BE 4100 Study Guide (Part 1)
BE 4100 Study Guide (Part 1) BE 4100
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This 20 page Study Guide was uploaded by Matthew Wieters on Sunday September 25, 2016. The Study Guide belongs to BE 4100 at Clemson University taught by Dr. Drapcho in Fall 2016. Since its upload, it has received 17 views. For similar materials see Biological Kinetics and Reactor Modeling Laboratory in Biosystem Engineering at Clemson University.
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Date Created: 09/25/16
BE 4100 -- Biological Kinetics and Reactor Modeling -- Exam 1 Study Guide (Thursday, 9/29) Tuesday, September 20, 20166:32 PM • This study guide will include the following ○ Lecture 1-6 (including 6a) review Including examples and lab review ○ Review problems from old tests ○ Equation sheet Lecture + Lab Review Tuesday, September 20, 2016 6:53 PM • This section contains concept reviewsfrom the following lectures/labs: ○ Part 1 Lecture 1 -- Mass balances Lecture 2 -- Chemical kinetics Lecture 3 -- Reversible reaction: Carbonate chemistry Open notes Section (problems) □ Problem 1 solution □ Problem 2 solution □ Problem 3 solution Closed notes Section (problems) □ No solutions yet ○ Part 2 Lab 2 -- Dynamic modeling of batch and continuous flow reactors using analytical and numerical technique calculated with Excel Lab 3 -- Analytical determination of pH, Alkalinity, and Total Inorganic Carbon Lecture 4 Closed notes section □ Problem 1 solution □ Problem 2 solution □ Problem 3 solution ○ Part 3 Lecture 5 Lecture 6a Lecture 6 Open notes section □ Problem 4 solution □ Problem 5 solution □ Problem 6 solution Lecture 1 --Mass balances -- Review Tuesday, September 20, 2016 6:50 PM • Definitions: ○ Mass balance --> a mathematicalrepresentationof a system that accounts for all movementof mass of a particular compound into and out of system and all formationor conversionof a compound within the system ○ Mass movement --> physical movementof mass due to: a) Bulk mass flows --> the movementof mass as a result of pump, conveyor,or fan etc. used to move mass into or out of system 1) Uses energy, not concentration gradient b) Mass transfer --> the movementof mass as a result of concentrationdifferences (i.e. diffusion) ○ Influent flow --> liquid flow entering a continuous flow system ○ Effluent flow --> liquid flow leaving a continuous flow system If there is only on influent and one effluent flow, we can use 'Q' to represent both flow rates: □ Q = liquid (or volumetric)flow rate, volume/time(L/hr, m^3/s) ○ Hydraulic retention time --> the average length of time that liquid remains in a continuous flow system.For a continuous flow system,the hydraulic retention time is calculated as: , where □ t = hydraulic retention time, [hr, min, sec] □ V = system volume,[L, m^3] ○ Dilution rate --> the inverse of the hydraulic retention time in a continuous flow system. Units of dilution rate are inverse time [hr^-1, etc] ○ Steady state --> state of a system when there is no change in the mass (or concentration)of the compound of interest within the system with respect to time. In other words, there is no net increase or decrease of mass within the system. Steady state conditions will occur when the rates of mass movementin/out of system are balanced with the reaction terms, so that there is no net increase or decrease in mass within the system Everything is balanced, no net change Accumulation term --> 0 ○ Transient (non-steady state) conditions --> state of system where there is a change in the mass (or concentration)of the compound of interest within system with respect to time. In other words, there is a net increase or decrease of mass of the compound within system • System types: a) Closed system --> system where there is no mass flow or mass transfer between system and surroundings. Energy may moveacross a closed system'sboundaries b) Open system --> system where there is mass movement(bulk mass flow and/or mass transfer) between system and surroundings c) Batch system --> system that has no bulk mass flows into or out of system;mass transfer between system and surroundings may occur. In batch chemical or biological systems, materials are added to the system at the start of the process, and the reactions proceed with time. Conditions in the reactor