3MS Multiphase Systems Problem Sheet 2024 Maximum THREE pages excluding cover page and references. The figures and table below present data from a study of a mixing vessel operated either with gas sparging or with solids. The details of the set up are shown in Figure 1 and Table 1. Experimental Setup and Data Air in Perspex Baffle Ring sparger Rushton 6-Blade Turbine ERT Linear Probe Electrode strip Figure 1. Experimental set up equipped with Linear Electrical Resistance Tomographic Apparatus. This geometry is different to the circumferential geometry used in 2nd year labs. The liquid is conductive (assume the density and viscosity are that of water and an interfacial tension of 0.04 N m¹), and the probe measures the distribution of conductivity in a 2-D radial slice from the impeller axis to close to the vessel wall. When a conductive aqueous solution is sparged with (non-conductive) gas bubbles, the conductivity distribution can be converted to a tomogram showing the distribution of voidage (air bubbles). Table 1. Tank Dimensions. Note: Liquid Fill Height = 3/2T Vessel Property Ratio with Tank Diameter, T Absolute Value (m) Tank Diameter, T 0.14 Impeller Diameter, D 2/5 0.056 Baffle width, B 1/10 0.014 Impeller clearance, C 4/14 0.04 Fluid Height, H 3/2 0.21 Ring sparger diameter 7/10 0.04 1 Exercise You will be asked to perform calculations for a permutation of particle size, particle density, solids mass fraction and gas volume rate based on YOUR University ID Number as shown in the table below: Parameter selection based on LAST 4 digits of ID 1st digit 2nd digit 3rd digit 4th digit Solids dp Pp Mass vvm (mm) (kg m-3) Fraction (-) (wt%) 0 0.20 3500 4.0 1.00 1 0.23 4000 4.5 1.25 2 0.25 4500 5.0 1.50 3 0.28 5000 5.5 1.75 4 0.30 5500 6.0 2.00 5 0.33 6000 6.5 2.25 6 0.35 6500 7.0 2.50 7 0.38 7000 7.5 2.75 8 0.40 7500 8.0 3.00 9 0.43 8000 8.5 3.25 For example, if your ID is 2013679 you would take the digits 3, 6, 7 and 9 to choose dp = 0.28 mm, pp = 6500 kg m³, mass fraction solids = 7.5wt% and air flow = 3.25 vvm. IMPORTANT: you must state your ID and the corresponding parameters on the cover page of the submission). Figures 2 and 3 show observations and measurements of gas distribution at various characteristic conditions as impeller speed increases for fixed gas volume rate. Figure 2 shows an image of the gas in the vessel and the corresponding tomogram of voidage (εg). (a) Flooding (b) Loading (c) Loading (d) Completely Dispersed/Recirculation (e) Completely Dispersed/Recirculation The average voidage vs depth has been determined from the tomograms and is shown in Figure 3. 2 70 (a) (b) (c) (d) (e) εg (%) 0.00 3.75 7.50 11.25 15.00 Figure 2: Vessel and tomogram images at increasing impeller speed (left to right) and constant gas volume rate. The tomogram shows voidage (gas holdup) in a radial slice. Relative height 1 0.9- 0.8 * * 0.7- Flooding Loading Loading * Recirculation + Recirculation 0.6 0.5 0.4 0.3 * + * + 0.2- 0.1- 0 0 5 10 15 20 ε (%) g Figure 3: Voidage vs height at increasing impeller speed (left to right). The voidage at each height is the average across the radius taken from the figure 2 tomograms. 3 1. Using your value for vvm, estimate the likely ranges of impeller speeds for each of the three conditions observed in Figures 2 and 3. [25%] 2. Pick a speed in each range (flooding, loading and complete dispersion/recirculation) and at each determine the power input, assuming no losses due to gassing. [15%] 3. Estimate the maximum bubble size at each of your three speeds [HINT - see UNIT 10 of Prof. Simmons' notes]. Compare qualitatively with Figure 2. [15%] 4. For ERT to work it is necessary that the liquid is conductive. If we are using water, then electrolytes must be added. Discuss the effect on bubble size versus a pure liquid. [15%] Stainless steel balls were added to the vessel and mixed without sparging. In this case the particles are conductive. Figure 4 shows mean conductivity in the radial plane vs height for three impeller speeds NJS, 2/3NJs and Njs. Relative height 0.9- 0.8- 0.7- 0.6- 0.5- 0.4- 0.3- 0.2- 0.1 2.725 2.73 2.735 2.74 2.745 Conductivity mS cm-1 Figure 4. Mean conductivity in the radial plane vs height for dispersion of stainless-steel spheres at different impeller speeds. 5. For your permutation of particle characteristics and loading, determine Njs. You can assume a Zwietering constant of 6 for the Rushton turbine. [10%] 6. The three impeller speeds in Figure 4 are NJS, NJs and NJs. Suggest which data curve corresponds to which speed. [10%] 7. With reference to Figure 4, comment on the suitability of ERT to determine Njs. [10%] 4

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3MS Multiphase Systems Problem Sheet 2024 Maximum THREE pages excluding cover page and references. The figures and table below present data from a study of a mixing vessel operated either with gas sparging or with solids. The details of the set up are shown in Figure 1 and Table 1. Experimental Setup and Data Air in P

