In coalbed methane (CBM) reservoirs, permeability changes dynamically throughout the life of the reservoir as the pressure depletes due to production. The dynamic variation of coal permeability mainly depends on the combined effect of effective stresses and coal matrix shrinkage caused by gas desorption. Under the conditions of pressure-dependent diffusivity in coal reservoirs, the flow mechanism in CBM reservoirs complicates the solution of the two-phase diffusivity equation. In this study, the authors present a new approach to describe the CBM reservoir diffusivity equation in a form that fully couples the pressure-dependent diffusivity and time-dependent desorption effects in the transport mechanism of CBM reservoirs. This paper presents a semi-analytical solution of the fully coupled diffusivity equation under pseudo-steady state flow conditions. The proposed solution is then leveraged to predict the performance of a two-phase CBM well using an approach that is alternative to the conventional method for CBM reservoirs. The proposed semi-analytical model presents a computational method not only to predict the performance but also to evaluate the performance of a producing CBM well. The model presented in this study has been used to investigate the impact of pressure-dependent diffusivity and time-dependent desorption on the production behavior of CBM wells producing under pseudo-steady state conditions. The results of the semi-analytical solution have been verified using numerical simulator CMG-GEM as well as actual in-field data.

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Conventional laboratory core analysis tests on samples of two limestone reservoir rocks indicate that about 20 per cent of PV is in dead-end pores. These tests (electric logging formation factor. mercury injection capillary pressure and miscible displacement) were carried out on 3/4-in. diameter test plugs. Test results show a clear difference between these samples and sandstone or homogeneous limestone reservoir rock. Although the amount of dead-end pore space can be only roughly estimated, the presence of such pore space seems clearly indicated. Pressure transient studies also show presence of dead-end PV. Although they do not give quantitative results, pressure transient data yield a reasonable estimate of the size of the neck connecting dead-end pores to the main flow channels. Introduction Equations conventionally used to describe reservoir flow behavior contain the implicit assumption that all connected pore spaces contributed to both porosity and permeability. Several authors have pointed out the changes in pressure transient behavior and in electric log interpretation that may result if this assumption is incorrect and, instead, dead-end or cul-de-sac pores are present. There is a need for laboratory tests that can detect presence of dead-end pores in core samples. With such information on hand the petroleum engineer can make more rational use of the mathematical tools now available for analysis of reservoir flow behavior. This paper describes laboratory studies designed to detect and, if possible, give a quantitative measure of dead-end PV in laboratory-size core plugs. Three reservoir rocks were used, two of which were limestones suspected of having dead- end pore spaces and a well-known sandstone, used as a comparison standard, in which there is believed to be little or no dead-end pore space. All the studies were designed to measure the natural dead-end PV; i.e., the pore space which is dead-ended because of rock structure. During multiphase flow in a rock without dead-end pores, some parts of one of the phases can become surrounded by the other, thereby giving (for certain flow behavior) an effective dead-end PV 8,9. Such behavior will not be described here. FORMATION FACTOR THEORY One of the simplest laboratory measurements which can be made on core plugs is the electric logging formation factor F. By definition: (1) where Ro is the resistivity of the core plug saturated with a saline solution of resistivity Rw. Difficulties in using this definition of F may arise when the solid framework of the rock is electrically conducting. These difficulties may be largely circumvented by using a highly conducting saline solution so that the conduction contribution of the solid is negligible. There are no useful theoretical relationships between F and the porosity phi. A widely used empirical relation is the one given by Archie: (2) where m, called the cementation factor, is expected to be a constant for a given type of rock. Pirson shows that for reservoir rocks, m varies from about 1.3 for loosely cemented sandstones to 2.2 for highly cemented sandstones or carbonate rocks. SPEJ P. 206ˆ