Chapter 3, Problem 3.47P

To maximize production and minimize pumping costs. crude oil is heated to reduce its viscosity during transportation from a production field.

1. Consider a pipe-in-pipe configuration consisting of concentric steel tubes with an intervening insulating material. inner tube is used to transport warm crude oil through cold ocean water. The inner steel pipe $\left(k_s=35\text{W/m}\cdot \text{K}\right)$ an inside diameter of $D_{i,1}=150\text{mm}$ and wall thickness $t_i=10\text{mm}$ while the outer steel pipe has an inside diameter of $D_{i,2}=250\text{mm}$ and wall thickness to $t_o=t_i.$ Determine the maximum allowable crude oil temperature to ensure the polyurethane foam insulation $\left(k_{\rho }=0.075\text{W/m}\cdot \text{K}\right)$ between the two pipes does not exceed its maximum service temperature of $T_{p,\max }=70°\text{C}$ . The ocean water is at $T_{\infty ,\rho }=-5°\text{C}$ and provides an external convection heat transfer coefficient of $h_o=500{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ The convection coefficient associated with the flowing crude oil is $h_i=450{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$
2. It is proposed to enhance the performance of the pipe-in-pipe device by replacing a thin $\left(t_{\alpha }=5\text{mm}\right)$ section of polyurethane located at the outside of the inner pipe with an aerogel insulation material $\left(k_a=0.012\text{W/m}\cdot \text{K}\right).$ Determine the maximum allowable crude oil temperature to ensure maximum polyurethane temperatures are below $T_{p,max}=70°\text{C}\text{.}$