1. GBH Enterprises, Ltd.Process Engineering Guide: GBHE-PEG-SPG-304SEDIMENTATIONProcess Information Disclaimer Information contained in this publication or as otherwise supplied to Users is believed to be accurate and correct at time of going to press, and is given in good faith, but it is for the User to satisfy itself of the suitability of the Product for its own particular purpose. GBHE gives no warranty as to the fitness of the Product for any particular purpose and any implied warranty or condition (statutory or otherwise) is excluded except to the extent that exclusion is prevented by law. GBHE accepts no liability for loss, damage or personnel injury caused or resulting from reliance on this information. Freedom under Patent, Copyright and Designs cannot be assumed.Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com

2. Suspensions Processing Guide:SEDIMENTATIONCONTENTS 0INTRODUCTION - The Phenomenon of Sedimentation1THE IMPORTANCE OF SEDIMENTATION TO SUSPENSION PROCESSING 1.1 Gravity Thickening 1.2 Clarification 1.3 Centrifugal sedimentation2THE SCIENCE OF SEDIMENTATION - STATE OF THE LITERATURE 2.1 2.22.33Clarification - Settling in Fairly Dilute Suspensions The Zone Settling Regime - Kynch Theory 2.2.1 Construction of Curve APBC from a Particle Settling Model 2.2.2 Analysis of Sedimentation Curve to Yield Particle Settling Function Zone Settling and Compression - The Sediment StructureTESTS, CHARACTERISATION PROCEDURES AND DESIGN METHODS 3.1 Batch Settling Tests 3.2 Suspension Characterization - Prediction of Sedimentation Behavior 3.2.1 Equilibrium Degree of Concentration 3.2.2 Use of a Compression Cell 3.2.3 Pulse Shearometry 3.2.4 Slow-speed Centrifugation [44-46] 3.2.5 Kinetics of Thickening 3.3Design Methods - Gravity ThickenersRefinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 3. 4EXAMPLES 4.1 The Purification of Brine 4.2 Distiller Blow-Off, DBO [52]5REFERENCES6FIGURESFigure 1The Different Sedimentation Regimes (Schematic)Figure 2Parameters used in the Kynch Theory of SedimentationFigure 3Kynch Model for Sedimentation Showing Propagation of Constant Concentration CharacteristicsFigure 4Sedimentation behavior of a weakly flocculated suspension (polystyrene latex + sodium carboxymethylcellulose) under various Centrifugal fields. Points are experimental data, continuous curves Derived from Kynch theory (see text).Figure 5Two Interface Description of Sedimentation (supernatantsuspension and suspension-sediment) as proposed by Tiller (schematic)Figure 6Concentration Dependence of Uniaxial Modulus, K, for a Model Suspension (polystyrene latex coagulated with RaCl2 ) before (open symbols) and after (solid symbols) shearing treatmentFigure 7Sedimentation Behaviors of Attapulgite Clav Suspensions at Two Gravitational Forces - Influence of Tube Diameter on Equilibrium Sediment Concentration of SolidsFigure 8The Pulse ShearometerFigure 9Schematic Illustration of the Centrifuge ExperimentRefinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 4. Figure 10Schematic View of a Typical Circular Basin Thickener Illustrating the Various Sedimentation ProcessesFigure 11Schematic Graph of Variation of Solids Flux, G, with Concentration of Solids, CFigure 12Batch Settling TestsFigure 13(a) Conventional Flow Sheet for Thickener Sizing Figure 13(b) Schematic Diagram of Procedure for Estimating Compression Time and Hence Depth of Compression Zone in Thickener (after Fitch in [3]) Figure 13(c) Thickener Sizing Procedure from Batch Settling Data Figure 13(d) Estimation of Critical Flux, Gc, Based on the Coe and Clevenger Equation Figure 14(a) The Yoshioka Construction for Thickeners based on the Batch Flux versus Concentration Graph (after reference [49]) Figure 14(b) Influence of Flocculants on Batch Flux Curve (Schematic) Figure 15Effects of Various Flocculant Types on Settling Velocity of Particles during Brine Clarification (Schematic)Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 5. 0INTRODUCTION - THE PHENOMENON OF SEDIMENTATIONSedimentation is the physical process whereby solid particles, of greater density than their suspending medium, will tend to separate into regions of higher concentration under the influence of gravity. As a solids/liquids separation technique it therefore possesses the great advantage of utilizing a natural, and therefore costless, driving force. This section of the suspension processing Guide is Intended to provide an Introduction to the science of the subject, and the means to judge where and how best to exploit sedimentation as a separation (or other processing) technique. As a scientific discipline the subject of sedimentation is vast with perspectives ranging from the field of chemical engineering through to theoretical physics being covered In the literature [1-11]. Good reviews of the subject, with a bias towards the engineering aspects, have been written by Fitch and Koz [12, 13]. A short summary of some of the more relevant contributions from the literature is also provided in GBHE-SPG-PEG-302 Basic Principles & Test Methods, of the Suspensions Processing Guides. . The sedimentation process is traditionally divided into settling within four regimes which are schematically depicted In Figure 1. At very low concentrations of solids, and in the absence of interparticle forces, each particle will settle independently of all others at a limiting velocity given by Stoke's formula [2], provided that the fluid flow is laminar. That is,where the symbols have their conventional meanings. The above limiting velocity is found for particles sedimenting under conditions where the Reynolds Number, defined as,is small (NRE < 1). Here L is the density of the suspension medium. This is the commonest behavior for systems of Interest to this manual. Where NRE is large 0 - 1000) the settling process involves turbulent flow of liquid around the settling particles and the limiting, so called Newtonian, velocity is: Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 6. For values of NRE between the above limits, the "transition zone", intermediate behavior is observed [2]. Extension of these results to non-spherical particles and further details are provided in Section GBHE-PEG-SPG-300.2- Intro Fundamentals of Suspensions & Dispersions. As the concentration of the solid phase is gently increased, particles or flocs may still settle essentially independently but now terminal velocities substantially lower than those predicted from equations (1) to (3) are observed. This is because each settling entity is buoyed by the rising stream of fluid generated by the others. That is, the particles or flocs interact through hydrodynamic mechanisms although direct interparticle forces have negligible effect at such average separations. This concentration regime is normally described as that corresponding to clarification; depending upon the degree of interparticle cohesion (during collisions) the clarification may be of primary or flocculated particles. At a phenomenological level the clarification mechanism may be distinguished in a suspension by a thinning out of the upper regions of the sample and by the deposition of a solid sediment at the base of the containing vessel. A detailed discussion of clarification is provided in GBHE SPG PEG 304 Centrifugation, of Suspensions Processing Guides. If the proportion of solids in the suspension is increased further the zone sedimentation regime results. Within this range of concentrations the suspension has structure (though