Prompt Title: Velocity-flow rate-back pr3essure

I want you to rewrite the code below so that it determines the velocity and the gas flow rate of the gas core associated with a particular percentage of hydrate growth and blockage. The code has to calculate the velocity of the gas and the back-pressure associate to every addition of 0.001% addition of gas hydrate growth, and store the data of each velocity of the gas core and back-pressure corresponding to a 0.001% increment of gas hydrate growth. Please stop the calculations when the gas hydrate velocity will be 0. Here are the formulas: The efficient tubing diameter: R_eff=R(1- α_H ) Shen et al. (2018) correlation of flow behavior and consistency index: n=0.99268-〖1.98 ϕ〗_H m=0.04199 exp(56.40 ϕ_H^2 -2.582 ϕ_H) average slurry thickness δ_avr=Rα_sl α_sl=0.01 the radius of the gas core R_g=R_eff-δ_avr The gas core density is as follows: ρ_c=ρ_g ε_cr+ρ_sl (1-ε_cr ) The density of the slurry is as follows: ρ_sl=100/(ϕ_H/ρ_h +(100-ϕ_H)/ρ_l ) ρ_sl=ρ_h ϕ_H+ρ_l (1-ϕ_H ) The gas core viscosity is as follows: μ_c=μ_g ε_cr+μ_l (1-ε_cr ) We adopt Ling (2012) model to compute the gas core viscosity as follows: μ_g=Ca×〖10〗^(-3) exp⁡[X((〖6.24×10〗^(-2) ρ_g)/(62.4))^Y ] Ca=(〖10〗^(-4) (9.18999+3.0893 (1000M_g )) 〖T(R)〗^(1.2288))/(208.99+18.83922 (1000M_g )+T(R) ) X=3.56014+((1000.01)/(T(R)))+0.124465 (〖1000M〗_g ) Y=2.47862-0.12294 X For calculations consistencies, we adopt the Brill and Beggs (1978) viscosity model for computation of the water phase viscosity, which is as follows: μ_w=exp[1.003-1.479×〖10〗^(-2) T+ 1.982×〖10〗^(-5) T^2 ] For computations consistencies, the gas-water interfacial friction factor developed by Fore et al. (2000) is adopted and expressed for the case of average and non-average hydrate slurry thickness f_w=0.005{1+300[(1+17500/R_eG ) 〖δ_cr〗_avr/2R-0.0015]} f_w=0.005{1+300[(1+17500/R_eG ) (δ_cr (α,β))/2R-0.0015]} Moreover, the gas-hydrate interfacial friction factor developed by Shi et al. (2018) f_h=K(u) ρ_h/ρ_lb [(φ_h+φ_w^' ) (d_p/d_o )^(3-f_r ) ] (d_p/D)^2 φ_w^'=(m_w-n_g NM_w)/(ρ_w V_Total ) K(u)=(23.59e^(-u⁄(0.158))+1.028)×〖10〗^4 Therefore, the interfacial friction factor is as follows: f_i=f_w+f_h Thus, the velocity of the gas core associated with a particular percentage of hydrate growth and blockage could be expressed as follows v_g=(n/(n-1)) (1/2m (-dP/dz+ρ_sl g sin⁡α ))^(1/n) [R_g^((n-1)/n) R_eff^(2/n) (_2^1)F (-1/n,(n-1)/2n;3/2-1/2n;(R_g^2)/(R_eff^2 ))- R_eff^((n+1)/n) (_2^1)F (-1/n,(n-1)/2n;3/2-1/2n;1)] With: (_2^1)F (-1/n,(n-1)/2n;3/2-1/2n;1) and (_2^1)F (-1/n,(n-1)/2n;3/2-1/2n;(R_g^2)/R^2 ) The hypergeometric FUNCTION (_2^1)F (-1/n,(n-1)/2n;3/2-1/2n;(R_g^2)/(R_eff^2 ))= 1-((n-1)/n)((R_g^2)/(R_eff^2 ))[(1/(3n-1))+((n-1)/(2n(5n-1)))((R_g^2)/(R_eff^2 ))] (_2^1)F (-1/n,(n-1)/2n;3/2-1/2n;1)= 1-((n-1)/n)[(1/(3n-1))+((n-1)/2n)(1/(5n-1))] the gas flow rate Q_g=2.5×〖10〗^8 ((APv_g)/ZT) The determination of the back-pressure is performed with the Schellhardt and Rawlins (1936) correlation by adopting Darcy’s flow. By assuming a laminar flow and low flow rate, and low-pressure conditions, the expression of the back-pressure could be expressed as follows: p_r^2-p_wf^2=Q_g/C C=(0.703kh)/(Tμ_g Z[ln⁡(r_e/r_w )-0.75+s] )