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E2A.6(a) A sample of 4.50g of methane occupies 12.7 dm3 at 310 K. (i) Calculate the work done when the gas expands isothermally against a constant external pressure of 200 Torr until its volume has increased by 3.3 dm². (ii) Calculate the work that would be done if the same expansion occurred reversibly. E2A.6(b) A sample of argon of mass 6.56g occupies 18.5 dm3 at 305 K.(i) Calculate the work done when the gas expands isothermally against a constant external pressure of 7.7kPa until its volume has increased by 2.5 dm3.(ii) Calculate the work that would be done if the same expansion occurred reversibly. F=\frac{k T}{2 l} \ln \left(\frac{1+v}{1-v}\right) \quad v=\frac{n}{N} where k is Boltzmann's constant, N is the total number of units, and l= 45 nm for DNA. (a) What is the magnitude of the force that must be applied to extend a DNA molecule with N=200 by 90 nm? (b) Plot the restoring force against v, noting that v can be either positive or negative. How is the variation of the restoring force with end-to-end distance different from that predicted by Hooke's law? (c) Keeping in mind that the difference in end-to-end distance from an equilibrium value is x = nl and, consequently, dx = ldn= Nldv,write an expression for the work of extending a DNA molecule. Hint: You must integrate the expression for w. The task can be accomplished best with mathematical software.

A gas stream containing 3 mol% Ammonia (NH3) in Air is to be passed to a packed absorption columnat a rate of 5 kg s1. The column is to use Water (H20) as the solvent to reduce the ammonia content in the air leaving the column to 0.01 mol%. The gas and water streams can be assumed to be at 25 °C.The column operates at 1 bar pressure. The relationship that describes the equilibrium between Ammonia and Water at these conditions is given by: y = Hx Where the Henry's Law constant, H = 1.3 (mole frac NH3 in gas) (mole frac NH3 in liquid)1 From pilot scale experiments the Overall Mass Transfer Coefficient, KG, has been found to remain constant with a value of 200 × 10--6 kmol m² s-1 Using the protocol outlined on Page 55 of the gas absorption notes, specify an absorption column to achieve the required separation using 1 inch Raschig Rings (See Table 1 in attached data sheets). Your Design Specification must clearly show the following: Any assumptions made must be stated clearly. What the minimum liquid rate for the column is. What the liquid rate of solvent is under normal operating conditions. Based on the assumption of operating at 60% of the flooding gas flow rate, what the diameter of the column should be in meters. Confirmation that the wetting rate of your column falls within the acceptable range. The values of HTU, NTU and thus the total height of packing required in the column.

Two tanks are connected together in the following unusual way in Fig. E2.3. Develop a model for this system that can be used to find hj, h2,W2, and w3 as functions of time for any given variations in inputs. 1. The density of the incoming liquid,p, is constant. 2. The cross-sectional areas of the two tanks are A1 and A2. 3. w2 is positive for flow from Tank 1 to Tank 2. 4. The two valves are linear with resistances R2 and R3.

The steady-state temperature distribution in a one-dimensional wall of thermal conductivity 50 W/m-K and thickness 50 mm is observed to be T(°C) = a + bx²,a = 200°C, b = -3,500°C/m2, and x is in meters.where Determine the heat fluxes at x = 50 mm in W/m-

P2E.1 Calculate the final temperature, the work done, and the change of internal energy when 1.00 mol NH,(g) at 298 K is used in a reversible adiabatic expansion from 0.50 dm³ to 2.00dm².

A completely enclosed stirred-tank heating process is used to heat an incomingstream whose flow rate varies. The heating rate from this coil and the volume areboth constant. Develop a mathematical model for the process if the heat losses tothe atmosphere occur. 1. p and Cpare constants. 2. U, the overall heat transfer coefficient, is constant. 3. A, is the surface area for heat losses to ambient. 4. T; > Ta (inlet temperature is higher than ambient temperature).

When measuring small pressure differences with a manometer, often one arm of is inclined to improve the accuracy of the reading. The air pressure in a circular duct is to be measured using a manometer whose open arm is inclined 32° from the horizontal, as shown in The figure. The density of the liquid in the manometer is 0.86 kg/L, and the vertical distance between the fluid levels in the two arms of the manometer is 12 cm. Determine the gage pressure of air in the duct (in Pa) and the length of the fluid column in the inclined arm above the fluid level in the vertical arm (in cm).

E1A.3b) A perfect gas undergoes isothermal compression, which reduces its volume by 1.80 dm". The final pressure and volume of the gas are 1.97 bar and 2.14 dm', respectively. Calculate the original pressure of the gas in (i) bar,(ii) torr.

4.36.) A gas mixture of methane and steam at atmospheric pressure and 500°C is fed to a reactor, where the following reactions occur: \mathrm{CH}_{4}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{CO}+3 \mathrm{H}_{2} \quad \text { and } \quad \mathrm{CO}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} The product stream leaves the reactor at 850°C. Its composition (mole fractions) is: y_{\mathrm{CO}_{2}}=0.0275 \quad y_{\mathrm{CO}}=0.1725 \quad y_{\mathrm{H}_{2} \mathrm{O}}=0.1725 \quad y_{\mathrm{H}_{2}}=0.6275 Determine the quantity of heat added to the reactor per mole of product gas.

4. 8.20 Engine oil flows through a 25-mm-diameter tube at a rate of 0.5 kg/s. The oil enters the tube at a temperature of 25°C, while the tube surface temperature is maintained at100°C. Determine the oil outlet temperature for a 5-m and for a 100-m long tube. For each case, compare the log mean temperature difference to the arithmetic mean temperature difference.