This paper presents new guidelines for determining net pay thickness in low-permeability, multilayered gas wells. These criteria were developed from a sensitivity study performed with an analytical solution for compmlex multilayered reservoirs. The purpose of this study was to determine whether many layers now considered to contribute to net pay actually have transmissibilities too low for the layer to be productive, causing performance projections from current single-layer descriptive models to be too optimistic.


Devonian shales are multilayered, frequently naturally fractured reservoirs with a large variance in permeability between layers. Many Devonian shale wells have had hydraulic fracture treatments to increase productivity; however, the fractures may exist only in some of the many layers of the reservoir. According to conventional post-fracture pressure-buildup test analysis, stimulation of the Devonian shale wells has fallen short of design expectations. This paper presents results from a study using an analytical solution for multilayered wells that suggest that conventional analysis of tests from these wells is inadequate because of the simplicity of the reservoir model used to describe them.

We developed a new analytical solution, based on Laplace transform methods, similar to Spath et al.'s1 recent solution. This solution accurately models the complexity of Devonian shale wells. Devonian shale completions frequently consist of at least five layers commingled at the wellbore. Some layers are naturally fractured, interspersed with homogeneous-acting silt layers. Some or all of the layers may contain a hydraulic fracture, and some layers may be of limited areal extent. Gas production from these wells is at a constant bottomhole pressure (BHP). The analytical solution we have programmed can model all these conditions.

We studied two-layer systems systematically to find a minimum transmissibility for a layer to be considered part of the net pay thickness. This study considered homogeneous or naturally fractured layers, with and without a hydraulic fracture in the layer. The results from this two-layer study were extended and confirmed for multilayered cases.

Unless layers are tested individually, conventional pressure-buildup analysis results in a total transmissibility, kh, and an equivalent fracture half-length for the entire net pay zone. When these results are used in performance projections with a single-layer model, forecasts have consistently proved to be optimistic.

We used the analytical solution to compare the impact of a fracture treatment that affects only one layer in a five-layer system with a fracture of the same length in the total system. The input parameters for the analytical simulation for the five-layer case were obtained from geophysical logs, production logs, and well tests in typical eastern Devonian shale wells. We illustrate the power of the model through a field case described with individual-layer test results.

Here, we first describe the model used to simulate the complex Devonian shale formation. We verified this model using examples from the literature2-6 and a commercial analytical simulator; detailed results are given in Ref. 3. We then present our results from both the two-layer and the multi-layer studies. Finally, we state conclusions drawn from the results of the research.

Model Description

The analytical solution can model n layers. Each layer can be either naturally fractured, with pseudo-steady-state or transient interporosity flow, or homogeneous-acting. Individual layers may have hydraulic fractures of various lengths, with either infinite conductivity or uniform flux. The layers can be infinite-acting or can act as closed systems with various drainage areas. Each layer can have a different permeability, thickness, porosity, wellbore radius, skin, fracture half-length, or natural fracture characteristics. The multilayered system is commingled at the wellbore, with no crossflow between layers. The well may be produced at constant BHP or at constant total flow rate. The solutions were developed for slightly compressible liquids, but the use of normalized pseudopressure in the solution allowed us to consider gas production. Isothermal conditions, negligible gravitational effects, production of a single-phase fluid, laminar flow behavior (gas velocities low enough that non-Darcy flow effects are negligible), permeability independent of pressure, and a viscosity/compressibility, µct, product that is constant with pressure were assumed.

The Appendix presents a derivation of the analytical solution. This reservoir model will have many applications in reservoir description beyond those discussed.

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