3r-reac_absorp - Reactions and Separations Modeling Eugeny...

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Unformatted text preview: Reactions and Separations Modeling Eugeny Kenig Univ. of Paderborn Panos Seferlis Aristotle Univ. of Thessaloniki R Effective modeling of reactive absorption enhances system design, improves experiment planning for parameter estimation, and facilitates process operation and control decisions. eactive absorption — i.e., the absorption of gases in liquid solutions accompanied by chemical reactions — is an important industrial operation for the production of basic chemicals (e.g., sulfuric or nitric acid) and for the removal of harmful substances (e.g., H2S) from gas streams. In recent decades, this process has become especially important for the purification of gases to high purities. Unlike physical absorption (without reactions), reactive absorption is able to provide high throughput at moderate partial pressures and without requiring large amounts of solvent. The advantages of combining chemical reactions with absorption are realized only in the region of low gas-phase concentrations due to the liquid-load limitations imposed by the reaction stoichiometry or equilibrium. Other factors that may limit the efficiency of reactive absorption are the heat liberated by exothermal reactions and the difficulty of solvent regeneration. Most reactive absorption processes are steady-state operations involving reactions in the liquid phase, although some applications involve both liquidphase and gas-phase reactions. Reactive absorption is a complex rate-controlled process that occurs far from thermodynamic equilibrium. Therefore, the equilibrium concept is often insufficient to describe it, and instead, accurate and reliable models involving the process kinetics (rate-based models) are required. The effectiveness of online model-based applications, such as process control and optimization, depends strongly on the quality of the available model predictions. Equilibrium stage model Modeling and design of reactive absorption processes are usually based on the equilibrium stage model, which assumes that each gas stream leaving a tray or a packing segment (stage) is in thermodynamic equilibrium with the corresponding liquid stream leaving the same tray or segment. For reactive absorption, the chemical reaction must also be taken into account. With very fast reactions, the reactive separation process can be satisfactorily described assuming reaction equilibrium. A proper modeling approach is based on the nonreactive equilibrium stage model, which is extended by simultaneously considering the chemical equilibrium relationship and the tray or stage efficiency. If the reaction rate is slower than the mass-transfer rate, the influence of the reaction kinetics increases and becomes a dominating factor. This tendency is taken into account by integrating the reaction kinetics into the mass and energy balances. This approach is widely used today. In real reactive absorption processes, thermodynamic equilibrium is seldom reached. Therefore, correlation parameters such as tray efficiencies or height equivalent to a theoretical stage (HETS) values are introduced to adjust the equilibrium-based theoretical description to real column conditions. However, reactive absorption occurs in multicomponent mixtures, for which this simplified concept often fails (1). The acceleration of mass transfer due to chemical reacCEP January 2009 www.aiche.org/cep 65 Reactions and Separations Two-Film Model Stage 1 A similar equation can be written for the gas phase. Thus, the gas-liquid mass transfer is modeled as a yiI yiB combination of the film model Stage S I B presentation and the Maxwellxi xi Stefan diffusion description. In this Liquid Phase Gas Phase stage model, equilibrium is δy δx Stage N assumed at the interface only. The film thickness represents a Packed Tray Column Column model parameter that can be estimated using the mass-transfer ■ Figure 1. The column discretization and the two-film model for the stage description. coefficient correlations governing the mass transport dependence on physical properties and process hydrodynamics. These tions in the interfacial region is often accounted for via socorrelations are usually obtained experimentally and are called enhancement factors (2, 3). These are either obtained available from the literature. Another important parameter by fitting experimental results or derived theoretically of the film model is the specific contact (interfacial) area, based on simplified model assumptions. However, it is not which is also estimated