APPLICATION OF EQUILIBRIUM STATE RHEOLOGICAL DATA IN THE RED MUD DISPOSAL PROCESS
Fiona Sofra and Prof D.V. Boger
Department of Chemical Engineering
The University of Melbourne
Parkville, Vic 3052
Ph 9344 7440
Fax 9344 4153
Accurate prediction of transport energy requirements for a non-Newtonian material involves overcoming a number of inherent problems. For a complex thixotropic material such as bauxite tailings (red mud), the major problem is a result of the difficulty in obtaining rheometric parameters which are representative of the structural state of the material in the pipeline.
The rheological behaviour of a suspension is generally summarised by the construction of a flow curve relating the shear stress to the shear rate. The present study identifies significant time dependent characteristics of the flow curve and outlines a method for simplifying pipeline design. The results obtained suggest that the yield stress at the pipeline conditions, as measured by the simple slump test (Pashias et al, 1996) and a single flow curve at any structural state can be used to calculate the shear stress, hence pumping energy, at the shear rate of interest.
Red mud rheology is dependent on shear and compression history, elapsed time since shearing and the dose and method of flocculant addition. Although the viscosity is a function of all of these factors, it also varies with shear rate for non-Newtonian slurries such as red mud. The yield stress however, is a singular point for each curve that also reflects the materials history and additives used. As such, it is proposed that the yield stress is a unique parameter, which may be used to eliminate the need for quantification of slurry history.
The proposed prediction method is applied to a wide range of pipeline data and good agreement with measured pipeline data is obtained.
red mud, pressure drop prediction, rheology, thixotropy, non-Newtonian, slurry
APPLICATION OF EQUILIBRIUM STATE RHEOLOGICAL DATA IN THE RED MUD DISPOSAL PROCESS
Fiona Sofra and Prof D.V. Boger
The use of rheological data to predict pumping energy requirements is difficult for thixotropic materials. Due to the changing behaviour of the material with shear history, extreme care must be taken to ensure that laboratory results will be representative of the state of the material in the pipeline.
Laboratory measurements are undertaken in order to generate a flow curve, ie. a plot of shear stress versus shear rate. This curve provides a means of determining the pressure drop-flowrate and the viscosity-flowrate relationships, hence the pumping energy required for a particular application. As these relationships are not unique for all times of shear for time dependent materials, methods must be devised to ensure that results are meaningful in terms of real pipeline flow.
For many industrial slurries, the shear stress-shear rate behaviour is dependent on shear and compression history, elapsed time since shearing, particle size distribution and the dose and method of flocculant addition. Although the viscosity is a function of all of these factors, it varies with shear rate for non-Newtonian slurries such as red mud. The yield stress however, is a singular point for each curve, which also reflects the history of the material. As such, it is proposed that the yield stress is a unique parameter, which may be used to eliminate the need for complex quantification of slurry history.
The present study aims to identify significant time dependent characteristics of the flow curve and to determine how the yield stress may be used to reflect the history of the material. The application of fully sheared state parameters on a partially sheared material is investigated.
2.0 PSEUDOPLASTICITY AND THIXOTROPY
Shear thinning of industrial slurries such as red mud is attributed to the alignment of particles or flocs. An increase in the shear rate from rest results in alignment of particles in the direction of shear, therefore providing a lower resistance to flow. As such, the suspension will show a decreasing viscosity with increasing shear rate. Although knowledge of this behaviour is imperative, the most significant influence on the application of flow curves is the time dependent nature of red mud, which results in thixotropic behaviour.
Thixotropy is the result of structural breakdown under shear and manifests itself as a decrease in the viscosity with time for a given, constant shear rate. As time of shear elapses, the rate of breakdown will decrease, as fewer structural bonds are available for breakdown. Structural reformation does take place and the rate of this process increases with time of shear due to the increasing number of bonding sites available.
A state of dynamic equilibrium, where the breakdown and reformation rates are equal, is possible, however this state is not generally achieved in industrial applications due to the extended times required. Generally, the material in the pipe will be in a partially sheared state, where the shear stress-shear rate behaviour is still changing with the time of shear. Problems arise when using flow curves generated in a lab environment due to the difficulties in ensuring that the material is in the same structural state as in the pipeline.
The only region in which one can be sure of the structural state of the material is the equilibrium state; thus the equilibrium state provides a good point of reference. Flow curves are shown to be reliable in this state, with the viscosity and yield stress being reproducible. As such, it is recommended that lab measurements be undertaken on a fully sheared slurry. For fully sheared results to be applied to a partially sheared slurry, the effect shear history on the generated flow curves must be determined.