change (reactant concentrationsdecreases and product concentrationsincrease) as the reactions proceed (changes over time -- transient) d) Fed-batch system --> variation of batch system where materials are added to the system while process is occurring, but no materials are removeduntil completionof process. As reactions proceed, the substrate concentrationmay be held relativelyconstant but product concentrationswill increase with time concentrationswill increase with time e) Continuous flow system --> system that has a continuous mass flow into and out of system; mass transfer between system and surroundings may also occur. In batch chemical or biological systems,after initial startup of system, conditions in system will be constant (reactant and product concentrationsin the system will not change with time) Main types of continuous flow systems: □ Plug flow --> system where there is not complete mixing, so that concentration gradients develop along the length of the system Will have concentrationgradient □ Completely mixed systems --> in a completelymixed reactor,no gradients of concentrationexist within the reactor. To achieve completelymixed conditions, some type of mechanical stirring or agitation is needed. A continuous flow, completelymixed reactor is called a chemostat,a CSTR (continuous, stirred- tank reactor), or a CFSTR (continuous flow, stirred-tank reactor) Uniform mixture, no concentration gradient • Mass balance types (focusing on one component) ○ Integral mass balance --> represents the amount of a componentthat enters and leaves the system and the amount of the componentthat was formed/convertedwithin the system over a defined time period *Insert picture description here* ○ Differential mass balance --> represents the rate of mass movemententering and leaving the system and rates of reaction that occur in a system *Insert picture description here* We will focus on differential mass balances in this class ○ Critical points to rememberfor constructing a mass balance equation (MBE): 1) A MBE represents an actual system;therefore,it will contain only the terms that are representative of the actual system 2) Each term in the MBE must have the same units. Regardless of whether the MBE is developed on an integral or differential basis, all rates of mass movementand reaction rate terms must be expressed on the same basis. For Differential MBEs, all terms must be expressed on a rate basis (per unit time) 3) Although a mass balance may be developed to account for ALL mass entering and leaving a system,it is often mostuseful to develop a mass balance equation with a focus on ONE compound of interest. In this case, include only those terms relevant to that compound of interest. We will develop MBE with respect to one compound of interest in this class • Procedure to solve mass balances 0) Draw sketch of system 1) Identify the component of interest 2) Identify system or control volume boundary 3) Identify all modes of mass movement (mass flow and mass transfer) of the component entering and leaving system 4) Identify processes or reactions that are occurring within the system which form or destroy the componentand formulate reaction rate expression 5) Identify time frame (or set the time frame of interest) 6) Determinewhether there is a net change in the mass (or concentration)of the compound within the system with respect to time (is the system at steady state?) • Means of expressing terms in a Differential Mass Balance Equation (MBE) ○ Mass-rate basis --> all terms in MBE are expressed in units of mass/time,such as mg/hr or kg/s or mol/hr Accumulation term --> Rate of reaction --> Concentration-rate basis --> all terms in MBE are expressed in units of mass/volume-time; ○ Concentration-rate basis --> all terms in MBE are expressed in units of mass/volume-time; for example mg/L-hr or kg/m^3-s. The concentration-ratebasis is often used for aqueous systems,when the compound of interest is dissolved or suspended in liquid Accumulation term --> Rate of reaction --> We will focus on how to do differential mass balances on this basis Lecture 2 -- Chemical Kinetics -- Review Tuesday, September 20, 2016 6:50 PM • Types of reactions: 1) Chemical --> acid/base; oxidation/reduction 2) Physical --> settling; shearing of cells 3) Biological --> Growth of cells, decay (death) of