ALWAYS BRING TUTORIAL NOTEBOOK AND CALCULATOR

Tutorial # 1 on 10 Jan 2007

1.  The ideal gas equation of state relates absolute pressure,  P (atm), gas volume, V (liters), number of moles of gas, n (mol) and absolute temperature, T (K):

                                                                                        PV = 0.08206nT

convert the equation to one relating P (psig), V(ft³), n(lb-mol) and T(^oF).

2.  Make the following conversions:

a) 2600 mm Hg to psi    b) 35.0 psi to cm of carbon tetrachloride    c) 1 atm to kgf/cm²    d) 15 cm Hg of vacuum to atm (absolute)

e) 300 K to Rankine

3.  A gas mixture has the following composition by mass: O₂, 16%; CO, 4%; CO₂, 17%; N₂, 63%.  This mixture is stored in a tank with a volume of 3.5 ft³ at a temperature of 85^oF.  The reading on a pressure gauge attached to the tank is 500 psi.  Calculate the mass of gas in lbs.

4.  The following equation relates heat and mass transfer coefficients:

                        hM/k = ρCpRT (ρCpD/ĸ)^-0.67

h is heat transfer coefficient, cal/(s cm^{2 o}C); M is molecular weight, g/gmol; ρ is density, g/cc; Cp is specific heat in cal/(g ^oC)

R is gas constant, atm cc/(g mol K); T is temperature, K; D is diffusivity, cm²/s; ĸ is thermal conductivity, cal/(cm s ^oC).

Find the units of mass transfer coefficient, k.

5.  A lethal dose of HCN in air is 300 mg/kg of air at room temperature.  How many HCN/kg air is 10 ppm?  what fraction of lethal dose is 10 ppm?

Tutorial # 2 on 17 Jan 2007

1.  The organic fraction in the wastewater is measured in terms of the biological oxygen demand (BOD), namely the amount of disolved oxygen required to biodegrade the organic matter.  If the dissolved oxygen (DO) concentration in a body of water drops too low, the fish may die.  The minimum summer levels for lakes is 5 mg/L of DO.  If a stream is flowing at 0.3 m³/s and has a BOD of 5 mg/L before reaching the discharge point of a sewage treatment plant, and the plant discharges 3.785 million liters/day of wastewater with a concentration of 0.15 g/L of BOD, what will be the concentration immediately below the discharge point of the plant?

2. If the percentage of fuel in a fuel-air mixture falls below a certain value called lower flammability limit (LFL), the mixture cannot be ignited.   For example, LFL of propane in air is 2.05 mole% C₃H₈.  If the percentage of propane is greater than 2.05 mole%, the gas can be ignited, otherwise not.  There is also an upper flammability limit, which for propane is 11.4 mole%.  A mixture of propane in air containing 4.03 mole% C₃H₈ is the feed to a combustion fyrnace.  If there is a problem in the furnace, a stream of pure air is added to the fuel mixture prior to the furnace inlet to make sure that ignition is not possible.

a) Draw and label a flowchart of the fuel-gas dilution mixing unit

b) If propane flows at a rate of 150 mol C₃H₈/s in the original fuel-air mixture, what is the minimum molar flow rate of the dilution air?  Would actual dilution of air feed rate be more than or less than what you calculated?

3.  Suppose that 100 mL/min are drawn from a fermentation tank and passed through an extraction tank in which the fermentation product (in the aqueous phase) is mixed with an organic solvent.  After mixing in the extraction tank, the mixture is allowed to separate into two phases--organic and aqueous--in a settling tank.  The concentration of the desired enzyme (3-hydroxybutyrate dehydrogenase) in the aqueous feed to the extraction tank is 10.2 g/L.  The pure organic phase runs into the extraction tank at 9.7 mL/min.  The ratio of the concentration of the enzyme in the exit product stream (the organic phase) from the settling tank to its concentration in the aqueous phase is 18.5.   Draw a flowchart for the process.  What is the fraction recovery of the enzyme and the amount recovered per min?  Assume negligible miscibility between the aqueous and organic liquids in each other.  Ignore any change in density on removal or addition of the enzyme to either stream.

Consider the extraction tank and the settling tank as one unit with the stream from extraction tank separating into two phases in the settling tank.  Draw two such units side-by-side and name them as first unit and second unit.  Now, the aqueous feed from the fermentation tank and the organic phase from the second settling tank are fed to the extraction tank of first unit.  The organic phase from the first settling tank is the final product.  The aqueous phase from the settling tank of the first unit is added to extraction tank of the second unit and fresh organic phase is also added to this tank.  Draw a flowchart of the two units.

