CHE499 TRANSPORT MODELING Spring 2008

Problem set #3

1. [1]Consider the anaerobic fermentation of glucose to ethanol by yeast. Glucose (C6H12O6) is converted into yeast, ethanol (C2H5OH), the byproduct glycerol (C3H8O3), carbon dioxide, and water. An empirical chemical formula for yeast can be taken as CH1.74N0.2O0.45. We can describe the fermentation by the following reaction:

C6H12O6 + aNH3b CH1.74N0.2O0.45 + c C2H5OH + d C3H8O3 + e CO2 + f H2O

Determine the stoichiometric coefficients of the above reaction if 0.21 moles of glycerol were formed for each mole of ethanol produced and 0.13 moles of water were formed for each mole of glycerol.

2. 1Consider the anaerobic fermentation of glucose to ethanol by yeast in a batch reactor.

C6H12O6 + 0.0462 NH3 0.2309CH1.74N0.2O0.45 + 1.6840C2H5OH

+ 0.2021 C3H8O3 + 1.7948 CO2 + 0.0162 H2O

The growth of yeast cell mass concentration Cc can be described by the Monod relationship

= Cc = max

In this equation, Cs is the substrate or glucose concentration with an initial value Cs0 = 100 g/L and the Monod constants are Ks = 1.5 g/L and max = 0.15 hr-1. The initial yeast cell concentration after inoculation of the fermentor is 0.2 g/L. Plot the concentration in the fermentor of the yeast cells Cc, glucose Cs, ethanol Cet, and glycerol Cgly. You can plot the yeast cell concentration as a function of time by varying Cc from 0.2 to 3.2 g/L and evaluating the corresponding time t.

3. [2]Air at400 kPa and 400 K passes through a turbine. The turbine is well-insulated. The air leaves theturbine at 125 kPa. Find the maximum amount of work that can be obtained from the turbine and the exit temperature of the air leaving the turbine. Assume air is an ideal gas with a Cp = 3.5 R (Gas constant).

4. Consider the slow adiabatic expansion of a closed volume of gas for which Cp = 3.5 R. If the initial gas temperature is 825 K, and the ratio of the final pressure to the initial pressure is 1/3, what is the change in enthalpy of the gas, the change in internal energy, the heat transferred Q, and the work W? Assume a basis of 1 mole of gas.

5.1Consider the anaerobic fermentation of glucose to ethanol by yeast in a CSTR.

C6H12O6 + 0.0462 NH3 0.2309CH1.74N0.2O0.45 + 1.6840C2H5OH

+ 0.2021 C3H8O3 + 1.7948 CO2 + 0.0162 H2O

The growth of yeast cell mass concentration Cc can be described by the Monod relationship

= Cc = max

In this equation, Cs is the substrate or glucose concentration and the Monod constants are Ks = 1.5 g/L and max = 0.15 hr-1. The feed stream to the fermentor contains no yeast cells, ethanol, or glycol. The concentration of glucose in the feed stream is 100 g/L. The fermentor has a volume of 2000 L and the feed flow rate F to the fermentor is 100 L/hr. Calculate the exiting concentrations of the yeast cells Cc, glucose Cs, ethanol Cet, and glycerol Cgly.

6.1The renal dialysis machine or artificial kidney can be used to treat patients with uremia or renal failure. During kidney dialysis blood flows through a system of tubes composed of a membrane permeable only to the smaller solutes but not the plasma proteins. On the outside of the dialysis tubes is a dialyzing fluid that contains the same concentration of solutes as the plasma, except for the metabolic waste products. As a result, metabolic waste products diffuse from the blood into the dialysis fluid due to the concentration (or more exactly chemical potential) gradient for these substances from the blood to the dialysis fluid. Blood is usually taken from an artery at a high pressure, passed through the dialysis machine, and then returned to a vein at a lower pressure. At some time during the dialyis of a patient in kidney failure, the aeterial and veuous blood conditions are as follows:

Arterial blood / Venous blood
Flow rate, ml/min
Urea concentration, mg/ml / 200
2.1 / 195
1.2

a)Calculate the rate at which urea and water are being removed from the blood.

b)If the dialyzing fluid enters at the rate of 1500 ml/min and the exiting dialyzing solution (dialysate) leaves at about the same rate, calculate the concentration of urea in the dialysate.

c)Suppose we want to reduce the patient’s urea level from an initial value of 2.7 mg/ml to a final value of 1.1 mg/ml. If the total distribution volume is 40 liters and the average rate of urea removal is that calculated in part (a), how long must the patient be dialyzed? (Neglect the loss in total blood volume due to the removal of water in the dialyzer.)

7. [3]At 50oC the vapor pressure of A and B as pure liquids are 268 and 236.2 mmHg, respectively. At this temperature, calculate the total pressure and the composition of the vapor, which is in equilibrium with the liquid containing a mole fraction of A of 0.25.

[1]Fournier, R. L., “Basic Transport Phenomena in Biomedical Engineering”, Taylor & Francis, 2007, p. 22.

[2]Fournier, R. L., “Basic Transport Phenomena in Biomedical Engineering”, Taylor & Francis, 2007, p. 86

[3]Fournier, R. L., “Basic Transport Phenomena in Biomedical Engineering”, Taylor & Francis, 2007, p. 87