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December Letters  

By Chemical Engineering |

More detail needed for VLE method

I read with interest Mr. Bahadori’s article in Chemical Engineering (August 2007; pp. 47 – 51) on the above subject. His new approach stated the algorithm for determining K i’s, x i’s and y i’s. However, he didn’t provide the constant values of A i, B i, C i, and D i or state where or how these constant values in Eq. (2 – 6) can be obtained or determined. Further the range of applicability of this new method in relation to reduced temperature ( T r) and pressure ( P r) was not mentioned and should in fact be provided since these constants ( A i, B i, C i, and D i) are dependent on the reduced parameters. Obviously, it’s essential for the reader to note where the available parameters in the polynomial equations are determined/obtained and their limitations in order to confirm the viability and accuracy of the technique. I didn’t observe these things in Mr Bahadori’s article. I hope that such important information will be provided in due course.

Sincerely,

A.K. Coker

Jubail Industrial College, Saudi Arabia

Author Replies:

An expanded procedure for determining tuning coefficients (Steps 1 – 4) is provided below. These coefficients can be tuned using the least-squares method for any experimental data set so that the model will predict a wide range of data accurately.

This approach has two main advantages in comparison to other models:

  1. We can retune the coefficients based on some available data to zoom for VLE calculations in a specific range of pressure and temperature.

  2. These coefficients can be retuned if more accurate data are reported in the future for a multicomponent system.

Determining tuning coefficients (Steps 1 – 4 revised). Repeat the following procedure for each component i:

Step 1. For each temperature (numbered from 1 to j), plot the experimental data x i as a function of partial pressure and use the least squares method to curve fit it per the following equation: x i = A ij + B ij P r + C ij P r 2 + D ij P r 3 This will yield j sets of A, B, C, and D coefficients for the given component.

Step 2. Next, plot all the A’s versus temperature and use the least squares method to curve fit them as a function of temperature (numbered from 1 to j) to determine the A temperature tuning coefficients ( A Aij, B Aij, C Aij and D Aij) for use in Equation (2)

Step 3. Repeat Step 2 for the B, C, and D coefficients to determine the B temperature tuning coefficients ( A Bij, B Bij, C Bij, D Bij) for use in Equation (3), the C temperature tuning coefficients ( A Cij, B Cij, C Cij, D Cij) for use in Equation (4) and the D temperature tuning coefficients ( A Dij, B Dij, C Dij and D Dij) for use in Equation (5).

Step 4. Repeat Steps 1 through 4 for each component
 

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