Mixing Lignocellulosic Slurries Presents Challenges
Lignocellulosic slurries have long been used for paper production as well as for feedstock for water-soluble polymer production, such as carboxy methyl cellulose. More recently, they have been used as the feedstock for cellulosic ethanol and other biofuels.
Such slurries usually behave as Herschel-Bulkley fluids, with pseudoplastic behavior above the fluid yield stress. Achieving complete fluid motion requires overcoming the yield stress everywhere in the vessel. Proper design with multiple impellers can avoid wasting energy caused by over-agitating some regions of the tank, and can be used to minimize total agitator power.
Several authors have reported the relationship between yield stress and cavern size in mechanically agitated complex fluids, and the minimum torque required to drive cavern size to the wall. Little has been published, however, on lignocellulosic slurries. Most studies were done with a single impeller, as opposed to the more common case of multiple impellers.
In practice, more torque is required of the bottom impeller than the upper impellers, due to the need to overcome yield stress on the tank bottom as well as the side wall. The result is that the lower impeller needs 2 to 10 times as much torque to create full motion out to the wall as each upper impeller, depending on the slurry. Without accounting for this result, too much torque overall will be applied, overagitating the top portions of the vessel needlessly and wasting power. The optimum aspect ratio of the tank for minimum power or torque is also affected by this phenomenon.
When such a fluid is agitated, a moving zone forms around the impeller. If torque is insufficient to overcome the yield stress throughout the vessel, a stationary area forms outside this zone. The moving area is often called a cavern. Its boundary is defined by the surface at which the fluid experiences its yield stress. P.E. Aratia and others illustrated this phenomenon in their paper, “Mixing of Shear-Thinning Fluids with Yield Stress in Stirred Tanks,” using fluorescent dye as shown in Figure 1.
Several researchers have found that when the cavern just reaches the wall, the aspect ratio (height/diameter) of the cavern is about 0.4 for Rushton impellers and other radial impellers, and up to 0.6 for high-solidity axial turbines. This author has found that the aspect ratio can be as high as 0.7 for low-solidity axial impellers. The flow patterns, however, do not stack up perfectly when multiple impellers are used. To get a seamless meshing of flow patterns without staging or intermittent dead zones between impellers, multiple axial flow impellers should be applied so as to control an aspect ratio of 0.5 to 0.6 maximum, each. The recommendations in this article are based on an aspect ratio of 0.5 per impeller for two or more impellers.
The shear thinning nature of these fluids above yield stress can result in highly localized movement if the tank diameter is too small. Also, dead areas often form around any in-tank flow obstruction, such as baffles. Thus, baffles are not recommended for cellulose slurries. This poses another problem. If the D/T ratio is too large (impeller diameter is D, tank diameter is T), the tank contents will tend to bodily rotate with the impellers, resulting in poor mixing. With solids content of 8 percent or higher prior to significant hydrolysis, the lower impeller should normally have a D/T ratio between 0.5 and 0.7. The upper impellers will be smaller, generally in the range of 0.4 to 0.6.
Bottom vs. Sidewall Agitation
Figure 1 illustrates the case where the cavern formed is well above the tank bottom. But what if we need to agitate the tank bottom? Due to the need to overcome the yield stress on the tank bottom as well as the side wall up to an aspect ratio of 0.5, the torque input needed from the bottom impeller to create complete motion is substantially more than that required of upper impellers, which need only overcome the yield stress at the sidewall. Though a theoretical model can be derived showing a 4/3 torque ratio should be required, actual experimental data show a larger torque share needed by the lower impeller.
Wet experiments were done on a variety of different cellulosic feedstocks, shown in Table 1. Most were not hydrolyzed, though some had undergone partial hydrolysis. Actual torque splits ranges of 68/32 are not unreasonably far off from the theoretical derivation of 57/43. Others, surprisingly, have power splits as high as 90/10 in favor of the bottom impeller. This means the ratio of upper impeller diameter to lower impeller diameter will generally be in the range of 0.64 to 0.86.
If test work done in the laboratory is scaled up to production equipment based on either a single impeller in a squat batch or dual, equal diameter impellers in a square batch, the resultant full-scale design will have much more vigorous agitation in the top of the tank than at the bottom. Such an agitator design will be more expensive than necessary, and consume far more power than needed. The problem gets worse rapidly as the aspect ratio of the production equipment gets higher. Table 2 illustrates this.
Tank Geometry Consequences
A proper torque split scale-up is needed. Normally, for flow-controlled processes, the required torque is about the same at a given volume, independent of aspect ratio (Z/T) of the vessel. The required power, however, increases as Z/T (liquid level is Z, tank diameter is T) increases at a constant tank volume. When the required torque is different for upper and lower impellers, the situation changes. Table 3 illustrates the effect for three cases: equal split, 70/30 and 90/10 ratios. All are based on equal tank volume. As expected, the torque remains the same and the power increases as a function of Z/T for the 50/50 case. For the 70/30 case, the power does not change much, but the torque diminishes as the aspect ratio increases. For the 90/10 case, both torque and power decrease as the vessel gets taller.
In lignocellulosic slurries, it is more difficult to agitate the bottom of the tank than the upper regions. More torque is therefore required from the bottom impeller than from the upper impellers. Failure to take this into account increases the capital and operating costs of the agitator used in the production equipment. Optimum tank geometry and production power required are also affected by the required torque split. Because the required torque split does not generally follow a theoretical derivation, it is necessary to do wet tests to determine the required torque split for any particular slurry.
Author: Gregory T. Benz
President, Benz Technology International Inc.
The claims and statements made in this article belong exclusively to the author(s) and do not necessarily reflect the views of Ethanol Producer Magazine or its advertisers. All questions pertaining to this article should be directed to the author(s).