Nonideal Flow in Complete-Mix and Plug-Flow Reactors. In practice the flow in complete-mix and olug- flow reactors is seldom ideal. For example, when a reactor is designed, how is the flow to be introduced to satisfy the theoretical requirement of instantaneous and complete dispersion? In practice, there is al ways some deviation from ideal conditions, and it is the precautions taken to minimize these effects that are important Nonideal flow occurs when a portion of the flow that enters the reactor during a given time period arrives at the outlet before the bulk of the flow that entered the reactor during the same time period arrives. Nonideal flow is illustrated on Fig 4-3a and 4-3b. The important issue with nonideal flow is that a portion of the flow will not remain in the reactor as long as may be required for a biological or chemical reaction to go to completion 4-2 Mass-balance Analysis The fundamental approach used to study the hydraulic flow characteristics of reactors and to delineate the changes that take place when a reaction is occurring in a reactor(eg, a container), or in some definable portion of a body of liquid, is the mass-balance analysis Inflow Outflow Q C ystem boundary amass balance Fig 4-4 Definition sketch for the balanc jsis for nix reactor with o are mixed completely The ph pical commplefe-mix actinated shudge reactor used for the biological treatment of wastewater The Mass-Balance Principle form of the mass can be altered (e. g. liquid to a gas). The mass-balance analysis affords a convenient way of defining what occurs within treatment reactors as a function of time. To illustrate the basic concepts involved in the preparation of a mass-balance analysis, consider the reactor shown on Fig 4-4. The system boundary is drawn to identify all of the liquid and constituent flows into and out of the system. The control volume is used to identify the actual volume in which change is occurring In most cases, the system and control volume boundaries will coincide. For a given reactant. the general mass-balance analysis is given by 1. General word statement Rate of accumulation Rate of flow of of reactant within reactant out of the tant within the e system boundary ystem boundary ystem boundary 2. The corresponding simplified word statement is Accumulation= inflow- outflow t generation (4) The mass balance is made up of the four terms cited above. Depending on the flow regime or treatment process, one or more of the terms can be equal to zero. For example, in a batch reactor in which there is no inflow or outflow the second and third terms will be equal to zero. A positive sign is used for the ecause the necessary (e.g. re=-kC for a decrease in the reactant or r.=+ kc for all increase in the reactant). Preparation of Mass Balances In preparing mass balances it is helpful if the following steps are followed, especially as the techniques involved are being mastered4-4 Nonideal Flow in Complete-Mix and Plug-Flow Reactors. In practice the flow in complete-mix and plug-flow reactors is seldom ideal. For example, when a reactor is designed, how is the flow to be introduced to satisfy the theoretical requirement of instantaneous and complete dispersion? In practice, there is always some deviation from ideal conditions, and it is the precautions taken to minimize these effects that are important. Nonideal flow occurs when a portion of the flow that enters the reactor during a given time period arrives at the outlet before the bulk of the flow that entered the reactor during the same time period arrives. Nonideal flow is illustrated on Fig.4-3a and 4-3b. The important issue with nonideal flow is that a portion of the flow will not remain in the reactor as long as may be required for a biological or chemical reaction to go to completion. 4-2 Mass-balance Analysis The fundamental approach used to study the hydraulic flow characteristics of reactors and to delineate the changes that take place when a reaction is occurring in a reactor (e.g., a container), or in some definable portion of a body of liquid, is the mass-balance analysis. Fig. 4-4 Definition sketch for the application of materials mass-balance analysis for a complete-mix reactor with inflow and outflow. The presence of a mixer is used to represent symbolically the fact the contents of the reactor are mixed completely. The photo is of a typical complete-mix activated sludge reactor used for the biological treatment of wastewater. The Mass-Balance Principle The mass-balance analysis is based on the principle that mass is neither created nor destroyed, but the form of the mass can be altered (e.g., liquid to a gas). The mass-balance analysis affords a convenient way of defining what occurs within treatment reactors as a function of time. To illustrate the basic concepts involved in the preparation of a mass-balance analysis, consider the reactor shown on Fig. 4-4. The system boundary is drawn to identify all of the liquid and constituent flows into and out of the system. The control volume is used to identify the actual volume in which change is occurring. In most cases, the system and control volume boundaries will coincide. For a given reactant, the general mass-balance analysis is given by 1. General word statement: ＝ － ＋ 2. The corresponding simplified word statement is Accumulation ＝ inflow － outflow ＋ generation (1) (2) (3) (4) The mass balance is made up of the four terms cited above. Depending on the flow regime or treatment process, one or more of the terms can be equal to zero. For example, in a batch reactor in which there is no inflow or outflow the second and third terms will be equal to zero. A positive sign is used for the rate-of-generation term because the necessary sign for the operative process is past of the rate expression (e.g., rc = -kC for a decrease in the reactant or rc = + kC for all increase in the reactant). Preparation of Mass Balances In preparing mass balances it is helpful if the following steps are followed, especially as the techniques involved are being mastered. Rate of accumulation of reactant within the system boundary (1) Rate of flow of reactant into the system boundary (2) Rate of flow of reactant out of the system boundary (3) Rate of generation of reactant within the system boundary (4)