Numerical Solution of a Moving Boundary Problem of One-Dimensional Flow in Semi-Infinite Long Porous Media with Threshold Pressure Gradient

Table 1

Calculation of dimensionless TPG 𝜆_𝐷 through experimental data [2] of eight samples.

Sample	𝜆; (psi/cm)	𝑘/𝜇; (md/cp)	Minimum flow rate 𝑞1 (cm^3/min)	Maximum flow rate 𝑞2 (cm^3/min)	Cross-sectional area 𝐴 (cm^2)	Average flow velocity 𝜈𝑤=(𝑞1+𝑞2)/𝐴/2 (cm/min)	𝜆𝐷=𝜆𝑘/𝜇/𝜈𝑤
Brown sandstone #1	0.00846	6520	8.83	30	20.2	0.961139	0.242
Brown sandstone #2	0.014	4810	13.19	32.32	20.2	1.126485	0.252
Brown sandstone #3	0.0203	4730	1.71	17.5	20.2	0.475495	0.852
Brown sandstone #4	0.017	3130	5.79	20.46	20.2	0.649752	0.345
Sandpack #1	0.0046	27900	3.81	34.3	11.4	1.671491	0.324
Sandpack #2	0.00789	23500	2.47	20.34	11.4	1.000439	0.782
Sandpack #3	0.00548	23800	4.57	29.92	11.4	1.512719	0.364
Shaly sandstone	0.813	56.6	2	6	11.4	0.350877	0.553