Praktikum Mechanical Engineering Spring semester 2016 Filtration Supervisor: Anastasia Spyrogianni ML F24 spyrogianni@ptl.mavt.ethz.ch Tel.: 044 632 39 52 1
1 Table of Contents 1 TABLE OF CONTENTS... 2 2 INTRODUCTION... 3 3 EXPERIMENTAL... 8 3.1 Suspension preparation... 8 3.2 Filter placing... 8 3.3 Measure suspension flow rate under constant pressure... 9 3.4 Measure the pressure-drop under constant flow-rate... 9 3.5 Shutting down and cleaning... 9 4 REPORT... 10 4.1 Specific tasks (in results and discussion)... 10 4.1.1 Constant pressure-drop measurements... 10 4.1.2 Constant flow-rate measurements... 11 4.2 Final discussions... 13 5 LIST OF SYMBOLS... 14 6 CONSTANTS AND GEOMETRICAL DATA... 17 7 BIBLIOGRAPHY... 17 Please note: This is a very brief summary of the filtration description in German. For theoretical background in English please refer to Ullmann s Encyclopedia of Industrial Chemistry, available online on www.ethbib.ethz.ch. Alternatively, you may ask your assistant for a hardcopy. 2
2 Introduction In many industrial processes dispersions of particles in a fluid (liquid or gas) need to be separated from their fluid, either for the removal of valuable product or for cleaning of a product liquid (e.g. water purification). One of the basic procedures for this is filtration. In this filtration practicum we will investigate the separation of CaCO 3 particles from an aqueous suspension (solid-liquid system) by filter pressing. Two different operation modes will be used: a) constant pressure drop and b) constant suspension volume flow rate. The suspension flow rate will be measured during constant pressure filtration whereas pressure drop across the filter is measured during constant suspension flow experiment. Information related to the structure of the resulting filter-cake can be extracted from this data. In the following you will find the equations based on the classic differential equations for cake-filtration: Darcy s law describes the flow of a liquid through a porous medium: V f = k p h k = p h η k k η (1) Here the term η *{hk/ k * η } describes the total resistance against flow through the filter. This law can be used to describe the build-up of a filter cake. The resistance term η * {hk / k * η } is now separated into a filter medium resistance β M and a filter cake resistance α c * h k. Here, α c is the height specific cake resistance and h k is the (time-dependent!) cake height. {h k / k * η} = (β M + α c * h k ) (2) Combining equation (1) and (2) results in 3
V f = 1 dv f dt = p η (β M + α C h k ) (3) For the integration of the differential equation (3) the following assumptions are made: a) The filtrate flow is laminar b) The built filtercake is incompressible, therefore its porosity is independent of the pressure (α c =const). c) The resistance of the filter medium β M is constant for the whole filtration process. d) The filter efficiency is 100% Based on these assumptions equation (3) can be integrated. The cake height h k is eliminated by a mass balance over the solid material: h k (1 ε) ρ solid =V f c (4) Substituting h k from equation (4) into equation (3): 1 dv f dt = p α η β M + C ρ sol (1 ε) c V f = p η β M + α c V f (5) In equation (5) the term α c / ρ sol (1-ε) is replaced by the area specific cake resistance α, which (for convenience) will be called cake resistance from now on. In this practicum two approaches will be used to solve equation (5): a) p = i.e. the filtrate volume flow rate decreases over time 4
b) Vf * = dvf / dt = i.e. the filtration pressure increases over time Following a), the solution for p = : For integration of (5) with the boundary conditions Vf = 0 at t = 0 : η p α c V A f +β M dv F f =dt (6) V η p α c f V 2 2 A f + β M V f =t (7) F 0 t = η ( α c V 2 +2 A f F β M V f ) 2 A 2 F p (8) For a graphical analysis of (8) use the following: t V f = η c α 2 2 p V f + η β M p (9) A graphic representation of t / V f as function of V f gives a straight line (Figure 4). From the slope the cake resistance α can be calculated, while from the intercept the filter medium resistance β M can be found. 5
t V f α β M V f Figure 4: t / Vf vs Vf for p = Following b), the solution for Vf * = dvf / dt = : With Vf = t. Vf * from (5) you get: p(t) = η α c V 2 f 2 t + β η V M f (10) This means the pressure increases linearly with time. By plotting p as function of t you can determine α as well as β M (Figure 5). 6
