Base + delta models

The main conversion units in a refinery are typically modelled via a linear Base + Delta representation. A reference point is chosen, by combining a typical feed with a typical set of operating conditions. The base vector provides the yields and properties for the reference point. The delta vectors indicate the linear yield and property response to changes in feed qualities and/or operating conditions from the reference point. When the response to one or more independent variables is highly non-linear, more than one set of base + delta tables might be required to adequately describe the behaviour of the process unit; for example, separate Base + Delta tables may be needed to represent changes in severity.

In DGS, you set up a series of process simulations, which represent different combinations of feed quality and operating conditions. These simulations can be generated in three ways:

• by routing different feeds to the unit and specifying the operating conditions

• by using DGS to automatically step the feed and operating parameters

• by generating a set of data externally and importing this into DGS.

One of the simulations is selected as the base vector. DGS then regresses the whole data set, using the selected feed and operating parameters as independent variables, to calculate the best base + delta representation of the unit. DGS also provides the means to analyse results and improve the model.

Selection of process model independents, and set-up of the sample cases used to derive the linear model, requires an intimate knowledge of the underlying process, feed quality covariance and process model responses. Hence, experts from the various skill groups typically perform this task.

Take for example a distillate hydrotreater.

In the Base situation the hydrotreater feed has a sulphur content of 1.8 % by weight. This might be the typical sulphur value of the unit's normal feed when running the standard crude basket. Under these conditions the yield of hydrotreated distillate is 98.38% by weight of the input feed. The remaining mass is lost as hydrogen sulphide.

When the sulphur content of the input feed increases to 2.8 % by weight, for example if the crude slate changed to much heavier, more sulphurous crudes, then the yield of distillate reduces to 97.93% by weight relative to the input feed. The mass of distillate must be reduced as more of the input is sulphur and this is all lost as hydrogen sulphide.

Using these values the gradient of the change can be determined. A change in (2.8 - 1.8) +1 for the sulphur yield leads to a change in distillate yield of (97.93-98.83) -0.9. Therefore the delta value for a +1 increase in feed sulphur by weight is -0.9. That is an increase in input feed sulphur by 1% by wgt leads to a 0.9% reduction in the amount of distillate produced (by wgt).

We have now established a linear relationship, and this can be used to calculate the effect of other input feed properties. For example if the input feed actually had a sulphur content of 2.3% then the distillate yield would be (98.83 + (2.3 - 1.8) * -0.9) 98.38.

The Base value should actually be in the middle of the expected range of input feed properties, and during regression the linear gradient is calculated to minimise the error between the entered property values and the values calculated using the final regression equation. The error is shown by the R2value in the results Grid where an R2value of 1 means the values calculated by the fitted equation are exactly equal to the entered values, and values less than this show an increasing error.

So in this case the distillate yields when sulphur is 2.8% and 0.8% by wgt would be used to fit the data over the entire range, where the base value lies in the middle of the expected values.