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The Equation method

This is the simplest indirect (calculation) method. It is a means to determine the base (reference temperature) viscosity using a single viscometer with or without the use of heat exchangers.

Key features:

- Only a single product stream
- single quality target
- Closed loop control
- Variation of viscosity with temperature is not pronounced
- A single viscometer is used

The viscometer can be installed directly into the process pipe line without a slip stream but if a heat exchanger is required, in a slip stream (bypass) installation.

How it works:

The viscosity at a reference temperature is calculated from the viscosity at the process temperature using the relationship from ASTM D341:

log10.log10.(+0.7)=A-

(Where is the kinematic viscosity at T°C.)

To solve this equation it is necessary to know the values of both constants A and B.

Both values can change significantly even with small changes in the product quality.

The equation method exploits the lesser sensitivity of the “B” value to a quality change by assuming that for a product that does not undergo significant quality change, especially when under closed loop control, and that has a very gradual change of viscosity with temperature, “B” can be considered a constant. This means that only the viscosity at a single temperature is required to solve for the other constant.

Now : “A” and “B” are both known; using these values and the reference temperature, “T”, the viscosity at the reference temperature is simply calculated.

Using this method, a new value for “A” is calculated in every calculation cycle using the real time measurement of kinematic viscosity at the process temperature.

In this application this value is is an indicator of the average molecular weight of the residuum.

Typical application:

The measurement of residuum viscosity for heating control of the quench oil in ethylene production.

Viscosity is an indicator of molecular weight.

More properly the molecular weight is a function of the viscosity at two different temperatures but in the same way the value of “b” is assumed constant, the molecular weight relationship may also be simplified. In this application the molecular weight indicates the composition of the residuum and is an indicator of the quality of the product streams.

A portion of the residuum is cooled and re-

By adjusting the temperature of the quench oil re-

Thus, in this measurement, as the temperature increases, so too does the viscosity.

This behaviour is such that simple viscometers cannot be used.

It is vital to discriminate a change in viscosity due to the quality change from a change in viscosity due to the temperature change.

This is done by determining the viscosity at a reference temperature. This viscosity is important because it is also an indicator of the average molecular weight of the residuum.

Limitations:

The assumption that “B” is constant depends on the stability of the product quality and control. It is periodically tested by taking a sample for laboratory evaluation and comparing this with the result given by the process viscometer and the equation method.

- If it falls within acceptable error limits then the assumption is good.
- If it does not then a new value for “B” is determined from the laboratory viscosity at the reference temperature and the kinematic viscosity at the process temperature measured by the viscometer.

- If, over a period of time it is found that “B” needs to be adjusted more often than
is preferred, then the system can be converted to a multi-
curve solution using the collected data and by simple changes to the program of the viscosity computer.