is naturally fractured or the well is horizontally intersecting a transverse vertical fracture, those assumptions are obviously violated and the published analysis techniques might not be applicable. Through the use of analytical and numerical solutions and application to actual field data, this paper investigates the analysis of after-closure data for heterogeneous formation, naturally fractured data, CBM, and fractured horizontal well.
This paper briefly reviews the various available techniques for after-closure analysis, pointing out the strengths and weaknesses of each. An analytical solution for injection falloff test for a naturally fractured formation has been developed and is presented. This solution might be used to analyze data for a MiniFrac test in a naturally fractured formation where the fractured has healed. Numerical simulation validated the developed solution for a fracture that has healed. The same numerical simulator was used to expand the solution to a situation where the fracture maintains residual conductivity.
The solution for a MiniFrac test in the case of a transverse fracture is also presented and discussed. Using a numerical simulator, MiniFrac tests are simulated and analyzed for both heterogeneous formations and a fractured horizontal well. Guidelines for analysis of such data have been developed and presented.
Field data are also presented. One case presents a MiniFrac test for a heterogeneous formation. A case for a transverse fracture intersecting a horizontal is also presented and analyzed. A third case for CBM is discussed.
The early development of fracture-diagnostic techniques (Nolte 1979; 1986; 1990 and Tan et al. 1988) aimed at the determination of fracture closure pressure and leakoff coefficient. Later development (Mayerhofer et al. 1995; Valkó and Economides 1999) concentrated on the transient analysis of the before-closure data, leading to the calculation of reservoir properties such as initial pressure and permeability. One major weakness in the before-closure analysis techniques is the strong dependence on the assumed fracture-propagation model. In addition, the change of model dimension (fracture length and width) during the test makes a unique analysis difficult to achieve. Analysis of after-closure data would, to some extent, eliminate this problem. Two basic approaches have been developed for analysis of after-closure data.
Abousleiman et al. (1994), Nolte et al. (1997) and Soliman et al. (2005) presented techniques to analyze the after-closure data. Those analysis techniques represent two basic approaches for analysis of data. Both approaches rely on the well-testing technology.
The first approach for after-closure analysis was developed by Nolte et al. (1997). In this approach, the after-closure analysis model was developed by assuming a constant injection pressure followed by shut-in. The solution of this problem can be found in the classical heat flow in solids. Manipulating the solution to account for closure time, the falloff equation was developed. The basic weakness of this approach is that one has to assume the prevailing flow regime during the after-closure period. In this approach, two models were developed for pseudo-radial or pseudo-linear flow conditions.
The second approach developed by Soliman et al. (2005) is grounded in well-test analysis technology and is similar to an approach that had been developed earlier for analysis of well-test data when the producing time is short (Soliman et al. 2004). Rather than considering the test as a constant pressure injection, as in the first approach, the test is considered to be a constant-rate test. This is actually a more realistic approach because most of those injection tests are conducted at a constant rate. Even if the rate is not exactly constant, Soliman et al. (2004) have shown that the effect of a somewhat varying rate on the final analysis is fairly minor.