g/s=g/s-g/s-g/s(units are consistent) The analytical procedures that are adopted for the solution of mass-balance equations usually are governed by(1)the nature of the rate expression, (2)the type of reactor under consideration, (3)the mathematical form of the final materials-balance expression (i.e, ordinary or partial differential equation), and(4)the corresponding boundary conditions Steady-State Simplificati Fortunately in most applications in the field of wastewater treatment. the solution of mass-balar that the steady-statelie. ong-term) concentration is of principal concern. If it is ass concentration is desired, then above equation can be simplified by noting that, under steady-state conditions. the rate accumulation is zero(dC/di=0). Thus, the equatin can be written as When solved for rc, the equation yields the following expression Q The solution to the expression given by the equation will depend on the nature of the rate expression(e.g 4-3 Analysis of Nonideal Flow in Reactors Using Tracers The discussion of nonideal flow in this section will serve as an introduction to the modeling of nonideal flow considered in the following section. Attention is called to this subject because often it is neglected o not considered properly. 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. Factors Leading to nonideal flow in reactors As noted previously, nonideal flow is often defined as short circuiting that 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. Factors leading to nonideal flow in reactors include ature differences. In flow reactors. nonideal flow( short circuiting) can rents due to temperature differenc or warmer than the water in the tank a portion of the water can travel to the outlet along the bottom of across the top of the reactor without mixing completely(see Fig 4-5a). 2. Wind-driven circulation patterns. In shallow reactors. wind-circulation patterns can be set on of the incoming water to the outlet in a ion of the actual detention time(see Fig 4-5 3. Inadequate mixing. Without sufficient energy input, portions of the reactor contents may not mix with the incoming water(see Fig. 4-5c). 4 Poor d the design of the inlet and outlet of the reactor relative to the reactor aspect ratio, dead zones may develop within the reactor that will not mix with the incoming water(see Fi 5. Axial dispersion in plug-flow reactors. In plug-flow reactors the forward movement of the tracer is due to advection and dispersion. Advection is the term used to describe the movement of dissolved or colloidal material with the current velocity. Dispersion is the term used to describe the axial and longitudinal transport of material brought about by velocity differences, turbulent eddies. and molecular diffusion. The distinction between molecular diffusion, turbulent diffusion, and dispersion is considered in the notion e subsequent discussion dealing with"Modeling Nonideal Flow In Reactors. "In a tubular plug-flow reactor(.g, a pipeline), the early arrival of the tracer at the outlet can be reasoned partially by remembering that the velocity distribution in the pipeline will be parabolic 八人 Ultimately, the inefficient use of the reactor
4-6 g/s=g/s-g/s-g/s(units are consistent) The analytical procedures that are adopted for the solution of mass-balance equations usually are governed by (1) the nature of the rate expression, (2) the type of reactor under consideration, (3) the mathematical form of the final materials-balance expression (i.e., ordinary or partial differential equation), and (4) the corresponding boundary conditions. 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). Thus, the equatin can be written as c dC V QC QC rV dt = − + 0 When solved for rc, the equation yields the following expression: 0 ( ) c Q r C C V = − The solution to the expression given by the equation will depend on the nature of the rate expression (e.g., zero-, first-, or second-order). 4-3 Analysis of Nonideal Flow in Reactors Using Tracers The discussion of nonideal flow in this section will serve as an introduction to the modeling of nonideal flow considered in the following section. Attention is called to this subject because often it is neglected or not considered properly. 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. Factors Leading to Nonideal Flow in Reactors As noted previously, nonideal flow is often defined as short circuiting that 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. Factors leading to nonideal flow in reactors include: 1. Temperature differences. In complete-mix and plug-flow reactors, nonideal flow (short circuiting) can be caused by density currents due to temperature differences. When the water entering the reactor is colder or warmer than the water in the tank, a portion of the water can travel to the outlet along the bottom of or across the top of the reactor without mixing completely (see Fig. 4-5a). 