Non-Newtonian flow simulation

Non-Newtonian and settling slurry flows occur across a number of industries, for example, food processing, pharmaceutical, wastewater and mining. Food and wastewater flows tend to be non-Newtonian/non-settling; mining flows tend to comprise a Newtonian carrier fluid (usually water) with a solids component which may be in full or partial suspension.

Simulating these types of flows in order to calculate pipe and pump sizes presents a significant challenge to the engineer. First, the broad divide between the two types needs to be established and then rheological and solids characteristics need to be determined.

Pipe friction loss models for non-Newtonian/non-settling flows are well established - Bingham, power-law or Herschel-Bulkley - depending on the stress/strain relationship of the fluid and are relatively easy to develop into a computer program. But for settling slurries (ie, a 'carrier fluid') conveying solid particles, the approach is considerably more complicated due to the wide range of variables involved, namely particle size distribution, solids density and shape; per cent solids; mixture velocity, etc. The accepted approach is to determine the 'solids effect', which is the extra friction loss caused by the solids content over that for an equivalent flow of the carrier fluid.

Typically, mining applications will involve a water-based settling slurry. A number of inter-related factors then influence the magnitude of the solids effect. The two main factors are the solids characteristics and the velocity of flow of the mixture, but pipe inclination is also important.

For solids of a size less than about 0.4 mm, and at higher velocities, the particles are distributed in a homogenous manner and the head drop can be considered directly proportional to that of water.

At the other extreme, with coarser particles moving as a sliding bed with none in suspension, the solids effect is considerable and the pressure loss much greater than for water alone. This is referred to as fully stratified flow. In between these extremes are two regimes, pseudo-homogeneous and heterogeneous. Pseudo-homogeneous flow contains particles between about 0.4 mm and 1.5 mm and displays a variation of solids concentration with height across the pipe diameter.

Again, the pressure drop is proportional to that obtained for an equal discharge of water. Heterogeneous flow (particle size around 1.5 mm to 4 mm and lower velocities) exhibits a greater non-uniformity of solids concentration. The solids are supported partly by fluid suspension and partly by inter-particle contact. The settling velocity of the solids and the per cent by volume in the mixture are important factors.

A mining slurry may contain a wide particle size distribution of solids and consequently all three regimes of flow - pseudo-homogeneous, heterogeneous and fully stratified - may be present at the same time.

The technique is to estimate the excess pressure drop separately for each of the three regimes and then sum them for the total. A further complication is that the very small particles may be in permanent suspension, thereby altering the friction characteristics of the water carrier fluid.

The design method is highly empirical. Slurry Transport Using Centrifugal Pumps, by KC Wilson, GR Addie, A Sellgren and R Clift, provides the best reference with a synthesis of the authors' many papers. Introduction to Practical Fluid Flow by RP King provides a useful summary of the Wilson, Addie, Sellgren, Clift method plus a comprehensive chapter on non-Newtonian slurries. Chemical Engineering Fluid Mechanics, by Ron Darby provides a very useful introduction to all types of flow.

These three references and a considerable amount of literature research provided the basis for the development of a slurry simulator as part of a more general fluid and process flow design package called FluidFlow3.

In the standard version of the package, calculations assume a Newtonian fluid but the optional slurry module addresses the issues described above. For non-Newtonian/non-settling slurries, the Bingham plastic, power-law and Herschel-Bulkley models are available.

For settling slurries, the Wilson, Addie, Selgren and Clift method is reproduced, utilising the empirical data presented in their text. The WASP model for coal slurries may be used. A correction routine necessary for the performance of centrifugal pumps is included.