from experimental data. possible to derive the enhancement factors properly from Balance equations. The component mass-balance equadata on binary experiments, and a theoretical description of tions of the rate-based models are written separately for reversible, parallel or consecutive reactions is based on each phase, and, due to the presence of chemical reactions, rough simplifications. include the reaction source terms (6). Considering the process dynamics, these equations become: Rate-based stage model B A more physically consistent way to describe a column ∂mLi ∂ B B =− LxiB + N Li a I + rLi φ L Ac i = 1 … n (2) stage is the rate-based approach (4). This approach directly ∂t ∂l considers actual rates of multicomponent mass and heat B transfer and chemical reactions. ∂mGi ∂ B B = GyiB − N Gi a I − rGi φG Ac i = 1 … n (3) Mass transfer at the gas-liquid interface can be described ∂t ∂l using different theoretical concepts (1, 5). Usually, the twoEquations 2 and 3 are valid for continuous systems film model or the penetration/surface-renewal model are (packed columns). For discrete systems (tray columns), used, and the model parameters are estimated via empirical the differential terms on the right-hand side become finite correlations. The advantage of the two-film model is that differences and the balances are reduced to ordinary difthere is a broad spectrum of correlations available in the litferential equations (5). erature for all types of column internals. If chemical reactions take place in the liquid phase only In the two-film model (Figure 1), it is assumed that the (which is true for most reactive absorption processes), the resistance to mass transfer is concentrated entirely in thin reaction term in Eq. 3 is omitted. films adjacent to the phase interface, and that mass transfer Equations 2 and 3 are supplemented by the summation occurs within these films by steady-state molecular diffuequation for the liquid and gas bulk mole fractions: sion alone. Outside the films, in the fluid bulk phases, the n n level of mixing is assumed to be sufficiently high so that (4) ∑ xiB = 1 ∑ yiB = 1 there is no composition gradient — i.e., one-dimensional i =1 i =1 diffusion transport normal to the interface takes place. The volumetric liquid hold-up, φL, depends on the gas Multicomponent diffusion in the films can be described by the Maxwell-Stefan equations that relate components’ and liquid flowrates in the column and is calculated by diffusion fluxes to their chemical potential gradients. In a empirical correlations. To determine axial temperature progeneralized form, the Maxwell-Stefan equations can be files, differential energy balances that include the product used for the description of real gases and liquids (1). For of the liquid molar hold-up and the specific enthalpy as the liquid phase: energy capacity are formulated. The energy balances for n xN −x N continuous systems are: xi d μi i Lj j Li i =1 … n di = =∑ (1) B ∂U L ∂ B B loss RT dz cLt Dij j =1 =− LhL + QL a I Ac - qL (5) ∂t ∂l Film Interface Film ( )( ) ( )( ) ( )( 66 www.aiche.org/cep January 2009 CEP ) B ∂UG ∂ B B loss = GhG − QG a I Ac - qG ∂t ∂l ( )( ) (6) Mass transfer and reaction coupling in the fluid film. The component fluxes, NiB, in Eqs. 2 and 3 are determined based on the mass transport in the film region. The description of the film phenomena is usually reduced to a steadystate problem (6). The key assumptions of the film model result in one-dimensional mass transport normal to the interface, and the differential component-balance equations including simultaneous mass transfer and reaction in the film are: dN Li − rLi = 0 (7) i =1 … n dz Equation 7 is generally valid for both liquid and gas phases if reactions take place in both phases. It represents the differential mass balance for the film region including the source term due to the reaction. The component fluxes are expressed in terms of concentrations using Eq. 1, whereas the source terms result from the reaction kinetics description and usually represent nonlinear dependencies on the mixture composition and temperature of the corresponding phase. The boundary conditions for Eq. 7 are those typical for the film model and specify the values of the mixture composition at both film boundaries. They are applicable to both phases; for the liquid phase they are: xi ( z = 0 ) = xiI xi ( z = δ L ) = xiB i =1 … n (8) Combining Eqs. 7 and 8 results in a set of vector-type boundary value problems that permits the component concentration profiles to be obtained as functions of the film coordinate. These concentration profiles allow the component fluxes