Hmmm have you tried looking at any undergraduate text on rheology. Coal/water slurries are invariably non-Newtonian, or at least they are if you don't look to closely, so normally a viscos-plastic model will suffice. ■

Well there is no average viscosity that is meaningful with non-Newtonians, the viscosity is a function of the shear rate (i.e. the velocity profile) and so varies across the duct and changes if the flow changes. The viscosity, which used to be called apparent viscosity but I think that term is now deprecated, is the local shear stress over the local shear rate. If you want to just look at the flow in the pipe then you can use the shear rate at the pipe wall, which is (3n'+1)/4n' x 8V/D where V is the bulk velocity, i.e. flow rate / area, D the pipe dianmeter and n' you will have too look up as its too long an explanation for this forum or else I'm just lazy

If you have a model that fits your data, say the Herschel Bulkley model, then of ccourse you can just use the analytical expressions for this model. ■

The corelation to be used will depend on type of slurry flow.

1. Heterogeneous flow is characterised by pronounced solids concentration gradient across the vertical axis of the pipeline, and it is encountered in a wide variety of commercial applications ranging from dredging to coal transportation. In such flows, the particles are coarser and hence are flown at moderate concentration and higher flow velocity. Such flows are always turbulent for keeping the coarser particles in suspension. Slurry behaves as Newtonian fluid as coarseness of particles at moderate concentration makes yield stress equal to zero. For modeling such a flow, you can fairly assume slurry flow as Newtonian considering influence of gravitational force and turbulent diffusivity on particles.

2. Homogeneous flow is characterised by uniform concentration across pipe cross-section, and it is generally encountered in iron-ore and tailings pipeline flowing slurries of very fine paticles at high concentrations in the paste form. Slurry generally behaves as power-law or Bingham-Plastic fluid with considerable yield stress. Such flows may be either laminar or turbulent depending on throughput requirement. Such flows are easy to model on the basis of slurry rheological properties only as described in the earlier post by Lionel P. ■

Yes you are absolutely right, the flow regimes are far more complicated than the original questioner had realized (I think). My understanding was that we were looking at coal slurries like coal/water mixtures which may be considered (grossly) to be a non-Newtonian. In reality they are all heterogeneous ranging from the water based systems you have described for relatively low concentration coarse solid flow to the hybrid Stab Flo type suspensions where the high concentrations and broad size distributions form a non-Newtonian slurry in which the remaining particles are conveyed. This latter regime usually appears to be like a homogenous non-Newtonain but is in reality a highly stratified flow.

So I guess a simple simulator, that was the basis of the original question can only go so far. ■

Dear Dr. Pullum,

I fully endorse your views. Have a look at two PSDs and their rheological properties, we obtained in our Lab. on coal-water slurries. It is interesting to note that maximum static concentration for 1 and 2 was 60% and 45% by weight, respectively. For the smooth flow without any operational difficulties related to choking, we need to keep the avearage concentration atleast 10% less than Cwss. Hence, we can go only upto 50% and 35% by weight in slurry pipeline for transporting particles 1 and 2, respectively.

Regards,

Kaushal

Attachments

1JPEG:forum_attachments/file_container/1_4.jpg (BMP)

2JPEG:forum_attachments/file_container/2_7.jpg (BMP)

■

Dear Dr Kaushal

Yes particle size distribution is very important. When non-Newtonian behaviour occurs it is dominated by the fine end of the distribution, and also by the surface chemistry of course and so other things, for example water quality become important. For the coarser particles it is the packing that is important. Consequently for high concentration suspensions it is more useful to express the concentration in the reduced form, i.e. volume concentration/ maxiumum concentration. This then takes into account both the packing and non-Newtonain effects. Unfortunately calculating the packing is not easy, and the non-Newtonian effects impossible so this normaly has to obtained by experiment. ■

The best way to determine the viscosity of any heterogeneous material such as the coal slurry you described is to use a rotational viscometer such as the Cannon DPV (Digital Paddle Viscometer). We offer equal quality, but half the cost Viscosity Standards used in the calibration of such instruments. Using glass capillary viscometers for measuring materials such as this are inappropriate for two reasons. First, the capillary may become clogged if a coal particle that was too large made it into one of your samples. Second, the turbulent flow of the fluid around the particles in the capillary would yield inconsistent/unreliable results. The flow inside the capillary must be uniformly laminar to be consistent with the viscometer constants provided with the instrument. You mentioned velocity. Simply running the slurry down a fixed incline and timing it would give a rough estimate of the viscosity, but would probably prove too inaccurate for any serious industrial application.

A good example of the rotational viscometer's practical use for a material like this is road crews mixing asphalt emulsions to build pavement roads. They must first measure the viscosity of the hot asphalt/water emulsion at the paving site before application to the road surface. If the viscosity is not within bounds the road surface is likely to fall apart many years sooner than if applied properly.

Please visit www.ViscosityStandard.com to learn more about viscosity standards and their role in the calibration of viscometers of all types and other viscosity verification purposes. ■

Well I didn't realise that this forum was a venue for advertising ones products, which is a shame as it reduces the impartiality of any replies.

Regarding the problem of measuring rheological properties of hetereogenosu suspensions, the first point to maker is that viscometers or all forms are designed to measure the properties of homogenous fluids, and each form will fail to indicate the rheology of the underlying carrier fluid, some geometries more than others. If it is not possible to remove the coarse particles, i.e. those over say > 40 micron, then appropriate modelling needs to be applied to account for the presence of these particles. For rotary viscometers some attempts have been made tc account for their presence in changing the average shear rate but I am unaware of any that have been able to remove the effects of particle migration within the gap to retrieve the carrier fluid viscosity, if anybody knows of any papers please upload details. Regarding capillary tube viscometers; for sufficiently large ones that will not block, there is sufficient knowledge from pipeline transport to get very close to these values, which can then be used with suitable mechanistic models to design the pipelines for the combined suspension. There will be a paper on this subject in the next Korean Australian Journal of Rheology.

Rotary viscometers are very useful, portable and have very small sample requirements but they suffer just as many issues as other forms.

Finally the answer is to stop strying to model complex solids fluids flows as viscometric ones■