1. Prepare a simplified schematic or flow diagram of the system or process for which the mass balance is to be prepared a system or control volume boundary to defi its over which mass balance is to be applied. Proper selection of the system or control volume boundary is extremely important because, in List all of the pertinent data and assumptions that will be used in the preparation of the materials balance on the schematic or flow diagram 4. List all of the rate expressions for the biological or chemical reactions that occur within the control volume 5. Select a convenient basis on which the numerical calculations will be based It is recommended that the above steps be fol slowed routinely. to avoid the errors that are often made in the preparation of mass-balance analyses Application of the Mass-Balance Analysis To illustrate the application of the mass-balance analysis, consider the complete-mix reactor shown on Fig 4-4. First, the control volume boundary must be established so that all the flows of mass into and out of the system can be identified. On Fig 4-4a, the control volume boundary is shown by the inner dashed line To apply a mass-balance analysis to the liquid contents of the reactor shown on Fig 4-4. it will be volumetric flowrate into and out of the control volume is constant 2. The liquid within the control volume is not subiect to evaporation(constant volume The liquid within the control volume is mixed completely. 4.A chemical reaction i a reactant a is occurring within the reacte The rate of change in the concentration of the reactant a that is occurring within the control volume is overned by a first-order reaction(rc=-KC). Using the above assumptions, the mass balance can be formulated as follows 1. Simplified word statement cumulation=回no-國uno+ generation 2. Symbolic representation(refer to Fig. 4-4) y=C-C+ry Substituting-kC for r'eyields =C0-C+(-kC where dC/dt=rate of change of reactant concentration within the control volume, MLT 0=volumetric flowrate into and out of control volume L'T-l Co=concentration of mactunt entering the control volume ML-3 C=concentration of reactant leaving the control volume ML-3 first-order reaction, k=first-order reaction rate coefficient, T-I 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. If the following units are substituted into the above. dC/dt=g/m's / Co, C=g/m the resulting unit check yie dt =wo-aC+(kC) (g/n.s)m'=m /s(g/m)-m(g/m)+(-1/s)(8/m)m4-5 1. Prepare a simplified schematic or flow diagram of the system or process for which the mass balance is to be prepared. 2. Draw a system or control volume boundary to define the limits over which mass balance is to be applied. 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 that will be used in the preparation of the materials balance on the schematic or flow diagram. 4. List all of the rate expressions for the biological or chemical reactions that occur within the control volume. 5. Select a convenient basis on which the numerical calculations will be based. It is recommended that the above steps be followed routinely, to avoid the errors that are often made in the preparation of mass-balance analyses. Application of the Mass-Balance Analysis To illustrate the application of the mass-balance analysis, consider the complete-mix reactor shown on Fig. 4-4. First, the control volume boundary must be established so that all the flows of mass into and out of the system can be identified. On Fig. 4-4a, the control volume boundary is shown by the inner dashed line. 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: Accumulation ＝ inflow － outflow ＋ generation 2. Symbolic representation (refer to Fig. 4-4): c dC V QC QC rV dt = − + 0 Substituting -kC for rc yields 0 ( ) dC V QC QC kC V dt = − + − where dC/dt = rate of change of reactant concentration within the control volume, ML-3T -1 V = volume contained within control volume, L3 Q = volumetric flowrate into and out of control volume, L3T -1 Co = concentration of mactunt entering the control volume, ML-3 C = concentration of reactant leaving the control volume. ML-3 rc = first-order reaction, (-kC). ML-3T -1 k = first-order reaction rate coefficient, T-1 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. If the following units are substituted into the above equations: V=m3 dC/dt = g/m3·s Q = m3 /s Co, C = g/m3 k = 1/s the resulting unit check yields 0 ( ) dC V QC QC kC V dt = − + − (g/m3·s)m3=m3 /s(g/m3 )-m 3 (g/m3 )+(-1/s)(g/m3 )m3