Abstract
When a gas well is drilled and stimulated in a coal seam, the gas flow goes through three regimes of flow: (1) unsteady flow, which is time-dependent, (2) steady flow, and (3) production decline, also time-dependent. Estimation of gas and water flow under each regime is essential for commercial marketing contracts. First, the unsteady state flow is mathematically modeled and solved to predict pressure decline in a reservoir, where the well is flowed at a constant pressure. Pseudo-porosity for coal is defined and shown to be about 0.55 for most coal. Next, the pressure decline in a coal seam where the gas well is produced at a constant flow rate is calculated. An equation for the cumulative gas flow when the well is produced at a constant pressure from an infinite reservoir is calculated. Then the mathematical derivation of permeability from (1) draw-down test and (2) build-up test are done to supplement the calculation of permeability in Chapter 3, Porosity and Permeability of Coal. In the steady-state flow regime, the gas production as well as water production is calculated theoretically. Production increases by hydrofracking a single coal seam and multiple coal seams in a single well are calculated. Finally, six models of production decline are presented. They are: (1) exponential decline, (2) harmonic decline, (3) hyperbolic decline, (4) power law exponential decline, (5) stretched exponential decline, and (6) power law decline. The last was proposed by the author, and three cases of gas production are modeled to confirm the accuracy of the model.
Published Version
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