2.1 The Herschel Buckley Model
For slurry in laminar tube flow, a flow curve is easily generated using the tube dimensions, flowrate and the pressure drop. A logarithmic plot of wall shear stress against apparent shear rate can then be used to predict the pressure drop at various shear rates.
The wall shear stress is a function of the pipe diameter and length (D and L) and the measured pressure drop (?P),
The apparent shear rate is based on the average flowrate (V) across the pipe,
In the case of red mud, which is a shear thinning, yield stress material, the equilibrium shear stress-shear rate relationship is well modelled by the Herschel Buckley equation;
where n is the slope of a log-log plot of ty vs Gy.
The constants k and n are found by iterative solution of the equation.
2.2 Shear History Effects
In order to identify variations in rheological parameters due to the thixotropic nature of the material, flow curves were generated for increasing durations of shear (Figure 1).
The sample tested was 47% thickener underflow taken from the Kwinana residue plant. The Herschel Buckley model was then fitted to each curve to assess the changes in
To reduce the amount of laboratory work required to predict the pressure drop at a given shear rate for design purposes, an investigation into the possibility of creating one master curve for each concentration was undertaken. The construction of a master curve to be used for pressure drop, therefore pumping energy estimation, involved vertically shifting all curves to a common yield stress (see figure 3). The exact shape of the curves was maintained (the same k and n) and curves were shifted so that the intercept was the yield stress of the equilibrium state. The point of the shifting process was to superimpose all curves to determine the variation in shape.
Shifted Flow Curves (Lines indicate 95% Confidence Limits)
The actual shifted data and the 95% confidence limits are shown in Figure 3. The maximum deviation of 25% occurs when a material in the initial state is approximated using the equilibrium state values of n and k. If the average n and k for all structural states is used, the maximum deviation reduces to 14%. Once the material is subjected to a shearing force, this deviation reduces significantly.
As would be expected, the curve using the average values of n and k gives results that are more accurate. However, the additional work required to analyse all structural states from the initial state to equilibrium is probably not warranted. Although a thorough error analysis has not been undertaken as part of this work, rheometer measurements and pumping energy control would undoubtedly be outside this level of accuracy.
The results obtained suggest that the thixotropic nature of red mud manifests itself primarily as a variation of the yield stress. As such, if both the yield stress at the pipeline conditions and any flow curve for the material are available, the shape of the curve can simply be shifted along the y-axis to coincide with that yield stress. The resulting curve and equation (1) can then be used to calculate the shear stress, hence the pumping energy required at the desired shear rate.
To ensure that the yield stress used is representative of the structural state of the material in the pipe, it is recommended that the slump test (Pashias et al., 1996) be used on site at the time of sample collection. This testing method eliminates further thixotropic breakdown during transport or recovery due to time delay. The slump test has the added advantage of being inexpensive and simple to perform and analyse.
Having obtained this representative yield stress, ty slump, it is simply substituted for ty in equation (3) to produce the flow curve that will approximate the material in the relevant structural state. It is then possible to simply read off the shear stress (hence pressure drop from equation (1)) for the desired shear rate.
The results indicate that a flow curve generated at any time can be used to predict the pressure drop. The maximum deviation in the wall shear rate of approximately 25% will occur when a material in the initial state is approximated by the equilibrium values of k and n. The deviation calculated is considered acceptable given the accuracy of capillary measurements.
The proposed method provides a significant reduction in laboratory work and data analysis required to determine the viscosity and pressure drop of a slurry at a given flowrate.
3.0 APPLICATION TO PIPELINE DATA
The pressure drop prediction method outlined above was applied to existing data obtained from various sources. The data available encompassed a range of both material types and operating conditions, therefore providing a good test of predicted values.
The first set of data used was collected from the carbonation pipeline at the Kwinana residue plant (D=0.15m, L=133m). Solids loadings of 35-45% were included in the data. For each concentration, the yield stress was measured immediately using a vane rheometer (Nguyen and Boger, 1983). The capillary rheometer was used to construct flow curves some time later. Due to the delay, some settling of the slurry had taken place so agitation was required to resuspend the solids. Because of the delay and added shear, it was difficult to determine the structural state of the material.
In order to predict the pressure drop, the vane yield stress was used to shift the flow curve to the appropriate shear stress corresponding to a zero shear rate. The wall shear stress was then determined for the shear rate of interest. Determination of the expected pressure drop was then relatively simple given the dimensions of the pipeline used. The calculated pressure drops were then compared with those measured during the pipeline runs. Results are summarised in Figure 4.