cells, products formed • Chemical reactions: 1) Reversible reactions --> reaction in which reactant is not totally converted to product, because products that are formed will convert back to the starting reactants, and an equilibrium between the reactants and products is achieved. Both the forward and reverse reactions will proceed simultaneously i. Examples 1) Water 2) Dissolved ammonia in water 2) Irreversible reactions --> reactions where the reactants are converted to products i. Lab: Blue dye --> colorless form of compound 1) A (reactant) --> B (product) • Chemical reaction rate for irreversible reaction ○ Generalized reaction for chemical compound A being converted to compound B is 1) A --> B ○ The reaction rate can be expressed as the rate of removal of reactant (A) or rate of formation of product (B) = rate of removal of reactant A, mass/volume-time = rate of formation of product B, mass/volume-time ○ For a unimolar reaction as shown in Equation 1, 2) ○ As a convention with chemical kinetics, the reaction rate is usually expressed in terms of removal rate of reactant A. Therefore, for an irreversible reaction, the generalized reaction rate expression is: 3) , where □ r = reaction rate, mass/volume-t (example mg/L-hr); □ K = reaction rate constant, units will depend on reaction order; □ A = concentration of A, mass/volume(example mg/L); □ n = reaction order, unitless ○ Many reaction can be described by a reaction order of 0, 1, or 2 If n = 0, then reaction is zero order; If n = 1, then reaction is first order; If n = 2, then reaction is second order ○ Therefore, the reaction rate for a zero, first or second order reaction would be: 4) ,for 0 order reaction (units of k are mg/L-hr); 5) , for 1st order reaction (units of k are ); 6) , for 2nd order reaction (units of k are L/mg-hr) 6) , for 2nd order reaction (units of k are L/mg-hr) ○ Several import points are: 1) The reaction rate constant, k, is a true constant and does not vary with the concentration of the reactant or product □ Does change with temp 2) The reaction rate is constant for a zero order reaction. For a first or second order reaction, the reaction rate will decrease as the concentration of reactant decreases 3) Any of these reaction types (zero, first or second order) can occur in any system (batch, continuous flow or closed). The order of the reaction is independent of the type of system • Experimental procedure for determining reaction order and rate constant for irreversible reaction ○ The reaction order and rate constant can be determined experimentally for many chemical reactions. One method to do this is to set up a batch experiment, measure the concentration of reactant with time, and then analyzing the data to determine the reaction order and reaction rate constant: Mass Balance for a Batch Experiment: 0) 1) A 2) Reactor (beaker) 3) No mass flow in/out (assume mass transfer = 0) 4) Oxidation of blue food coloring a) A --> B b) 5) Length of lab (1.5 hrs) a) Time frame after bleach is added 6) Transient Zero order reaction in batch reactor: First order reaction in batch reactor: Second order reaction in batch reactor • Summary of general procedure for determining reaction order and reaction rate constant in batch reactor: 1) Conduct batch 2) Measure reactant concentration with time 3) Plot (A) vs t --> if linear, n = 0 Ln(A) vs t --> if linear, n = 1 (1/A) vs t --> if linear, n = 2 ○ In all cases, k = slope of regression The important concept to remember is that k, the reaction rate constant, is a constant, and does not change with change in concentration of reactant A or product B, no matter what the reaction order • Using analytical solutions for system analysis and design ○ Once we have determined the reaction order and reaction rate constant for a specific reaction, then we can use that rate expression in a mass balance equation for engineering analysis and design Example of using solution for system analysis: Example of using solution for system analysis: • A batch reactor is used to oxidize the dye from industrial wastewater. If the initial wastewater contains 1,000 mg/L of dye compound, calculate the dye concentration at t = 5 hours if the reactor volume is 50 L, and the reaction can be described as first order with reaction rate constant k = 1.2 MBE 1) Dye 2) Batch system 3) No