A comparison of filtration characterisation devices for compressible suspensions using conventional filtration theory and compressional rheology
Graphical abstract
Introduction
Solid-liquid separation is a common process in industries such as mining, water and wastewater treatment, life sciences and in the production and recycling of paper, for example. The aim of solid-liquid separation is to increase the solids concentration by applying a driving force for consolidation of the suspended solid phase. Such driving forces can be gravity in sedimentation, centrifugal acceleration in centrifugation, negative mechanical displacement through vacuum filtration or positive mechancial displacement through pump pressure or a movable membrane. These processes are widely applied in industry with varying objectives ranging from product specification to waste handling and disposal.
In a suspension with low solids content, particles are far from each other with no direct interaction between them. During solid-liquid separation, the solids concentration increases and, at a certain point, particles are close enough to form a continuous load-bearing network structure that exhibits a strength against consolidation. This strength is a function of solids concentration, such that increasingly more energy has to be put in to consolidate further. At some point the process objectives and the process energy consumption can lie outside the economically feasible range. In order to reduce this discrepancy, optimisation of solid-liquid separation processes and equipment is necessary.
Currently, a variety of solid-liquid separation theoretical frameworks is applied worldwide. Most theories implement Darcy's law [1] to describe the rate of liquid flow through a porous solid phase based on the permeability of the solid phase. The assumption is then often made that the filter cake is homogenous and incompressible [2]. In the 1940's, Ruth [3] introduced and Grace [4] subsequently further developed the Compression-Permeability cell for the characterisation of material filterability, which demonstrated that the rate and extent of filtration were functions of the applied pressure for many materials. Suspensions can be ‘slightly compressible’ for hard, non-interacting or stabilised spheres [[4], [5], [6], [7]], ‘highly compressible’ for flocculated and coagulated inorganic suspensions [[4], [5], [6], [7], [8], [9], [10], [11], [12], [13]], and ‘extremely compressible’ for biological sludges [[13], [14], [15], [16], [17], [18], [19], [20]].
Conventional filtration theory for compressible materials, often attributed to Tiller et al. [19,[21], [22], [23]], considers the applied pressure as the explicit variable and uses the specific filter resistance α(p) as a measure of the rate of filtration and the filter cake porosity ε(p) (or solidosity, εs(p) = 1 – ε) as a measure of the extent of filtration. The null stress porosity ε0 is the porosity when the solids network forms, i.e. ε0 = ε(p = 0). Conventional theory [24] is also attributed to Shirato due to his contributions to the modified Darcy-Shirato Equation [25], the constant rate [26] and the variable pressure-variable rate descriptions [27,28].
Compressional rheology [29] also describes the dewatering behaviour of suspensions using two material functions, namely the compressive yield stress, Py(ϕ), and the hindered settling function, R(ϕ). Py(ϕ) represents the strength against consolidation and R(ϕ) describes the solid-liquid interphase drag, which is inversely proportional to the Darcian permeability. Both material functions are monotonically increasing with solid volume concentration ϕ, which is related to the porosity as ϕ = 1–ε. The solids volume fraction at which the solids network forms is called the gel point ϕg, such that Py(ϕg) = 0. Py(ϕ) then increases and becomes infinite at random close packing. R(ϕ), as a drag parameter, is 1 at infinite dilution, where the particles do not interact with each other, and infinite as ϕ approaches 1. The compressional rheology framework was developed by Buscall and White to describe the settling behaviour of flocculated suspensions [29] and was then extended to filtration by various other authors [16,17,[30], [31], [32], [33], [34], [35]]. Bürger and Concha [36] developed the same concept with different notation based on the Kynchian settling velocity [37].
An important conceptual difference between conventional theory and compressional rheology is how the solid-liquid separation is regarded. Grace, Ruth, Tiller, Shirato et al. consider the separation from a process point of view, while in contrast Buscall and White formulated it in a material-centred approach. This means that in compressional rheology the material functions are an explicit function of the solids concentration, while the conventional theory is expressed in dependence of the applied pressure and only implicitly as a function of the solids concentration. One of the key consequences of this is that compressibility is always acknowledged in compressional rheology and accounted for in its characterisation techniques.