it may be very weak) as a consequence of the direct interparticle forces [24-27]. As a result of this structure the particles sediment en masse with a velocity that depends only upon their relative height in the suspension and not on their lateral position. This zone settling (sometimes called line settling) is normally easy to distinguish from the clarification regime for it exhibits a clear falling zone boundary between concentrating suspension and (clear) supernatant. There may also be a rising layer of compacted sediment at the bottom of the vessel but the position of this is usually obscured by the opacity of the rest of the suspension. The final, and slowest, mechanism for sedimentation will occur when the suspension is sufficiently concentrated to present a significant structural resistance to densification [27]. At this point the suspension will develop a measurable modulus either In shear or compression; this point will be considered In more detail later. Apart from the relative rates of fall of the zone boundary, zone settling and consolidation in the compression regime are not, normally, visually distinguishable. Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 7. The various mechanisms for sedimentation which occur at Increasing solids concentrations are controlled by different physical factors and therefore impose diverse constraints on solids/liquids separation operations. For this reason a detailed consideration of clarification practice is deferred until GBHE SPG PEG 304 Centrifugation; separation operations occurring within the zone settling or compression regimes are treated In this chapter. It is important to stress here that many of the principles discussed in this section are pertinent to, and overlap with, other GBHE Suspensions Processing Guides, particularly the following: Centrifugation, Selection of Flocculants, Clarification, Suspensions of Controlled Rheology.1THE IMPORTANCE OF SEDIMENTATION TO SUSPENSION PROCESSINGAs has already been stated, the principal application of sedimentation to suspension processing is In the field of solids/liquids separation. Three main sorts of separation operation may be distinguished: 1.1 Gravity Thickening These operations generally involve the concentration of a suspension under gravity in a situation where the solid phase is initially at a moderately high concentration. The use of scientific tests to measure suspension properties relevant to this dewatering operation are described later in this section (3.3). 1.2 Clarification As shown by Figure 1, clarification is a separation operation occurring at much lower starting concentrations. An understanding of the clarification process requires knowledge of the sedimentation and Flocculation behavior of the suspension. A discussion of the latter is not relevant here but is provided in GBHE SPG PEG 304 Centrifugation together with some exemplification.Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 8. 1.3 Centrifugal sedimentation This is closely analogous to thickening except that the operation is carried out In an enhanced gravitational field. Much of the relevant Science is common to both and will be discussed here. Specific examples and centrifuge design theory will, however, be covered in section 3. In addition to the above direct applications of sedimentation to suspension processing, there are a number of other areas of science and technology where the phenomena and theory are relevant. These Include:(i)The theory of fluidized beds [17-19].(ii)Storage stability of suspensions (Chapter 7) [20-21].(iii)Particle size classification methods [22].(iv)Settling of dust/other solid particles from smoke etc [23].(VIMethods for determining the density of particulates, and/or the viscosity of a suspending medium.2THE SCIENCE OF SEDIMENTATION - STATE OF THE LITERATUREThe objective of this part of the section on sedimentation is to provide a brief outline of the state of the scientific (as opposed to chemical engineering) literature on the subject. For purposes of convenience the subject matter is classified into categories corresponding to the various regimes of Figure 1. Inevitably many of the papers discussed overlap more than one category, however,Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 9. 2.1Clarification - Settling in Fairly Dilute Suspensions The major factors affecting the rate of sedimentation for such cases are the particle or floe size, shape and hence density, the concentration of settling species and the presence of any added species that might modify floe structure [24-28] or the medium viscosity [29]. (In addition, for small scale work the dimensions of the containing vessel may also affect the sedimentation rate.) The contributions of various workers in quantifying the Influence of these factors will now be reviewed. For Colloidally stable particles a number of formulae have been proposed for the concentration dependence of the settling rate at moderate solids contents. Perhaps the most useful of these is that employed by Buscall ,Goodwin and Ottewill [291 amongst others. For suspensions of 1.55 m polystyrene latices the settling rate was found to be of the form:where p is the volume fraction at which the particles close pack and k is a numerical constant determined by Buscall et al to be equal to 5.4. (Note that under the artificial conditions where p = 1, this equation reduces to the well known Richardson and Zaki equation, U/US = (l - )4.7 much favored by engineers. The same workers also found that Stoke's formula for the sedimentation rate of a sphere In very dilute suspensions (see Introduction) could be extended to shear thinning supernatants by using the zero shear viscosity In the expression:The great value of expressions for sedimentation rates, such as (4) above, is that they illustrate the parallel behavior of the settling rate of suspensions with their shear rheological behavior.Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 10. For example the concentration dependence of the same suspensions conforms to a closely analogous equation, due to Dougherty and Krieger [30], for the shear viscosity:This latter feature has been developed and extended in subsequent work on weakly flocculated suspensions by Buscall and McGowan [31]. For these, slow speed centrifuge experiments and shear rheological measurements Indicated, a closely parallel relationship between the stress dependence of the viscosity and the dependence of the collective friction coefficient on the ambient gravitational field. Thus, in principle, with this result established it should be possible to snake accurate predictions of sedimentation rates, for weakly flocculated suspensions, from shear rheological measurements. The influence of floc structure and container dimensions on settling rate was investigated thoroughly by Michaels and Bolger [32] in a study of the sedimentation properties of flocculated kaolin suspensions, By controlling the pH of the suspending medium these workers were able to control the degree of "openness" of the floc structure and correlate this with the settling properties. Furthermore, they found that the flow conditions under which the flocs were formed were also an important factor. In fact the Influence of floc structure and the kinetics determining it are often the main variables in a clarification context. For more details of the factors that control them, the reader is referred to GBHE Suspensions Processing Guides, particularly the following: Centrifugation, Selection of Flocculants, Clarification, which also contain many additional references. All the work discussed above refers either to particles with a narrow size distribution or flocculated suspensions. Substantial progress has been made by a number of workers in elucidating the factors that determine the settling behavior of suspensions containing bimodal or polydisperse size distributions of non-flocculating particles [34-38].Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 11. 2.2The Zone Settling Regime - Kynch Theory [39] In many senses the first real attempt to produce a theory of sedimentation away from the simpler clarification regime was due to Kynch. His theory, though It contains some conceptual errors and gross oversimplifications, is the foundation of much of the present understanding of the subject. Furthermore, the Kynch analysis of sedimentation remains the basis of most contemporary engineering algorithms for the sizing of full-scale thickeners (Section 3.3). It is therefore well worthwhile outlining the principles and results of his contribution. Kynch's principal starting assumption was that the settling velocity of a single particle, u, was a function of its local concentrations only; that is:where c is the particle number concentration at that point. It was further assumed that all the settling entitles were of the same size and shape. By considering the particle flux, S = c.u, through a horizontal element of thickness dx, Figure 2, in the settling column, he derived the basic continuity equation:where x is the vertical height of the element within the column. This may be re-expressed In the form:Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 12. Kynch now considered the behavior of the height, x, as a function of time, t, for any element of constant concentration. Such an element is described by a characteristic line following the equation:Combining (9) and (10) yields the beautifully simple result for the slope of the characteristic equation of a zone element of constant concentration:This result is indicated schematically In Figure 3. It can be seen that all the concentration zones are propagated upwards at the constant velocity, V, which is a simple function of that concentration. Provided that the concentration function is continuous, no two characteristics will cross. The equation of these characteristics is then:X 0 being the Intercept of the characteristic on the height axis. Two other relations enable Kynch's theory to be exploited in order to understand the fall of the zone boundary, ABC. At any general point P, the speed of fall is given by:A conservation equation based on the total number of particles to pass through a given rising characteristic, (n(xo)), concentration may be written in the form:Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 13. Equations (12) and (14) apply only for characteristics terminating on the part of the curve, APB. For the region BP the further assumption is made that the concentration at the bottom of the bed, x = 0, reaches a maximum value, Cm, very rapidly after sedimentation has commenced. These characteristics therefore extrapolate back towards, but do not actually originate from, the point x = t = 0. Similar reasoning indicates that equations (12) and (14) still hold provided that xo = 0 in this region. After C, sedimentation ceases since the whole bed has reached the uniform, maximum concentration, Cm. (As will be seen later, these assumptions are erroneous since they do not allow for consolidation. Having outlined the basis of the theory and presented the salient equations, we now describe how to apply it in two important situations:2.2.1 Construction of Curve APBC from a Particle Settling Model In order to construct a zone boundary decay curve as a function of time, two additional pieces of information are required: The initial concentration profile; c(x0) at t = 0. An expression for the settling rate as a function of concentration, i.e. u(c). This constitutes the settling 'model". Kynch's Theory may then be applied as follows to generate pairs of (x,t) points from which the curve is composed: (1) Choose a value of XO, XO , or equivalently a starting concentration, c', which may be associated with XO. The initial choice should be close to XO, ie In the A-B part of the curve. (2) The local settling velocity, u' , on the characteristic intercepting at the chosen XO is evaluated from the model for settling rate. (3) V(c') ray now be calculated from V = - ds/dc'. Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 14. (4) The characteristic equation is now defined:(5) The time, t', is now evaluated from equation (14) thus:(6) It remains only to apply the characteristic equation, as in (iv), and the height x' corresponding to time t' is obtained. (7) A new, incremented value of Xo or c Is chosen. (8) Go back to (1). NB As soon as c reaches the value at the bottom of the bed, Xo is set to zero in equations (12) and (14).2.2.2 Analysis of Sedimentation Curve to Yield Particle Settling Function In this case It Is assumed that the experimental sedimentation curve Is known as is the starting concentration distribution, c(xo) at t = 0. The analysis proceeds as follows: (1) A point, P, is chosen fairly close to t = 0 so as to lie in the region APB, Figure 3. Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 15. (2) The quantity, (x - t. dx/dt)p, is evaluated, This may be simply measured as the Intercept of the tangent at P on to the height axis. (This is a useful result, see Section 3.3) (3) The following equation is then obtained from a combination of equations (12) to (14):(The subscript, p, indicates the local evaluation of the expression in brackets.) (4) Hence xo is obtained and thus the concentration of the characteristic from the known distribution of starting concentrations. (5) Thus the functions u(c) or S(c) may be evaluated by taking further points, P.A detailed discussion of the deficiencies of Kynch's theory will be deferred until the next section: where attempts by various authors to remedy them are described. However, it is instructive to list Kynch's own assumptions and therefore limitations: (i)Uniform particle concentration across any horizontal layer.(ii)Initial concentration function c(x0)at t = 0, is uniform or increases towards the bottom of the dispersion.(Iii)Velocity of settling u(c) tends to zero as c -- > Cm, the maximum allowed concentration in the sediment.(iv)u is a function of c only for a given dispersion.(v)Wall effects are negligible.(vi)All particles are the same shape and size.Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 16. Having just presented Kynch's own limitations to the theory, and before discussing the criticisms of others, it redresses the balance somewhat to restate the value of the theory in appropriate sedimentation regimes. A good example of this is provided in the work of Buscall and McGowan [56] on weakly flocculated latex suspensions. These workers were able to model the sedimentation curves resulting from centrifugation experiments very effectively using Kynch's theory. The form of the settling function, u(c), was derived from the hypothesis that the settling collective friction coefficient, fc(c)-1 U (c)' (and viscosity coefficient n(c), had similar concentrations dependencies. The experimental points and fitted sedimentation curves from the paper of Buscall and McGowan is reproduced in Figure 4.2.3Zone Settling and Compression - The Sediment Structure The most restraining assumption within Kynch's theory is (iv) above which requires that settling velocity be a function of concentration, i.e. u(c), only. Unfortunately this means that the theory is incomplete as soon as a sediment with any structural strength Is formed. In an attempt to revise and clarify the theory, Tiller [40] presented new arguments which may be interpreted in terms of Figure 5. This diagram may be understood as follows. Assuming uniform starting concentration, the sedimentation starts with a constant rate section analogous to the part of the curve of Kynch's Figure 3 denoted APB. At the height, H1, the characteristic emanating from the origin intersects the H(t) curve and thereafter a sediment begins to build up on the base of the containing vessel. It is this sediment, which is itself undergoing the much slower consolidation process, which causes the rate of fall to decrease and which leads to the breakdown of Kynch's analysis. By point H2 the whole sediment Is undergoing consolidation and the Kynch approach is completely inappropriate; means of treating this section of the curve for compression are given later. Tiller argued that the characteristics developed by Kynch for the first falling rate section should emanate not from the origin but from the top of the rising sediment. He then revised the theory to take account of the rising sediment as well as the falling zone boundary.Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 17. However, Tiller's theory suffers from many disadvantages, the most notable being a failure to provide simple solutions to the complicated partial differential equations which he derived. In addition he failed to adequately treat the question of the compressive strength of the sediment itself and its ability to withstand some of the consolidating driving pressure. Finally, from a practical point of view, any application of the theory suffers from the disadvantage of requiring knowledge of the sediment rise with time, L(t), a quantity which is difficult to observe visually. A subsequent paper by Fitch [41] developed Tiller's extension of Kynch Theory so as to make the numerical analysis more straightforward. In particular he developed graphical constructions in order to yield a settling function, u(c), for the first falling rate section of a sedimentation curve. Unfortunately, in common with Tiller's analysis, the construction requires a knowledge of L(t) and Fitch conceded that this removed much of the practical advantage of the new approach. He suggested two means of extracting L(t) by experiment. The first, originally developed by Gaudin and Fuerstenau [16], uses an X-Ray absorption Instrument scanning up and down in height at a speed appreciably faster than the sedimentation rate. The alterntative tack is to identify "compression points" by a whole series of batch settling tests at different Initial heights. Unfortunately the use of a battery of batch tests sacrifices the advantage that the Kynch approach originally conveyed. The above discussions are concerned either with zone settling or a combination of zone settling occurring simultaneously with compression. There are, however, many circumstances where an understanding of the compression or consolidation process occurring in isolation is what is required. This regime, corresponding to heights less than H2 in Figure 5, involves the collapse under gravitational forces of a continuous particulate network. The kinetics of the collapse are strongly Influenced by the drag forces operating on the liquid which is being expressed from the consolidating structure. Clearly then the consolidation process depends primarily on the structure, and thereby compressive strength, of the particulate network. The factors that can modify the network structure, e.g. particle size, shape, extent and mechanism of flocculation, degree of shear, etc, [24-28], are those that will allow control of the consolidation process. Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 18. Details of the Influence of simple properties of the particles and means of flocculation on the structure and strength of flocculated networks are given in a series of reports by Buscall, Wills, Sutton and Stewart [24-27]. A brief discussion of these issues is also given in Sections 2.4 and 2.5. A detailed investigation of the effects of prolonged shear on particulate suspension structure has been provided by Mills [28]. In order to apply an understanding of the consolidation process for a given sediment structure it is useful to consider two aspects of the process: (1) The final solids content, , (or conversely porosity) that results when the compressive strength of the network can fully support its own weight. This represents the ultimate degree of dewatering that can be achieved via sedimentation. In the parlance of Section 3.2 of the manual (Basic Principles and Test Methods, this is the Structurally-Limited S-L, regime). (2) The rate at which the consolidation takes place up to that ultimate limit, i.e. the kinetics of the process, (the so-called Kinetically-Limited, K-L, Regime). The first aspect is fairly readily approached provided that a means of quantifying and measuring the strength of a particulate suspension is available. One fundamental parameter that can be used for this purpose is the uniaxial compressional modulus, K, defined as [46]:where and V are the volume fraction or network volume resulting from an application of consolidating pressure p. The advantage of using K as a network parameter Is that Its functional dependence upon solids content is often known or can be measured, hence equation (15) may be integrated to give a yield pressure, Py, which must be applied before a certain ultimate degree of consolidation, *, can be attained:Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 19. Predicting the form of the function, K(), from first principles is beyond current art even for simple model experimental systems such as electrolyte-coagulated, monodisperse latex particles. It is, however, straightforward to measure It experimentally. This experimental determination Is facilitated by the observation that K is numerically almost equivalent to the infinitesimal shear modulus, Go (). Thus pulse shearometry, creeping flow measurements, centrifugation tests or the use of a pressure cell may be used. Alternatively, Py may be measured directly by a slow-speed centrifugation experiment. All of these techniques are described in more detail in Section 3 (Basic Principles and Test Methods) of the dewatering chapter and In the next section. K () Is experimentally found to be a very strong function of solids concentration often following the sort of dependence:where 0 is the volume fraction at which a space-filling network can form and the exponent, n, is typically 3 or larger. This sort of relationship is illustrated in Figure 6 where the influence of shear on the modulus is also shown. A change in the strength of flocculation of a particulate network also has a profound influence on the modulus curve and consequently on the final sediment volume. Thus weakly flocculated systems, eg polymerflocculated particles or simply larger particles, are more easl ly rearranged and yield smaller sediment volumes than the strong, open structures that result from electrolyte-coagulation of small particles. Further details regarding the various mechanisms and structures of flocculated systems are provided