xSPE 49225

A Generalized Material Balance Equation for Coal Seam Gas ReservoirsG. Penuela, SPE, U. Industrial de Santander; A. Ordonez, SPE, U. Industrial de Santander, and A. Bejarano, SPE,Instituto Colombian del Petroleo - ECOPETROL

Copyright 199S, Society of Petroleum Enginaers, lnc

rhis paper was prepar~ for presenlatiti al the 1998 SPE Annual Te*nical Conference andExhibtion held in New Orleans, Louisiana, 27-30 September 199a

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AbstractDuring the Iast few years, research has been done ongeneralized material balance equations for conventional oiland gas reservoirs in order to improve the reservoirperformance analysis. However, those equations areinappropriate for coal seam gas (CSG) reservoirs. To addressthis limitation, a generalized material balance equation(GMBE) for CSG reservoirs was developed. This work isbased on a mathematical development and the straight-linemethod, published previously md widespread used forconventional reservoirs.

Three validation examples of the proposed equation weredesigned. They show the new equation has the followingadvantages: (1) it is applicable to CSG reservoirs in saturated,equilibrium, and undersaturated conditions, (2) it is applicableto any type of coalbed without restriction on especial diffusionconstant values, (3) existent equations are particular cases ofthe generalized equation evaluated under certain restrictions,and (4) its reorganization is analogous to the popular straight-line method for conventional reservoirs.

IntroductionThe material balance technique is one of fundamental methodsused to analyze the reservoir performance, to determine theoriginal gas-in-place, and to make future reservoir predictions.Schilthuis, in 1936, was among the first to formulate andapply material balances. Later, Walsh2presented a generalizedapproach for oil-and-gas conventional reservoirs, However,the assumption of non-reactive gas-rock makes the use oftraditional equations for conventional gas reservoirs

Society of PetroleumEngineers ~1

inappropriate for CSG reservoirs due to the large inte_m_alsurface area contained within the coal seam. This area allowsmany potential sorption sites exist and large quantities of gascan be adsorbed.

King3 presented the development of two material balanceequations using the traditional assumptions associated with thematerial balance approach and including the effects ofadsorbed gas. One of these equations is appropriated forestimating gas in-place, but an additional assumption ofequilibrium between the free and adsorbed gas phases is

-.

required. This equation has the form

(Vba+Zsc TscGp = P,, T )-1(1 - ~.,) pi + RTCE, -Zi

1 -= ==1

[1 - C+(Pi - P~Q - SW)Pz

R TCE+

4,

..(1)

where

Swi[l+ C. (Pi - P)] + 5.615 (We- BwWp)3.=

& Vb,[(- C,@i: i)]- --()

In the present work, the above equation has been calledconventional material balance equation (CMBE) for CSG.

me second expression proposed by King is a lessrestrictive equation that is useful for making fiture reservoirpredictions, It can be obtained by considering a gas resorptionterm, Gd. This equation has the form

[

(l-Sw,)Pi -

(Vb, + Zsc Tsc

)

z,Gp =

P,. T [1C$(Pi-P)](l 9Pz

+Gd..(3)

621

2 G. PENUELA, A. ORDONEZ, A. BEJARANO SPE 49225

md Gd = Vb,(GI, - GI) ....... . . . ..... . . ..............................(4)

or GJ = V~,Da~(Glt - V~)e-D-r)dr .....................(5)o

Although the aforementioned equations are goodapproximations, they do not help us analyze differentreservoir conditions in which a CSG reservoir may be foundor can undergo throughout its productive life. Therefore,based on a generalized material balance equation forconventional reservoirs,2 a GMBE for CSG reservoirs wasdeveloped.

Behavior of a Coal Seam Gas ReservoirCoal seam gas reservoirs are unconventional gas reservoirs,where natural gas, comprised and predominantly compound ofmethane (95-98?%), exists as a monomolecular layer in nearliquid-like state, adsorbed on the internal surfaces of the coaImatrix.

Most natural occurrences of coalbed methane gas are incoal seams that are submerged in aquifers. The gas resorptionmechanism is controlled by the hydrostatic head of theaquifer. As water is pumped from the seam at a well bore, thepressure (head) is reduced and methane released. Once thisgas is desorbed from the matrix, it diffises to the cleat systemand flows to the producing well according to Darcys law 5(Fig. 1).

Coal seam gas reservoirs may be found in three possibleinitial states (Fig. 2): 6 (A) Equilibrium, (B) saturated, and (C)undersaturated conditions. In the tower portion of Fig. 2, aLangmuir isotherm is shown. Point A, equilibrium state,occurs when the amount of adsorbed gas is equal to theamount given by the isotherm. A pressure drop in the cleatsystem causes gas to desorb from the micropore surfaces andto difise into the macropores. As production continues, a freegas phase wilI be formed in the cleats. Point B represents thesaturated state. It is similar to the equilibrium state in terms ofadsorbed voIume; however, free gas is present in the cleatsystem. As production continues, the reservoir is retained inthe saturated condition. The third possibility, described asPoint C, is the existence of undersaturated condition. In acoalbed reservoir described as point C, the amount of gasadsorbed onto the coal is less than the amount depicted by theisotherm at reservoir pressure and temperature. In this case, nogas can be produced until its critical resorption pressure hasbeen reached. As water production continues, and pressuredecreases over the course of time, the reservoir enters into thesaturated condition.

The upper portion of Fig. 2 shows gas saturation in thesecondary-porosity system (fracture system) for theabovementioned cases. For cases A and C, there is no initialfree gas; hence, gas saturation is marked as zero. For case B,the gas phase saturation is larger than zero.

Generalized Material Balance Equation for CoalSeam Gas ReservoirsIn the mathematical development of the GMBE for CSGreservoirs, the following assumptions were used1.2.

3.

4.

5.

6.7.

8.

9.10,

11