bulk flow in/out -- assume no mass transfer 4) Oxidation 5) t = 5 hrs 6) Transient MBE □ □ Solution Example of using solution for system design: • A batch reactor is used to oxidize the dye from industrial wastewater. If the initial wastewater contains 1,000 mg/L of dye compound, calculate the time required for the dye concentration to be reduced to 10 mg/L if the reactor volume is 50 L, and the reaction can be described as first order with reaction rate constant k = 1.2 MBE ○ ○ ○ ○ ○ Solving for t, we get t = 3.84 hrs • Irreversible chemical reactions in CSTR ○ Mass balance for a continuous (flow), stirred tank reactor (CSTR): If an irreversible chemical reaction is occurring in a CSTR and there is no mass transfer between the system and surrounds, the general MBE with respect to compound A (reactant) is as shown below for a simple CSTR. In most cases that we will cover, we will assume there is reactant in the influent flow, but no product 1) General MBE for irreversible chemical reaction in CSTR □ Concentration/Differential basis ◊ Where, = initial concentration = flow rate in/out of system = flow rate in/out of system = reaction rate constant t = hydraulic retention time 2) MBE for zero order chemical reaction in CSTR □ □ Steady state solution: ◊ Where, is not changing with time (constant) 3) First order chemical reaction in CSTR □ □ Steady state solution: 4) Second order chemical reaction in CSTR □ □ Steady state solution: • Using analytical solutions for system analysis and design ○ Just as with batch reactors, once the reaction order and reaction rate constant for a specific reaction are determined, then we can use that rate expression in a mass balance equation for a CSTR for engineering analysis and design Example of using solution for system analysis: • A CSTR is used to oxidize the dye from industrial wastewater. If the influent water flow contains 1,000 mg/L of dye compound, calculate the effluent dye concentration at steady state if the volumetric flow rate is 10 L/hr, the reactor volume is 50 L, and the oxidation reaction can be described as first order with reaction rate constant k = 1.2 ○ □ Lecture 3 -- Reversible reaction: Carbonate chemistry -- Review Tuesday, September 20, 2016 6:50 PM Reversible reactions: • Reversible reaction are those where the reaction proceeds in a forward and reverse direction. Equilibrium is established when the rate of forward reaction is equal to the rate of reverse reaction. We will focus on calculating the equilibrium concentrationsof individual compounds ○ For a general reversible reaction: 1) 1) Where = stoichiometricvalue ○ The rate of forward reaction is defined as: 2) ○ The rate of reverse reaction is defined as: 3) 1) Where = reaction constant ○ With reversible reactions, equilibrium is reached after a certain period of time. Equilibrium is defined as the state when the rate of forward reaction is equal to the rate of reverse reaction 4) or ○ Which can be rearranged to: 5) ○ This ratio is defined as the equilibrium constant, , for a given reaction: 6) 1) Where a) [A], [B], [C], [D] represent the molar concentrationsof compounds A, B, C and D at equilibrium, mol/L;and ○ The most commonreversible reaction in aqueous systemsis the hydrolysis of water: 7) ○ The for this reaction is important and is given a special designation as , and is also called the ion product of water 8) ○ Recall that the concentration of in water is essentially constant and is much greater than the concentration of or , so to avoid making the calculation of unnecessarily complex,it is typically given as shown below (applies to water only): 9) ○ The value of is = at 25 degrees C. Therefore,if either or is known, the other concentration can be calculated from Equation 9. Since we can easily measure the pH of a solution, we can calculate the as: Carbonate chemistry • Reactions ○ The dissociation of carbonate compounds in aqueous systemsis an example of a reversible reaction that is important to bioprocessing and ecological applications. The reactions involve a series of reversible reactions, a simplified version of which is shown below 10) Where, □ = carbon dioxide gas □ = carbon dioxide aqueous (dissolved ) □ = carbonic acid □ = bicarbonate □ = carbonate ○ The concentrationof total inorganic carbon concentration is defined as the sum of the