Module 1: CHAPTER FOUR PHYSICAL PROCESSES Objectives: To know physical processes that are important in the movement of pollutants through the environment and processes used to control and treat pollutant emissions. 3 Major Sections: Mass Balances Energy Balances Mass Transport Processes MASS BALANCES Law of Conservation of Mass states that mass can neither be produced nor destroyed. General Equation: Mass Accumulation Rate Mass Flux Mass Flux = in out + Net Rate of Chemical Production a. Basics: be able to write the mass balance on a control volume: dm m m m in out reaction *Mass Accumulation Rate dm = rate of change of mass within the control volume Control Volume = boundaries across m in and m out Mass Flux = the rate at which mass enters / leaves a system *Mass Flux in (m in ) m in = Q in x C in where: Q in = volumetric flowrate of input stream entering the control volume, m 3 /s C in = concentration, mg/l If Q, volumetric flowrate is UNKNOWN Q = v x A where: v = velocity, m/s A = cross sectional area, m 2 1
*Mass Flux out (m out ) m out = Q out x C out where: Q in = volumetric flowrate of input stream entering the control volume, m 3 /s C out = concentration, mg/l @ well mixed control volume: C out = C m out = Q out x C where: C = concentration in the control volume *Net Rate of Chemical Reaction (m rxn ) or Mass Flux Due to Reaction m rxn = V rxn only where: V = control volume = rate of change in concentration that would occur if the reaction rxn only took place in isolation, with no influent/effluent flows Obtained from the rate law for the reaction Mass Flux Due to Reaction (m rxn ) may take various forms: Conservative Compound compounds with no chemical formation or loss within the control volume. rxn only = 0 m rxn = V = 0 rxn only Zero-order decay the rate of loss of the compound is constant. rxn only = -k m rxn = V = -Vk rxn only First-order decay the rate of loss of the compound is directly proportional to its concentration. rxn only = -kc m rxn = V = -VkC rxn only Production @ a rate dependent on the concentration of the other compounds in the CMFR in this situation, the chemical is produced by reactions involving other compounds in the CMFR. rxn only 0 2
Steps in Mass Balance Problems 1. Draw schematic diagram of the situation, and identify the control volume and all influent and effluent flows. 2. Write the mass balance equation in general form. dm m m m in out reaction 3. Determine whether the problem is steady state ( dm / = 0) or non-steady state ( dm / = V / rxn only) 4. Determine whether the compound being balanced is conservative (m rxn =0) or non-conservative (m rxn = V / rxn only). 5. Replace m in and m out with known or required values. 6. Finally, solve the problem. a. If in steady state problem, solve in algebraic in algebraic equation. b. If in non-steady state problem, solve in differential equation. *Retention Time and Other Expressions for V / Q. Retention time Dentention time Residence time Retention time, 0 V 0 = Q refer to the average period spent in a given control volume Where: V = volume of the reactor, m 3 Q = total volume volumetric flowrate exiting the reactor,m 3 /s 0 = retention time, s REACTOR ANALYSIS Reactor Analysis refers to the use of mass balances to analyze pollutant concentrations in a control volume that is either a chemical reactor or a natural system modeled as a chemical reactor. *Ideal Reactors Completely Mixed Flow Reactors (CMFR) Plug Flow Reactors (PFR) Batch Reactor Semi-batch Reactor 2 most common types CMFR/CSTR used to model well mixed environmental reservoir, eg. dam PFR used to model the chemical transformation of compounds as they transport in system resembling pipe. - Behave like pipes and are used to model situations such as downstream transport in a river in which fluid is not mixed in the upstream-downstream direction. Batch Reactor all component mixed up in a reactor that has no inlet or outlet flows. Semi-batch Reactor one component is gradually entering a batch reactor. 3
