Filtration. Praktikum Mechanical Engineering. Spring semester ML F16 Tel.:

Transcription

1 Praktikum Mechanical Engineering Spring semester 2018 Filtration Supervisor: Davide Stucchi ML F16 Tel.:

2 1 Table o Contents 1 TABLE OF CONTENTS INTRODUCTION EXPERIMENTAL Suspension preparation Filter placing Measure suspension low rate under constant pressure Measure the pressure-drop under constant low-rate Shutting down and cleaning REPORT Speciic tasks (in results and discussion) Constant pressure-drop measurements Constant low-rate measurements Final discussions LIST OF SYMBOLS CONSTANTS AND GEOMETRICAL DATA BIBLIOGRAPHY Please note: This is a very brie summary o the iltration description in German, which can be ound on the PTL homepage. For theoretical background in English please reer to Ullmann s Encyclopedia o Industrial Chemistry, available online on Alternatively, you may ask your assistant or a hardcopy. 2

3 2 Introduction In many industrial processes dispersions o particles in a luid (liquid or gas) need to be separated rom their luid, either or the removal o valuable product or or cleaning o a product liquid (e.g. water puriication). One o the basic procedures or this is iltration. In this iltration practicum we will investigate the separation o CaCO 3 particles rom an aqueous suspension (solid-liquid system) by ilter pressing. Two dierent operation modes will be used: a) constant pressure drop and b) constant suspension volume low rate. The suspension low rate will be measured during constant pressure iltration whereas pressure drop across the ilter is measured during constant suspension low experiment. Inormation related to the structure o the resulting ilter-cake can be extracted rom this data. In the ollowing you will ind the equations based on the classic dierential equations or cake-iltration: Darcy s law describes the low o a liquid through a porous medium: V k p h k p h k k (1) Here the term η * {hk / k * η } describes the total resistance against low through the ilter. This law can be used to describe the build-up o a ilter cake. The resistance term η * {hk / k * η } is now separated into a ilter medium resistance β M and a ilter cake resistance α c * h k. Here, α c is the height speciic 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

4 V 1 dv dt p ( M C h k ) (3) For the integration o the dierential equation (3) the ollowing assumptions are made: a) The iltrate low is laminar b) The built iltercake is incompressible, thereore its porosity is independent o the pressure (α c =const). c) The resistance o the ilter medium β M is constant or the whole iltration process. d) The ilter eiciency 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 ) solid V c (4) Substituting h k rom equation (4) into equation (3): 1 dv dt p M C sol (1 ) c V p M c V (5) In equation (5) the term α c / ρ sol (1-ε) is replaced by the area speciic cake resistance α, which (or convenience) will be called cake resistance rom now on. In this practicum two approaches will be used to solve equation (5): a) p = i.e. the iltrate volume low rate decreases over time 4

5 b) V * = dv / dt = i.e. the iltration pressure increases over time Following a), the solution or p = : For integration o (5) with the boundary conditions V = 0 at t = 0 : p c V M dv dt (6) V p c V 2 2 A M V t (7) F 0 t c V 2 2 A F M V 2 A 2 F p (8) For a graphical analysis o (8) use the ollowing: t c V 2A 2 F p V M p (9) A graphic representation o t / V as unction o V gives a straight line (Figure 4). From the slope the cake resistance α can be calculated, while rom the intercept the ilter medium resistance β M can be ound. 5

6 t V M V Figure 4: t / V vs V or p = Following b), the solution or V * = dv / dt = : With V = t. V * rom (5) you get: p(t) c V 2 2 t V M (10) This means the pressure increases linearly with time. By plotting p as unction o t you can determine α as well as β M (Figure 5). 6

7 p M t Figure 5: p versus t, or V * = Plotting the speciic cake resistance α rom dierent experiments at dierent constant p in double logarithmic scale as unction o p, you will ind a near to linear dependency according to the ollowing ormula: o (p / p o ) n (11) From this you can calculate the compressibility n: n log / o logp / p o (12) For incompressible ilter cakes n becomes 0, or compressible cakes n increases rom 0 to approximately 1.2. At n = 1 the iltrate volume is ater a certain time quasiindependent o the iltration pressure. 7

