THE THEORY OF THERMODYNAMICS
The Abbott Power Plant uses a loop called the Rankine Cycle to generate power. This cycle consists of four main components, a pump, boiler, turbine, and condenser. Shown above is the layout of the cycle and the order in which the processes interact with each other. The process is summarized well by the following, the pump delivers liquid water to the boiler, after which the boiler converts water to superheated steam which is then used to run the turbine which powers the generator, then the steam leaves the turbine and becomes cooled to its original liquid state in the condenser (Fedkin, Dutton). For the purposes of these calculations, the cycle will be assumed to be idealized to detail the thermodynamic processes that occur. The diagram above gives a basic idea of how the power plant operates with this cycle. We can see that there are a total of four stages and because the water is undergoing a thermodynamic process in between each of these stages, the water is generating energy.
The first step from stage 1-2 is when the water goes through a feed-water pump. Looking at these points on the graph, point one lies on the saturated water curve and point two lies in the compressed liquid water area. The stage going from step 1 to step 2 is an isentropic process because no volume changes here and the water remains in liquid form. As written by M. Bahrami in Vapor Power Cycles, in the isentropic compression process, water enters the pump as state 1 as saturated liquid and is compressed isentropically to the operating pressure of the boiler (Bahrami). Specifically, the pump pressurizes the water flowing into it from 0.88 bar to 68.9476 bar while keeping everything else like temperature and volume the same under the idealized conditions. Therefore, the enthalpy change here is from 402.33kJ/kg to 407.835kJ/kg. This gives us the work done on the water during this process, --5.401kJ/kg through pump.
The second step from stage 2-3 is when the water goes through a boiler. This stage of the Rankine Cycle can be referred to as constant pressure heat addition in a boiler. As stated in 7.6 Rankine Cycle, “the energy balance in the boiler can be expressed as the change in enthalpy of the fluid from the ‘before’ state (compressed liquid” to ‘after’ state (superheated steam)” (Fedkin,Dutton). This step occurs isobarically, meaning the process has constant pressure. The state of water changes here from liquid to steam. The boiler takes the cool liquid from the pump and heats it at a constant pressure, heating the saturated water leaves it as superheated vapor at state 3 (Bahrami). Since there is volume change here, the mechanical work done by the boiler is zero. And since the enthalpy changes from 407.835kJ/kg to 3162.166kJ/kg, the heat added to water Q is 2754.33kJ/kg.
The third step from stage 3-4 is when the water goes through a turbine. This step shows isentropic expansion in the turbine which produces work, this work done is useful and the main purpose of the cycle. This is an adiabatic process which means that heat doesn’t leave or enter during this process, because of this, the system does not have to deal with excessive moisture which is ideal for higher boiler pressure (Bahrami). Here, the turbine uses the steam from the boiler to spin and expand the blade in order to produce work, which is then released to the condenser with low pressure. The blades spin to generate electricity. The pressure drops from 58.60 bar to 5.17 bar, therefore the enthalpy drops from 3162.166kJ/kg to 2846.015 kJ/kg. Looking at this data we can conclude that the total work done here is 316.15 kJ/kg and the work is positive, which is significant since it essentially reverses the process form stage 1-2.
The final step from 4-1 has the water go through a condenser, and involves steam cooling and condensation. This process includes constant pressure heat rejection in a condenser which means the extra heat is withdrawn from the system, and water returns to its liquid state, returning the process to its initial stage. This is an isobaric process meaning the process is at a constant pressure. The cooled pipes will cool down the steam, thus changing it into liquid water. Since the whole process is isobaric, there is no change in pressure which causes the work done to be zero. The net heat change here is -2443.58kJ/kg. This is negative because the heat is removed from water to condense.
References:
Vapor Power Cycles Ideal Rankine Cycle
https://www.sfu.ca/~mbahrami/ENSC%20461/Notes/Vapor%20Power%20Cycles.pdf
Thermodynamics eBook: Ideal Rankine Cycle
http://www.ecourses.ou.edu/cgi-bin/ebook.cgi?topic=th&chap_sec=10.1&page=theory
Rankine Cycle: Utility Solar Power and Concentration