Thickener Model Class

This model class is one of the most complex in the process module. It implements an approximate characteristic for a thickener, sufficient to test basic thickener control strategies as well as thickener "farms" such as mud washing train (Counter-Current Decantation train). The characteristics are sufficient to generate values for all the standard measurements found on a thickener. The model makes little attempt to model the complex 3-dimensional dynamics in a real thickener (which would need CFD anyway), but instead attempts to lump the resulting characteristics into a model much more suitable for process control engineers.

This documentation should be read in conjunction with the docstring documentation from the class definition ("built-in documentation").

Objectives

• Create a thickener class that is useful to Process Control Engineers but relatively low computational load.
• Lump the operating states and parameters sufficiently to enable these to be reasonably mapped to commonly available thickener measurement instruments.

Philosophy

Major Assumptions

• The bed is a single mass of solids pulp with a volumetric solids density which varies linearly with vertical position in the thickener. The top density is zero and represents what is commonly called the "interface" level. The bottom density is the UF density. The low number of parameters and states in this formulation is quite a good match with the typical set of measurements around a thickener. Specifying the solids mass in the thickener and the UF volumetric solids density completely defines the mud density profile in the thickener.

  • It is commonly thought that the density is relatively constant in the compaction layer and relatively constant (but different to compaction layer) in the settling layer. However, it is likely that these layers are mixed up with each other to the extent that they can be considered a continuous variation in density from the top of the bed to the bottom. The practical arguments for this model (apart from reducing complexity) are:
    • At a particular level in the thickener, there is a large variation in the density along the radius of the thickener because of variable rake effectiveness. Similarly, the discharge of the feed-well does not distribute itself evenly across the radius - its reasonable to assume that the settling layer is deeper in the centre of the thickener compared to the outer edge. So even though a bed level measurement might be at a particular radius, it is not necessarily representative of the level of "mud" across the whole thickener.
    • While a laboratory scale thickener may have well defined layers, a practical thickener's layers will suffer from significant inter-layer mixing due to turbulence. One source of turbulence is caused by the feedwell flow patterns spilling out into the settling layer, making its top surface less well defined as well as disturbing the top surface of the compaction layer. A second source is the entrained air, from imperfect deaeration in the feed-well, causing some solids in the settling layer to rise above the nominal interface surface. It is common to see air bubbles extending out from the feed-well wall. A third, large source of turbulence is the rake rotation, and this causes waves and recirculation of the mud around this layer. Finally, the UF pumping rate (perhaps compared with rake effectiveness) distorts the shape of the surface of the compaction layer in the centre of the thickener compared with the perimeter.
    • Anecdotally, it is known that under-floccing events causes the bed level measurement to rise, with a corresponding drop when the flocc flow is restored. This indicates that the compaction layer IS NOT already settled and unaffected by flocc-rate.

• "Mud-level" is the level at which a nominated volumetric solids density occurs - i.e. the level that a mud-level "float" (of a nominal SG) will settle at. This is not at the top of the solids bed in the thickener.

• "Interface-level" is the level of the top of the solids bed (~zero solids density).

• Solids already in the thickener compact over time to increase the UF volumetric solids density. There is an upper limit on the UF vol solids density, related to the settling characteristics of the specific type of mud and flocculant being used. This upper limit is for the dynamic case of nominal solids flow in and out of the thickener and applies to the maximum possible operating case of 100% pulp level in the thickener (interface at thickener surface). The compression of the mud bed occurs with a time-constant (proportional to solids residence-time and inversely proportional to sqrt(flocc rate)) applied to the UF volumetric solids density. Effectively, this assumes that if the UF stops pumping, the UF density will stay constant (analogous to needing to pump out (say) underflocc'ed mud before seeing flocc'ed mud)

• A mass-balance of solids and liquid are enforced.