p α β M t Figure 5: p versus t, for Vf * = Plotting the specific cake resistance α from different experiments at different constant p in double logarithmic scale as function of p, you will find a near to linear dependency according to the following formula: α = α o ( p/ p o ) n (11) From this you can calculate the compressibility n: n = log α/ α o log p/ p o (12) For incompressible filter cakes n becomes 0, for compressible cakes n increases from 0 to approximately 1.2. At n = 1 the filtrate volume is after a certain time quasiindependent of the filtration pressure. 7
Figure 7: Piping and Instrumentation diagram (P&ID) of the plate filter setup. 3 Experimental Figure 7 shows the piping and instrumentation diagram of the filter press used for the experiments. Make yourself familiar with the setup before operation. Find the relevant valves and its proper position on the P&ID for the two modes of operation. 3.1 Suspension preparation Weigh 250 g of CaCO 3, add some water and stir to make a rather thick presuspension. Before water is filled in through valve B, make sure the outlet valve A is closed and the pressure release valve of the stirrer tank is opened properly. Then fill approximately 60 L of water through valve B and add the pre-suspension through valve B as well and fill in water until 70 L are in the tank. Start the stirrer C and the recirculation pump D to achieve a homogeneous suspension. 3.2 Filter placing Check that the filter (degas) valves E are closed. Place the filter between the plates (smooth surface towards the incoming flow). Press the plates together with 8
the clamp. After the filter is wetted it might be needed to reinforce the clamp pressure as the filter settles a bit when wet. 3.3 Measure suspension flow rate under constant pressure First close the pressure release valve E and the filling valve B on the tank. Switch the pressurized air supply on (main valve on the wall). Next, the tank needs to be pressurized to the required pressure level for the corresponding experiment. This can be done by adjusting the pressure control valve (PIC). Turning clockwise will increase the pressure and vice versa (please lift the red plastic ring while adjusting). Air flows into the tank and fills up the volume above the liquid (give it some time to reach equilibrium). Once the tank is pressurized, check that the flow through the flow controller (FIC) is bypassed. Let some suspension pass through the filter press by opening the final valve to the plate filter (valve J) and simultaneously open the degas valves E until suspension runs out. Close degas valves and start the measurement. Measure the flow under constant pressure for 8-12 minutes, recording the flowrate every 15 s. Change the filter (release overpressure through valve E before opening the press) and redo the measurement at p = 2 bar (set valve F to 2 bar). After the second experiment you have to drain the remaining suspension in the tank through valve A and prepare a new 70 L batch of suspension. Change the filter and redo the measurement at p = 3 bar (set valve F to 3 bar). 3.4 Measure the pressure-drop under constant flow-rate Set the pressure to 3 bar (valve F) and replace the filter. Set the flow rate on the FIC to 80 l/h. Open the path leading through the flow meter (G) and close the path through the bypass line. Measure the pressure drop during approximately 10 minutes every 15 s. After all experiments have been carried out you can compare the appearance of the filter cakes like cake thickness and porosity. 3.5 Shutting down and cleaning Close the valve to the pressurized air (F). Drain the rest of the suspension by opening the valve A. Shut down the stirring (C) and suspension circulation (D). Disconnect all electrics (stirring, pump, flow and pressure-meters). Clean the working place. 9
4 Report Each group has to write one report. The report should be approximately 8 pages long and include the following chapters: 1. Abstract (describe shortly what was done and what were the major findings) 2. Theory (equations which will be used in the result part must be introduced) 3. Experimental (describe the experimental procedure) 4. Results (plot the result curves and perform the needed calculations) 5. Discussions (discuss the results and refer to literature if needed) 6. Conclusions (what are the discoveries of the experiment, what does it mean in practice) 4.1 Specific tasks (in results and discussion) 4.1.1 Constant pressure-drop measurements a) Neglecting the filter resistance β M in equation (8), the filtration for constant pressure is then described by t = η c α V 2 f 2 A 2 F p (13) V f = 2 t p c η α (14) Plot the filtrate volume V f [m 3 ] per filter area A f [m 2 ] as a function of time t [s] in double logarithmic scale. Following equation (13) you should get a linear dependency with a slope of 0.5. Discuss the results and draw some qualitative conclusions from the plotted results. 10