2. Wind-driven circulation patterns. In shallow reactors, wind-circulation patterns can be set up that will transport a portion of the incoming water to the outlet in a fraction of the actual detention time (see Fig. 4-5b). 3. Inadequate mixing. Without sufficient energy input, portions of the reactor contents may not mix with the incoming water (see Fig. 4-5c). 4. Poor design. Depending on the design of the inlet and outlet of the reactor relative to the reactor aspect ratio, dead zones may develop within the reactor that will not mix with the incoming water (see Fig. 4-5d). 5. Axial dispersion in plug-flow reactors. In plug-flow reactors the forward movement of the tracer is due to advection and dispersion. Advection is the term used to describe the movement of dissolved or colloidal material with the current velocity. Dispersion is the term used to describe the axial and longitudinal transport of material brought about by velocity differences, turbulent eddies, and molecular diffusion. The distinction between molecular diffusion, turbulent diffusion, and dispersion is considered in the subsequent discussion dealing with"Modeling Nonideal Flow In Reactors." In a tubular plug-flow reactor (e.g., a pipeline), the early arrival of the tracer at the outlet can be reasoned partially by remembering that the velocity distribution in the pipeline will be parabolic. Ultimately, the inefficient use of the reactor
volume due to short circuiting resulting from temperature differences. the presence of dead zones resulting from poor design. inadequate mixing, and dispersion(see Fig 4-6) can result in reduced treatment rformance. Morrill examined the effects of short circuiting on the performance of sedimentation tanks Fig 4-5 Definition sketch for short circuiting caused by(a) density currents caused by temperature differences;(b)wind circulation patterns;(c)inadequate mixing;( fluid advection(via)and dispersion Need for Tracer Analysis One of the more important practical considerations involved in reactor design is how to achieve the ideal conditions postulated in the analysis of their performance. The use of dves and tracers for measuring the residence time distribution curves is one of the simplest and most successful methods now used to assess ce of full-scal tors.(2)the contact time in chlorine contact basins. 3) the assessment of the hydraulic approach co lIons Ir reactors and (4)the assessment of flow patterns in constructed wetlands and other natural treatment svstems. Tracer studies are also of critical importance in assessing the degree of success that has been d with corrective measures Types of Tracers Over the vears. a number of tracers have been used to evaluate the hydraulic performance of reactors. Important characteristics for a tracer include: The tracer should not affect the flow (should have essentially the same densi when v The tracer must be conservative so that a mass balance can be performed. It must be possible to inject the tracer over a short time period The tracer should be able to be analyzed conveniently on or react with the exposed reactor surfac v The tracer should not be absorbed on or react with the particles in wastewater. Dves and chemicals that have been used successfully in tracer studies include congo-red fluorescein fluorosilicic acid(H2SiF6), hexafluoride gas( SF6). lithium chloride( LiCD. Pontacyl Brilliant Pink B. tassium, potassium p anate, rhodamine WT, and sodium chloride( NaCD). Pontacvl Brilliant Pink B(the acid form of rhodamine WD) is especially useful in the conduct of dispersion not readily adsorbed onto surfaces. Because fluorescein. rhodamine WT and Pontacyl Brilliant Pink B can be detected at very low concentrations using a fluorometer, they are the dye tracers used most common in the evaluation of wastewater-treatment facilities lithium chloride is commonly used for the study of dium chloride. used commonly in the past. has a tendency to form density currents less mixed Hexafluoride gas(SF6) is used most commonly for tracing the movement of groundwater Conduct of Tracer Tests In tracer studies, typically a tracer(i.e, a dye, most commonly) is introduced into the influent end of the Tracer response reactor or basin to be studied. The time of its arrival at the effluent end is determined by collecting a series of grab samples for a given Mixer to period of time or by measuring the arrival of a Uy banks tracer using instrumental methods(see Fig. 4-6) FLuent weir The method used to introduce the tracer will control the type of response observed at the downstream end. Two types of dye input are used, the choice depending on the influent and effluent configurat Stacked plan view of Fig 4 tic of setup used to cont of tracer using positive curve for continuous nput tracer studies of plug-flow reactor (a)slug of tracers added to flow; (b)continuous input of tracer added to flow. Tracer response curve is measured continuousl The first method involves the injection of a quantity of dye(sometimes referred to as a pulse or slug of dye)over a short period of time. Initial mixing is usually accomplished with a static mixer or an auxiliary mixer. With the slug injection method it is important to keep the initial mixing time short relative to the 4-7