Tutorial # 3 on 24 Jan 2007

1.  Methanol is synthesized from carbon monoxide and hydrogen in a catalytic reactor.  The fresh feed to the process contains 32.0 mole% CO, 64.0% H₂ and 4.0% N₂.  This stream is mixed with a recycle stream in a ratio 5 mol recycle/1 mol fresh fed to produce the feed to the reactor, which contains 13.0 mole% N₂.  A low single pass conversion is achieved in the reactor.  The reactor effluent goes to a condenser from which to streams emerge: a liquid product stream containing essentially all the methanol formed in the reactor, and a gas stream containing all the CO, H₂ and N₂ leaving the reactor.  The gas stream is split into two fractions: one is removed from the process as a purge stream, and the other is the recycle stream that combines with the fresh feed to the reactor.

a) Draw and label a flowchart for the above problem description

b) calculate the production rate of methanol (mol/h), the molar flow rate and composition of the purge gas, and the overall and single pass conversion.

c) briefly explain in your own words the reasons for including (i) the recycle stream and (ii) the purge stream in the process design

d) scale up the process and calculate the moles of CO and H₂ required to produce 235 kmol/h of methanol.

2.  Ethane is chlorinate in a continuous reactor:

                                C₂H₆ + Cl₂                              C₂H₅Cl  +  HCl

    Some of the product monochloroethane is further chlorinated in an undesired side reaction:

                                C₂H₅Cl + Cl₂                           C₂H₄Cl₂ + HCl     

a) Suppose your principal objective is to maximize the selectivity of monochloroethane production relative to dichloroethane.  Would you design a reactor for a high or low conversion of ethane? Explain your answer. (Hint: If the reactor contents remained in the reactor long enough for most of the ethane in the feed to be consumed, what would be the main product)  What additional processing steps would almost certainly be carried out to make the process economically sound?

b) The reactor is designed to yield a 15% conversion of ethane an a selectivity of 14 mol  C₂H₅Cl per mol C₂H₄Cl₂ with negligible amount of chlorine gas in the product stream.  Calculate the feed ratio (mol Cl₂  per mol C₂H₆) and the fractional yield of monochloroethane.

c) Suppose the reactor is built and the conversion is only 14%.  Analysis of reactor outlet stream shows no Cl₂ but another species with a molecular weight higher than dichloroethane.  Offer a likely explanation for these results.

3.  n-pentane is burned with excess air in a combustion chamber.

a) A technician runs an analysis and reports that the product gas contains 0.270 mole% pentane, 5.3% oxygen, 9.1% carbon dioxide and the balance nitrogen on a dry basis.  Assume 100 mol of dry product gas as a basis of calculation, draw and label a flowchart.

b) Use balances to prove that the reported percentages could not possible be correct.

c) The technician reruns the analysis and reports new values of 0.304 mole% pentane, 5.9% oxygen, 10.2% carbon dioxide and the balance nitrogen on a dry basis.  Verify that this result could be correct and, assuming that it is, calculate the percent excess air fed to the reactor and the fractional conversion of pentane.

Tutorial # 4 on 7 Feb 2007

1.  On a hot summer day the temperature is 35^oC, barometric pressure is 103 kPa and the relative humidity is 90%.   An air conditioner draws in outside air, cools it to 20^oC, and delivers it at a rate of 12,500 L/h.  Calculate the rate of moisture condensation (kg/h) and the volumetric flow rate of the air drawn from the outside.  Antoine constants for water are A = 8.10765, B = 1750.286 and C = 235.000, Use T in ^oC; Vapour pressure is in mm Hg.

2.  The solubility coefficient of a gas may be defined as the number of cubic centimeters (STP) of the gas that dissolves in 1 cm³ of a solvent under a partial pressure of 1 atm.  The solubility coefficient of CO₂ in water at 20_oC is 0.0901 cm³ CO₂ (STP)/cm³ H₂O(l). 

a) calculate the Henry's law constant in atm/mole fraction for CO₂ in water at 20^oC from the given solubility coefficient.

b) How many grams of CO₂ can be dissolved in a 330 mL can at 20^oC if the gas above the soda is pure CO₂ at a gauge pressure of 2.5 atm.  Assume the liquid properties are those of water.

