Satya Harpalani

A new theoretical approach to model sorption-induced coal shrinkage or swelling

The shrinkage or swelling of coal as a result of gas desorption or adsorption is a well-accepted phenomenon. Its impact on permeability changes has also been recognized for two decades. Its importance has increased significantly because of the potential of coals that are not likely to be mined and depleted or nearly depleted coalbed methane reservoirs to serve as CO2 repositories. This article proposes a new theoretical technique to model the volumetric changes in the coal matrix during gas desorption or adsorption using the elastic properties, sorption parameters, and physical properties of coal. The proposed model is based on the theory of changes in surface energy as a result of sorption. The results show that the proposed model is in excellent agreement with the laboratory volumetric strain data presented in the literature during the last 50 yr. Furthermore, the proposed model can be extended to describe mixed-gas sorption behavior, which can be applied to enhanced coalbed methane and CO2 sequestration operations.

Evaluation of in situ stress changes with gas depletion of coalbed methane reservoirs

A sound knowledge of the stress path for coalbed methane (CBM) reservoirs is critical for a variety of applications, including dynamic formation stability evaluation, long-term gas production management, and carbon sequestration in coals. Although this problem has been extensively studied for traditional oil and gas reservoirs, it is somewhat unclear for CBM reservoirs. The difference between the stress paths followed in the two reservoir types is expected to be significant given the unique sorption-induced deformation phenomenon associated with gas production from coal. This results in an additional reservoir volumetric strain, which induces a rather “abnormal” loss of horizontal stress with depletion, leading to continuous changes in the subsurface formation stresses, both effective as well as total. It is suspected that stress changes within the reservoir triggers formation failure after significant depletion. This paper describes an experimental study, carried out to measure the horizontal stress under in situ depletion conditions. The results show that the horizontal stress decreases linearly with depletion under in situ conditions. The dynamic stress evolution is theoretically analyzed, based on modified poroelasticity associated with sorption-induced strain effect. Additionally, the failure tendency of the reservoir under in situ conditions is analyzed using the traditional Mohr-Coulomb failure criterion. The results indicate that depletion may lead to coal failure, particularly in deeper coalbeds and ones exhibiting large matrix shrinkage.

Determination of the Effective Stress Law for Deformation in Coalbed Methane Reservoirs

Effective stress laws and their application are not new, but are often overlooked or applied inappropriately. The complexity of using a proper effective stress law increases when analyzing stress variation in coal as a result of gas production or mining. In this paper, an effective stress law is derived analytically for coalbed methane reservoirs, combining the concepts of matrix shrinkage/swelling and external stress by including the effect of sorbing gas pressure on the elastic response of the reservoir. The proposed law reduces to that of Terzaghi when the compressibility of bulk material is sufficiently greater than the compressibility of the solid grain, and without the strain associated with matrix shrinkage/swelling effect. Moreover, it is shown that the Biot coefficient (α) can have a value larger than unity for self-swelling/dilation materials, such as coal. The proposed stress–strain relationship was validated using experimental results. Overall, the effective stress law for deformation was extended for sorptive materials, providing a new and unique technique to analyze the elastic behavior of coal by reducing three variables, namely, external stress, pore pressure and matrix shrinkage/swelling along with the associated stress, down to one variable, “effective stress”.

Compressibility of sorptive porous media: Part 2. Experimental study on coal

This paper, second of a two-part series, discusses the results of the experimental work conducted to estimate the different compressibilities of coal under both unconstrained and constrained conditions. Under unconstrained conditions, the shrinkage or swelling compressibility (C m) was measured, which was found with certainty to be a pressure-dependent parameter. The model proposed to estimate was able to effectively predict the variation trend, although the modeled values were larger than those calculated using experimental results. The pore-volume compressibility under uniaxial strain conditions for helium depletion was found to be a constant positive value. The value of for methane depletion, however, was found negative, indicating that the pore volume (cleat) increases with depletion. Moreover, its absolute value increased with decreasing methane pressure. Consistent with field permeability observations, the permeability increases with methane depletion, and the rate of increase at lower pressures is higher than at high pressures. The proposed pore-volume compressibility model was well able to predict the variation.

Evaluation of Various Pulse-Decay Laboratory Permeability Measurement Techniques for Highly Stressed Coals

The transient technique for laboratory permeability measurement, proposed by Brace et al. (J Geophys Res 73:2225–2236, 1968) and widely used for conventional gas reservoir rocks, is the preferred method when testing low-permeability rocks in the laboratory. However, Brace et al.’s solution leads to considerable errors since it does not take into account compressive storage and sorption effect when applied to sorptive rocks, such as, coals and shales. To verify the applicability of this solution when used to characterize fluid flow behavior of coal, an in-depth investigation of permeability evolution for flow of helium and methane depletion was conducted for San Juan coals using the pressure pulse-decay method under best replicated in situ conditions. Three permeability solutions, Brace et al.’s (1968), Dicker and Smits’s (International meeting on petroleum engineering, Society of Petroleum Engineers, 1988) and Cui et al.’s (Geofluids 9:208–223, 2009), were utilized to establish the permeability trends. Both helium and methane permeability results exhibited very small difference between the Brace et al.’s solution and Dicker and Smits’s solution, indicating that the effect of compressive storage is negligible. However, methane permeability enhancement at low pressures due to coal matrix shrinkage resulting from gas desorption can be significant and this was observed in pressure response plots and the estimated permeability values using Cui et al.’s solution only. Therefore, it is recommended that Cui et al.’s solution be employed to correctly include the sorption effect when testing coal permeability using the transient technique. A series of experiments were also carried out to establish the stress-dependent permeability trend under constant effective stress condition, and then quantify the sole contribution of the sorption effect on permeability variation. By comparison with the laboratory data obtained under in situ stress/strain condition, it was verified that accelerated CBM production can be achieved by reducing the horizontal stresses.

Compressibility of sorptive porous media: Part 1. Background and theory

This paper, the first of a two-part series, provides a sound background of the volumetric response of sorptive porous media to gas depletion under in situ boundary conditions in producing reservoirs. As a first step, the overall rock matrix deformation is split into two separate components, elastic deformation caused by mechanical decompression and the nonelastic swelling or shrinkage strain induced by adsorption or desorption of gas. The shrinkage or swelling compressibility is estimated by the first derivative of pure adsorption or desorption strain with variations of gas pressure. The pore volume, or fracture, compressibility is then estimated by application of a semi-empirical model under uniaxial strain conditions. Based on the proposed model, both shrinkage or swelling and pore volume compressibilities show strong pressure dependence for sorbing gases and are thus variables for which gas production is controlled by desorption of gas. In Part 2, the experimental work under best-replicated in situ conditions is described in detail along with the results obtained and application of the theory presented in this paper.