to be determined. Thus, the boundary value problems describing the film phenomena have to be solved in conjunction with all other model equations. An analytical solution of this boundary value problem in a closed matrix form can be obtained (5) if some further assumptions concerning the linearization of the diffusion and reaction terms are made. On the other hand, the boundary values need to be determined from the total system of equations describing the process. The bulk values in both phases are found from the balance relationships, Eqs. 2 and 3. The interfacial liquid-phase concentrations are related to the relevant gas-phase concentrations, yiI, by the thermodynamic equilibrium relationships and by the continuity condition for the molar fluxes at the interface (1, 5). Due to the chemical conversion in the liquid film, the molar fluxes at the interface and at the boundary between the film and the bulk of the phase differ. The system of Nomenclature aI = specific contact area, m2/m3 Ac = cross-sectional column area, m2 c = molar concentration, kmol/m3 d = mass-transport driving force, m-1 D = Maxwell-Stefan diffusivity, m2/s F = Faraday’s constant = 9.65×104 C/mol G = gas-phase stream molar flowrate, kmol/s h = molar enthalpy, kJ/kmol l = axial coordinate, m L = liquid-phase stream molar flowrate, kmol/s m = length-specific molar hold-up, kmol/m n = number of components, dimensionless N = molar flux, kmol/(m2-s) P = pressure, Pa = length-specific heat loss, kJ/(m-s) qloss Q = heat flux, kW/m2 r = reaction rate, kmol/(m3-s) R = universal gas constant = 8.3144 kJ/(kmol-K) t = time, s T = temperature, K U = length-specific energy hold-up, kJ/m x = mole fraction of component in liquid phase y = mole fraction of component in gas phase z = normal coordinate, m zi = ionic charge, dimensionless Greek Letters δ = film thickness, m φ = volumetric hold-up, m3/m3 ϕ = electrical potential, V η = film coordinate, dimensionless μ = chemical potential, kJ/kmol Subscripts G = gas phase i, j = component or reaction index L = liquid phase t = mixture property Superscripts B = bulk phase I = interface equations is completed with the continuity equations for the mass and energy fluxes at the phase interface. Handling electrolyte systems Reactive absorption processes occur mostly in aqueous systems, with both molecular and electrolyte species. These systems demonstrate substantially nonideal behavior. Two basic models are employed for the thermodynamic description of electrolyte-containing mixtures, the Electrolyte NRTL model and the Pitzer model. The Electrolyte NRTL model is able to estimate the activity coefficients for both ionic and molecular species in aqueous and mixed-solvent electrolyte systems based on the CEP January 2009 www.aiche.org/cep 67 Reactions and Separations Rate-Based/Staged Model Rate-Based/OCFE Model binary pair parameters (7). The Pitzer model (8, 9) can be used for aqueous electrolyte systems up to 6 mol/kg ionic strength. The models require different parameters, such as pure-component dielectric constants of nonaqueous solvents, Born radii of ionic species, and binary and (for the Pitzer model) ternary interaction parameters. The electrolyte solution chemistry involves a variety of chemical reactions in the liquid phase. These reactions occur very rapidly, so chemical equilibrium conditions are often assumed. Therefore, chemical equilibrium calculations are of special importance for electrolyte systems. Concentration or activity-based reaction equilibrium constants as functions of temperature can be found in the literature. The presence of electrolyte species makes calculation of relevant diffusion coefficients crucial. The effective diffusion coefficients for electrolyte components can be obtained from the Nernst-Hartley equation for dilute solutions and from the Gordon equation for higher electrolyte concentrations (10). The driving force due to electrical potential difference also needs to be taken into account (1), which is done by introducing the electrical potential gradient into the generalized driving force di: x 1 d μi F 1 dϕ di = i + xi zi i =1 … n (9) RT δ L dη RT δ L dη In dilute electrolyte systems, the diffusional interactions can usually be neglected, and the generalized MaxwellStefan equations are reduced to the Nernst-Planck equations (1). In all cases, the electroneutrality condition must be met at each point of the liquid phase: n ∑ xi zi = 0 (10) i =1 Reducing the size of the model The models described in the previous sections, when applied to a tray or packed absorption column (Figure 1), will eventually result in a large set of complex and