**Statistical Analysis of FCCU
Data to Monitor and Optimize Unit Performance**

**Introduction**

The Fluid Catalytic Cracking (FCC) process is a series of complex and highly coupled interactions between catalyst, hardware, feed and products. Effective monitoring of these interactions can determine the key variables of the catalyst, feed and operating conditions which will result in optimum performance for a given set of economic conditions and unit constraints.

Statistical Analysis of FCC unit operating data can help the refiner to determine these key variables rapidly and without the need for sophisticated and expensive FCC models.

BASF has developed a system, which takes its customers' database spreadsheets and performs step-wise regression analysis of their data to derive mathematical equations describing the current operation of the unit.

The equations determined by this analysis are linked together in a spreadsheet model by heat, mass and elemental balances to give a robust, simple and accurate unit-specific trend model.

This article describes examples of how regressions were performed for two refineries to improve their units' performance.

**Optimum FCC Performance
Requires Accurate Catalyst Selection**

Analysis of the operating history of an FCC unit over a period of time covering several catalyst changes can identify the interaction of catalyst design variables with the feed and unit hardware. Such analysis has historically been done in fixed bed and circulating pilot plants and the results used to select catalyst and/or derive equations for trend models. Such work is expensive in terms of investment, manpower and lapsed time. With the advent of personal computers in the technical departments of refineries, however, historical data of FCC performance is readily available for analysis. Merging the fresh and equilibrium catalyst databases allows determination of feed/catalyst interactions on a unit by unit basis without necessarily the need for extensive pilot plant studies.

A major benefit is that correct catalyst reformulation to achieve specific unit objectives can be determined more accurately on a unit specific basis.

**Curve Fit of Kinetic Conversion
Model (1)**

The following cracking model assumes a second order rate for conversion.

X/(1-X) = (FEED/CAT FACTORS)*(CTO)^n*(WHSV)^n-1*EXP(-k/R(T+273))

- Where

X = Wt Fraction Conversion

CTO = Catalyst to Oil Weight Ratio

WHSV = Space Velocity, 1/hr

T = Kinetic Avg. Reaction Temperature, Deg C

R = Gas Constant, 1.9872 cal/mol/Deg K

k = Activation Energy for Cracking, 13900 cal/mol

n = Decay Exponent, 0.65

With the exception of space velocity there is usually sufficient data available from a refiner's database to curve fit this equation. Space velocity can be replaced in this equation with catalyst to oil ratio as follows:

- WHSV= 3600/CTO/Q

where Q = Catalyst Contact Time, seconds

The original equation becomes:

X/(1-X) = (FEED/CAT FACTORS)*(CTO)* Q^1-n*EXP(-k/R(T+273))

Catalyst contact time in this equation can be determined by either catalyst circulation rate (assuming constant reactor holdup) or by total feed rate (assuming constant catalyst backmixing or slip).

**Refinery A Conversion Model**

The regression of the database from Refinery A found that total feed rate gave the best correlation for catalyst contact time. The following equation for conversion was derived:

A/X/( l-X)=(CTO)^1.24/(FDSG-0.78)/(FDRI-1.41) * (FDMPH)^-0.29*(MAT/(100-MAT)^0.16*EXP ( -2700/T)

- Where

FDSG = Feed Specific Gravity

FDRI = Feed Refractive Index

MAT = MAT Activity, Wt %

FDMPH = Feed Rate, M3/Hr

In the above regression, the activation energy has been increased from 13900 to 5400 while the catalyst decay exponent increases from 0.65 to 0.71. Using a generic trend model, where original values were deter-mined as in reference (1), we would have seriously underestimated the conversion incentives for a higher operating temperature in this unit. Figure 1 shows the historic trend of observed and predicted conversion. Average error of prediction is +/-2.5 Wt %. which is quite reasonable for a 2 parameter feed model.

**Refinery B Conversion Model**

In the regression of Refinery B's database the catalyst circulation rate gave the best correlation for catalyst contact time and the following was derived for conversion:

X/( l-X)=(CTO)^O.88/(FDSG-0.87)*(FDS+6.05) ^0.5 *(CCR)^-0.14* (SA)^0.56* EXP( -5610/T)

- Where

FDS = Feed Sulphur content, Wt %

SA = Equilibrium Surface Area, M2/g

CCR = Catalyst Circulation Rate, Tons/min

In this regression, the activation energy is approximately the same as that found in reference (1) while the catalyst decay exponent is increased from 0.65 to 0.86. Figure 2 shows the historic trend of observed and predicted conversion. Average error is +/-2.3 Wt %.

**Refinery A Motor Octane Model**

A simple linear model was found to describe Refinery A's Motor Octane Number (MON):

MON=44.7=0.065 * T+0.038* PREDCONV-0.018* FBP+0.00117*CATNI

- Where

PREDCONV = Conversion predicted by the above equation

FBP = Gasoline Final Boiling Point, Deg C

CATNI = Equilibrium Nickel Level on Catalyst, Wppm

Figure 3 shows the historic trend of observed and predicted MON. Average error of prediction is +/-0.6 which is near the combined practical variability of the process and test method. Based on this information the refiner subsequently increased reaction temperature 10 Deg C and reduced gasoline end point 10 Deg C thereby increasing MON by approximately one number, consistent with this model.

**Refinery B Motor Octane Model**

A simple linear model was also found to describe Refinery B's MON:

MON=60.3+0.036* T+0.091* PREDCONV-0.0061*FBP-0.00043*CATNI+7.3*CATCRC-2.16*REO-0.01* CATSA-0.0004*FDTPD

- Where

CATCRC = Carbon on Regenerated Catalyst, Wt %

REO = Rare Earth Oxide Level on Equilibrium Catalyst, Wt %

CATSA = Equilibrium Catalyst Surface Area, M2/g

FDTPD = Total Feed Rate, Tons/day

Figure 4 shows the historic trend of observed and predicted MON. Average error of prediction is +/-0.7 which is again quite good. Again the refinery subsequently used this model to increase MON by approximately 0.7.

**FCC Spreadsheet Trend Model**

With the use of either published or linear equations most FCC product yields and qualities can be predicted by similar regressions. References for lumped kinetic forms are given in articles (2) and (3). A simple spreadsheet program can then be written which integrates the predictions to meet mass, heat and elemental (eg. Sulphur, Hydrogen) balances. Inclusion of feedstock costs and product prices allows the user to optimize the unit to meet any prevailing economic environment.

Inclusion of catalyst parameters into the model allows the determination of optimum catalyst properties for a given set of unit constraints. For example, increasing rare earth lowers MON but also reduces wet gas compressor load which in turn allows an increase in reaction temperature. Statistically regressing MON and gas yield permits the determination of the rare earth direction in which to go in the FCCU to maximize MON, provided the reactor temperature can change.

**Summary**

While this article outlines how BASF has applied statistical regression to assist several refiners in optimizing operating conditions the unit can only achieve this improvement if the actual operating conditions are changed. This in turn generates new data for inclusion into the database and allows recorrelation and confirmation of the magnitude and direction of each of the independent variables.

This analytical process should, therefore, be considered as an ongoing evolution of the FCC unit's performance in an environment where the price spreads between feed and products do change and fast simple operating responses can capture the credits associated with these changes.

**References**

1. Wollaston, E.G., Haflin, W.J., Ford, W.D. and D'Souza, G.J., Hydrocarbon Process,54(No 9), Page 93 (1975).

2. Weekman, V.W., AIChE Series. 75, No 11, Page 1 (1979).

3. Jacob, S.M., Gross, B., Voltz, E.E. and Weekman, V.W., AIChE Journal 22, Page 701 (1976).