Using the shift method, the deviation from the measured value ranges from 20% to 44% and although this may seem high, it should be noted that pressure drop predictions based on friction factors (Darby et al, 1992) give much larger deviations (Sofra, 1996). Deviations ranged from 43% to 78% using friction factor methods. As such, it is considered that the proposed semi-empirical method provides a much-improved prediction of the pressure drop for red mud in laminar pipe flow, especially at higher flowrates.
In both cases, a large contribution to the discrepancy between predicted and measured pressure drops is the frictional losses due to valves and fittings. The pipeline used contained six tee pieces and associated valves, causing significant frictional losses. The small diameter of the sampling port and valve would also have subjected the slurry to high shear stresses. This high stress resulted in the pressure drop calculated from sampled material properties being higher than the true value. In the case of non-Newtonian slurries, the pressure loss due to these fittings is very difficult to estimate.
Pressure drop versus flowrate data for the Paranam washer #7 underflow in a long (19.5m), predominantly straight pipe were also available. These data were used along with the yield stress measured at the operating conditions (Cooling, 1997) and capillary rheometer data measured in an unknown structural state (see figure 5).
An average deviation from the measured pressure drop of 11% was obtained using the shifted curve. The slight overestimate calculated compares very favourably to the deviations observed when using the power law model with no vertical translation of the curve (which was originally used in this case). The unshifted power law is currently used in a number of software packages in the Alumina industry (Cooling 1997). An average pressure drop underestimation of 94% resulted when power law parameters gained from capillary rheometer results were used.
The significant underestimation is consistent with expectations if the sample had been subjected to large shear forces before testing, resulting in a breakdown of the material structure. The shearing could have been due to the sampling method, transport and/or resuspension of the solid material.
Using the more accurate Herschel-Buckley model in combination with shifting the curve to the pipe yield stress value allows the structural state of the material to be taken into account. Consequently, the pipeline pressure drop may be predicted far more accurately.
The above trend is also seen in pressure drop predictions for trials undertaken at Alcoa, Wagerup on the 7th and 9th of November 1995. The slump test yield stress measured at the pipeline conditions was then used to shift the curves in the previously mentioned manner (see figure 6).
The pressure drop was overestimated by 63% and 84% when the unshifted power law model was employed. In contrast, the shift method produced much smaller deviations of 25% and 28%.
The shift method was used to predict the pressure drop for a nickel tailings pipeline. The tailings were pumped over a distance of approximately 60 meters at a flowrate of 953 m3/hr and a concentration of 43% by weight. The yield stress at the pipeline conditions and a flow curve generated at The University of Melbourne were used to calculate the expected pressure drop in the line. The predicted pressure drop was then compared with the measured value, also shown in figure 6.
Measurements for flow curve generation were taken some weeks after sampling and after transport from Perth to Melbourne. Therefore, the material was in a structural state, which did not relate to the process conditions at all. This resulted in a significant underestimation of the pressure drop using the unshifted curve. By employing the shift method outlined, the difference between the calculated and measured pressure drops was notably reduced, as can be seen in figure 6 above. The use of the yield stress at the process conditions resulted in a significant increase in the accuracy of the predicted pressure drop from an underestimate of 16% to an overestimate of just 2.5%.
Of the samples tested, there was considerable variation in the deviations between predicted and measured pressure losses. The variation observed is in part due to the different structural states of each of the samples. Some samples had been subjected to extensive pumping and flow over long distances, whereas others were closer to initial (fully structured) state. As the equilibrium state rheological parameters were used in all calculations, the samples closest to the initial state will show the greatest deviations
4.0 CONCLUSIONS AND RECOMMENDATIONS
The results obtained suggest that the thixotropic nature of red mud primarily manifests itself as a variation of the yield stress. As such, the yield stress at the pipeline conditions and a flow curve for the material may be used to calculate the pumping energy at any shear rate. This allows rheometric parameters measured in the fully sheared state to be applied to a partially sheared material.
Comparison with pumping energy requirements calculated using friction factors or the unshifted power law show the proposed shift method to be preferable. For solids loadings of 35-45%, greater accuracy was obtained for all shear rates encountered. Furthermore, the proposed method provides a significant reduction in laboratory work and data analysis required to determine the viscosity and pressure drop of a slurry at a given flowrate.
It is recommended that pumping energy calculations be undertaken using the shift method outlined. This method may be used with acceptable accuracy for design purposes. Measurement of the yield stress, using the slump test (Pashias, 1996), should take place on site immediately after sampling.
The authors wish to acknowledge Alcoa of Australia for their continuing long-term support and the Australian Research Council for the Research Student Scholarship.
Particular thanks to David Cooling of Alcoa of Australia for providing much of the pipeline data.
Cooling, D. Private communication. July, 1997.
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