Preparation of Mass balances Prepare a simplified schematic or flow diagram of the system or process 2. Draw a system or control volume boundary to define the limits. Proper selection of the system or control volume boundary is extremely important because, in many situations, it may be possible to simplify the mass-balance computations 3. List all of the pertinent data and assumptions 4. List all of the rate expressions for the biological or chemical reactions 5. Select a convenient basis It is recommended that the above steps be followed routinely
Preparation of Mass Balances 1. Prepare a simplified schematic or flow diagram of the system or process 2. Draw a system or control volume boundary to define the limits . Proper selection of the system or control volume boundary is extremely important because, in many situations, it may be possible to simplify the mass-balance computations. 3. List all of the pertinent data and assumptions 4. List all of the rate expressions for the biological or chemical reactions 5. Select a convenient basis It is recommended that the above steps be followed routinely
application of the Mass-Balance Analysis To apply a mass-balance analysis to the liquid contents of the reactor shown on Fig. 4-4, it will be assumed that 1. The volumetric flowrate into and out of the control volume Is constant 2. The liquid within the control volume is not subject to evaporation(constant volume) 3. The liquid within the control volume is mixed completely 4. A chemical reaction involving a reactant A is occurring within the reactor 5. The rate of change in the concentration of the reactant A that is occurring within the control volume is governed by a first-order reaction(r=-kC)
Application of the Mass-Balance Analysis To apply a mass-balance analysis to the liquid contents of the reactor shown on Fig. 4-4, it will be assumed that: 1. The volumetric flowrate into and out of the control volume is constant. 2. The liquid within the control volume is not subject to evaporation (constant volume). 3. The liquid within the control volume is mixed completely. 4. A chemical reaction involving a reactant A is occurring within the reactor. 5. The rate of change in the concentration of the reactant A that is occurring within the control volume is governed by a first-order reaction (rc = -kC )
Using the above assumptions, the mass balance can be formulated as follows 1. Simplified word statement 2. Symbolic representation Before attempting to solve any mass-balance expression, a unit check should always be made to assure that units of the individual quantities are consistent
Using the above assumptions, the mass balance can be formulated as follows 1. Simplified word statement 2. Symbolic representation Before attempting to solve any mass-balance expression, a unit check should always be made to assure that units of the individual quantities are consistent
Steady-State Simplification Fortunately, in most applications in the field of wastewater treatment, the solution of mass-balance equations, such as the one given by the equations, can be simplified by noting that the steady-state(i.e, long-term) concentration is of principal concern. If it is assumed that only the steady-state effluent concentration is desired, then above equation can be simplified by noting that, under steady-state conditions, the rate accumulation is zero(dc/dt=0)
Steady-State Simplification Fortunately, in most applications in the field of wastewater treatment, the solution of mass-balance equations, such as the one given by the equations, can be simplified by noting that the steady-state(i.e., long-term) concentration is of principal concern. If it is assumed that only the steady-state effluent concentration is desired, then above equation can be simplified by noting that, under steady-state conditions, the rate accumulation is zero (dC/dt = 0)
4-3 Analysis of Nonideal Flow in Reactors Using Tracers Because of a lack of appreciation for the hydraulics of reactors, many of the treatment plants that have been built do not perform hydraulically as designed
4-3 Analysis of Nonideal Flow in Reactors Using Tracers Because of a lack of appreciation for the hydraulics of reactors, many of the treatment plants that have been built do not perform hydraulically as designed