How to add murphree efficiency to Column Inside-Outside method?

[Long Cloud]

To add murphree efficiency to column IO method, I modify the triangle dialog matrix, and calculate K in outside by bubble point, not by TPXY. when I converged the outside and re-calculate the the inner variable, such as Sb, I found the Sb is changed. So the column results is not stable. Anyone can give any suggestion?

private void CalcLvByV_MurphreeEff()
 {
     double[,] Vij = new double[info.NumComp, info.NumStage];
     double[] Rl = (double[])info.Rl.Clone();
     double[] Rv = (double[])info.Rv.Clone();

     for (int i = 0; i < info.NumComp; i++)
     {
         if (info.Zm[i] < info.MinZ || (info.IsWaterColumn && i == info.WaterIndex))
             continue;

         double[,] matrix = new double[info.NumStage, info.NumStage];
         double[] arrFi = new double[info.NumStage];
         double[] alphaSj = new double[info.NumStage];
         double[] effTerm = new double[info.NumStage];

         for (int j = 0; j < info.NumStage; j++)
         {
             alphaSj[j] = 1 / (info.Eff[i, j] * info.Alpha[i, j] * info.Sb * info.Sr[j]);
             effTerm[j] = (1 - info.Eff[i, j]) * alphaSj[j] / Rv[j];
         }

         for (int j = 0; j < info.NumMainStage; j++)
         {

             if (j > 0 && !info.TotalPaFromTray[j - 1])
                 matrix[j, j - 1] += alphaSj[j - 1];

             if (j == 0 && info.IsTotalCondenser) 
                 matrix[j, j] += -Rl[j] * alphaSj[j] - Rv[j];
             else
             {
                 matrix[j, j] += -Rl[j] * alphaSj[j] - Rv[j];
                 if (j > 0)
                     matrix[j, j] += -effTerm[j - 1];
             }

             if (j < info.NumMainStage - 1)
                 matrix[j, j + 1] += 1 + Rl[j] * effTerm[j];

             arrFi[j] = -info.F[j] * info.Z[i, j];
         }
         if (info.WaterIndex == i)
         {
             for (int j = 0; j < info.NumMainStage; j++)
             {
                 arrFi[j] += info.Water[j];
             }
         }

         double[] Vi = matrixCalc.Calc(matrix, arrFi);
         for (int j = 0; j < info.NumStage; j++)
         {
             if (Vi[j] < 0)
                 Vi[j] = 0;
         }
         clip(Vi);
         Vij.SetRow(i, Vi);

         double[] Li = new double[info.NumStage];
         for (int j = 0; j < info.NumStage; j++)
         {
             if (j < info.NumStage - 1)
                 Li[j] = Vi[j] * alphaSj[j] - effTerm[j] * Vi[j + 1];
             else
                 Li[j] = Vi[j] * alphaSj[j];

         }
         for (int j = 0; j < info.NumStage; j++)
         {
             if (Li[j] < 0)
                 Li[j] = 0;
         }
         info.Li.SetRow(i, Li);
     }

     for (int i = 0; i < info.NumComp; i++)
     {
         for (int j = 0; j < info.NumStage; j++)
         {
             if (Vij[i, j] < 0)
             {
                 info.LstMessage.Add($"comp {i} in tray {j} is negative");
                 return;
             }

             if (double.IsNaN(Vij[i, j]) || double.IsInfinity(Vij[i, j]))
                 return;
         }
     }
     info.Vi = Vij;
     for (int j = 0; j < info.NumStage; j++)
     {
         info.V[j] = 0;
         for (int i = 0; i < info.NumComp; i++)
         {
             info.V[j] += info.Vi[i, j];
         }
     }
  
     for (int j = 0; j < info.NumStage; j++)
     {
         info.L[j] = 0;
         for (int i = 0; i < info.NumComp; i++)
         {
             info.L[j] += info.Li[i, j];
         }
     }

     for (int i = 0; i < info.NumComp; i++)
     {
         for (int j = 0; j < info.NumStage; j++)
         {
             if (info.Li[i, j] < 0)
             {
                 info.Li[i, j] = 0;
             }
             if (info.Vi[i, j] < 0)
             {
                 info.Vi[i, j] = 0;
             }
         }
     }

 }

 

[georgeverghese]

The procedure for the use of the I/O method and worked examples and references are well narrated on page 13-49 onwards in Perry Chem Engg Handbook 7th ed. See if this helps. I have used this method only on Pro-II from Simsci, so I cant comment only specific details.

 

[PaoloPemi]

you may consider this old thread

Russell inside out for Dist column - Chemical process engineering

Hi all, I was wondering if anyone can direct me to a good reference on how to implement the Russells inside out algorithm for distillation column model calculations. What I need is to learn the theory and how it works. Also possibly get into the numeric method... Alternatively, is there any...

www.eng-tips.com

it's about the version proposed by Richard (Dick) Russell which (as far as I know) has been the standard procedure in most simulators and thermo libraries,
there are different ways to modify the amount of liquid condensed on each tray depending from tray efficiency, those depend from the simplified model you adopt to describe vapor/liquid equilibria...

Paolo