3.  A stream of 5.00 wt% oleic acid in cottonseed oil enters an extraction unit at a rate of 100 kg/h.  The unit operates as an equilibrium stage (the streams leaving the unit are in equilibrium) at 85^oC.  At this temperature, propane and cottonseed oil are essentially immiscible, and the distribution coefficient (mass fraction of oleic acid in propane/mass fraction of oleic acid in cottonseed oil) is 0.15.

a) calculate the rate at which liquid propane must be fed to the unit to extract 90% of the oleic acid.

b) estimate the minimum pressure of the extraction unit (i.e., the pressure required to keep the propane liquid at 85^oC).

Tutorial # 5 on 28 Feb 2007

The following diagram shows a simplified version of how a refrigerator works:

In a liquid receiver, a liquid refrigerant (any one of a number of halogenated hydrocarbons such as CCl₂F₂) is contained at high pressure and temperature.

The liquid passes through an expansion valve where it flashes to a low pressure, cooling to its boiling point at this pressure and partially evaporating.

The liquid-vapour mixture passes through an evaporator coil (shown as a box).  Air from the food storage area circulates over the coil, and the heat absorbed

by the evaporating refrigerant in the coil causes the air to cool.  The cold refrigerant vapour emerging from the coil passes to a compressor where it is brought

back to high pressure and in the process is raised to a high temperature.  The hot vapour then passes through a condenser, where it is cooled and condensed at

constant pressure.  The air that absorbs the heat given up by the condensing fluid is discharged outside the refrigerator, and the liquefied refrigerant returns to the

liquid receiver.

    Suppose refrigerant R-12 (the standard name for CCl₂F₂) undergoes this cycle at a circulation rate of 40 lb_m/min, with the temperatures and pressures at the different

points of the cycle being those shown on the flow diagram.  Thermodynamic data for R-12 are as follows:

Saturated fluid:  T = 5^oF, H_liq = 9.6 Btu/lb_m, H_vap = 77.8 Btu/lb_m

                                    T = 86^oF, H_liq = 27.8 Btu/lb_m, H_vap = 85.8 Btu/lb_m

Superheated vapour: T = 114^oF, P = 93.3 psig, H_vap = 90 Btu/lb_m

a) Suppose the expansion valve operates adiabatically (no heat loss or heat gain) and ΔE_k is negligible.  Use an energy balance about the valve to calculate the fraction of the

refrigerant that evaporates in this stage of the process.

b) Calculate the rate in Btu/min at which heat is transferred to the refrigerant that evaporates in the coil. (this is the useful cooling done in the system.)

c) If the heat loss in the condenser is 2500 Btu/min, how much horsepower must the compressor deliver to the system?

Tutorial # 6 on 7 Mar 2007 (Bring psychrometric chart to tutorial class)

Wet wood chips are dried in a continuous drier that operates at 1 atm.  The chips enter at 19^oC with a water content of 40 wt% and must leave with a moisture content of less than 15%.  Hot air is fed to the drier at a rate of 11.6 m^{3 (}STP) per kg of wet chips.

    To monitor the performance of the drier by sampling the exiting ships and determining their moisture content directly would be a cumbersome procedure and almost impossible to automate.  Instead, wet and dry bulb thermometers are mounted in both the inlet and outlet airlines, and the moisture content of wood chips is determined by a material balance.

After the unit goes on stream, the inlet dry bulb temperature is found to be 100^oC and the wet bulb temperature is low enough so that the moisture content of the air may be neglected.  The dry bulb temperature of the exiting air is found to be 38^oC and the wet bulb temperature is 29^oC.

a)  Use the psychrometric chart to determine the absolute humidity (kg H₂O per kg dry air) and specific enthalpy (kJ per kg dry air) of outlet air stream.  Then calculate the mass of water in the exiting air per kg of wet chips fed, assuming dry air has a molecular weight of 29.0.

b)  Calculate the moisture content of emerging chips and determine whether the design specification of les than 15% has been achieved.

c)  If the unit operates adiabatically (no heat loss or heat gain) and the heat capacity of dry chips is 2.10 kJ/(kg ^oC), what is the exit temperature of the chips? (In estimating the specific enthalpy of the entering air, recall that the reference temperature for dry air used in constructing the psychrometric chart id 0^oC).

Tutorial # 7 on 14 Mar 2007

Ammonia is oxidized with air to form nitric oxide in the first step of the production of nitric acid.  Two principal reactions occur.  In one reaction, ammonia reacts with oxygen to form nitric oxide and water; in another ammonia reacts with oxygen to form nitrogen and water.  100 mol NH₃/min enter the reactor at 25^oC and 8 bar and 900 mol/min of air at 150^oC and 8 bar also enters the reactor.  The product gas at 700^oC and 8 bar contains the following: 90 mol NO/min, 150 mol water (v)/min, 716 mol N₂/min, 69 mol O₂/min.

a) Taking elemental species [N₂(g), H₂(g), O₂(g)] at 25^oC and 1 atm as references conditions, prepare and fill in an inlet-outlet enthalpy table.

b) Calculate the required rate of heat transfer to or from the reactor in kW.

