## AspenTech Case Solution

## Aspen Tech Case Study Solution

**Memorandum**

To: Mr. Sean F. Askebom

From: Your Name

The task I will be explaining in this memorandum is the curve fitting using MATLAB on the data of the four species I was given. The four speciesthat were given to me as the task were Ethane, Cyclopropane, Iso-Butane and n-Butane. The data of their vapor pressure were taken from the Perry’s handbook. The minimum temperature that was allowed to note was 170 K and the maximum was the species critical temperature.

The problem have to solved using Matlab so I, made the *.m script files for all these species separately. The equations will be derived once a great line fitting technique was found. The Matlab gives the best solution to the Equation finding. Once I input the data on to the .m file, the curve fitting function that is ‘fit’ was used. This function syntax allowed me to demonstrate the curve true equation. I give the function 4 different methods, namely linear that is the linear line equation (y = x) poly1, that is the first order polynomial equation (y = ax + b), ploy2, that is the second order polynomial equation (y = ax^2 + bx + c),and the best result producing method was poly3, the third order polynomial equation (y = ax^3 + bx^2 + cx + d).

Once the data is fitted using the ploy3 method, one can simply plot the data using plot () function. The data is plotted along with the curve on the graph and can be view as soon as the program is executed. After the plot function, the code also asks you if you want to know the vapor pressure of a particular specie at any particular temperature that has to be in kelvin. Once the user input his desired temperature value the command window in the Matlab software will show the result for you query.

For example, if a user opens Psat1 file that has Ethane C2H6 data, and inputs a value of 245.5 in temperature, the answer would be like ‘The vapor pressure at temperature 245.50 K is 11.36 bar’.Now the equations corresponds with different coefficient values, as I have fitted the data with 3^{rd} order polynomial equation, the equation found out to be,PSat1(x) = p1*x^3 + p2*x^2 + p3*x + p4. The coefficients calculated by Matlab are p1 = 1.558e-05 p2 = - 0.007734 p3 =1.319 and p4 = - 76.88. The Matlab function will also show the error rates with 5 different error rate determining techniques. The most commonly used and understood method of all these 5 are root means square error that is found out to be 0.0625 at this particular curve fitting.

AspenTech Harvard Case Solution & Analysis

Similarly for the other 3 species, same code was used but with their respective datasets, and all of these data, has been fitted best with the third order polynomial functions. The goodness of the fit is used to determine the errors that affects the plotting of the curve...........

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