Method of optimizing product output rate of packed columns

1. A method of optimizing a product output rate from a distillation column having a top and a bottom, comprising:

(a) setting a desired product output rate from the distillation column having a packing;

(b) calculating a fraction of flood point of the distillation column at a reflux ratio;

(c) determining a two-phase pressure drop value within the distillation column at the fraction of flood point;

(d) calculating a pressure at the bottom of the distillation column for a pressure at the top of the distillation column, and calculating the two-phase pressure drop value within the distillation column of a given length;

(e) calculating a temperature corresponding to the calculated pressure at the bottom of the distillation column; and

(f) adjusting the desired product output rate or the reflux ratio or the pressure at the top of the distillation column.

2. The method of claim 1 , wherein the distillation column is a subject packed column.

3. The method of claim 2 , wherein the subject packed column is operated with gas as vapor continuous phase and liquid as dispersed phase.

4. The method of claim 1 , wherein determining a two-phase pressure drop value within the distillation column at the fraction of flood point includes using a plot of two-phase pressure drop value as a function of fraction of flood point, the plot obtained by the computer-implemented steps of:

(aa) providing a reference data set of two-phase pressure drop values as a function of gas and liquid flow rates for a reference liquid and a reference gas at several liquid flow rates through a reference packed column containing the same packing being used in the distillation column;

(bb) converting the reference data set to dimensionless two-phase pressure drop values as a function of the density of the liquid phase of a subject packed column thereby making the two-phase pressure drop values at flood inversely proportional to the density of the liquid phase;

(cc) providing a known flood point value for one liquid flow rate in the reference data set;

(dd) setting working flood point values for higher liquid flow rates at values lower than the known flood point value;

(ee) setting working flood point values for lower liquid flow rates at values higher than the known flood point value;

(ff) expressing gas flow rates for liquid flow rates as fractions of the working flood point value for each respective liquid flow rate in the reference data set; and

(gg) at a constant two-phase pressure drop value:

i) from the fractions of the working flood point value calculating an average fractional flood point value for the liquid flow rates; and

ii) minimizing the standard deviation between the fractional flood point value at different liquid flow rates and the calculated average fractional flood point value by repeating steps (cc)-(gg) over reference two-phase pressure drop and liquid flow rate data.

5. The method of claim 4 , wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about one and a half inches of water per foot of column for the gas being air and the liquid being water.

6. The method of claim 4 , wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about two inches of water per foot of column for the gas being air and the liquid being water.

7. The method of claim 4 , wherein the known flood point value for one liquid flow rate equals a gas flow rate at which a slope of dimensionless two-phase pressure drop values as a function of gas flow rate is equal to or greater than about two.

8. The method of claim 4 , wherein the known flood point value for one liquid flow rate includes a user observation of an accumulation of liquid at the top of the packing.

9. The method of claim 1 , wherein determining a pressure drop within the distillation column at the fraction of flood point includes using a mathematical expression of two-phase pressure drop as a function of fraction of flood point, the expression obtained by the computer-implemented steps of:

(aa) providing a reference data set of two-phase pressure drop values as a function of gas and liquid flow rates at several liquid flow rates through a packed column;

(bb) converting the reference data set to dimensionless two-phase pressure drop values as a function of the density of the liquid phase of a subject packed column thereby making the two-phase pressure drop values at flood inversely proportional to the density of the liquid phase;

(cc) providing a known flood point value for one liquid flow rate in the reference data set;

(dd) setting working flood point values for higher liquid flow rates at values lower than the known flood point value;

(ee) setting working flood point values for lower liquid flow rates at values higher than the known flood point value;

(ff) expressing gas flow rates for liquid flow rates as fractions of the working flood point value for each respective liquid flow rate in the reference data set; and

(gg) at a constant two-phase pressure drop value:

i) from the fractions of the working flood point value calculating an average fractional flood point value for the liquid flow rates; and

ii) minimizing the standard deviation between the fractional flood point value at different liquid flow rates and the calculated average fractional flood point value by repeating steps (cc)-(gg) over reference two-phase pressure drop and liquid flow rate data.

10. The method of claim 9 , wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about one and a half inches of water per foot of column for the gas being air and the liquid being water.

11. The method of claim 9 , wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about two inches of water per foot of column for the gas being air and the liquid being water.

12. The method of claim 9 , wherein the known flood point value for one liquid flow rate equals a gas flow rate at which a slope of dimensionless two-phase pressure drop values as a function of gas flow rate is equal to or greater than about two.

13. The method of claim 9 , wherein the known flood point value for one liquid flow rate includes a user observation of an accumulation of liquid at the top of the packing.

