Table of Contents
This paper will review thickening theory, from the study but of the practicing engineer, with particular emphasis on areas of uncertainty or disagreement. It will attempt to outline broadly what we know and what we don’t know. This should serve two purposes. First, it will warn the process engineer where he might get into trouble. At least it will alert him to the risk involved in uncritically accepting any of the recommended design procedures. Second, it will identify for researchers some areas in which further work might be fruitful.
“Thickening” means different things to different people. For this paper we define it to mean sedimentation behavior characterized by line settling. Solids subside with a clear line of demarcation between settling solids and supernatant. Although the supernatant will usually be clear, in some cases it may be turbid.
Coe and Clevenger believed that throughout “free settling” the settling velocity u was a function of C only. In mathematical terms, u = u(C). About compression they made the following statement:
“The water liberated by compression finds its way out of zone D” (their compression zone) “through tubes or channels which form drainage systems upwards through the zone.”
Thus they conceived channeling to be symptomatic of compression. If you saw channeling, you knew you had reached compression.
Recently it has become apparent that channels must form, either permanently or intermittently, in a concentration range which is not yet in compression, at least as we have conceived compression in the past. And in this range u is not a function of C only. This divides Coe and Clevenger “free settling” into two regimes, giving three altogether:
- Zone settling – Coe and Clevenger “free settling” in which u = u(C)
- Phase settling – Free settling with channeling, u ≠ u(C)
- Compression – Floc structure supports compressive stress
Scott who has done more to prove experimentally the reality of phase settling in thickening than any one else, calls these regimes “dilute”, “intermediate”, and “thick” respectively.
In zone settling, there is some velocity u, fixed by concentration C, which can be ascribed to the rate at which solids settle with respect to the pulp as a whole. It is the solids subsidence rate one would observe in a batch test. The corresponding downward flux of solids is uC. In a thickener there is also a down-ward velocity v of the settling pulp as a whole past any level below the feed, because underflow is withdrawn at the bottom. This gives an additional component of solids flux equal to vC. Therefore, the total solids flux downward past any level in the thickener must be:
Gt = uC + vC……………………………………………………..(1)
From material balance:
Gt = vCu………………………………………………………….(2)
Kynch started from the postulate that u = u(C). As noted above, this was assumed true by Coe and Clevenger for their “free settling”, and we have used it as the defining relationship for the zone settling regime. Using a continuity approach, Kynch showed that:
- A concentration discontinuity would propagate with a velocity:
U = ΔG/ΔC
- A locus of constant concentration in a concentration gradient will propagate with a velocity:
U = dG/dC
Lower Conjugate Concentration Zone
The lower conjugate concentration poses an unresolved problem. Continuity would demand that this concentration exist between the feed point and whatever higher concentration zones exist below. But there is no necessity to assume continuity. And many thickeners show a mud line far below’the feed point, with clear supernatant above, at least near the periphery where sample lines are commonly provided, so a lower conjugate concentration does not have to exist. Yet Scott reports finding concentrations apparently corresponding to upper conjugate in some test operations.
If feed is more concentrated than a lower conjugate concentration, there is a large body of literature in the Civil Engineering field which says it will plunge to the bottom of such a zone like a submerged waterfall – as a density current. It will spread out at the level of hydrostatic equilibrium. And it can be shown mathematically that by the time it has spread out over the entire thickener area Its load of solids will have settled out, regardless of how fast or slow it spreads, providing u = u(C).
Comings long ago showed solids profiles in a continuous thickener. Concentration varies with depth, and such behavior was common industrial knowledge. Theory based on the postulate that u = u(C) does not permit this. Therefore the idea that zone settling could explain all thickening behavior was never logically tenable.
Classically, pulps not in zone settling were assumed to be in compression. Coe and Clevenger defined a compression zone as “that portion of the pulp where the flocs considered as integral bodies, have settled to a point where they rest directly one upon another. After pulp enters zone D, further separation of liquid must come through liquid pressed out of the flocs and out of the interstitial spaces between the flocs”.
Classically it was believed that channeling accompanied compression. This has always been hard to rationalize, and leaves several questions. First, what holds channels open, when solids pressure necessarily exceeds the yield value of the solids structure to cause compaction? If it is hydraulic pressure, what pressure gradients then remain to push water out of the floc structure into the channels? And why should channels open up to begin with, when the structure is being crushed together overall? As far as we know, nobody has thought this through and come up with a completely plausible explanation.
On the other hand, there can be no doubt that channeling does occur in sedimenting pulps. In the first place, you can often see it. Particularly with metallurgical pulps it visibly takes the form described by Coe and Clevenger, great drainage systems upward through the pulp. At their mouths these rivers of fluid may be of the order of a millimeter across, and they erupt through the surface as “volcanoes”. After eruption there is a steady and rapid streaming of fluid upward through them, evidenced occasionally by flutter of semi-detached floccules fluidized in channels which form next to the glass column wall.
The Compression Point
In batch settling, the “compression point” has been generally conceived as that at which solids just below the pulp supernatant interface pass into the compression regime. It is identified with a discontinuity in the slope of a batch settling curve of H vs t. From a to b the subsidence plot is linear, corresponding to initial concentration. At b higher concentration or Kynch zones start appearing at the interface, giving a first slope discontinuity. At some point c there is a second discontinuity in slope, which is taken as the compression point. The slope discontinuities are usually more easily spotted on a log log plot of H vs t.
Experience shows, however, that in many loosely flocculant pulps there is no discontinuity apparent to identify as the compression point. This gives rise to considerable uncertainty in the Coe and Clevenger procedure, and also to the idea that if the results were wrong, it was because the compression point had not been properly identified.
What Is an Engineer to Do?
From the foregoing it will be apparent that there are many unresolved problems in the theory of thickening. But the practicing engineer cannot cease specifying thickener size until theoretical types get them straightened out. He must do the best he can with the information available. Fortunately things are not quite as bad practically as this paper makes them sound. The announced idea of the paper was to emphasize what we do not know.
In most metallurgical applications the Coe and Clevenger procedure will continue to yield thickeners of adequate design, as it has for the past fifty years. However, the Talmage and Fitch procedure should be preferred for determining thickener area. It is simpler, and even though it has been shown to be theoretically not quite valid in the vicinity of the compression point, empirically it has been shown to predict area more accurately, (and more rapidly) than the Coe and Clevenger procedure.