highly coupled nonlinear equations whose solution may become quite tedious. Several online applications, such as operator training, and process control and optimization, require the solution within a reliably defined timeframe. This can be achieved by formulating the rate-based model in a compact form, for example by using the orthogonal collocation on finite elements (OCFE) model. The OCFE formulation reduces the overall size of the reactive absorption process model (in terms of the total number of equations) while preserving the model’s structure and accuracy. The basic concept behind this efficient approximating technique (mathematical details can be found in Refs. 68 www.aiche.org/cep January 2009 CEP Rate-Based Interface Gas Bulk Gas Film Liquid Liquid Film Bulk Materials Streams Energy Streams ■ Figure 2. Schematic of the OCFE and the full column model formulation for a configuration with multiple feed and recycle streams (blue lines) and heat-transfer streams (orange lines). 11–15) is that the stagewise domain within a column section, defined as the part of the column between two consecutive streams entering or leaving the column, is considered to be a continuous analog. Subsequently, molar and enthalpy flowrate profiles within such a column section are treated as continuous functions of the longitudinal coordinate in the column. The approximating power of the OCFE model lies in the fact that the behavior within a specific column section can be accurately approximated by fewer balance equations (applied only at selected points — namely the collocation points) than a traditional stage-by-stage formulation. The greatest advantage is that the form of the balance equations at the selected collocation points is entirely preserved; hence, the rate-based model formulation as previously described is fully maintained. An important feature of the OCFE approximation model shown schematically in Figure 2 is that stages at which feed or side-draw material streams are attached are treated as discrete stages, thus isolating abrupt and sharp changes in the concentration and temperature profiles in the column approximating scheme. The extent to which the model order is reduced is dictated by the shape of the approximated concentration and temperature profiles along a given column section. Consequently, column sections with steep temperature and concentration profiles generally require a denser pattern of collocation points than column regions with relatively flat profiles. In design optimization, the decision variables involve the overall column configuration (e.g., the number of stages in each column section, the locations of material and energy feed and side-draw streams, etc.) and the column operating conditions (e.g., solvent flowrate, stage cooling/heating, recycle scheme, etc.). The OCFE model formulation transforms the otherwise discrete decision problem (e.g., calculation of the optimal number of discrete stages in the column) to a continuous design optimization problem, where the size of the column sections becomes a continuous degree of freedom, thus facilitating solution of the problem. Rounding up to the next-highest integer value leads to the optimal number of stages. This is of particular interest in synthesis problems where the optimal interconnectivity of multiple sequential separations is sought (16) as the overall number of required integer decision variables is significantly reduced. Enhancing the predictive power of a reactive absorption model Liquid- and gas-side film thicknesses depend strongly on the flow pattern in the column, the type of column internals, and gas and liquid physical properties, such as surface tension, diffusivity and viscosity. Similarly, specific contact area, which, in general, differs from the geometric surface area of the column internals, strongly depends on the flow pattern and physical properties of the fluids. In simple packed beds (e.g., packed with rings or saddles), it is possible that, at moderate liquid loads, the packing surface is not completely covered, so the mass transfer occurs through a smaller area than the geometric surface area. The opposite situation, in which the phase interface is larger than the geometric surface area, is also possible. Values of film thicknesses, specific contact area, and mass transfer coefficients are most often determined by empirical correlations, which allow scale-up to different operating states. The liquid- and gas-phase mass-transfer coefficients are usually related to Sherwood number (Sh); the latter is represented as a function of Reynolds number (Re), Schmidt number (Sc) and other