8 Figure 7: Piping and Instrumentation diagram (P&ID) o the plate ilter setup. 3 Experimental Figure 7 shows the piping and instrumentation diagram o the ilter press used or the experiments. Make yoursel amiliar with the setup beore operation. Find the relevant valves and its proper position on the P&ID or the two modes o operation. 3.1 Suspension preparation Weigh 250 g o CaCO 3, add some water and stir to make a rather thick presuspension. Beore water is illed in through valve B, make sure the outlet valve A is closed and the pressure release valve o the stirrer tank is opened properly. Then ill approximately 60 L o water through valve B and add the pre-suspension through valve B as well and ill 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 ilter (degas) valves E are closed. Place the ilter between the plates (smooth surace towards the incoming low). Press the plates together with the clamp. Ater the ilter is wetted it might be needed to reinorce the clamp pressure as the ilter settles a bit when wet. 8

9 3.3 Measure suspension low rate under constant pressure First close the pressure release valve and the illing valve B on the tank. Switch the pressurized air supply on slowly (main valve on the wall). Next, the tank needs to be pressurized to the required pressure level or the corresponding experiment. For the irst experiment, set the pressure to 1 bar. This can be done by adjusting the pressure control valve (PIC). Turning clockwise will increase the pressure and vice versa. Air lows into the tank and ills up the volume above the liquid (give it some time to reach equilibrium). Once the tank is pressurized, check that the low through the low controller (FIC) is bypassed. Let some suspension pass through the ilter press by opening the inal valve to the plate ilter (valve J) and simultaneously open the degas valves E until suspension runs out. Don t stand directly in ront o the valves to avoid getting wet! Close degas valves and start the measurement. Check again the pressure o the tank and adjust i necessary. Measure the low under constant pressure or 6 minutes, recording the low-rate every 10 s or the irst minute, and every 20 s or the next 5 min. Change the ilter (release overpressure through valve E beore opening the press) and redo the measurement at p = 2 bar (valve F). Change the ilter and redo the measurement at p = 3 bar (valve F). 3.4 Measure the pressure-drop under constant low-rate Set the pressure to 3 bar (valve F) and replace the ilter. Set the low rate on the FIC to 80 l/h. Open the path leading through the low meter (G) and close the path through the bypass line. Measure the pressure drop during approximately 9 minutes, every 10 s in the irst minute and every 20 s in the next 8 min. Ater all experiments have been carried out you can compare the appearance o the ilter cakes like cake thickness and porosity. 3.5 Shutting down and cleaning Close the valve to the pressurized air (F) and release the overpressure. Drain the rest o the suspension by opening the valve A. Shut down the stirring (C) and suspension circulation (D). Disconnect all electrics (stirring, pump, low and pressure-meters). Clean the working place. 9

10 4 Report Each group has to write one report. The report should be approximately 8 pages long and include the ollowing chapters: 1. Abstract (describe shortly what was done and what were the major indings) 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 perorm the needed calculations) 5. Discussions (discuss the results and reer to literature i needed) 6. Conclusions (what are the discoveries o the experiment, what does it mean in practice) 4.1 Speciic tasks (in results and discussion) Constant pressure-drop measurements a) Neglecting the ilter resistance β M in equation (8), the iltration or constant pressure is then described by t = h c a V 2 2 A 2 F Dp (13) V 2tp A c F (14) Plot the iltrate volume V [m 3 ] per ilter area A [m 2 ] as a unction o time t [s] in double logarithmic scale. Following equation (13) you should get a linear dependency with a slope o 0.5. Discuss the results and draw some qualitative conclusions rom the plotted results. b) Plot t/v [s/m 3 ] as a unction o V [m 3 ] and ind the speciic cake resistance α rom the regression. Additionally, determine the resistance o the ilter medium β M 10