14. A method of optimizing a product output rate from a distillation column having a top and a bottom, comprising:

(a) setting a desired product output rate from the distillation column having a packing;

(b) calculating a fraction of flood point of the distillation column at a reflux ratio;

(c) determining a two-phase pressure drop value within the distillation column at the fraction of flood point;

(d) calculating a pressure at the top of the distillation column for a pressure at the bottom of the distillation column, and calculating the two-phase pressure drop value within the distillation column of a given length;

(e) calculating a temperature corresponding to the calculated pressure at the top of the distillation column; and

(f) adjusting the desired product output rate or the reflux ratio or the pressure at the bottom of the distillation column.

15. The method of claim 14 , wherein the distillation column is a subject packed column.

16. The method of claim 15 , wherein the subject packed column is operated with gas as vapor continuous phase and liquid as dispersed phase.

17. The method of claim 14 , wherein determining a two-phase pressure drop value within the distillation column at the fraction of flood point includes using a plot of two-phase pressure drop value as a function of fraction of flood point, the plot obtained by the computer-implemented steps of:

(aa) providing a reference data set of two-phase pressure drop values as a function of gas and liquid flow rates for a reference liquid and a reference gas at several liquid flow rates through a reference packed column containing the same packing being used in the distillation column;

(bb) converting the reference data set to dimensionless two-phase pressure drop values as a function of the density of the liquid phase of a subject packed column thereby making the two-phase pressure drop values at flood inversely proportional to the density of the liquid phase;

(cc) providing a known flood point value for one liquid flow rate in the reference data set;

(dd) setting working flood point values for higher liquid flow rates at values lower than the known flood point value;

(ee) setting working flood point values for lower liquid flow rates at values higher than the known flood point value;

(ff) expressing gas flow rates for liquid flow rates as fractions of the working flood point value for each respective liquid flow rate in the reference data set; and

(gg) at a constant two-phase pressure drop value:

iii) from the fractions of the working flood point value calculating an average fractional flood point value for the liquid flow rates; and

iv) minimizing the standard deviation between the fractional flood point value at different liquid flow rates and the calculated average fractional flood point value by repeating steps (cc)-(gg) over reference two-phase pressure drop and liquid flow rate data.

18. The method of claim 17 , wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about one and a half inches of water per foot of column for the gas being air and the liquid being water.

19. The method of claim 17 , wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about two inches of water per foot of column for the gas being air and the liquid being water.

20. The method of claim 17 , wherein the known flood point value for one liquid flow rate equals a gas flow rate at which a slope of dimensionless two-phase pressure drop values as a function of gas flow rate is equal to or greater than about two.

21. The method of claim 17 , wherein the known flood point value for one liquid flow rate includes a user observation of an accumulation of liquid at the top of the packing.

22. The method of claim 14 , wherein determining a pressure drop within the distillation column at the fraction of flood point includes using a mathematical expression of two-phase pressure drop as a function of fraction of flood point, the expression obtained by the computer-implemented steps of:

(aa) providing a reference data set of two-phase pressure drop values as a function of gas and liquid flow rates at several liquid flow rates through a packed column;

(bb) converting the reference data set to dimensionless two-phase pressure drop values as a function of the density of the liquid phase of a subject packed column thereby making the two-phase pressure drop values at flood inversely proportional to the density of the liquid phase;

(cc) providing a known flood point value for one liquid flow rate in the reference data set;

(dd) setting working flood point values for higher liquid flow rates at values lower than the known flood point value;

(ee) setting working flood point values for lower liquid flow rates at values higher than the known flood point value;

(ff) expressing gas flow rates for liquid flow rates as fractions of the working flood point value for each respective liquid flow rate in the reference data set; and

(gg) at a constant two-phase pressure drop value:

i) from the fractions of the working flood point value calculating an average fractional flood point value for the liquid flow rates; and

ii) minimizing the standard deviation between the fractional flood point value at different liquid flow rates and the calculated average fractional flood point value by repeating steps (cc)-(gg) over reference two-phase pressure drop and liquid flow rate data.

23. The method of claim 22 , wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about one and a half inches of water per foot of column for the gas being air and the liquid being water.

24. The method of claim 22 , wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about two inches of water per foot of column for the gas being air and the liquid being water.

25. The method of claim 22 , wherein the known flood point value for one liquid flow rate equals a gas flow rate at which a slope of dimensionless two-phase pressure drop values as a function of gas flow rate is equal to or greater than about two.

26. The method of claim 22 , wherein the known flood point value for one liquid flow rate includes a user observation of an accumulation of liquid at the top of the column.