Both theoretical foundations analyse filtration tests of some sort to measure filterability. The Compression-Permeability cell (shown in Fig. 1 a) introduced by Ruth [3] and further developed by Grace [4] initially uses a piston to consolidate the material at a known pressure, followed by a second stage using the liquid flowrate through the filter cake at a given applied permeation pressure to measure the permeability. This is then repeated at increasing consolidation pressures. In the piston-driven dead-end Filtration Rig [38] (shown in Fig. 1 b), the suspension is filtered at a constant pressure with a solid piston. The change in piston height is tracked with a linear encoder. Measurement can be carried out as single pressure tests or as stepped pressure tests [39]. A third device that is often used is the Nutsche Filter [40,41] (shown in Fig. 1 c), which uses an applied air pressure as the driving force for the solid-liquid separation. The mass of filtrate is measured as a function of time. At some point, the air pressure exceeds the capillary pressure of the particulate network, leading to air breakthrough and cake desaturation [34,42,43], which halts further consolidation.
All three techniques use a filter cake that is built-up and consolidated. Dead-end filtration can be divided into two stages; cake formation (or filtration) and cake consolidation (or expression). In the first stage, solid particles form a filter cake at a semi-permeable surface. During cake formation, the volume of filtrate v varies with the square-root of time t (t ∝ v2). Both conventional and compressional rheology theories have methods for extracting the permeability from dt/dv2 [2,45]. At some time, all the particles are in the filter cake and the cake begins to compress. The transient behaviour, to first order, decays logarithmically during cake consolidation (t ∝ lnv) [31]. The cake concentration is determined after a trial terminates preferably on a differential mass basis before and after oven drying to mass equilibrium.
This paper compares the two frameworks of the conventional filtration and the compressional rheology theories, with emphasis on the characterisation generally carried out in practice. Therefore, the Compression-Permeability cell, the piston-driven Filtration Rig and the air-driven Nutsche Filter are compared based on their characterisation performance. In order to do this, a chalk suspension screened to different particle sizes is used (Omyacarb 2, 10 and 40). Because of the varying particle size the suspensions show differing degrees of compressibility and allow comparison of the devices in regards to their performance for compressibility and permeability.
Section snippets
Conventional filtration theory
The specific filtration resistance macroscopically describes the drag between solid and fluid phase. Darcy [1] established a fundamental law describing the fluid flow through a porous bed as,where dV/dt is the specific flow rate, Δp is the applied pressure, η is the fluid viscosity, hc is the filter cake height, kD is the Darcy-permeability and Rm is the membrane resistance. Note that, in this formulation, V is the specific volume or volume per unit area, V = v/A.
During
Materials and methods
Experimental data to compare the results from both filtration frameworks was obtained by characterising a calcite suspension. The suspension was prepared from commercial calcium carbonate (Omyacarb 2, 10 and 40 supplied by Omya Australia Pty Ltd. and Omyacarb 2-LU, 10 and 40, Omya California Inc.) and a 0.01 M potassium nitrate electrolyte solution out of Milli-Q water (Millipore™ Synergy®, 0.22 μm filter) and KNO3 (Chem-Supply, analytical reagent, min. 99% purity, Product Code: PA011). The
Results and discussion
The experiments from the Compression-Permeability and the Filtration Rig and the Nutsche Filter are analysed and compared using the equations given in the theory section. In compressional rheology, the compressibility is described with the compressive yield stress, Py(ϕ) whereas in the conventional framework it is described as the pressure dependence of the porosity, ε(p). As outlined in the theory with Eq. (14), the two concepts are translatable. For simplicity, only the compressive yield
Conclusion
The results in this paper show that the conventional filtration theory developed by Tiller, Shirato and Ruth and the compressional rheology framework developed by Buscall, White and Landman describe the same phenomena and are interchangeable, provided the material is not too compressible. Data from different filtration devices can be analysed using both theoretical approaches. Whilst the Nutsche Filter can be used to give an estimate of the permeability, it desaturates for applied pressures
Acknowledgement
The authors would like to acknowledge the funding of the project through the Australia-Germany Joint Research Co-operation by the German Academic Exchange Service (DAAD) and Universities Australia. The University of Melbourne and the Particulate Fluids Processing Centre (PFPC) in Melbourne, Australia and the Institute for Mechanical Process Engineering and Mineral Processing, Freiberg (Saxony), Germany provided access to facilities and supply of equipment.
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