def Stichlmair_flood(Vl, rhog, rhol, mug, voidage, specific_area, C1, C2, C3, H=1.0): r'''Calculates gas rate for flooding of a packed column, using the Stichlmair [1]_ correlation. Uses three regressed constants for each type of packing, and voidage and specific area. Pressure drop is given by: .. math:: \frac{\Delta P_{irr}}{H} = \frac{\Delta P_{dry}}{H}\left(\frac {1-\epsilon + h_T}{1-\epsilon}\right)^{(2+c)/3} \left(\frac{\epsilon}{\epsilon-h_T}\right)^{4.65} .. math:: h_T = h_0\left[1 + 20\left(\frac{\Delta Pirr}{H\rho_L g}\right)^2\right] .. math:: Fr_L = \frac{V_L^2 a}{g \epsilon^{4.65}} .. math:: h_0 = 0.555 Fr_L^{1/3} .. math:: c = \frac{-C_1/Re_g - C_2/(2Re_g^{0.5})}{f_0} .. math:: \Delta P_{dry} = \frac{3}{4} f_0 \frac{1-\epsilon}{\epsilon^{4.65}} \rho_G \frac{H}{d_p}V_g^2 .. math:: f_0 = \frac{C_1}{Re_g} + \frac{C_2}{Re_g^{0.5}} + C_3 .. math:: d_p = \frac{6(1-\epsilon)}{a} Parameters ---------- Vl : float Superficial velocity of liquid, Q/A [m/s] rhog : float Density of gas [kg/m^3] rhol : float Density of liquid [kg/m^3] mug : float Viscosity of gas [Pa*s] voidage : float Voidage of bed of packing material [] specific_area : float Specific area of the packing material [m^2/m^3] C1 : float Packing-specific constant [] C2 : float Packing-specific constant [] C3 : float Packing-specific constant [] H : float, optional Height of packing [m] Returns ------- Vg : float Superficial velocity of gas, Q/A [m/s] Notes ----- A numerical solver is used to solve this model. Examples -------- Example is from [1]_, matches. >>> Stichlmair_flood(Vl = 5E-3, rhog=5., rhol=1200., mug=5E-5, ... voidage=0.68, specific_area=260., C1=32., C2=7., C3=1.) 0.6394323542746928 References ---------- .. [1] Stichlmair, J., J. L. Bravo, and J. R. Fair. "General Model for Prediction of Pressure Drop and Capacity of Countercurrent Gas/liquid Packed Columns." Gas Separation & Purification 3, no. 1 (March 1989): 19-28. doi:10.1016/0950-4214(89)80016-7. ''' guess = [Vl * 100., 1000.0] return newton_system(_Stichlmair_flood_f_and_jac, x0=guess, jac=True, args=(Vl, rhog, rhol, mug, voidage, specific_area, C1, C2, C3, H), ytol=1e-11)[0][0]
def Stichlmair_flood(Vl, rhog, rhol, mug, voidage, specific_area, C1, C2, C3, H=1.0): r'''Calculates gas rate for flooding of a packed column, using the Stichlmair [1]_ correlation. Uses three regressed constants for each type of packing, and voidage and specific area. Pressure drop is given by: .. math:: \frac{\Delta P_{irr}}{H} = \frac{\Delta P_{dry}}{H}\left(\frac {1-\epsilon + h_T}{1-\epsilon}\right)^{(2+c)/3} \left(\frac{\epsilon}{\epsilon-h_T}\right)^{4.65} .. math:: h_T = h_0\left[1 + 20\left(\frac{\Delta Pirr}{H\rho_L g}\right)^2\right] .. math:: Fr_L = \frac{V_L^2 a}{g \epsilon^{4.65}} .. math:: h_0 = 0.555 Fr_L^{1/3} .. math:: c = \frac{-C_1/Re_g - C_2/(2Re_g^{0.5})}{f_0} .. math:: \Delta P_{dry} = \frac{3}{4} f_0 \frac{1-\epsilon}{\epsilon^{4.65}} \rho_G \frac{H}{d_p}V_g^2 .. math:: f_0 = \frac{C_1}{Re_g} + \frac{C_2}{Re_g^{0.5}} + C_3 .. math:: d_p = \frac{6(1-\epsilon)}{a} Parameters ---------- Vl : float Superficial velocity of liquid, Q/A [m/s] rhog : float Density of gas [kg/m^3] rhol : float Density of liquid [kg/m^3] mug : float Viscosity of gas [Pa*s] voidage : float Voidage of bed of packing material [] specific_area : float Specific area of the packing material [m^2/m^3] C1 : float Packing-specific constant [] C2 : float Packing-specific constant [] C3 : float Packing-specific constant [] H : float, optional Height of packing [m] Returns ------- Vg : float Superficial velocity of gas, Q/A [m/s] Notes ----- A numerical solver is used to solve this model. Examples -------- Example is from [1]_, matches. >>> Stichlmair_flood(Vl = 5E-3, rhog=5., rhol=1200., mug=5E-5, ... voidage=0.68, specific_area=260., C1=32., C2=7., C3=1.) 0.6394323542746928 References ---------- .. [1] Stichlmair, J., J. L. Bravo, and J. R. Fair. "General Model for Prediction of Pressure Drop and Capacity of Countercurrent Gas/liquid Packed Columns." Gas Separation & Purification 3, no. 1 (March 1989): 19-28. doi:10.1016/0950-4214(89)80016-7. ''' guess = [Vl*100., 1000.0] return newton_system(_Stichlmair_flood_f_and_jac, x0=guess, jac=True, args=(Vl, rhog, rhol, mug, voidage, specific_area, C1, C2, C3, H), ytol=1e-11)[0][0]