48 CEE 453: Laboratory Research in Environmental Engineering Fall 2006 Reactor Characteristics Introduction Chemical, biological and physical processes in nature and in engineered systems usually take place in what we call "reactors." Reactors are defined by a real or imaginary boundary that physically confines the processes. Lakes, segments of a river, and settling tanks in treatment plants are examples of reactors. Most, but not all, reactors experience continuous flow (in and out). Sequencing batch reactors have a sequence of states including fill, react, and empty. It is important to know the mixing level and residence time in reactors, since they both affect the degree of process reaction that occurs while the fluid (usually water) and its components (often pollutants) pass through the reactor. Chlorine contactor tanks are designed to maximize the contact time between chlorine and pathogens before the water is delivered to consumers. Thus the design objective is to maximize the time that it takes for water to travel from the tank influent to the effluent. Tracer studies can be used to determine the hydraulic characteristics of a reactor such as the disinfection contact tanks at water treatment plants. The results from tracer studies are used to obtain accurate estimates of the effective contact time. In this laboratory students will experiment with different reactor designs with the goal of maximizing the contact time. Reactor Classifications Dispersion Mixing levels give rise to three categories of reactors; completely mixed flow (CMFR), plug flow (PFR) and flow with dispersion (FDR). The plug flow reactor is an idealized extreme not attainable in practice. All real reactors fall under the category of FDR or CMFR. Boundary Conditions The reactor inlet and outlet boundary conditions significantly affect the reactor response to the addition of a pulse of tracer. If dispersion is possible across a boundary, then the boundary is open. An example of a reactor with open boundaries is a section of a river. If a tracer is added to a section of a river it is possible for some of the tracer to move upstream, illustrating that an arbitrary section of a river is an open reactor (Figure 5-1). This is equivalent to letting the reactor be DdReactorDdDd Figure 5-1 Schematic of a reactor with open boundary conditions49 Reactor Characteristics defined as a section of a long reactor. One of the characteristics of open boundaries is that some of the tracer introduced at the reactor inlet can be carried upstream and thus the residence time for a conservative tracer can be greater than the hydraulic residence time! A "closed" reactor is one where the reactor has a diffusion or dispersion coefficient different than those of the entrance or exit (Figure Error! Reference source not found.). Typically exit and entrance diffusion/dispersion are much less than the diffusion/dispersion in the reactor. An example of a reactor with closed boundaries is a tank with small inlet and outlet pipes. Reactor Modeling Reactors can be studied by measuring the effluent concentration after the addition of a spike or pulse of a tracer in the influent or after a step function change in input concentration. The resulting response curves can be non dimensionalized by plotting ()rttr trCCθ∀∀ as a function of tθ where θ is the hydraulic residence time. The term tθ will be defined as *t . The non dimensional response curves from pulse inputs and step inputs are know as E curves and F curves respectively. The E curve is the exit age or residence time distribution curve and the F curve represents the fraction of tracer molecules having an exit age younger than*t. The E and F curves are related by () ()****0tttFEdt=∫ 5.3 The ()*tF curve can either be obtained by integrating ()*tE or by applying a step function change in influent concentration to a reactor and monitoring the effluent concentration. In that case ()*tF is defined as ()*tinCFC= 5.4 The following sections will include typical E and F curves for different reactor types. Completely Mixed Flow Reactor Complete mix flow regimes can be approximated quite closely in practice. In the case of CMF reactors, there is not an analytical solution to the advective dispersion equation Dd entranceDd reactorDdexitReactor Figure 5-2 Schematic of a reactor with closed boundary conditions50 CEE 453: Laboratory Research in Environmental Engineering Fall 2006 so we revert to a simple mass balance. For a completely mixed reactor a mass balance on a conservative tracer yields the following differential equation: ()rindCCCQdt∀=− 5.5 where Q is the volumetric flow rate and r∀ is the volume of the reactor. Equation 5.5 can be used to predict a variety of effluent responses to tracer inputs such as the pulse input used in this experiment. If a volume of tracer is discharged directly into a reactor so that the initial concentration of tracer in the reactor is 0tr trrCC∀=∀and the input concentration is zero (Cin = 0) the solution to the differential equation is: ()()trtttr trCECeθθθ−⎛⎞⎜⎟⎝⎠∀==∀ 5.6 or in the dimensionless form ()()()***rttttr trCECe−∀==∀ 5.7 where ()*tE is the exit age or residence time distribution curve, r∀ is the reactor volume, tr∀ is the tracer volume, and trC is the tracer concentration. If a reactor has a complete mix flow regime its response, ()*tE , to a pulse input should plot as a straight line on a semi-logarithmic plot. Response curves for a CMFR are shown in Figure 5-3) The time for 10% of the pulse to arrive at the effluent of a CMFR is approximately 0.1*t . Plug Flow Reactor Plug flow regimes are impossible to attain because mass transport must be by advection alone. There can be no differential displacement of tracer relative to the average advective velocity. In practice some mixing will occur due to molecular diffusion, turbulent dispersion, and/or fluid shear. For the case of the plug flow reactor the advective dispersion equation 5.11 reduces to: 0.100.00.20.40.60.81.00.0 1.0 2.0 3.0t*E00.20.40.60.81FEFt* at F=0.1 Figure 5-3 Exit age (E) and Cumulative exit age (F) curves for completely mixed flow reactors.51 Reactor Characteristics CCUtx∂∂=−∂∂ 5.9 The velocity, U, serves to transform the directional concentration gradient into a temporal concentration gradient. In other words, a conservative substance moves with the advective flow of the fluid. The solutions to