Chemical and Biological Engineering (CBE 101) Exam 2 Study Guide

Transcription

1 Chemical and Biological Engineering CBE 101) Exam 2 Study Guide What is Chemical and Biological Engineering? S&H Ch. 1) Chemical and Biological Engineering is combining math, physics, chemistry, biology and engineering to benefit society by providing safe, economical solutions to a wide range of technological problems. Important concepts from this chapter include: Chemical and biological engineers make contributions to many industries. See Figure 1.1 on p. 3 of S&H.) Table 1.2 on p. 5 of S&H list great achievements of chemical and biological engineering, primarily from the past century. In the future, chemical and biological engineers will contribute to addressing the Grand Challenges for Engineering, described in As a student in our undergraduate program, you will study the core CBE topics listed in Engineering is a profession; its practitioners have extensive training, which gives them vital skills. They meet rigorous qualifications. Because of their specialized expertise, they have a relative degree of autonomy and monopoly. This requires that they abide by a code of ethics. Chemical Processing S&H Ch. 2) Important ideas from this chapter include: What is a chemical process S&H p. 13)? What are batch, continuous, and steady-state processes S&H p. 15)? Three types of diagrams are used to describe chemical and biological) processes: block diagrams, process flow diagrams PFDs), and piping and instrumentation diagrams P&IDs). PFDs are usually accompanied by stream tables. Know the salient features of each of these, as described in

2 Engineering Problem Solving S&H Ch. 3 and Group Lab Activity) Important ideas from these include: Engineering problems solving does not mean solving problems using some of the familiar strategies you have practiced in our science and math courses e.g. finding a similar problem with a known solution, asking what equation do I need?, etc.). These are problem solving methods, but they are not engineering problem solving strategies. Engineering problem solving involves designing, building, and testing systems. A more detailed list of steps is found in 3.1 of S&H. Many engineering problems are solved by teams of people with different expertise. 3.3 of S&H covers stages of team development Table 3.1), characteristic work temperaments common on a team Table 3.2), and roles within teams Table 3.3). Essentials for successful group work are found on pp of the course packet. These include common-sense tips for preventing, identifying, and resolving conflicts within groups. Describing Physical Quantities S&H Ch. 4 and Lab 1) Important ideas include: Physical quantities have: a value reported on a scale Dimensions indicated by the units The scale indicates where the zero is, how the measurement is incremented relative to other scales), and which directions are positive and negative. Quantities can be converted from one scale to another using scale conversion equations), and from one unit system to another using unit conversions). It is meaningless to attempt to convert a measurement to a different dimension. A conversion factor is a quantity equal to one, that can be multiplied by a quantity to change the units. This is a slightly different definition than the one our textbook authors use.) 2

3 Most dimensions we will use in this class can be defined by combination of the fundamental dimensions of mass, length, time, and temperature. Some units we use may be initially unfamiliar or confusing to you. Study them! E.g. lb m, lb f, gmol, lbmol, kgmol, horsepower, psi). Systems of units we use include the SI, cgs, and American Engineering system. Know how mass, length, time, and temperature are combined to derive common dimensions e.g. volume, density, force, pressure, velocity, concentration, energy, power, etc.). The units used for these combined dimensions are the defined units on p. xxi of S&H. The defined units can also be used to figure out how to combine the fundamental dimensions. E.g. if you know power can be measured in Watts, look up how a Watt is defined to discover how it combines mass, length, and time. An equation is dimensionally consistent if and only if: terms added, subtracted, or on opposite sides of an equal sign have the same dimensions; and arguments of transcendental functions e.g. exponents, logarithms, trigonometric functions) are dimensionless. Measured variables have an uncertainty. The uncertainty is the larger of: the reproducibility of the measurement; or the resolution or precision of the instrument used. When a value is calculated from multiple measured values, the uncertainty of the calculated value is propagated from the uncertainties of the measured values using the root-sum-of-squares formula. Uncertainties should be reported with one significant digit, and this should be the last significant digit in the value. See pp of the course packet for information on uncertainties.) 3

4 Material Balances S&H Ch. 5 and Lab 2.1) Chemical and biological processes can neither create nor destroy mass. Important concepts include: For continuous processes the conservation of mass principle can be expressed: In Out = Accumulation At steady state, Accumulation = 0, so: In = Out Mass balance equations can be used to derive relationships among many other important process variables e.g. molar flow rates, volume flow rates, molar concentrations, densities, molecular weights, mass fractions, etc.) if we know how those quantities are related to mass flow rates. Chemical and biological processes do not necessarily conserve other quantities e.g. volume, total moles, masses and moles of individual components). Individual component balances can be written, as long as their generation and consumption are accounted for. At steady state: ṅ A,in + r A,formation = ṅ A,out + r A,consumption The molar rates of generation and consumption of different species can be related to one another via chemical reaction stoichiometry. Follow the steps for solving material balance problems S&H p. 65 and p. 76). Material balances can be written around parts of a process, including individual unit operations and groups of unit operations. Be careful to include all streams entering and leaving the part of the process around which the balance is performed. 4

