Chemical Engineering - Chemical Plants II

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Pretest homemade 1)In a three-effect evaporators the boiling points are respectively: BP1= 383K ; BP2=95°C; BP3=80°C; Which are the thermal coefficients of each effect? (Boiling point elevation negligible) Utot= 850 W/m2/K ; TV0= 393 K [sol: W/m2/K U1=3400; U2=2267 ; U3=2267 ] DTtot=TV0-BP3=40 Utot*DTtot=U1*(TV0-BP1) ---> U1 Utot*DTtot=U2*(BP1-BP2) ---> U2 Utot*DTtot=U3*(BP2-BP3) ---> U3 2)In a once-through evaporator an aqueous solution of NaNO3, a very soluble salt, must be concentrated. The temperature inside the unit is 105,72 °C and Tv = 104,3 °C. Which is the molal concentration of the solute obtained? Considering that, Keb [°C*kg/mol] = 9, doesn’t take into account the van’t Hoff factor, but during calculations you should consider it. [sol: m=0,079 mol/kg] deltaTeb = Keb * m * i , where i = 1+ alfa*(n-1) is the van’t Hoff factor, and alfa = 1 since is very soluble and n = 2 since this salt splits in two ions → m 3) A crystallizer operates for 2h to have a growth of 0,052 mm. Give a first estimation of the total mass transfer coefficient knowing that: deltaC = 5 kg/m3 ; rhos=1500 g/dm3 ; volume shape factor= 0,80 ; surface shape factor= 0,85 ; [sol: K = 6,12*10^-6] dL/dt = K/3rhos * psi/phi * deltaC → first estimation deltaL/deltat → K = deltaL/deltat * 3rhos * volume shape factor/surface shape factor *1/deltaC 4)In the graph T vs mole fraction (y), for a crystallizer, highlight the driving force requested for the surface reaction. [solution guideline: ] the difference segment between red - green → y’-ys 5)According to the given data for a centrifugal filtration, decantation will be a problem to filtrate 95% of the liquid? rhos[kg/m3]=2000 ; rhow[kg/m3]=1001 ; w [round/s] = 1,05 ; mu [Pa*s] = 1,19*10^-3 ; Dp[m]=1,11*10^-3 ; R0/R=0,7 ; V0/K = 5 s [sol: tf=10,22 s tD= 0,14 s , therefore decantation is a problem] just the two last usual formulae from practical session 6)DeltaL = 0,003 m is the thickness of the cake formed on a centrifugal filter, how does it change when the solid concentration doubles and the basket diameter is the half of the previous case? [sol: DeltaL*= 0,012 m] mcake=Cs*Vloaded Vcake=mcake/rhos DL=Vcake/(2*pi*R*H) ---> DL=Cs/Diameter * const DL*=Cs*2/(Diameter/2)*const=4*Cs/Diameter *const ---> DL*/DL = 4 ---> DL*=4*DL 7)An air stream with 20% relative humidity is employed in a cooling tower. Water is cooled from 50 to 15 °C; which is the maximum allowed inlet air temperature? Consider a ΔTmin of 5°C with respect to equilibrium condition. [Sol: ~ 22 °C, use of the psychrometric chart ]. Maximum allowed T-> Twb and Tdb for 20% relative humidity Twb=Tair,out-DTmin=10°C Tdb is obtained from the chart knowing Twb and humidity 8)An abatement chamber with L=6 m and B=1.5 m is able to separate particles which diameter is higher than 20 ������m . It’s desired to design a radial abatement chamber to treat the same gas-solid stream with critical diameter equal to 15 ������m ; which is the radius of the chamber? [Sol: 2.257 m] Ratio between the diameter of the normal abatement chamber and the radial one: everything simplifies out except for BL and pi*R^2. By knowing the ratio of the diameter, B and L you can find R. 9)A stream made of water (ρ1=1000 kg/m3) and oil (ρ2=890 kg/m3) of 1 kg/s is separated in a centrifugal decanter which spins at ⍵=10 rad/s . By considering the following geometrical properties of the decanter (R is the position of the interface): ●R^2-R0^2=5.5*10^-2 m^2; ●RT^2-R^2=7.4*10^-2 m^2; determine the mass fractions of the two liquids. Assume that both liquids have the same outlet section. [Sol: x1=0.373, x2=0.627] -See the practical session on the centrifugal LL separation; -From the relation between radius and velocities, get v1 and v2 (the key is to not replace the mass flowrate in the expression); -Get the area from W[kg/s]=(v rho A) for both liquids; -W1/(rho1 v1)=W2/rho2 v2); -W1=Wtot w1 … 10) The critical diameter of a Cyclone is Dpc1 which is that one of a cyclone with the half height of the inlet with respect to the previous one? [sol: Dpc1/2] [note that N=A/B ;) ] 11)A hot and a cold fluid enter a 1-2 heat exchanger respectively at 240 °C and 60°C and they both exit at 140 °C. Use the following graph to evaluate the correction factor FG. [FG=0.9250.01]± N.B: this exercise has been recently modified 12)A cold stream is heated-up from 100°C to 130°C by an hot stream that enters at 150°C and has an heat capacity of 17 kJ/°C. Quantify the heat exchanged by knowing that FG is equal to 0.925 . [use the graph above, Qex=459 kJ] 13) A slice of eggplant should be freeze dried in a lyophilization chamber. Given a certain Ts,max, in order to not lose the quality of the product, write down the expression of the best temperature profile for the radiative plate as to minimize the lyophilization time and prevent the loss of quality of the product. ​Given the steady state equation for the thermal fluxes: h*S*(Tp-Ts)=lambda/x*S*(Ts-Tf) By setting Ts=Ts,max the optimal temperature profile for the radiative plate is: Tp,opt=Ts,max + lambda/h/x*(Ts,max-Tf) 14)In a heat pump, the stream leaving the condenser undergoes a isoenthalpic expansion, after which it reaches a pressure of 40 psia and a specific enthalpy of 49 btu/lb. By exploiting the graph calculate the percentage of vaporized liquid. [%v = 32%] Lever rule: Ha = xv*HV+(1-xv)*HL