Implementation

Ideas

The thickener model is still evolving over time, so the ideas below seek to improve the fidelity of the thickener model without increasing its lumped-state complexity:

• Calibration of the thickener model against a real one is a problem. One way to do this would be to nominate an operating state from actual steady thickener operation: UF density, mud level, interface level, torque, flocc rate and feed solids flow. For the above formulation, all calibration parameters and states can be calculated from these, including the mud mass, the mud level density threshold, flocculation and torque calibration points.
• Compression time-constant (similar to settling rate) would probably have a non-linear effect w.r.t. flocc (normalised) rate. Perhaps use a square-root function here? Normalising would mean that the influencing factor (of floccing) would be w.r.t. (flocc-flow / feed-solids-flow) / (nominal-flocc-flow / nominal-feed-solids-flow). The square-root function still results in 1.0 output for nominal (1.0) input of normalised flocc flow!
• The compression time-constant could also represent the settling-time parameter commonly measured by Clarometer units. This settling-time is not an absolute measure, but is only with respect to the size of the cell in the Clarometer. So an external "transmitter" scaling and zero needs to be applied to yield the correct range of settling-rate values expected from the Clarometer.
• If the thickener is in steady-state, the drive of compression time-constant increasing the UF Vsolidsdensity is matched by an opposite effect of the addition of new (low density) feed. Over dt, the feed adds new pulp at feed solids density. Similarly, the UF pumping is removing pulp at the UF solids density.
  • without feed and without compression, the UF pumping would simple result in the density profile of the bed emptying out in a plug-flow fashion down towards the thickener UF. At the moment, the only way UF density reduces is through the reduction of inventory, which is not close to reality.
    • At each timestep we could reduce the UF Vsolidsdensity corresponding to the loss of mass from the bottom of the density "triangle" (UF solids density at base, 0 density at top). Can we calculate the height of the piece of triangle to truncate, so that we can calculate the density at the new base?
  • Perhaps, new feed should just add sufficient height to the bed to accommodate the additional mass of solids (UF density shouldn't be affected). However, something should account for the actual feed density - that is, a very low feed density should have a different effect to a very high feed density? Perhaps it doesn't matter - low density will report to the highest point in the bed and high density feed will fall through to a lower part of the bed.
  • On reflection, the above interpretations are not accurate - the current model with just the inventory mass manipulating the density "drive" target should have roughly the correct characteristics:
    • i.e. the mass inventory must come down before the UF density will come down - it won't come down because some of the highest density material has been removed.
    • assumes the pctVSolidsUFmax applies to the dynamic case of nominal solids feed/discharge rate. This is a bit different to above where it assumes that pctVSolidsUFmax is for a no feed/discharge situation and pctVSolidsUFmax is the ultimate density that it could ever achieve in a laboratory.
    • But, presently the SS UF density doesn't depend on the feed/discharge rate of solids (see next major point)
• Perhaps the timeconstant of compression shouldn't be set by the user - perhaps it should be set as the residence time of solids in the thickener (based on the UF solids discharge rate). I.e. as the inventory gets less, the thickener responds faster.
• Further on the response-time, some cone geometry should be implemented to represent the significant dynamic changes that occur when operating at very low solids levels
• Mechanism to explain relatively fast response of UF density to UF flow:
  • The normal view of a thickener with flat surfaces of mud and interface means that an increase in UF flow would have to appreciably lower the mud level before the UF density would change.
  • However, observation indicates that UF density is generally the earliest thickener variables to change - so a mechanism is required to replicate.
  • It is likely that, at high UF flows, the mud bed is not flat, and that there is a draw-down cone or rathole that develops, causing lower density material higher in the bed to bypass through to the UF pumps.
  • Replicate by allowing the UF density to be drawn from a point up in the mud bed with a height proportional to the UF flow - the higher the flow the higher the draw point and the lower the density. However, this would be instantaneous, so apply a time-constant proportional to the bed height (a deep bed will take longer to establish a rat-hole).