5 Reactor Design S&H Ch. 9) The rate of a chemical reaction is related to the molar concentrations of components by a rate law. The rate law describes how frequently collisions between reactants occur with the right conditions energy, orientation, etc.) to cause the reaction to proceed. For elementary reactions, the rate is proportional to the concentrations of the reactants each raised to the power of their respective stoichiometric coefficients e.g. the oxidation of nitric oxide reaction on p. 144). Not all reactions are elementary. So some rate laws may have a very different form e.g. the oxidation of carbon monoxide reaction on p. 144). The reaction rate, r reaction, has dimensions of moles volume 1 time 1. The dimensions of the rate coefficient, k, depend upon the order of the reaction. The rate coefficient accounts for the effects of temperature and other conditions on the reaction rate. Rate coefficients vary with temperature. One relationship used to describe this variation is the Arrhenius equation equation 9.3, on p. 144 of S&H). Designing continuous, stirred-tank chemical reactors requires finding the reactor volume. The reactor volume can be found from a material balance on one of the reactants, if the rate law is known e.g. according to equation 9.8 on p. 147 of S&H). When a reaction rate is related to component molar concentrations in a continuous, stirred-tank reactor, these concentrations are the same as the concentrations in the reactor effluent not the reactor feed). 5

6 Mass Transfer S&H Ch. 8 and Lab 2.2) We considered to mechanisms of mass transport, molecular diffusion and mass convection. Both of these mechanisms can be described by: transport rate = driving force resistance Ordinary molecular diffusion is a result of random dispersion of molecules associated with their random motions and collisions. It can be described by: Ṅ A = D A,B A dc ) A dx = D ca,2 c A,1 A,BA = D A,B A c A x 2 x 1 x Mass convection is when the transport is enhanced by the bulk flow of a fluid. This convective transport is not necessarily in the direction of the bulk flow. See figure 8.5 on p. 129 of S&H). Mass convection can be described by: Ṅ A = h m A c A,s c A, ) = h m A c A In both molecular diffusion and mass convection, the driving force is an apprpriate concentration driving force c. Therefore, the resistance is the reciprocal of everything else on the right-hand side of the governing equation.) These mechanisms of mass transport are very important for industrial chemical and biological processes, including absorption, stripping, liquid-liquid extraction, membrane separations, and many biological transport phenomena, such as oxygen transport from blood vessels to cells in tissues. In many cases there are multiple diffusive and convective) resistances to mass transport in series, as in figure 8.7 on p. 132 of S&H. The blood oxygenator and hemodyalizer are examples. Multistep mass transport can be described by: transport rate = overall driving force overall resistance where the overall driving f orce and overall resistance are the sums of the driving forces and resistances for the individual steps. 6

7 The largest resistance will have dominant effects on the transport rate. Changing very small resistances will have little effect on the transport rate when a larger resistance dominates. 7

8 Heat Transfer and Conservation of Total Energy S&H Ch. 10 and Labs 3 and 4) Chemical and Biological processes can neither create nor destroy energy. Important concepts include: For continuous processes, the conservation of energy principle can be expressed: In Out = Accumulation At steady state, Accumulation = 0, so: In = Out Energy balance equations describe how energy is converted from one type to another. For continuous processes, mass flowing into and out of the process carries energy with it, in the unique forms of internal energy, kinetic energy, and gravitational potential energy. Energy can also enter or leave a process as heat and work. The mass balance equation for such a process may be written: ṁ out Û αv2 + gz ) in ṁ Û + 1 ) 2 αv2 + gz = Q + Ẇ Terms in the above equation have dimensions of [Power]. We described three mechanisms whereby thermal energy can be transferred. They can all three be described as: transport rate = driving force resistance The three mechanisms of thermal energy transfer heat transfer) we described are: conduction - thermal energy transported through a conducting solid Q = ka dt ) dx = ka T2 T 1 = ka T x 2 x 1 x convection - thermal energy transport enhanced by a bulk fluid flow Q = hat s T ) = ha T 8