dimensionless process characteristics (17, 18). It is important that the correlations are applied to conditions within their range of validity. Additional parameters related to the empirical correlations are the liquid hold-up on the relevant column internals and the pressure drop caused by the flow resistance in the column. The liquid hold-up is necessary both for the liquid-phase reaction description and for the estimation of the gas-phase hold-up in the case of gas-phase reactions. The pressure drop can influence primarily the phase equilibrium and hold-up. These parameters also depend on the operating conditions, column internals type, and physical properties. In some cases, hold-up and pressure drop are coupled and cannot be calculated explicitly, so they are determined iteratively (18). The range of application for each correlation depends on the actual column loads, as both hold-up and pressure drop strongly depend on hydrodynamic interactions. Selecting the proper correlation is mostly a question of column operating regime and user experience. Masstransfer correlations must be compared and validated with experimental data generated through experiments in the reactive absorption column. During the experimental runs (planned using statistical design of experiments techniques (19)), one or more input process variables to the reactive absorption column are changed deliberately in order to record the effect these changes have on the output process variables (responses). The accuracy of model parameter estimates is improved by centering the joint confidence region (JCR) of the model parameter estimates on their true values, and their precision is subsequently increased by reducing the volume of the multi-dimensional JCR. Statistical correlation of model parameter estimates provides a measure of the degree to which two or more parameters co-vary under certain experimental conditions, and is mainly characterized by the orientation of the JCR. In general, a small (with respect to volume) and spherical JCR centered at the true values of the model parameters is the most desirable situation. To satisfy (all or a subset of) the aforementioned objectives, the inputs to the process system should be selected in such a way that the system response becomes sensitive to its major model parameters. Reactive absorption process models can then be utilized in the calculation of optimal experimental runs. Several techniques are available (19) based on a variety of objective functions that are intended to improve the quality of parameter estimates. Key decisions in designing new steady-state and dynamic experiments involve the choice and characteristics of the input variables to the system (usually these are the manipulated variables of the control system), the selection of a suitable set of measured variables (e.g., stages with temperature sensors or composition analyzers), and the sampling rate. The duration of an experimental run depends on the system dynamics and the time it takes to reach the final steady state (which is proportional to the dominant system time constant). Combining all these elements within a unified optimal experimental-design framework that utilizes the rate-based model provides a well-defined context for improving the predictive power of the model for reactive absorption columns. NOx absorption example Absorption of nitrous gases is an important operation in the chemical process industries, used mainly in the production of nitric acid and in the purification of exhaust gas streams. It is a highly complex process due to the interaction of several components and chemical reactions in both the liquid and gas phases. This example demonstrates the ability of the rate-based modeling approach to accurately predict the steady-state and dynamic column behavior of CEP January 2009 www.aiche.org/cep 69 Reactions and Separations Table 1. Nitric acid is produced through a series of reactions. Table 2. Design parameters for the industrial sieve tray column. Gas-Phase RR1 2 NO + O2 → 2 NO2 RR2 2 NO2 ↔ N2O4 RR3 3 NO2 + H2O ↔ 2 HNO3 + NO RR4 NO + NO2 ↔ N2O3 RR5 NO + NO2 + H2O ↔ 2 HNO2 Column Diameter Number of Trays Plate Spacing Weir Height Weir Length Flow Path Number of Holes Hole Diameter Distance between Holes (Pitch) Hole Diameter industrial and experimental columns. Chemical reactions are important in NOx absorption because they enhance the absorption of components that are otherwise insoluble in water (e.g., NO) through their chemical transformation to more soluble components (e.g., NO2). Nitric acid is produced through the complex reaction mechanism detailed in Table 1 (20–22). The