in GBHE-SPG-PEG-302 Basic Principles & Test Methods, of our Suspensions Processing Guides (SPG). As far as the kinetics of consolidation are concerned, the situation is far more complex; a recent piece of work by Buscall and White has done much to clarify it, however [44, 45]. The theory is presented in some detail in Section 3; a brief overview is reproduced here for completeness. Starting from a force balance on an element of the consolidating network they derived the relation:Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 20. The terms represent respectively the viscous drag forces on the sedimenting element, the structural pressure gradient resisting consolidation and the weight of unit volume of suspension. The main thrust of the Buscall and Mite model for the kinetics may be summarized In the constitutive equation that they employed:In this equation, D/Dt is the material derivative, () a dynamic drag coefficient for the squeezing out of water from the collapsing network, p the applied pressure and Py the "yield pressure". The assumption implicit in (19) is that the driving pressure for consolidation Is attenuated by the full elastic strength of the particle network. Once again (cf 3) the analogy between the concentration dependence of sedimentation rate with shear rheology may be drawn since equation (19) may be cast into a form reminiscent of the Bingham plastic constitutive equation. By combining equations (18) and (19) with Kynch-like continuity equations, Buscall and White produced a rather complicated 2nd Order partial differential equation. By considering just the t = 0, or initial rates solution, the problem was, however, considerably simplified yielding the following coupled pair of 1st Order equations:Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 21. and X represents the point In the bed where the consolidating pressure, p = Py(). Hence below X the bed will consolidate; above it the sediment falls uniformly without compaction. R() is a (collective) drag factor depending upon the concentration dependence of the permeability of the consolidating sediment. Drawing upon approximations that demonstrate that A x Ho is very large (103 104) equations (20a) and (20b) may be combined to yield a simple result for the Initial consolidation rate:The above overview of Buscall and Whltes model has been given here mainly for completeness. For a detailed appreciation of the interpretation and assumptions implicit in equations (18) to (21) the reader is strongly urged to refer to GBHE-SPG-PEG-302 Basic Principles & Test Methods of the Suspensions Processing Guides (SPG). Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 22. The detailed theory is presented in Section 3; strategies for scaling rules based on the yield stress concept are described in Sections 3.2.6 to 3.2.8. Following experimental verification, it is anticipated that improved and refined scaling relationships may be forthcoming from the new understanding implicit In the Buscall-White mode 1.3TESTS, CHARACTERIZATION PROCEDURES AND DESIGN METHODS 3.1Batch Settling TestsThe first and most basic application of a batch settling test on a given suspension Is to Identify the class of sedimentation that prevails at that concentration, Thus If the upper regions of the sample are seen to thin out gradually with a visibly rising sediment, it may be safely assumed that, for at least the initial stages, the process may be regarded as clarification. If, on the other hand, a fairly distinct boundary develops with relatively Clear supernatant above an opaque, falling sediment boundary then zone settling is occurring. To distinguish between zone settling proper and consolidation the most obvious criterion Is the rate of fall of the sediment; consolidation is much slower. In many cases, of course, the type of sedimentation process occurring is obvious from the initial concentration of the suspension, Figure 1. In the context of this chapter on dewatering, it will usually be a zone settling or consolidation regime which is being investigated. The setting up of such tests is normally fairly straightforward involving placing a sample of the suspension in a graduated tube or measuring cylinder and monitoring the fall of the zone boundary with time. A number of precautions are necessary, however, If the results are to be free from artifacts of scale etc. Perhaps the greatest danger in these tests is the risk of having an appreciable "wall effect" [46]. Two means of minimizing such effects are to steam-clean the glass very thoroughly and to use a graduated sample container of sufficient diameter. In practice the best way to gauge such effects is to perform otherwise identical tests in a series of containers of different diameter. Typical results from such a series of tubes containing suspensions of attapulgite clay (rod-like particles) are given in Figure 7. It is quite clear that wall effects are playing no significant role in the observed sedimentation volumes provided that the diameter is greater than about 6 cms. It is also observed that the test in a centrifuge at 5 g shows negligible wall effects for even smaller tubes. Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 23. Likewise suspensions of more spherical particles tend to be less prone to such artifacts. Clearly the data of Figure 7 is only yielding information regarding the influence of such effects on the equilibrium sediment height; for a batch settling experiment to investigate the sedimentation kinetics, the whole settling curve should be compared. Most of the other precautions relating to scale-up from small scale tests merely reflect the need to parallel plant operation as closely as possible in the laboratory. Thus for example if the test involves addition of a flocculant then it must be added and mixed in a well defined manner such that flocculation occurs under the same conditions on both scales. Likewise, stirrers etc may be employed in the laboratory tests to gain at least a qualitative idea of the Influence of "raking" on a large scale thickener. In all these considerations the main feature is to ensure that the structure of the suspension in the batch test is not perturbed by any factors other than the controlled sedimentation process. It is therefore wholly unsatisfactory to re-slurry a settled suspension in order to carry out some further experimentation. In some cases the re-suspended material will behave in the same way as fresh suspension, but this should not be assumed for all samples. Likewise good mixing (eg of a flocculant) is relatively easily accomplished on a laboratory scale but is often less satisfactory on the plant. As far as the actual application and analysis of batch settling tests to specific problems Is concerned, It will already be clear from the section on Kynch's theory and the subsequent modifications to It, that these procedures enable the particle settling-concentration, u(c), relationship to be evaluated. An outline of how these sorts of tests and models are then used for design purposes for thickeners is given in Section 3.3.4(c). In addition, very detailed instructions on how to conduct batch settling tests for a variety of applications, including both clarification and thickening, are given in Purchas' book "Solid/Liquid Equipment Scale-Up", Centrifugation [3].Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 24. 