Mass Balances around Reactor CSTR Batch Reactor PFR Semi-batch Reactor C A 4
Sample Problem [4-1] A pond is used to treat a dilute municipal wastewater before the liquid is discharged into a river. The inflow to the pond has a flow rate of Q = 4,000 m 3 /day and a BOD concentration of C in = 25 mg/l. The volume of the pond is 20,000 m 3. The purpose of the pond is to allow time for the decay of BOD to occur before discharge into the environment. BOD decays in the pond with a first-order rate constant equal to 0.25/day. What is the BOD concentration at the outflow of the pond, in units of mg/l? 5
Sample Problem [4-8] In the winter, a stream flows at 10 m 3 /s and receives discharge from a pipe that contains road runoff. The pipe has a flow of 5 m 3 /s. The stream's chloride concentration just upstream of the pipe's discharge is 12 mg/l, and the runoff pipe's discharge has a chloride concentration of 40 mg/l. Chloride is a conservative substance. (a) Does wintertime salt usage on the road elevate the downstream chloride concentration above 20 mg/l? (b) What is the maximum daily mass of chloride (metric tons/day) that can be discharged through the road runoff pipe without exceeding the water quality standard? 6
Sample Problem [4-5] In the simplified depiction of an ice rink with an ice resurfacing machine operating (shown in Figure 4-19), points 1 and 3 represent the ventilation air intake and exhaust for the entire ice rink, and point 2 is the resurfacing machine's exhaust. Conditions at each point are (C indicates the concentration of carbon monoxide, CO): point 1: Q 1 =3.0 m 3 /s, C 1 =10 mg/m 3 ; point 2: emission rate = 8 mg/s of nonreactive CO; point 3: Q 3, C 3 unknown. The ice rink volume (V) is 5.0 x 10 4 m 3. (a) Define a control volume as the interior of the ice rink. What is the mass flux of CO into the control volume, in units of mg/s? (b) Assume that the resurfacing machine has been operating for a very long time, and that the air within the ice rink is well mixed. What is the concentration of CO within the ice rink, in units of mg/m 3? 7
Sample Problem [4-10] The total flow at a wastewater-treatment plant is 600 m 3 /day. Two biological aeration basins are used to remove BOD from the wastewater and are operated in parallel. They each have a volume of 25,000 L. In hours, what is the aeration period of each tank in hours? 8
Sample Problem [4-11] You are designing a reactor that uses chlorine in a PFR or CMFR to destroy pathogens in water. A minimum contact time of 30 min is required to reduce the pathogen concentration from 100 pathogens/l to below 1 pathogen/l through a first-order decay process. You plan on treating water at a rate of 1,000 gal/min. (a) What is the first-order decay rate constant? (b) What is the minimal size (in gallons) of the reactor required for a plug flow reactor? (c) What size (in gallons) of CMFR would be required to reach the same outlet concentration? (d) Which type of reactor would you select if your treatment objective stated that "no discharge can ever be greater than 1 pathogen/l? Explain your reasoning. (e) If the desired chlorine residual in the treated water after it leaves the reactor is 0.20 mg/l and the chlorine demand used during treatment is 0.15 mg/l, what must be the daily mass of chlorine added to the reactor (in grams)? 9
KINETICS Rate Law expresses the dependence of the reaction rate on measureable, environmental parameters; also, on the concentration of the reactants. a[a] + b[b] c[p] Rate of Reaction R = k [A] a [B] b Where: [A], [B] = reactant A,B a,b = mole of A,B order of A, B Over-all order of rxn = (a+b) Elementary Reaction - the reaction order is controlled by the stoichiometry of reaction. In reality, order of reaction is determined experimentally! Order Rate Law Integration Rate Law Half Life (t 1/2 ) 0 r = k [A] = -kt + [A] o [A] o / 2k 1 r = k [A] [A] = -kt + ln [A] o ln [A] / k 2 r = k [A] 2 1 / [A] = kt + 1 / [A]o 1 / k[a]o Plot [A] vs. t ln[a] vs. t 1 / [A] vs. t 10