b) Plot t/vf [s/m 3 ] as a function of V f [m 3 ] and find the specific cake resistance α from the regression. Additionally, determine the resistance of the filter medium β M (m -1 ), for each pressure drop 1, 2 and 3 bar by using equation (9). Discuss the results. 4.1.2 Constant flow-rate measurements c) Plot the pressure drop p [Pa] as a function the time t [s]. Find the cake specific filter resistance α C [m -2 ], and resistance of the filter medium β M (m -1 ), using the graph and equation (10) where V f * [m 3 /s] is the filtrate volume flow. d) Solve the compressibility n [-] using equation (11) or (12). e) Find the porosity ε (ratio of void volume to total cake volume) of the filter cake using the Carman-Kozeny theory. Carman (1939) calculated the pressure loss in the bulk and modeled the porous filter cake as numerous continuous parallel channels. The pressure loss in such channels is: p Kanal liq 2 hk = ξ (Re) ρ vkanal (15) 2 d h The pressure drop coefficient is here 64/Re (laminar flow) The Reynolds number for such channel is: v Kanal d h ρ liq Re = (16) η The mean velocity in the channel is determined by the continuity equation: 11
V * f = vkanal AF 23 = v { 0 AF freie Lehrrohr Querschnittsfläche Geschwindigkeit 1 ε (17) In reality there are no single and continuous channels. In fact, in porous filter the channels are curved with changing dimensions depending on the particle properties. Thus, the main inaccuracy comes from the use of the hydraulic diameter d h which can be defined as: d h = 4A U h k h k (18) here A is the channel cross section area [m 2 ] and U is the wetted channel circumference [m]. Another definition of the hydraulic diameter is: d h = 4 (ε h k ) F (19) where F is the total wetted surface: (20) F = S (1 { ε) AF hk 123 solid volume total cake fraction volume S= Specific particle volume surface ε = porosity With (4) and inserting the above in (15) you get: The pressure drop is: 12
p = η α C K c V f v 0 (21) With given equations derive the specific cake resistance, α C-K [m/kg]. Using the solved cake resistances from the pressure constant experiments α [m/kg] one can solve for the porosities for each p=const experiment. Which porosities do you get and what conclusion can be drawn? 4.2 Final discussions Discuss your results and compare your experimental data to the theory: Are the assumptions made for the integration of the filter differential equation reasonable comparing the observed results here? How would the porosity change if instead of ideal monodisperse ( single sized) particles, polydisperse ( several sizes) particles with broader size distribution would be used? How would the plot of t/v f as a function of V f change if the filter media resistance (β) would change over time? Compare the results of four different filter cake (α) and media (β) resistances, their order of magnitude and ratio to each other. How does the magnitude of the cake (α) and filter media (β) resistances affect the values of the compressibility (n) and porosity (ε)? 13
5 List of symbols A channel cross section [m 2 ] area of the filter [m 2 ] c solids concentration, mass of solid per total volume [kg/m 3 ] d h hydraulic diameter [m] F wetted surface [m 2 ] h k cake height (channel lenght) [m] k Durchlässigkeitskoeffizient after Darcy [m 3 *s/kg] n compressibility [-] p pressure drop over filter and cake [N/m 2 ] S specific surface area (surface per volume of the particles) [m -1 ] t filtration time [s] U wetted curcumferance [m] mean velocity in the channel (pore) [m/s] 14
v 0 void tube velocity [m/s] V f suspension volume [m 3 ] V f * suspension volume flow [m 3 /s] a C cake height specific cake resistance [m -2 ] 15
α area based cake resistance [m/kg] α C-K flächenmassenspezifischer Kuchenwiderstand nach Carman-Kozeny [m/kg] β M resistance of the filter media [m -1 ] ε porosity [-] η dynam. viscosity [kg/(ms)] ρ liq fluid density [kg/m 3 ] ρ sol solid density [kg/m 3 ] x pressure drop constant [-] 16
6 Constants and Geometrical Data ρ sol = r CaCO3 = 2710 kg/m 3 ρ liq (Wasser bei 14 C) = 1000 kg/m 3 S = 9.18 * 10 5 m 2 /m 3 η = 1197.8. 10-6 kg/(ms) = 0.0324 m 2 7 Bibliography [1] Darcy, H.: "Les Fontaines Publique de la Ville de Dijon", Herausgeber Victor Dalmont, Paris, 1856 [2] Carman, P. C.: "Fundamental Principles of Industrial Filtration", Transactions-Institution of Chemical Engineers, 1939, 168-188 [3] Müller, E.: "Mechanische Trennverfahren", Band 2, Sauerländer, 1983, (IVUK-Bibliothek CIT 219/II) 17