inorganic carbon compounds, or: 11) With [ ] designating molar concentrations.Since each compound in Equation 11 contains 1 mol C per mol of compound, you can sum the molar concentrationsof the compound to obtain the total concentrationof inorganic carbon in solution • Carbonate reactions in open systems ○ If the system is open to the atmosphere,Henry's law (equation 12) is used to calculate the equilibrium concentrationof dissolved gas in solution 12) Where, □ = concentrationof dissolved gas A in liquid, M □ = Henry's law constant at given temp for gas A, M/kPaor M/atm □ = partial pressure of gas A in gas phase, kPa or atm ○ Example: Calculate the concentrationof dissolved in a water sample at sea level. If there are no other inputs of inorganic carbon to the system,then Henry's law can be used to determinethe equilibrium concentration of dissolved carbon dioxide in water □ Where ◊ = concentrationof dissolved in liquid, M ◊ = Henry's law constant for , M/kPa or M/atm ◊ = partial pressure of gas in atmosphere, kPa or atm In general, the solubility of gases decreases with increasing temperatureand increasing salinity, and the value of the Henry's constant reflects these changes Step 1: Determinepartial pressure of in atmosphere □ (atmospheric □ (atmospheric concentrationof is 440 ppm or 0.04%) Step 2: Find the Henry's law constant for in water. See handout (from class) □ The value for (page 57 of handout) Step 3: Calculate the equilibrium concentration in water □ Therefore,the equilibrium concentrationof dissolved in freshwater open to atmosphereis: □ Converting to mg/L units: • Carbonic reactions in closed systems ○ If the system is closed to the atmosphere,then no transfer of gas will occur between the atmosphereand the liquid. This situation applies to many systems in reactors,and also to samples collected from lakes, oceans when the measurementof the total inorganic carbon is done in the lab. We will focus on carbonate chemistryfor closed systemsbecause of the complexity of the calculations for open ○ In closed systems, the term is often used to refer to the sum of to simplify the overall reaction modeling. The equilibrium for this reaction lies very far to the left, so very little carbonic acid will be present, with majoritypresent as ○ is the equilibrium constant for the dissociation of carbonic acid and is the equilibrium constant for the dissociation of bicarbonate. The values of and are and , respectively,at 25 degrees C and 1 atm pressure ○ The concentrationof each of the carbon compounds present at equilibrium in a closed aqueous system can be calculated if the pH and alkalinity values are known, through use of the following equations. These equations were obtained through mass balances for a closed system: 13) 14) 15) 16) 17) 18) 19) ○ Where, = hydrogen ion concentration,mol/L = alkalinity, mol equivalence/L = hydroxyl ion concentration, mol/L = total inorganic carbon concentration,mol/L = total inorganic carbon concentration,mol/L ] expressed as mol/L ○ Alkalinity is defined as the sum of base compounds minus the acid compounds 20) Importance of carbonate chemistry to ecological and bioprocessingsystems • Carbonate chemistry is important to both bioprocessing and ecological applications, because biological growth affects the pH of aqueous systems and is in turn affected by that pH change. Organisms that respire and produce will cause a decrease in pH if the solution is not buffered. The pH is often controlled through addition or natural presence of sodium bicarbonate (baking soda - ), calcium carbonate (limestone - ), calcium magnesium carbonate (dolomite - ) or other compounds such as phosphates. Thus, the alkalinity is an important considerationin natural lakes, wastewater treatmentand bioprocessing. If the wastewateror media contains insufficient alkalinity and pH is not controlled, the pH may drop below the normal physiological range, retarding the activity of autotrophic and heterotrophic microorganisms. • Organisms that consume will cause the equilibrium to shift to the left, reducing the concentrationof and raising the pH. Autotrophic organisms use inorganic carbon as their C source. pH values of 10 or 11 in autotrophic algal culture are not uncommon. Chemistry review ○ Molarity (M) defines the number of mol of compound per L; M = mol/L ○ Normality (N) defines the number of mol of equivalent charge (or equivalence) per L; N = equ/L Normality is most often used as concentrationunit for acids and bases ○ Examples Review problems from Old Tests Tuesday, September 20, 2016 6:59 PM • This section will include problems from some old tests ○ Two sub sections: Open notes Closed notes Open Notes Section Tuesday, September 20, 2016 7:00 PM 1. For a 25 mL sample of freshwater from a closed system, the following information was obtained in lab after titration: Initial buret reading: 50.00 mL Initial pH: 9 Final buret reading: 38.00 mL Final pH: 4.5 Normality of acid added: 0.02 equ/L Calculate: a. The alkalinity of the water sample expressed as mol equ/L and mg/L CaCO 3 b. The total inorganic carbon concentration of the original sample 2. You have been asked to prepare a 1 N solution of Ca(OH) . Calcu2ate the mass of Ca(OH) 2 required per liter of water needed to prepare this solution. 3. China recently surpassed the US in terms of annual energy consumption. However, between 1980 to 2000, the US consumed far more energy than China. Provide a rough estimate of the total energy consumption (in EJ) for the US and China between 1980 and 2000. 4. For a sample of freshwater that has a pH of 9.5 and an alkalinity of 5,000 mg/L as CaCO , at 3 25ºC, calculate: a. The total inorganic carbon concentration b. The carbonate concentration 5. You have been asked to prepare a 2 N solution of NaOH. Calculate the mass of NaOH required per liter of water needed to prepare this solution. 6. Calculate the equilibrium concentration of dissolved oxygen (in units of mg/L) in a beaker of water at 25ºC that is open to the atmosphere. Problem 1 solution Tuesday, September 20, 2017:04 PM Problem 2 solution Tuesday, September 20, 2017:10 PM Problem 3 solution Tuesday, September 20, 2017:01 PM Closed Notes Section Tuesday, September 20, 2016 7:00 PM 1. Vegetable oil can be chemically converted to biodiesel (O → BD) in an irreversible chemical reaction. Data from a batch experiment are shown in Figure 1. a. Determine the reaction order and reaction rate constant that best describes this reaction. b. Develop the mass balance equation for a batch reactor that has been set up to carry out this reaction. c. Using forward finite difference, solve the MBE for a batch system to solve for the concentration of oil at 0.2 hours if the oil concentration at time t = 0 is 600 g/L and the time step (▲t) = 0.1 hour. d. Now, develop the MBE and calculate the steady state concentration of oil in a CSTR that has been operated at a retention time of 0.5 hours, with influent oil concentration of 600 g/L. 2. In a few words or symbols, define, explain, or give chemical structure for the following: a. Bicarbonate vs carbonate b. Aerobic vs anoxic conditions c. Autotrophic vs heterotrophic d. Lithotroph vs organotroph e. Oil refinery vs biorefinery f. 1 order reaction rate expression vs 2 order reaction rate expression 3. Use the definition of equilibrium constant for reversible reactions to calculate the molar concentration of carbonate in a freshwater sample if the concentration of bicarbonate is 0.001 M and the pH is 11.25 (closed, 25ºC, 1 atm pressure). 4. Bisphenol A (BPA) is a chemical that leaches from certain plastics. BPA has been identified as an Endocrine Disruptor Compound, a term used to describe a class of compounds that have hormone-mimicking or hormone-blocking activity in humans and other animals. BPA is not excreted in urine in an appreciable amount. a. Data from a batch study of BPA metabolism in humans are shown in Figure 1. i. Determine the reaction order and reaction rate constant that best describes this reaction. ii. Give the mass balance equation for a human who ingests a one-time dose of BPA (for time frame after ingestion). iii. Using forward finite difference, solve the MBE to calculate the concentration of BPA in plasma of a human at 0.2 hours if the BPA concentration at time t=0 is 10 mg/L using a time step (▲t) = 1 hour. b. If a person drinks 8 glasses of water a day for a month from a plastic bottle resulting in an ingestion of 4.8 mg of BPA per day, calculate the steady state concentration of BPA in the person’s plasma, assuming no excretion of BPA in urine and a plasma volume of 6 L.
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