Gas-Well Testing in the Presence of Desorption for Coalbed Methane and Devonian Shale

Abstract

Summary. Very large potential gas reserves are present in both coalbeds and Devonian shales. In both formation types, long-term gas production is the result of gas desorption from the matrix. Experiments on core samples show that the desorption obeys a Langmuir isotherm. An approximate analytic solution is derived for single-phase gas flow when gas is present as both free gas and gas adsorbed on the matrix. The solution was verified against a finite-difference solution; the agreement between the two methods is excellent. The analysis of test data is simplest if the test is conducted at a constant mass flow rate. It is shown that the effect of desorption cannot be detected in production testing; therefore, analysis can be performed to obtain permeability as if the desorption effect is absent. The procedure to obtain desorption parameters is also given. The effect of desorption shows up in an increased compressibility, of the form, which can be much larger than the gas compressibility. The effect of desorption on total production is substantial. When gases are adsorbed. total production over the life of a well can be an order of magnitude higher. Introduction In recent years, coalbeds and Devonian shales have been looked to as potential unconventional sources of gas. These sources of gas differ from conventional sources in that gas (methane) is present as free gas and is also held within the porous matrix by an adsorption mechanism that is controlled by the reservoir pressure. Fig. 1 shows methane sorption isotherms at 82 deg. F [28 deg. C] for shale samples from the Illinois basin. The solid curves measure only adsorbed gas as a function of pressure (adsorption isotherm), While the dashed curves measure the total gas content (free and adsorbed gas). Figs. 2 and 3 show sorption isotherms for coal. It is evident from the curves presented in these figures that in coalbeds as well as Devonian shales, long-term gas production is the result of gas desorption from the matrix. These figures also demonstrate that adsorption isotherms are highly nonlinear. Consider, for example, a reservoir with an initial reservoir pressure of 870 psi [6000 kPa] and a sorption isotherm given by Fig. 3. If the pressure is lowered to 435 psi [3000 kPa], the amount of methane adsorbed on the coal changes from 18.47 to 16.18 cm/g, a mere 12.4% decrease. The pressure must be reduced to 260 psi [1790 kPa] (a 70% reduction in external pressure) before one-fourth of the adsorbed methane can be released. The remaining three-fourths of the methane can be released only when the pressure is reduced the remaining 260 psi [ 1790 kPa]. This demonstrates that desorption phenomena play a key role in releasing as, and thus, in gas production. Hence, gas content is not the only factor to consider in estimating reserves. Desorption will ultimately affect current assessment of recoverable gas from both coal and Devonian shale. While gas production decreases with time for conventional sandstone reservoirs, it can increase with time when gas is present as adsorbed gas in unconventional gas reservoirs as a result of desorption phenomena. Objective Some coalbed methane reservoirs and most Devonian shale reservoirs have low or no water content. This paper therefore focuses on single-phase gas flow when any water present is immobile. Flow equations and an approximate analytic solution are developed for gas flow in gas reservoirs where gas is present as both free gas and adsorbed gas. This analytic solution is then compared with a numerical solution. The analytic solution is then used to develop testing procedures for obtaining information on reservoir properties, and to show the effects of desorption on gas production. Adsorption Isotherm The adsorption data that describe the volume of gas adsorbed as a function of pressure at constant temperature are known as the adsorption isotherm. Many functional forms have been proposed in the literature. Two popular forms are the Langmuir and Freundlich isotherms. The Freundlich isotherm is a power-law relationship between adsorbed volume and pressure, and thus it does not limit the total volume adsorbed. Figs. 1 through 3 show that the adsorbed volume reaches a limit at high pressure: therefore, the Freundlich isotherm may be unsuitable when the reservoir pressure is high. The Langmuir isotherm does limit the total methane adsorbed, It can be written as (1) where Pg = gas pressure, PL = Langmuir pressure, the pressure at which totalvolume adsorbed, V, is equal to one-half of theLangmuir volume, V, VE = volume of gas adsorbed per unit volume of thereservoir in equilibrium at pressure p, and VL = Langmuir volume, the maximum sorption capacityof the coal. VE and VL are normally measured under standard temperature and pressure (STP) conditions. Data presented in Fig. 3 can be represented by Eq. 1 if V is 21.53 cm (STP)/g coal and p1 is 144 psi [993 kPa]. Mathematical Model Most unconventional gas reservoirs where gas desorption is important consist of very tight porous formations. The mathematical model used here assumes the following.The reservoir is horizontal with homogeneous properties.The reservoir has single-phase gas flow. SPEFE P. 179^