Standard heats of formation: NH₃ = -46.19 kJ/mol; NO = +90.37 kJ/mol; H₂O(v) = -285.84 kJ/mol

Specific heats of various species, T in ^oC and C_p in kJ/(mol ^oC): NH₃: 35.15 x10^-3 + 2.954 x 10^-5T + 0.4421 x 10^-8T² - 6.686 x 10^-12T³

                                                                                                                      NO: 29.50 x10^-3 + 0.8188 x 10^-5T - 0.2951 x 10^-8T² + 0.3652 x 10^-12T³

                                                                                         O₂: 29.10 x10^-3 + 1.158 x 10^-5T - 0.6076 x 10^-8T² + 1.311 x 10^-12T³

                                                                                         N₂: 29.00 x10^-3 + 0.2911 x 10^-5T + 0.5723 x 10^-8T² - 2.871 x 10^-12T³

                                                                                         H₂O(v):33.46 x10^-3 + 0.6880 x 10^-5T + 0.7604 x 10^-8T² - 3.593 x 10^-12T³

Tutorial # 8 on 21 Mar 2007

Ammonia scrubbing is one of the many proceses for removing SO₂ from flue gases (product gases from furnace).  The gases ar bubbled through an aqueous solution of ammonium sulphite, and the SO₂ reacts to form ammonium bisulphite:

                    (NH₄)SO₃ (aq)    +    SO₂(g)    +    H₂O(l)                                    2NH₄HSO₃ (aq)

Subsequent process steps yield SO₂ and regenerate ammonium sulphite, which is recycled to the scrubber.  The SO₂ is either oxidized and absorbed in water to form sulphuric acid or reduced to elemental sulphur.

    Flue gas from a power plant boiler containing 0.30% SO₂ by volume enters a scrubber at a rate of 50,000 mol/h at 50^oC.  The gas is bubbled through an aqueous solution containing 10.0 mole% ammonium sulphite that enters the scrubber at 25^oC.  The gas and liquid effluents from the scrubber both emerge at 35^oC.  The scrubber removes 90% of the SO₂ entering with the flue gas.  The effluent liquid is analyzed and is found to contain 1.5 moles (NH₄)SO₃ per mole of NH₄HSO₃.  The heat of formation of (NH₄)SO₃ (aq) at 25^oC is -890.0 kJ/mol, and that of NH₄HSO₃ (aq) is -760.0 kJ/mol.  the heat capacities of all liquid solutions may be taken to be 4.0 J/(g ^oC) and that of the flue gas may be taken to be that of nitrogen = 1.237 kJ/(mol ^oC).  Evaporation of water may be neglected.  Calculate the required rate of heat transfer to o from the scrubber (kW).

Tutorial # 9 on 4 Apr 2007

1.  The catalyst in a fluidized-bed reactor of 200 cubic meter volume is to be regenerated by contact with hydrogen stream.  Before the hydrogen can be introduced in the reactor, the O₂ content of the air in the reactor must be reduced to 0.1%.  If pure N₂ is fed to the reactor at the rate of 20 cubic meter per minute and an equal volume of the gas flows out, , for how long should the nitrogen be flown into the reactor?  Assume that the catalyst solids occupy 6% of the reactor volume and that the gases are well mixed.

2.  A steam radiator is used to heat a 60 m³ room.  Saturated steam at 3.0 bar condenses in the radiator and emerges as a liquid at the saturation temperature.  Heat is lost from the room to the outside at a rate given by Q (kJ/h)  = 30.0 (T-T_o), where T(^oC) is the room temperature and T_o is the outside temperature.  At the moment the radiator is turned on, the temperature in the room is 10^oC.

a) Let m_s (kg/h) denote the rate at which steam condenses in the radiator and n (kmol) the quantity of air in the room.  Write a differential energy balance equation on the room air, assuming that n remains constant at its initial value, and evaluate all numerical coefficients.  Take the heat capacity of air (C_v) to be constant at 20.8 J/(mol ^oC).

b) Write the steady stat energy balance on the room air and use it to calculate the steam condensation rate required to maintain a constant room temperature of 24^oC.

c) Integrate the transient balance to calculate the time required to achieve a temperature of 23^oC, assuming that the steam rate is that calculated in part (b).