Response to “Comments on ‘Gas Permeability of Fractured Sandstone/Coal Samples under Variable Confining Pressure’, Transport in Porous Media 83:333–347, 2010”

Abstract

We are thankful that Dr. Cook invested strong interests in our recent TIPM article. Dr. Cook’s figures and comments would be undoubtedly correct if the scatter-fitting used in his analysis could truly play an effective role similarly for insufficient data. Differently, we employed a line-based fitting considering therewere only five data per sample, and thus interpolated some points as complementary data by a straight-line law between every two adjacent measured data. In line-based fittings, the regression coefficients (R2) of full-range power functions for different samples are all just between 0.7 and 0.85, but the R2 of first-4-datum power fitting can be more than 0.9 or even 0.95. To double check the conclusions presented in that article, we also measured two more samples, Sandstone 3# and Coal 4# we call them. Their unload steps have been increased to 9 and 11, respectively, so now we can utilize 10 or 12 data points, double the past 5 points, to develop a fitting curve. The data measured or calculated for the two samples are shown in Tables 1 and 2. Figure 1 gives the permeability-confining pressure relationship of Sandstone 3#, respectively, by full-range power fitting, last-5-point power fitting, or last-5point exponential fitting. These fittings are all scatter based. Obviously, both of the fittings in Fig. 1a and c can make sense, because the regression coefficients in such two fittings are both >0.95. For the coal sample 4, it cannot be luckily deduced from Fig. 2 that a power function would fit all the data well. The regression coefficient of full-range fitting is just about 0.78. On the contrary, in Fig. 3 the data under 2MPa can still contribute a better exponential fitting, with R2≈0.9. Figure 4 shows the relationship between the ratios of pressure drop and permeability growth, respectively, for Sandstone 3# or Coal 4#. For Sandstone 3#, the relationship follows an exponential curve, with R2 =0.95. However, a power function better represents the relationship of Coal 4#, with R2 =0.98. Therefore, we think that the sandstone and coal samples have different sensibilities of permeability reaction to unloading.