ENGG$682,$ Applied Heat Transfer

Design Problem #

Fall $2024$

Crude oil is to be transported overland in Alaska. One of the workable methods is shown in Figure $1.$ The distance between

the pumping stations is $32$ km and the required oil flow rate is $44k\frac{g}{s}.$ To facilitate pumping, a heater will be installed at

The permafrost is not to be melted. Insulation may be used on the pipe to reduce the heat loss. The external surface

temperature of the pipe or insulation in contact with the permafrost must be maintained at $0C$ or below. The inside diameter

of the pipe should not be less than $400$ mm and more than $600$ mm $.$ The outer diameter of the pipe with insulation should not

exceed $800$ mm $.$ Heat transfer data applicable to the pipe and insulation are shown in Figure $2.$ The overall heat transfer

coefficient, U $,$ between the oil and the permafrost in $\frac{W}{m^2}-K$ based on inside area, $A_t,$ is given by

$\frac{1}{U_i{A}_i}=\frac{1}{113A_i}+\frac{}{k\frac{A_i+A_o}{2}}+\frac{1}{7\mathrm{.}2A_o}$

where $A_o$ is the outside area of the insulation. The temperature change $dT$ in a differential length of pipe is expressed by:

$m^{}{c}_p(-dT)=UD[T-(-4^{o}C)]dL$

where, $m^{}=$ mass flow rate$=44k\frac{g}{s}$

$c_p=$ specific heat of oil $=1\mathrm{.}93k\frac{J}{k}g-K$

${?}^2={?}^2$

$dT=$ change in oil temperature in length $dL$

$U=$ overall h$.$ t$.$ coefficient between oil and permafrost in $\frac{W}{m^2}-K$

$D=$ inside pipe diameter, between $0\mathrm{.}4$ m and $0\mathrm{.}6$ m

$L=$ length of the pipe, $m$

$=$ insulation thickness, $m$

The pump is operating with $75\%$ efficiency and heater is an electrical heater with $95\%$ efficiency. Consider the minor losses

to be $10\%$ of the friction losses in the piping.

Review the design criteria for pipe sizing and the thickness of insulation and indicate the satisfactory design conditions.

Optimize your design $($for best combination of pipe size and insulation thickness$)$ based on minimum daily consumption cost

due to heating and pumping. Your final report should include:

Size of the pipe chosen,

mm

Insulation thickness,

Inlet oil temperature, $T_1=$

$C$

Outlet oil temperature, $T_2=C$

Pressure drop between stations, $P=$

Daily energy consumption

Daily consumption cost $

$k\frac{J}{?}$ day

Temperature of surface in contact with permafrost $($highest in $32$ km run$)$

$C.$

Due Monday, October $14,2024$

Figure $1.$ Oil Pipeline