Organic Rankine Cycle efficiency issue

[enter802]

hi all. just to give you a background story - i am graduate student at U of Calgary in the ECE department. My colleague, from the Mechanical department did not show up yet, because of which I have to work alone on my project, including the mechanical part at which i am no expert but have some basic ideas.

so here is what i am trying to figure out - i am trying to do optimization on ORC efficiency (thermal and exergy) and hence I need equations which are related to parameters/variables that I have control over (e.g. evaporator inlet pressure, mass flow rate of the working fluid,etc). All now i have are equations with enthalpies which really does not help for formulating an optimization problem, also I have equations related to heat source and cooling source temperatures (both inlet and outlet). but none of these aspects can be controlled right? i hope you understand my problem here, or else let me know may be I can try explain more elaborately. it will be great to come up with some useful equations for an optimization formulation.

and anyone with any other suggestion or direction that i can work with, will be also very helpful. thank you all in advance...hoping to get some awesome feedback soon.take care!

 

[SteamKing]

It's not clear what you are asking here. The thermal efficiency of any cycle, ORC or otherwise, is related to the maximum temperature and the minimum temperature between which the cycle operates.

For steam turbines, the higher the pressure and temperature of the steam at the inlet, the higher the thermal efficiency. There is usually a point at the exhaust end of the turbine, at the condenser inlet, where for practical reasons, a minimum exhaust pressure is set so that the exhaust steam does not contain too much moisture, which leads to erosion of the turbine blades. In large turbine installations, this minimum pressure is usually about 1.5 in Hg absolute, but it can be higher for smaller turbines.

For steam at a certain temperature and pressure, there is one enthalpy value. This makes it easier to calculate the cycle thermal efficiency in terms of enthalpy, rather than pressures and temperature.

 

[enter802]

I am trying to formulate an optimization problem. As you already know, with increasing inlet pressure at the evaporator (i.e. P₂) (see the image file attached), while the thermal efficiency increases (due to increase in size in area), exergy efficiency decreases. So, let us just say - I want to draw a curve for Thermal Efficiency vs Inlet Pressure (P₂) and Exergy Efficiency vs Inlet Pressure (P₂) and find out a value for P₂ which will give me the combined maximum efficiency. But without having equations which relate this inlet pressure P₂ with the thermal efficiency and exergy efficiency (individual equations), I cannot find that optimal working point of P₂. So I basically need equations that connect both the efficiencies with P₂.

I will give you an example I have solved for T_s,in. With increasing T_s,in, Q_in increases and eventually thermal efficiency increases. So I need to find a relation between T_s,in and the thermal efficiency (while the other parameters are constant) which shows the previous statement is correct. And I have done it as you can see from image 002. I have found out equations for both Q_in and Q_out in terms of temperature (eliminating enthalpies) and now I can easily use this for the thermal efficiency equation (1-Q_out/Q_in). Similarly, I found an equation for exergy efficiency as well related to T_s,in. Now I can find out a value of T_s,in using the two equations for which I will have the maximum combined efficiency.

So basically, I am trying to derive relations between the two efficiencies (eliminating any enthalpy or entropy term from the equation) and any other relevant parameters. I hope I could clear myself. Or else, I will probably try again. Please cope up with me a bit - I told you I am an Electrical Engineering student and hence cannot discuss at the same level as you guys are. Cheers!

P.S. one more hint of what I am trying to achieve: you may notice, for the turbine work, I still have enthalpies over there in the equation - I am trying to get rid of those enthalpy terms.

 

[SteamKing]

I think what you are trying to do is optimize your ORC by means of doing a heat balance on the cycle. You want to be able to vary certain properties and have the calculations spit out the thermal efficiency.

There is software which will allow you to do such calculations, for things like steam propulsion plants for ships or power generation cycles for land-based generating plants. The software has property tables built into look up the properties of the working fluid in the different phases encountered in the cycle.

Here is a like to one such software which can be used to design operating cycles using a number of different working fluids. I don't think there's a lot of choices out there, and most software is usually custom-developed for a particular cycle layout.

http://www.softinway.com/product-and-services/product/axcycle/

NIST/ASME/IAPWS have worked together to produce software which can calculate the properties of water and steam at various conditions:

http://www.nist.gov/srd/upload/STEAM30-2.pdf

 

[enter802]

You are exactly right - but I need to solve it in terms of equations rather than using data. Because using data, we can never guarantee the working condition obtained is THE OPTIMAL working condition. But with the help of equations, formulating an optimization problem and solving it to find the optimal working condition, we will always be right. Thanks for your responses though. Really appreciate your quick responses. Hoping to get some more perspectives on this.

 

[SteamKing]

I'm afraid I don't understand your comment about using 'data'. You have to use something in the way of thermodynamic properties for your efficiency calculations; you can't just use conditions like temperature or pressure alone. If the latter were true, the choice of working fluid wouldn't matter much, but it has a huge impact on the design of the machinery itself.

Now NIST/ASME/IAPWS have developed equations which accompany tables of the properties of steam, which equations can be used in a mathematical model of a given cycle.

I wouldn't get too hung up on squeezing the last iota of efficiency out of this cycle. You do have some control over the inlet and outlet conditions of the turbine, which in large part determine the upper limit on the efficiency of the cycle as a whole. About the best efficiency a high pressure high temperature power station turbine can obtain is about 63%, and the overall cycle efficiency is about 42%. Using lower inlet pressures and temps. means lower efficiency for the turbine and the cycle as a whole.

http://en.wikipedia.org/wiki/Rankine_cycle

http://en.wikipedia.org/wiki/Organic_Rankine_cycle

This latter article has some links about modelling ORC which might be of use to you.