4-7 volume due to short circuiting resulting from temperature differences, the presence of dead zones resulting from poor design, inadequate mixing, and dispersion (see Fig. 4-6) can result in reduced treatment performance. Morrill examined the effects of short circuiting on the performance of sedimentation tanks. Fig. 4-5 Definition sketch for short circuiting caused by (a)density currents caused by temperature differences; (b)wind circulation patterns; (c)inadequate mixing; (d)fluid advection(平流) and dispersion Need for Tracer Analysis One of the more important practical considerations involved in reactor design is how to achieve the ideal conditions postulated in the analysis of their performance. The use of dyes and tracers for measuring the residence time distribution curves is one of the simplest and most successful methods now used to assess the hydraulic performance of full-scale reactors. Important applications of tracer studies include (1) the assessment of short circuiting in sedimentation tanks and biological reactors, (2) the assessment of the contact time in chlorine contact basins, (3) the assessment of the hydraulic approach conditions in UV reactors, and (4) the assessment of flow patterns in constructed wetlands and other natural treatment systems. Tracer studies are also of critical importance in assessing the degree of success that has been achieved with corrective measures. Types of Tracers Over the years, a number of tracers have been used to evaluate the hydraulic performance of reactors. Important characteristics for a tracer include : ✓ The tracer should not affect the flow (should have essentially the same density as water when diluted). ✓ The tracer must be conservative so that a mass balance can be performed. ✓ It must be possible to inject the tracer over a short time period. ✓ The tracer should be able to be analyzed conveniently. ✓ The molecular diffusivity of the tracer should be low. ✓ The tracer should not be absorbed on or react with the exposed reactor surfaces. ✓ The tracer should not be absorbed on or react with the particles in wastewater. Dyes and chemicals that have been used successfully in tracer studies include congo-red, fluorescein, fluorosilicic acid (H2SiF6), hexafluoride gas (SF6), lithium chloride (LiCl), Pontacyl Brilliant Pink B, potassium, potassium permanganate, rhodamine WT, and sodium chloride (NaCl). Pontacyl Brilliant Pink B (the acid form of rhodamine WT) is especially useful in the conduct of dispersion studies because it is not readily adsorbed onto surfaces. Because fluorescein, rhodamine WT, and Pontacyl Brilliant Pink B can be detected at very low concentrations using a fluorometer , they are the dye tracers used most commonly in the evaluation of wastewater-treatment facilities. Lithium chloride is commonly used for the study of natural systems. Sodium chloride, used commonly in the past, has a tendency to form density currents unless mixed. Hexafluoride gas (SF6) is used most commonly for tracing the movement of groundwater. Conduct of Tracer Tests In tracer studies, typically a tracer (i.e., a dye, most commonly) is introduced into the influent end of the reactor or basin to be studied. The time of its arrival at the effluent end is determined by collecting a series of grab samples for a given period of time or by measuring the arrival of a tracer using instrumental methods (see Fig. 4-6). The method used to introduce the tracer will control the type of response observed at the downstream end. Two types of dye input are used, the choice depending on the influent and effluent configurations. Fig 4-6 Schematic of setup used to control tracer studies of plug-flow reactors (a)slug of tracers added to flow; (b)continuous input of tracer added to flow. Tracer response curve is measured continuously. The first method involves the injection of a quantity of dye (sometimes referred to as a pulse or slug of dye) over a short period of time. Initial mixing is usually accomplished with a static mixer or an auxiliary mixer. With the slug injection method it is important to keep the initial mixing time short relative to the