Application of Matchstick Geometry To Stress Dependent Permeability in Coals

Abstract

SPE Members Abstract Several investigators have reported coal permeability decreases with increasing stress, but no conceptual model has been advanced to explain this effect. To better understand the permeability of stressed coal, a theoretical and experimental program was undertaken. A common naturally fractured reservoir geometry, a collection of matchsticks, was extended to stressed coalbeds and tested against laboratory measurements using samples from the San Juan and Warrior Basins. Good agreement was obtained between theoretical behavior and laboratory data, Equations are presented for converting laboratory measured stress-permeability data to (a) in-situ permeability as a function of depth of burial in a basin, and (b) to reservoir permeability during coalbed depletion. Coal cleat compressibility, analogous to pore volume compressibility of conventional reservoirs, has historically been difficult and expensive to measure and the results of such measurements are often ambiguous. A method is presented for calculating cleat volume compressibility from stress permeability experiments, resulting in considerable savings of both time and money. Stress-permeability and cleat volume compressibility results reported here are compared with those published in the literature. Evidence in the literature indicates that coal matrix shrinks when gas is desorbed, increasing cleat permeability. Assuming a matchstick geometry and using a coal matrix shrinkage coefficient reported in the literature, the increase in cleat permeability due to matrix shrinkage was calculated. The increase in permeability due to matrix shrinkage during depletion is compared with the decrease in permeability due to increased stress. Introduction Coal deposits are an important gas resource. Producibility of that gas depends on many factors, one of the most important being coalbed permeability. Several previous studies of coal permeability and compressibility have been published and are reviewed in Puri and Seidle. In summary, nine studies showed permeability decreased exponentially as net confining stress increased. All previous experimental work encountered similar difficulties in (1) obtaining well cleated, competent samples, (2) development of sample preparation techniques which did not harm coal samples, (3) equipment constraints which dictated use of experimental stress regimes not representative of in-situ coals, and (4) extreme hysteresis, precluding replication of results from a sample. Theoretical models of coal permeability were based upon conventional sedimentary rock models, not those of naturally fractured reservoirs. The present study was undertaken to:develop a theoretical expression for coal permeability as a function of stress which reflects the naturally fractured nature of a coal deposit, andto measure permeability as a function of stress for selected coals. As work progressed, it became apparent cleat volume compressibility and matrix shrinkage effects could be addressed and the following objectives were added:to fit laboratory results to the theoretical relation to determine cleat volume compressibilities, andto calculate the effect of desorption-induced matrix shrinkage on coal permeability. 1. Theoretical Permeability-Stress Relation Coal deposits are naturally fractured gas reservoirs. These natural fractures form a closely-spaced, orthogonal network called cleats. P. 433^