Tham khảo tài liệu 'natural gas part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 472 Natural Gas 4W 4 X E - 6 Then RNP ----------- ---------------------------------- g g dp X X E - 7 X Alternatively RNP P. Q g b b X 1 X X 144 X E - 5 Rgdp ggZbTb X E - 7 X 1 X 530 X The equation of continuity for gas flow in a pipe is W Y A1 V1 Y2 A 2 V2 Constant 10 Then W Y A V. In a cylindrical homogeneous porous medium the equation of the weight flow rate can be written as W Y A p v. 11 Equation 11 can be differentiated and solved simultaneously with the lost head formulas equation 2 3 and 4 and the energy equation equation 1 to arrive at the general differential equation for fluid flow in a homogeneous porous media. Regarding the cross sectional area of the porous medium A p as a constant equation 11 can be differentiated and solve simultaneously with equations 2 and 1 to obtain. d p d p cÌ c v u Y Sind k k J c T. 2 _ W2 d Y k Y2 Ap2gdp 12 Equation 12 is a differential equation that is valid for the laminar flow of any fluid in a homogeneous porous medium. The fluid can be a liquid of constant compressibility or a gas. The negative sign that proceeds the numerator of equation 12 shows that pressure decreases with increasing length of porous media. The compressibility of a fluid C f is defined as Steady State Compressible Fluid Flow in Porous Media 473 Cf 1 d 7 7 dp 13 Combination of equations 12 and 13 leads to d p d p J . c v p -2- 7 sin0 k k7 .2 1_ W k 7 Ap2 g 7 14 Differentiation of equation 11 and simultaneous solution with equations 2 1 and 13 after some simplifications produces d p d p . 32 c v p 2------- 7 sin1 d p 2 k p 7 . 2 - 1 c f 1_-----f 7 Ap2g k 7 15 Differentiation of equation 6 and simultaneous solution with equations 4 1 and 1 3 after some simplifications produces d p d p 9 f W 2 -----------------Ĩ 7 sin0 2 7 A p2 d p 7 Í t_2 A W 2 Cf 1 - 7 Ap2 g k 7 16 Equation 16 can be simplified further for gas flow through homogeneous
