## October 2016

## Special Focus: Process Control and Information Systems

# Optimize a CDU using process simulation and statistical modeling methods

A methodology was implemented to optimize the operation of a refinery crude distillation unit (CDU) using a combination of process simulation and statistical modeling methods.

A methodology was implemented to optimize the operation of a refinery crude distillation unit (CDU) using a combination of process simulation and statistical modeling methods. The primary objective was to estimate a set of operating targets for column pumparound and bottoms stripping steam flows. These targets were established to maximize the unit profitability over a typical range of crude rate and crude quality operating conditions.

The crude unit has an advanced process control (APC) application that maximizes product draw rates, but does not optimize the variables above. Process simulation was used to evaluate the CDU performance over a feasible range of pumparound and bottoms stripping flows, as existing operating data did not provide sufficient data. Crude quality and crude feed rate were sampled randomly from actual operating data to account for their inherent process variability.

To develop a robust set of operating targets that would perform well under varying market conditions, alternate market scenarios were considered—where gasoline margins exceeded diesel margins, and vice versa—when calculating the unit profit function. Several statistical modeling methods were used to build 3D profit response surfaces as a function of the operating targets to determine the economic optimum. The estimated optimum operating targets for pumparound and bottoms stripping steam flows are being implemented.

## Study goals and parameters

A crude distillation unit takes a crude stream and separates it into boiling point fractions, which include naphtha, kerosine, diesel and tower resid bottoms. A process diagram for a typical crude distillation unit, which has four tower pumparounds, is shown in **FIG. 1.** Pumparounds remove heat from the column to preheat the incoming crude prior to the crude entering the crude heaters, and to generate internal reflux for distillation.^{1} The optimum targets for pumparounds and bottoms stripping steam flows depend on the impact of these variables on both product yields and energy use. As the amount of heat removed from the column via pumparounds increases, the heater duty requirements are reduced at the expense of column fractionation efficiency.

This study is based on the use of process simulation to evaluate the performance of the unit over a range of pumparounds and tower bottoms stripping steam flows. Process simulation was selected, as unit operating data did not provide a sufficiently wide range to allow the determination of the optimum targets.^{2} Pumparound flows were represented as the ratio of the pumparound to the crude flowrate. The bottoms stripping steam flow was represented as the ratio of the pounds of steam per gallon of tower resid bottoms. The process simulation results were used to construct response surfaces using multiple regression methods for product yields and heater duty requirements to validate the simulation results prior to building the profit response surfaces. Profit response surfaces were then built using the predicted product yields, heater duty requirements and product prices for different market scenarios with multiple regression methods. The profit response surface mapped out the crude distillation unit profit as a function of the pumparound ratios and the tower bottoms stripping steam ratio.

The following methodology was used in the study:

- Develop a set of simulation cases that covers the range of pumparounds and stripping steam ratios considered
- Randomly draw the crude feed composition, as well as the crude feed rate, for each simulation case
- Run process simulations for the cases defined above
- Use simulation results to build multiple regression models of product yields and crude heater duty requirements as a function of pumparound and stripping steam ratios
- Produce 3D response surfaces based on the regression models to map out the product yields and the heater

duty requirements as a function of pumparound and stripping steam ratios - Generate profit response surfaces for market conditions where gasoline margins exceed diesel margins, and

vice versa - Validate results obtained with multiple linear regression models with those obtained with other statistical modeling methods that model non-linear behavior, including multivariate adaptive regressive splines (MARS) and classification and regression trees (CART).

Detailed descriptions of the process simulation and statistical modeling of product yields and heater duty requirements are provided here, followed by the economic optimization analysis and key findings.

## Process simulation

To conduct simulations, proprietary software was selected for a user-friendly spreadsheet interface that provides the capability to run multiple cases.^{a} **TABLE 1** summarizes the model specifications common to all of the simulation cases.

The process variables that were modified for each simulation include crude feed composition, crude feed rate, pumparound flowrates and bottoms stripping steam mass rate. A total of 60 simulation cases were initially configured to define the range of operations with respect to pumparound flowrates and bottoms stripping steam mass rates. The 60 cases covered pumparound flowrates ranging from 20 Mbpd–50 Mbpd for kerosine, and diesel and bottoms stripping steam mass rates ranging from 6,500 lb/hr–12,500 lb/hr.

To model the variability in crude feed composition, three different crude assays were used, corresponding with the refinery’s three most typically run crudes. The percentages of two of the crudes were varied randomly, and the percentage of the third crude was calculated by difference so that the total crude volume percentage added to 100%. Crude feed rates were modeled using a normal distribution, with the mean and standard deviation estimated from operating data.

A second set of 60 simulation cases was defined after preliminary analysis indicated that the direction of the optimum was at high diesel pumparound flowrates and high bottoms stripping steam mass rates. The impact of kerosine pump-around was not found to be as significant, so the second set of cases kept the same range of kerosine pumparound flowrates as the initial configuration. The second set of runs covered diesel pumparound flowrates of 40 Mbpd–50 Mbpd, and stripping steam mass rates of 10,500 lb/hr–12,500 lb/hr.

## Modeling of product yields, heater duty requirements

The impact of tower pumparound and bottoms stripping stream ratios on product yields and heater duty requirements was first assessed to validate the process simulation results prior to building the profit response surfaces. **FIG. 2** is a scatter plot matrix illustrating the relationships between product yields and heater duty requirements against tower pumparound ratios, reflux ratio and bottoms stripping steam ratio. The strong impact of the diesel pumparound ratio on product yields and on heater duty requirements can be seen. The impact of the kerosine pumparound ratio was not found to be as significant. A strong correlation between product yields and duty requirements with reflux ratio can also be observed.

