Page 262 - Advanced Mine Ventilation
P. 262

Reservoir Properties of Coal Seams                                239

              The two processes work in series, and the one with a lower rate will control the net
           flow. Thus, in a shallow reservoir with high permeability and a low diffusion coeffi-
           cient, the diffusivity determines the flow rate. In a deeper coal of high rank, the diffu-
           sivity is one or two orders of magnitude higher, and the permeability is lower. Hence,
           permeability determines the flow rate. It is, therefore, important to analyze the diffu-
           sion of gas from coal. It also determines how much methane can be ultimately drained
           from a coal seam.



           14.3.1 The Diffusion Process
           When a gas composed of molecule A (methane) comes in contact with gas composed
           of molecule B (air), the contact will cause diffusion of A into B and B into A. The pro-
           cess tends to produce a mixture of a uniform composition. Many enhanced methane
           production techniques from coal use a gas driver, such as carbon dioxide (CO 2 ) or he-
           lium (He), to increase production. Gas-to-gas diffusion is an important part of the study
           to predict the diffusion process. Similarly, when gas is passed through a porous me-
           dium wet with liquid (oil), the rate of attaining equilibrium between the gas and liquid
           phases depends on the diffusion process.
              Fig. 14.8 shows a simple diffusion process. Container A has CO 2 at 100% concen-
           tration. Container B has 99% methane with 1% carbon dioxide. If the two vessels are
           connected by a conduit 1   1 cm and 1 cm long, CO 2 will try to go into container B
           and likewise methane will try to go into container A.
              Assuming the containers are large in relation to the diffusion rate, the process is
           expressed mathematically as
               dc       dc
                  ¼ DA                                                   (14.15)
               dt       dx

           where c ¼ number of molecules diffusing; t ¼ time; D ¼ diffusivity coefficient;
           A ¼ area; dc/dx ¼ concentration gradient.


           14.3.2 Determination of Sorption Time

           The rate of gas diffusion from coal matrix to bore spaces in coal is, of course, deter-
           mined by the diffusivity coefficient, D. Because it is not certain what the coal “mole-
                                                           2
                                                                              1
           cule” diameter, a, is, the diffusivity is often expressed as D/a that has a unit of sec .







           Figure 14.8 Diffusion process for gases.
   257   258   259   260   261   262   263   264   265   266   267