as seen in previous Sections, gas sorption and swelling have complex effects on the variation of coal porosity and permeability and therefore on the performance of an ECBM operation. an accurate description of Co2/CH4 displacement dynamics in the coal seam is essential for the development of reliable ECBM simulators used to history-match field test data obtained during ECBM operations. the amount of Co2 stored and CH4 recovered, and the time needed for the Co2 to break through at the production well, constitute some of the information needed when designing an ECBM process. input parameters for these models are the laboratory results presented above.
Coal reservoirs are fractured systems often saturated with water, consisting of a low-permeability matrix and a high-permeability fracture network. One can distinguish up to four types of pores in coal, namely cleats where gas and water are present, macro- and mesopores where there is only free gas, and micropores where sorption takes place. The complexity of this pore structure also impacts mass transfer mechanisms and how to describe them in ECBM models. the general assumption is that the displacement of CH4 by Co2 results from a multistep process. the gas injected in the coalbed diffuses from the fracture network, through the matrix and macropores and finally to the internal surface of the coal. Here, partial pressure with respect to the adsorbed gas is reduced, causing desorption, and gas exchange takes place. the desorbed gas diffuses through the matrix and micropores, out to the fracture network where it flows to the production well (Gentzis, 2000;
totsis et al., 2004; Seto, 2007).
as in the case of Equation 5.5, this mass transfer can be described through a linear driving force model by lumping gas diffusion in the different types of pore using a single mass transfer coefficient or the corresponding time constant (Bromhal et al., 2005; Sams et al., 2005). For the sake of better visualization, Fig. 5.8 shows concentration profiles in a coal seam obtained by solving the model presented in Section 5.5, where this relatively simple description of mass transfer is complemented by the description of porosity and permeability changes in the coal during injection and displacement through Equation 5.3. a typical ECBM scenario has been simulated: the coalbed was originally saturated with CH4 and the model is solved for three different compositions of the injected gas, namely pure Co2, pure n2 and a mixture of the two. important insights into coalbed displacement dynamics emerge from the figure. In agreement with field observations and more
CO2
CH4
0 50 100
z (m) 2
1.5
1
0.5
0 ci (kmol/m3)
(a)
CO2 N2
CH4
0 50 100
z (m) 1
0.5
0 ci (kmol/m3)
(b)
5.8 Density profiles in the coal seam obtained by solving the 1D model described in Section 5.5 for different injection compositions:
(a) pure CO2 injection, (b) 50 % CO2/50 % N2 and (c) pure N2 injection.
Parameters: initial reservoir pressure P0 = 15 bar, injection pressure Pinj
= 40 bar, production pressure Pp = 1 bar, initial permeability k0 = 1 mD.
Permeability changes are described using Equation 5.3, for which the constants C1 and C2 are given in the caption of Fig. 5.6.
N2
CH4
0 50 100
z (m) 1.5
1
0.5
0 ci (kmol/m3)
(c)
detailed simulations, injection of pure Co2 displaces the CH4 through a sharp front, due to the higher adsorptivity of the former compared to the latter.
in contrast, when pure n2 is injected the front is much smoother, resulting in a produced stream of CH4 polluted with n2. as expected, injection of a mixture of Co2 and n2 results in the appearance of both the above-mentioned phenomena.
interestingly, the same trends presented above can be obtained by applying a completely different approach, where the so-called local equilibrium assumption is made, i.e. by assuming that sorption and desorption occur quickly enough that the fluid phase and the coal matrix are always in equilibrium (no mass transfer) (Seto et al., 2006; Seto, 2007; orr Jr, 2007; Jessen et al., 2008).
By neglecting dispersion phenomena and swelling effects, the equations presented in Section 5.5 are further simplified and a powerful mathematical technique, i.e. the method of characteristics, can be used to calculate the multiphase multicomponent flow in a coal bed. Even though it represents a strong simplification of the real coal seam, this model is able to describe the EBCM process in a way that sheds light on the complex injection/
displacement dynamics. in particular, the Co2/CH4 displacement mentioned in the previous section can be described by a sharp front the so-called ‘shock front’, whereas the N2/CH4 is characterized by a much broader front, i.e. the so-called ‘simple wave’.
In order to take into consideration the complexity of the pore structure of coal, more detailed approaches have been proposed. these include, for example, the use of a bidisperse pore diffusion model accounting for the diffusivity of both macro-/mesopores and micropores through the corresponding time constants (Shi and Durucan, 2003, 2005a). Such a model has been further improved by extending mass transfer to the overall pore size distribution of the coal, i.e. including convective flow in cleats, convective and diffusive flows in meso- and macropores, sorption and surface diffusion in micropores, whereby diffusion is described using the Maxwell–Stefan equations (Wang et al., 2007). However, a more compact version of such a model has been shown to describe with good agreement a number of displacement experiments carried out on coal cores in different laboratories (Wei et al., 2007a,b).
The 1D single-component description of a dry coal core presented above can be extended to a 3D multicomponent multiphase (coal, gas and water) model.
Such models have to be solved in a 3D domain that comprises the coalbed and accounts for its geological structure and possibly heterogeneous physical features as well as for the configuration of the injection and production wells.
One such reservoir simulator, namely PSU-COALCOMP developed at The Pennsylvania State university and based on a 2D description of the coalbed that assumes vertical homogeneity, has been used to study the effect of the well configuration and design on the amount of stored CO2 as compared to
its theoretical amount, given in principle by the sorption isotherm (Bromhal et al., 2005; Sams et al., 2005). it was shown that depending on the sorption time constant used, at the end of the project lifetime a significant portion of the swept region can still be far from equilibrium, resulting in a reduced amount of Co2 stored, i.e. down to 50 % as compared to the thermodynamic limit predicted by the sorption isotherm. By investigating different well configurations, this situation can be improved and useful design criteria can be derived.
the MEtSiM2 simulator has also been used to analyze and optimize ECBM performance (Shi and Durucan, 2007; Durucan and Shi, 2009). With reference to Fig. 5.9, different ECBM schemes, comparing pure Co2 injection with mixed n2/Co2 injection, were investigated for a three-spot pattern of horizontal wells using public-domain coalbed reservoir properties (Durucan and Shi, 2009). For a five-year time period, mixtures rich in N2 significantly improved CH4 production compared to primary recovery, whereas pure Co2 injection led to no enhancement of CH4 production (Fig. 5.9a). this effect was attributed to the higher permeability following n2 injection in the coal- bed compared to Co2. For the same reason, injection of a 25 % n2 / 75 % Co2 or 50 % n2/50 % Co2 mixture led to a larger amount of Co2 stored compared to that stored if pure Co2 was injected (Fig. 5.9b). Due to the early breakthrough of N2 at the production well, however, there is a trade- off between the enhanced CH4 recovery and the purity of the produced gas (Durucan and Shi, 2009).