Tower pumparounds were expressed as a ratio of pumparound flow to crude flow (P/A ratio). Heater duty requirements were expressed as MBtu/bbl of crude. Note that the diesel product yield was positively correlated, and the kerosine product yield negatively correlated with the diesel P/A ratio, as expected. The diesel P/A ratio was also found to be highly correlated with reflux ratio, as the top tray temperature was assumed to be constant and the simulator adjusted the reflux ratio to maintain this temperature.

Since the reflux ratio was found to be highly correlated with the diesel P/A ratio, the reflux ratio was excluded as a regressor to minimize the effects of multi-collinearity on the multiple linear regression models. The tower bottoms stripping steam ratio was found to be highly correlated with the resid bottoms yield, diesel yield and naphtha yield. As expected, the diesel P/A ratio and the heater duty requirements were found to be negatively correlated, as high P/A ratios translate to lower heating requirements. The scatter plot matrix illustrating these relationships was generated using a statistical graphics procedure.^{b}

To examine the relationships between product yields and heater duty requirements against the key factors, second-order linear regression models were constructed with both quadratic and interaction terms.^{3,4} These models were then used to build response surfaces to examine the unit performance over the operating range prior to proceeding with the economic optimization analysis. **FIGS. 3, 4, 5** and **6** provide 3D surface contour maps of product yields as a function of bottoms stripping steam ratio and diesel P/A ratio. Note that naphtha yield is maximized at maximum diesel P/A ratio, kerosine yield at minimum diesel P/A ratio, diesel yield at maximum diesel P/A ratio, and resid bottoms yield at minimum diesel P/A ratio. In terms of the bottoms stripping steam ratio, diesel yields were maximized at maximum stripping steam ratio, and resid bottoms yield at minimum steam ratio. **FIG. 7** shows that maximum heater duty requirements occur when the diesel P/A ratio is at a minimum, as expected.

## Economic optimization analysis

Once the process simulation results were validated based on the second-order linear regression model results, profit response surfaces were built to determine optimum targets. Profit response surfaces were constructed for scenarios where gasoline margins exceeded diesel margins, and vice versa, to develop a set of robust targets that would perform well under varying market conditions and minimize the need to adjust these targets. **FIG. 8** illustrates the average product margins used to estimate product revenues, as well as the natural gas prices used to estimate the crude heaters fuel costs and stripping steam costs. This data was based on actual pricing data from November 2014 to October 2015. The resid bottoms product margin was estimated as 70% of the gasoline margin and 30% of the diesel margin.

Profit response surfaces were first constructed based on second-order linear regression models. **FIGS. 9** and **10** provide the profit per barrel of crude for both market scenarios considered. Note the higher density of points at the higher values of diesel P/A ratio and stripping steam ratio, which represent the second set of simulation runs configured.

When gasoline margins exceeded diesel margins, the profit function was maximized at maximum diesel P/A ratio (**FIG. 9**). The profit response surface was found to be relatively flat as a function of bottoms stripping steam ratio for this scenario. When diesel margins exceeded gasoline margins, the profit function was maximized at the highest diesel P/A ratio and at the highest bottoms stripping steam ratio (**FIG. 10**).

To validate the results obtained with the multiple linear regression models, a model based on the MARS method, which uses piecewise linear basis functions to allow for the modeling of non-linear behavior, was also constructed. **FIGS. 11** and **12** show profit response surfaces based on the MARS method for both market scenarios. Note that the behavior of both profit response surfaces was consistent with the results obtained with the multiple linear regression models. A proprietary procedure^{c }was used to build the model, and two procedures^{d} were used to generate the profit response surfaces.

As an additional verification of the analysis results discussed here, the CART method^{e} was used to map out the unit profitability as a function of the key drivers. The CART method is based on binary recursive partitioning, which also models non-linear behavior. **FIGS. 13** and **14** are regression trees predicting unit profitability for both market scenarios considered. Note that profit is maximized in either case at higher diesel P/A ratios. The CART regression tree results show that the range between the maximum and minimum terminal node values was $0.08/bbl when gasoline margins exceed diesel margins, and $0.06/bbl when diesel margins exceeded gasoline margins.

## Key findings

This work has determined optimum operating targets for crude distillation unit pumparound flowrates and bottoms stripping steam mass rates using process simulation combined with statistical modeling. Diesel P/A ratio and the bottoms stripping steam ratio were found to be the key drivers impacting unit profitability. The analysis estimated maximum diesel P/A ratio and maximum bottoms stripping steam ratio as the optimum operating targets for the range of market scenarios considered.** HP**

**NOTES**

^{ a} KBC’s Petro-SIM 4.1 process simulation software.^{b} SAS PROC SGSCATTER procedure.^{c} SAS PROC ADAPTIVEREG procedure.^{d} SAS PROC TEMPLATE and PROC SGRENDER procedures.^{e} R rpart procedure

**REFERENCES**

^{ }Gary, J. H., G. E. Handwerk and M. J. Kaiser,*Petroleum Refining: Technology and Economics,*5th Ed., CRC Press, Boca Raton, Florida, 2007.^{}Montgomery, D. C., E. A. Peck and G. G. Vining,*Introduction to Linear Regression Analysis,*5th Ed., John Wiley & Sons Inc., Hoboken, New Jersey, 2012.^{}Montgomery, D. C. and R. H. Myers,*Response Surface Methodology: Process and Product in Optimization Using Designed Experiments,*1st Ed., John Wiley & Sons Inc., New York, 1995.^{}Del Castillo, E.,*Process Optimization—A Statistical Approach,*Springer, 2007.

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