3.2Suspension Characterization - Prediction of Sedimentation BehaviorThe prediction of the sedimentation behavior of suspensions at very low concentrations is usually the province of the clarification mechanism and is thus treated in another Engineering Guide of the SPGs (Centrifugation). The prediction work described here refers to samples that are initially at concentrations such that the predominant mechanism is zone settling (including consolidation). As explained in Section 3.3.3(c), it is usually helpful to consider the sedimentation behavior In two parts: the equilibrium degree of concentration by sedimentation and the kinetics of the process.3.2.1 Equilibrium Degree of Concentration As explained previously the guiding principle in this area is that sedimentation, in the form of the consolidation process, will cease when the sediment has acquired sufficient compressive strength to completely resist the gravitational forces acting upon it. This will correspond to:where H Is the height of the consolidating sediment and * the equilibrium degree of concentration. Variations in the degree of densification down the bed will of course arise and, where the consolidating pressure arises from a centrifugal gravitational field (Section 3.4), g" itself will vary through the sediment. Despite these problems the equilibrium degree of consolidation, *, can usually be calculated, or at least estimated as described in Section 3.2. All that is needed, apart from the relative density and height of the sediment, Is a knowledge of the uniaxial, compressional yield function, Py(). There are three general approaches to gaining this information:Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 25. 3.2.6 Use of a Compression Cell This Is a classic way of obtaining the uniaxial, compressional modulus, K. This technique, although widely used, e.g. by Sutherland, Borrish and Ottewill [47], has a number of serious disadvantages. Its use will therefore not be described in detail here; further information in the experimental technique is provided in the references.3.2.7 Pulse Shearometry This technique measures the propagation speed of a very small strain shear wave through a small sample ("50 cm3) of the suspension of interest [46]. From this speed, u, and p, thedensity of the sample, a quantity known as the wave rigidity modulus, , may be derived:Under circumstances where the shear wave propagation time can be measured, gives a good approximation to the instantaneous (i.e., high frequency limiting> shear modulus, . Invoking the very close numerical agreement between and K [46] permits the yield pressure, Py(), to be deduced:Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 26. Thus is measured for a series of sediments at varying concentrations and application of (27) enables the evaluation of Py, typically by graphical or numerical integration. This function once known may then be used in the predictive sense of equation (25). The great advantage of the Pulse Shearometer is that measurements may be made in a very short time (a few minutes) compared with the timescale of a normal consolidation process under unit gravity. Thus the influence of any conditioning process (e.g. additives such as flocculants, or physical processes such as shearing) on the final sediment volume and solids concentration can be assessed very efficiently. In addition, time dependent effects such as "ageing" of the sediment can be readily followed over extended periods if necessary. 3.2.8 Slow-speed Centrifugation [44-46] The centrifugation method measures the yield function, Py(), directly. The experiment consists of measuring the equilibrium height of the sediment in a centrifuge as a function of the centrifuge speed and hence the applied consolidating field, Figure 9. Two approaches may be used to calculate the results. The old and original approach is simple since it requires no numerical differentiation to evaluate the function, Py, which is simply calculated from the equilibrium and initial sediment heights (H, HO), the relative density (), centrifuge angular velocity (w) and the distance R from the axis of rotation to the bottom of the centrifuge tube:Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 27. The disadvantage of this analysis is evident; that is, only a mean solids concentration, , is evaluated down the sediment profile. A new means of analyzing the data, which is less fast but more accurate, has recently been described by Buscall and White. The same two quantities, Py and , are now calculated parametrically according to the relations:Whichever of the two means of analysis is used, the result is a series of values of the yield function at various concentrations. Clearly, in order to obtain data to enable prediction under unit gravity, an extrapolation is required to low values of Py. This tends to be somewhat unsatisfactory since the $-dependence of Py at low is a power law-type function of varying Index. However, provided that the centrifuge is capable of stable, slow-speed operation, this extrapolation may provide at least a useful estimate of the yield point at low solids concentration. In general, however, the Pulse Shearometry method is to be preferred at low $ for these reasons.3.2.9 Kinetics of Thickening Using the experimental methods just described, the equilibrium degree of concentration may usually be straightforwardly determined. However, prediction of the kinetics of the sedimentation process is generally far more problematical and this Is undoubtedly an area where further research will be most valuable.Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 28. The kinetic model due to Buscall and White (described already in Section 3.3.3(c)) is of considerable value as a starting point for deriving scaling rules for the initial rate of sedimentation. Unfortunately, however, the relevant solutions, equations (22) and (23), require a knowledge of certain drag functions, e.g. R() and (), before the model can be used predictively. Means of estimating these were given in Section 3.2.10. Another possible means of tackling the problem for gravity thickeners is to determine the form of these functions using accelerated settling tests conducted in a centrifuge, and then applying the theory to obtain the Initial settling rate at unit gravity. The validity of such an approach has yet to be tested but it is an attractive one because of the relative ease and speed with which settling curves at higher gravitational forces can be obtained. The experimental data is easily available from the Stroboscopic Centrifuge [53]. This device uses an electrical or mechanical triggering of a stroboscope which illuminates the interior of the centrifuge for a very short time once per revolution. The decay of the zone boundary in a sample tube Is easily observed as a "frozen Image" through a perspex window In the lid of the machine. Commercial machines are available (Triton VRC Type TV161) but It Is a relatively simple matter to modify an ordinary bench top centrifuge for the purpose. Some words of caution are necessary, however, regarding the use of accelerated tests to predict unit gravity sedimentation. Many problems may arise from features of the various sedimentation mechanisms which scale differently with "g". For example the settling of a single Inert particle in a non-Newtonian fluid may not so easily be correlated with the zero shear viscosity n(0), at high accelerations. Likewise, the structure and shape of flocculated suspensions Is liable to be perturbed In a nonlinear fashion at high centrifugal fields. Thus, although accelerated tests may prove very valuable in the future, great care must be taken in their application and interpretation.Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 29. A number of alternative and largely empirical scaling relationships have been utilized in the past to Interpret accelerated settling tests. These have proved particularly useful for centrifuge scale-up in the kinetically-limited regime. Further details of these may be found in Section 3; worked examples based on the approach are given In Section 4.3.3 Design Methods - Gravity Thickeners Although the design of gravity thickeners is a broad and mature subject and perhaps better regarded as the province of the chemical engineer, many features impinge on the principles already established in this section. Figure 10 shows a schematic view of the sedimentation process in a typical continuous thickener. It can be seen that all or some of the sedimentation mechanisms of Figure 1 may be simultaneously operating at different levels. In order to understand the origin of the zone labeled as the "critical zone", and its implications on design, one-dimensional continuity equations for the solids flux are derived. Coe and Clevenger [50] were the first workers to tackle large-scale thickener operation in this way and they arrived at the equation:Here G is the solids flux (i.e., mass rate per unit area) at a given point in the thickener where the ambient concentration is C. cu is the concentration of the underflow. The influence of equation (28) on the operation of continuous thickening devices Is Illustrated in Figure 11, which shows the variation of solids flux with concentration for a given value of Cu. Coe and Clevenger obtained curves of this sort by making measurements of U(C) using a whole series of batch settling tests at different starting concentrations. In doing so they relied upon the assumption, explicit also in Kynch's theory, that the settling velocity, u, was a function of concentration only. It is this assumption which allows the results from batch-type experiments to be translated into predictions of continuous thickening operation, The origin of the "critical zone" in Figure 8 may now be understood in terms of the minimum In the function G(c).Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 30. If the feed flux to the thickener exceeds GC, which represents the limiting flux or "solids handling capacity", at some point in the device a zone will develop where the solids flux cannot be passed in a steady state operation. The result is that a zone of the critical concentration, Cc, propagates upwards. This critical zone can eventually lead to loss of solids in the overflow If it continues to propagate upwards. Thus one of the basic criteria in design is to provide a sufficient cross-sectional area for the thickener such that the feed flux is comfortably less than the critical flux. Thus an understanding of the form of U(c) is essential so as to enable the derivation of a series of flux versus concentration diagrams at various underflow concentrations. In addition it may be noted that as long as sufficient area is provided to prevent the flux exceeding GC, the zone settling region, (i.e., that in which u = u(c) as opposed to any compression or consolidation zone,) imposes no depth requirement on the design of the thickener. In practice, as a result of the theory due to Kynch and subsequent modifications and applications to it, the area required to prevent critical zone occurrence can in principle be deduced from a single batch settling test. (Recall that in essence the Kynch theory permits the function U(c) to be derived for a whole series of concentrations greater than the Initial one. These standard design procedures involve simple graphical constructions based on Kynch's theory; the most famous being due to Oltmann, and to Talmage and Fitch. Details and worked examples may be found In references [1, pp147-160] and [3, pp108 et seq]. In addition to the area demand of the non-compression, zone settling regime in a gravity thickener, It Is often necessary to identify constraints arising from other sedimentation mechanisms. Thus both clarification (If the feed is at a concentration below that at which zone settling commences) and compression impose a detention time constraint on the continuous operation. Clarification is the subject of GBHE SPG PEG 304 Centrifugation but the required detention time for any compression regime is straightforwardly derived from a simple batch test as shown in Figure 12. First of all the so-called "compression" or "critical sedimentation" point must be identified; this may be associated with the onset of the second falling rate section of Figure 5. At this point the whole of the sediment starts to undergo compression. In favorable cases the compression point is identified as a pronounced discontinuity in the batchsettling, height versus time curve. Where its position is less obvious a "loglog plot" or some other device may assist. Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 31. Once the time corresponding to the compression point, c, is known the detention time, d, is given simply by:a Is the time at which the required underflow concentration is reached in the batch experiment. From the detention time, d, and the area and flux of the thickener, the height, H comp required for a compression zone is easily estimated. The sorts of sizing procedure outlined above are summarized in a simple flow diagram and schema 1c constructions shown in Figure 13a-d. Much greater detail for both the experimentation and calculation for these is provided In Purchas' book, "Solid/Liquid Separation Equipment Scale Up". In addition a detailed description of the various limitations to the thickening process in the analogous situation of centrifugal sedimentation is given In Section 3.4. A variant on the sizing procedure here-described, due to Yoshioka is also given in that section. Although all these techniques employ some level of fundamental understanding of sedimentation, it is evident that there is great scope for progress In the area. Thus although it is well known that Kynch's theory is not rigorously applicable to zone settling, no simple alternative is yet in widespread use. Likewise the sort of calculation of compression height, Hcomp, described above fails to take explicit account of the influence of sediment height on consolidation rate itself. Application of some of the results of the Buscall and White theory for consolidation kinetics might well improve the situation here. Finally, it should be remembered that other considerations based either on economies of space or the need to wash the sedimenting solids may in themselves Introduce new design constraints in terms of height and area.Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 32. 4EXAMPLESAccording to Bash, [51], in a 1977 survey of solid/liquid separation practice, most of the plant based on sedimentation has been supplied in the form of proprietary clarifiers or thickeners bought in from external European. Thus in most cases the suppliers have been largely responsible for design considerations at least with respect to sizing etc. This naturally leads to something of a paucity of suitable inhouse examples of these procedures. However, two European companies provide exemplification of both typical operating procedures and also of a novel application of a thickener. 