...of flowing pulp suspensions.

Friction loss for pipes with pulp slurries can be very difficult for dynamic simulators to calculate because of certain anomalies. For example, friction loss can actually decrease with increased velocity or it can exhibit unexpected behavior with a change in consistency.

CADSIM Plus uses a novel empirical method which normalizes each curve fitted through the friction loss maximum, minimum and point of crossing of the water curve. This method calculates the friction loss through the difficult region where the friction loss dips as the velocity increases. The results shown in Figure 1 demonstrate a good fit of the various methods that CADSIM Plus uses, when compared to measured data.

Many friction loss calculations have been based on the TAPPI method TIS 0410-14. This method uses a formula, given below, to calculate friction loss up to the velocity at which the maximum friction loss is observed. Beyond this point the TAPPI method suggests a straight line be drawn to where it crosses the friction loss curve for water.

The TAPPI method may be fine for design because it is very conservative (it overstates the friction loss in the region where it dips) but it is not acceptable for dynamic simulation. A more realistic response to changing flows is required by dynamic simulation to more accurately predict pressure flow networks and control responses.

In the region of consistency depicted in Figure 1, the first section of pulp slurry friction loss is calculated using the TAPPI method, given by the following formula:

The figure (at right: depicting slurry friction loss in pipes) shows the results of these calculations for the lower velocities which are linear on the log - log plot.

The lines shown are CADSIM Plus calculations for one to five percent consistencies. The points shown (pictured at right) are taken from Tappi Vol 33 No 9, Fig 6, p22A to show proximity to measured data.

The challenge is to calculate the dip in friction loss as the velocities increase, and the ultimate convergence back towards the curve for friction loss with just water. Water friction loss in CADSIM Plus is calculated by:

This method allows CADSIM Plus to deliver reasonable dynamic simulation results, while adhering to the TAPPI method at the lower velocities, observing the dip at medium velocities and approaching the more rigorous water friction loss calculations at higher velocities.