BACKGROUND

American Crystal Sugar Company's $($ACSC$)$ factory in Moorhead, MN$,$ is a prime example of Energy

Conversion system. To support ACSC's goal of processing beets into sugar the plant produces its own

power by means of steam generation and the Rankine cycle.

The power generation cycle can be summarized as follows. Coal is transported by rail from Midwest

locations, fed through underground scroll$/$elevator combo, and burned in one of the three available large

boilers. The combustion of coal transmits chemical energy into thermal energy with an average heating

value $11,500$ BTU$/$lb but less when coal gets wet due to weather or leakage underground. By having

three boilers in parallel the plant can have different levels of MW output through heat or to complete

repair work on one of the offline units. For normal operating parameters a heat generation of $17\mathrm{.}636MW$

can be achieved from the boilers. The boilers have an exit pressure of $400$ and exit temperature of $320$

$C.$ During normal operation in the fall, $90$ tons of high$-$pressure steam per hour is fed into two GE

turbines; thereby converting thermal energy into mechanical. Coupled with generators, one rated for

$3\mathrm{.}1$MW output and another for $3\mathrm{.}8MW$ output, rotational mechanical energy is converted to electrical

energy.

During typical operation, the first turbine outputs $2\mathrm{.}3MW$ and the second $2\mathrm{.}7MW.$ Minimal heat is lost

through the turbines and so they are assumed to be adiabatic. Their exit temperature and pressure are

$150C$ and $57\mathrm{.}04$ psi, respectively. They have separate shafts so that one or both turbines may be used

at a time. During excess production times, the factory will sell energy back to the power grid to the Xcel

Energy. During the time of low production, $($i$.$e$.$ wet coal$)$ the factory will supplement their power

production with the power purchased from Xcel Energy. The power produced in the factory "boiler$-$

house" $-$as it is called$-$powers lights, doors, and everyday uses in the offices and shop floor. The turbine

exhaust steam is then used throughout the factory for heat transfer in plate$-$frame heat exchangers and

calandria evaporators.

Much of the energy that originally left the turbine is returned to three water pumps and then the cycle is

started again. Due to make$-$up and high flow rate, only $7C$ is lost from the turbine outlet to the entrance

of the pumps. Just like the boilers the pumps are run in parallel to allow for repair or extra flow.

Redundancy is very important in a factory that is in operation $24$ hours a day for $120$ days straight. During

the cycle the water goes through different stages. After the boiler is superheated steam, after the turbine

and before it gets into the feedwater pumps it is assumed saturated liquid.

By$-$products of coal combustion include particulates, NOx,$S{O}_2,$ as well as $C{O}_2.$ The factory utilizes several

methods for reducing the inevitable carbon footprint. In the main boiler exhaust stacks with minimal

filters with selective catalytic reduction that removes most particulate matter up to $50ppm$ as well as

some hydrocarbons, while electrostatic precipitators remove a large majority of the rest, including heavy

metals such as mercury.

The low$-$pressure steam travels through the factory and uses up its heat capacity completely. By utilizing

redundant$/$multiple devices per stage, the factory can make just as much power as they require, adjusting

the cycle for better efficiencies. Many closed feedwater heaters are used in the factory as well. Inevitable

and irreversible losses include those due to friction of the steam moving through lines $($relatively minimal

as they are not long$)$ and though the turbine blades. The turbine is also not perfectly adiabatic so it loses

thermal energy.

ASSIGNMENT

Draw a simplified cycle schematic including the boilers, the pumps, the turbines and the

generators, and a the heat exchanger $($condenser$)$ to account for the heat lost through the

applications in the factory and showing the mass flow rates in the lines.

Draw the T$-$s diagram locating all points described in $1.$

Calculate the estimate of efficiency with this model and compare it to the accepted average value

of $30\%.$

Suggest methods of improvement for the efficiency