4.1The Purification of BrineThe clarification of brine is an important process operated by many companies. A typical feed stream to the clarifier might comprise a solution of 26.5% BaCl by weight (equivalent to -5 M), but containing suspended solids such as CaCO3 (in the particle size range, 5-25 m) and submicron Mg(OH)2. These solids are removed by flocculating with an anionic polyelectrolyte, typically hydrolyzed polyacrylamides or acrylamide copolymers, and then by sedimentation in a settler. In this context the main variables to be optimized are the settling rates and thereby the clarity of the overflow. The role of such flocculants may be understood by referring to the schematic batch flux curves shown in Figure 14a and 14b. As can be seen in the curve, the dependence of batch solids flux on concentration is described by a characteristic curve containing at least three of the mechanistic regimes for sedimentation: free settling, hindered settling and compression. The interpretation of the batch flux curve together with an associated operating line is illustrated in Figure 14a. In essence the curve a represents the experimentally measured property of the v. This flux, Gsusp (C) is equal to the product of the concentration, c, and settling velocity, u (c). Hence construction of the curve requires knowledge of u(c) which may be acquired experimentally by one of the variants on Kynchs procedure (Section 3) or any other suitable experimental approach. Thus it must be emphasized that a represents a physico-chemical bound which can be alleviated only by modification of the suspension properties as will be considered shortly (Figure 14b).Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 33. Also shown in Figure 14a are two operating lines b and c. These are representations of flux-concentration relationships that are necessary for a certain operating regime to provide a mass balance through the thickener. The equation of such an operating line is simply derived (see, for example [1] and [49]) and relates the required flux, Grequired, to concentration:Hence the operating line does not depend upon the suspension properties but merely on geometric and operating conditions. However, only if the line falls below the point X in the Figure will the suspension properties permit stable thickening operation. The maximum stable flux, and hence most efficient operation, results when the operating line is tangential to the suspension batch flux curve at X. This maximum, stable flux is called the critical flux, GC. The above arguments as summarized in Figure 14a are known as the Yoshioka construction by some authors. (The reader Is also referred to Section 3 for related discussion.) Turning to Figure 14b, It can be understood that a tangent to the batch flux curve intercepting the y-axis at flux G will yield an underflow concentration of Cl, The addition of a suitable flocculant translates the batch flux curve upwards as shown In the figure and hence yields an Improved underflow concentration and enhanced supernatant clarity. Alternatively an Improved feed rate, QF, can be achieved at fixed underflow concentration (see equation (30)). These batch flux curves, Flux, Gsusp = concentration, c x settling velocity, (u), may be generated either by a series of jar tests (see Section 3.3.4(a) and the paper of Coe and Clevenger and subsequent references to it) or in a single batch sedimentation experiment using the method of Kynch (Section 3.3.3(b)). In either case, the settling velocity as a function of concentration, u(c), can be deduced. The behavior of this function, u(c), is illustrated In the next figure, Figure 15, for typical brine based suspensions flocculated with polyelectrolytes of varying molecular weight and anionicity. Clearly the degree of anionicity requires careful control (optimum at 15%) and very substantial advantage is gained by the use of a polyelectrolyte of very high molecular weight. There is, of course, a significant economic trade-off here; high molecular weight flocculants tend to be more expensive.Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 34. The mechanism for flocculation by these anionic polyelectrolytes probably Involves a combination of both bridging and charge neutralization effects although relatively little fundamental work has been done in the area. What is known for certain is that the optimization of the flocculant anionicity is sensitive to particle size as exemplified by the following data taken from brine samples at two different locations:4.2 Distiller Blow-Off, DBO [52] Distiller Blow-Off, or DBO, is the name given to an effluent stream originating from an ammonia recovery still in a European ammonia-soda producer. This stream is hot (85 oC) and contains a wide range of suspended matter ranging from micron sized particles including CaC03, MgCO3 and CaSO4. to larger scale grit (total suspended solids "1%). To clean up this effluent a Dorr-Oliver clarifier is used in a somewhat unique fashion. The approach utilizes the fact that DBO is less dense than concentrated brine and hence when introduced on top of the latter in a settler, the two phases remain essentially distinct. By this means the DBO solids pass through the interface and are drawn off in the concentrated (10% solids) brine underflow. Once again anionic polyelectrolyte flocculants (with different optima from the brine purification process) are employed to enhance solids settling rates. In this DBO clarification both the relative position of, and the density difference across, the interface of the DBO and brine phases require careful control. The former affects the efficiency of continuous clarifier operation. The latter Involves co-optimization of solid settling rate through the Interface with a limitation on the level of Ca2+ Ions discharged In the underflow. Finally, for completeness, the reader who requires more detailed information, or worked examples, on the sizing of thickeners etc., is directed to references [3,48,49] or to the centrifugation section (3.4) of this chapter. Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 35. These sources contain analogous procedures based on the theory and experimental tests described previously applied to the sizing of continuous centrifuge capacity.Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 36. Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 37. Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 38. Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 39. FIGURESRefinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 40. FIGURE Figure 1 The Different Sedimentation Regimes (Schematic)Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 41. Figure 2 Parameters used in the Kynch Theory of SedimentationFigure 3Kynch Model for Sedimentation Showing Propagation of Constant Concentration CharacteristicsRefinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 42. Figure 4 Sedimentation behavior of a weakly flocculated suspension (polystyrene latex + sodium carboxy methyl cellulose) under various centrifugal fields. Points are experimental data, continuous curves derived from Kynch theory (see text).Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts / Process Technology Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology Petrochemicals Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries Web Site: www.GBHEnterprises.com 43. Figure 5 Two interface description of sedimentation (supernatantsuspension and suspension-sediment) as proposed by Tiller (schematic)Refinery Proce