There is a difference between exergy loss and exergy destruction. In order to calculate the exergy destruction rate, you can use Exergy Balance equation (EBE) for each of the component in your system let say for a power generation system, HVAC and ETC. Regarding the numerical methods, I am not sure what you meant however there are some commercial software such as Hysis, Thermo-flow, camel-pro than can quickly calculate the exergy flow. For other system, you can develop your own code using any languages as long as you have the thermodynamic properties. I would suggest Engineering Equation Solver (EES) in simple cases. In addition, if you are talking about numerical methods to determine and assess the exergy analysis again you can use entropy generation methods and as  Andreas pointed out you can then multiply by reference temperature to calculate the reversibility. I suggest you read the book titled (entropy generation minimization by Adrian Bejan).

In the distillation processes of LPG, the loss of exergy in the column constitued from 33 plates and an efficiency close to the 60 percent, can be evaluated using the exergetic efficiency. For the operating pressure estimated equal to 20 bar, the simulation results give an average exergetic efficiency closeto 35%. For more details, please read my paper on this aim.  

The book by Bejan et al. provides the necessary equations and examples to calculate and model exergy loss and exergy destruction. The book details can be found here: http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471584673.html

The destruction of exergy can be calculated using the balance principle on the control volume. This loss of exergy is named  Irreversibility function.

Irreversibility= Input exrgy flux - Output exergy flux

I think all the previous answers explain the basic concepts for the exergy analysis. So if you find interesting, I found this journal with an special issue for exergy analysis.There are many cases studies for different systems that you can check

http://www.mdpi.com/journal/entropy/special_issues/exergy

Best

Adhemar

You must take into account two thing:

1.- Exergy destruction is an internal phenomenon, refers to the exergy destroyed due to irreversibilities within a component system (like irreversibilities inside a combustion, exergy destruction during the combustion process as function of engine operating and design parameters)

2.- Exergy losse is seen as external irreversibilities (Transfer of exergy from the overall system to its surroundings. This exergy transfer is not further used in this or another system)