11 (m -1 ), or each pressure drop 1, 2 and 3 bar by using equation (9). Discuss the results Constant low-rate measurements c) Plot the pressure drop p [Pa] as a unction the time t [s]. Find the cake speciic ilter resistance α C [m -2 ], and resistance o the ilter medium β M (m -1 ), using the graph and equation (10) where V * [m 3 /s] is the iltrate volume low. d) Solve the compressibility n [-] using equation (11) or (12). e) Find the porosity ε (ratio o void volume to total cake volume) o the ilter cake using the Carman-Kozeny theory. Carman (1939) calculated the pressure loss in the bulk and modeled the porous ilter cake as numerous continuous parallel channels. The pressure loss in such channels is: p Kanal liq 2 hk (Re) vkanal (15) 2 d h The pressure drop coeicient is here 64/Re (laminar low) The Reynolds number or such channel is: v Kanal d h liq Re (16) The mean velocity in the channel is determined by the continuity equation: V * vkanal 0 AF v A F (17) reie Querschnitsläche Lehrrohr Geschwindigkeit 11

12 In reality there are no single and continuous channels. In act, in porous ilter the channels are curved with changing dimensions depending on the particle properties. Thus, the main inaccuracy comes rom the use o the hydraulic diameter d h which can be deined 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 circumerence [m]. Another deinition o the hydraulic diameter is: d h 4 ( h k ) F (19) where F is the total wetted surace: (20) F S (1 ) AF hk solid volume raction total cake volume S= Speciic particle volume surace ε = porosity With (4) and inserting the above in (15) you get: The pressure drop is: p C K c V v 0 (21) 12

13 With given equations derive the speciic cake resistance, α C-K [m/kg]. Using the solved cake resistances rom the pressure constant experiments α [m/kg] one can solve or the porosities or 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 or the integration o the ilter dierential equation reasonable comparing the observed results here? How would the porosity change i instead o ideal monodisperse ( single sized) particles, polydisperse ( several sizes) particles with broader size distribution would be used? How would the plot o t/v as a unction o V change i the ilter media resistance (β) would change over time? Compare the results o our dierent ilter cake (α) and media (β) resistances, their order o magnitude and ratio to each other. How does the magnitude o the cake (α) and ilter media (β) resistances aect the values o the compressibility (n) and porosity (ε)? 13

14 5 List o symbols A channel cross section [m 2 ] area o the ilter [m 2 ] c solids concentration, mass o solid per total volume [kg/m 3 ] d h hydraulic diameter [m] F wetted surace [m 2 ] h k cake height (channel lenght) [m] k Durchlässigkeitskoeizient ater Darcy [m 3 *s/kg] n compressibility [-] p pressure drop over ilter and cake [N/m 2 ] S speciic surace area (surace per volume o the particles) [m -1 ] t iltration time [s] U wetted curcumerance [m] v Kanal mean velocity in the channel (pore) [m/s] 14

15 v 0 void tube velocity [m/s] V suspension volume [m 3 ] V * suspension volume low [m 3 /s] a C cake height speciic cake resistance [m -2 ] 15

16 area based cake resistance [m/kg] C-K lächenmassenspeziischer Kuchenwiderstand nach Carman-Kozeny [m/kg] M resistance o the ilter media [m -1 ] porosity [-] dynam. viscosity [kg/(ms)] liq luid density [kg/m 3 ] sol solid density [kg/m 3 ] x pressure drop constant [-] 16

17 6 Constants and Geometrical Data sol = r CaCO3 = 2710 kg/m 3 liq (Wasser bei 14 C) = 1000 kg/m 3 S = 9.18 * 10 5 m 2 /m 3 = kg/(ms) = 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 o Industrial Filtration", Transactions-Institution o Chemical Engineers, 1939, [3] Müller, E.: "Mechanische Trennverahren", Band 2, Sauerländer, 1983, (IVUK-Bibliothek CIT 219/II) 17