9 radiaton - thermal energy radiated as electromagnetic waves Q = ɛσa Ts 4 Tsur 4 ) Work is done on a fluid or extracted from a fluid by equipment containing moving parts e.g. pumps, turbines, and compressors). This type of work is called shaft work, denoted Ẇs. Decomposing Ẇ into the shaft work and rate-of-flow work, and combining the P ˆV with the internal energy gives an alternative form for the total energy balance equation for a continuous process: ṁ Ĥ + 1 ) 2 αv2 + gz ṁ Ĥ + 1 ) 2 αv2 + gz = Q + Ẇs out in We discussed three ways in which the enthalpy per mass, Ĥ, of a fluid can change: sensible heat - energy associated with a change in temperature Ĥ = Cp T latent heat - energy required to change the phase of a material Ĥ = Ĥvap for vaporization 1) Ĥ = Ĥfusion or Ĥm for fusion or melting) 2) Ĥ = Ĥs for sublimation 3) heat of reaction - energy associated with change in composition accompanying a chemical reaction H reaction = ν i MW i Cpi T T ref ) i=products j=products ν j MW j Cpj T T ref ) The heat capacity, C p, is an intensive material property that describes the amount of energy required to raise the temperature of a standard mass of material by a certain amount on a temperature scale. 9

10 A calorimeter is an insulated vessel that can be used to measure the amount of thermal energy in a material, the heat capacity of an object, or the energy associated with process e.g. a phase change or chemical reaction). A heat exchanger is a device used to contact two streams, allowing thermal energy to be transmitted from one stream to the other, without the streams mixing. In a heat exchanger the thermal energy always goes from the hot fluid, to the cold fluid. Heat exchangers can be plumbed in either a counter-current or cocurrent configuration. Sizing a heat exchanger means finding the area required to achieve the necessary rate of heat transfer. The heat exchanger design equation is: Q duty = U O A T log mean where U O is the overall heat transfer coefficient, A is the heat exchange area, and T log mean is the log-mean temperature difference between the hot and cold streams. U O accounts for the heat transfer resistance in both the hot and cold streams and the heat transfer resistance across the wall separating the two streams. The T log mean is: T log mean = T 1 T ) 2 T1 log T 2 where T 1 and T 2 are the difference in temperature between the hot and cold streams on either side of the heat exchanger. 10

11 Fluid flow and mechanical energy S&H Ch. 7 and Lab 5) Flowing fluids can convert among different forms of mechanical energy. Important concepts include: The total energy balance can be modified to account only for mechanical energy, by neglecting the thermal energy terms. Typically the mechanical energy balance for a fluid is normalized by the mass flow rate, and written: P 2 P 1 ρ α2 v2,avg 2 α 1 v1,avg 2 ) + g z2 z 1 ) = w s w f where w f accounts for energy lost due to friction in the flowing fluid. Terms in this equation have dimensions of [Energy] / [Mass]. If both the friction and shaft work are neglected, then the equation above is referred to as the Bernoulli equation: P 2 P 1 ρ α2 v2,avg 2 α 1 v1,avg 2 ) + g z2 z 1 ) = 0 The mechanical energy balance or Bernoulli equation can be used to describe the interconversion among different forms of mechanical energy between any two points in a fluid system, whether the fluid is flowing or stagnant. The mechanical energy balance can be used to find the power required for a pump or compressor, or the power obtained from a turbine, as w s ṁ. Mechanical equipment like pumps, compressors, and turbines are usually not 100 % efficient. The pump efficiency is: pump efficiency = power delivered to fluid power consumed by pump The following two pages are the last two pages of your exam. 11

12 Unit conversions Energy 1 kj = Btu 1 Btu = kj Force 1 N = 1 kg m s 2 1 lb f = 32ft lb m /s 2 Length 1 cm = 0.01 m 1 in = cm 1 m = ft 1 ft = m 1 ft = 12 in Mass 1 kg = lb m 1 lb m = kg Power 1 W = Btu/s 1 Btu/s = W 1 W = hp 1 hp = W 1 hp = 550 ft lb f /s Pressure 1 P a = 1 N m 2 1 psi = P a 1 P a = lb f /in 2 Temperature T C) = 5 C 9 F [T F ) 32] T F ) = 9 F 5 C T C) + 32 Time 1 hr = 3600 s Gas constant J gmol 1 K kp a m 3 kgmol 1 K g cm 2 s 2 gmol 1 K 1 12

13 Stefan Boltzmann constant, σ W m 2 K 4 Defined units and useful equations 1 J 1 N m = 1 kg m 2 / s 2 1 lb f 32 ft lb m /s 2 1 N 1 kg m/s 2 1 P a 1 N/m 2 = 1 kg/m s 2 1 W 1 J/s g = 9.8 m/s 2 = 32 ft/s 2 Ṅ A = D A,B A c A x Ṅ A = h m Ac A,s c A, ) Q = ka T x Q = hat s T ) Q = ɛσa Ts 4 Tsur 4 ) [ ṁ Ĥ + 1 ] αv αv1 2 ) + g z2 z 1 )... out [ ṁ Ĥ + 1 ] αv αv1 2 ) + g z2 z 1 ) = Q + Ẇ in P 2 P 1 ρ αv 2 2 αv1 2 ) + g z2 z 1 ) = w s w f 13