oxidation of NO to NO2 (RR1) is the slowest reaction, and thus is the limiting step (21). Diffusion coefficients in the gas phase were estimated using the Chapman-Enskog-Wilke-Lee model (7) and in the liquid phase using the method proposed in Ref. 23. The liquid-phase activity coefficients were calculated using the NRTL activity model, and all other necessary thermodynamic calculations were based on the Soave-Redlich-Kwong equation of state. Validation for a packed column. The model was implemented using the commercial simulator Aspen Custom Modeler (www.aspentech.com), which utilizes Aspen Properties to calculate the required physical properties. Validation was performed by comparing simulation results with experimental data for three pilot-scale columns connected countercurrently (22). Simulations for two of these columns are presented here. The simulated units have a simple configuration, with one liquid inlet stream at the top and one gas inlet stream at the bottom. Both columns have a diameter of 0.254 m and are filled with a random packing (16-mm steel Pall rings) to a packing height of 6 m. In Column Packing Height, m 5 Column 1 NOx, Simulation NOx, Experiment 4 3 Column 2 NOx, Simulation NOx, Experiment 2 13 mm 2.2 mm 1, a gas stream containing 20 mol% nitrogen oxides is absorbed by an aqueous solution containing 5 mol% nitric acid. The inlet gas stream of Column 2 contains 10.2 mol% nitrogen oxides and is treated by an aqueous solution containing 2.65 mol% nitric acid. Figure 3 compares the simulated axial profiles of the total NOx concentration in the gas phase for Columns 1 and 2 with reported experimental measurements (shown with 5% error bars). For Column 1, the calculated total NOx concentration at the top of the column shows good agreement with the experiments, as the maximum deviation is less than 5%. Figure 4 presents the simulated axial profiles of the liquid-phase temperature and measured values for both columns. The liquid temperature profiles reveal a maximum in the lower section of each column, which is typical for NOx absorption processes (24). The absolute deviation between the simulated and measured liquid temperatures is 4.5°C for Column 1 and 3.8°C for Column 2, which can be attributed to heat losses through the column wall because the experimental column was not insulated. Validation for a tray column. The design details of a tray column are given in Table 2. A gas stream containing 0.77 mol% nitrogen oxides is treated with an aqueous solution containing 0.68 mol% nitric acid. To maintain a fairly constant temperature profile, seven trays in the lower part 5 Packing Height, m Liquid-Phase RR6 N2O4 + H2O → HNO2 + HNO3 RR7 3 HNO2 → HNO3 + H2O +2 NO RR8 N2O3 + H2O → 2 HNO2 RR9 2 NO2 + H2O → HNO2 + HNO3 3.8 m 20 0.9 m 0.25 m 3.015 m 2.3 m 54,000 2.2 mm Column 1 Simulation Experiment 4 Column 2 Simulation Experiment 3 2 1 1 0 0 0.04 0.06 0.08 0.10 0.12 Molar Fraction 0.14 0.18 0.22 www.aiche.org/cep January 2009 25 30 35 40 45 50 Temperature, ºC ■ Figure 3. An axial profile of the total gas-phase NOx concentration of Columns 1 and 2 and their measured values. 70 20 CEP ■ Figure 4. An axial profile of the liquid temperature of Columns 1 and 2 and their measured values. 55 18 Column Height, m Table 3. Stream data for the NOx absorption column shown in Figure 6. NOx, Simulation HNO3, Simulation NOx, Experiment HNO3, Experiment 16 14 12 Gas Inlet Stream (Bottom) 10 8 6 4 2 0 0.00 0.01 0.1 1 Liquid Inlet Stream (Top) NO NO2 N2O4 O2 N2 T P H2O T 21.83 mol/s 58.08 mol/s 20.11 mol/s 82.74 mol/s 1016.44 mol/s 332 K 5.6 bar Molar Fraction ■ Figure 5. An axial profile of the total NOx concentration in the gas phase, the nitric acid concentration in the liquid phase, and the measured values. of the column are equipped with cooling coils fed with 152 m3/h water at an average temperature of 23.6°C. The resulting rate-based model was solved using gPROMS, an integrated process modeling environment (www.psenterprise.com). Figure 5 shows the calculated axial profiles of the total NOx concentration in the gas phase and the nitric acid concentration in the liquid phase, as well as the measured inlet and outlet values (with a measurement error of 15%). The experimental and simulated values of the total NOx reveal a maximum deviation of 8.5%, and the deviation of the simulated HNO3 concentration from the experimental value is within 10%. Thus, the agreement is good, as all deviations lie within the measurement error margins. The simulated outlet temperature of the cooling water is 24.8°C. This agrees very well with the measured value of 24.9°C (deviation <1%). From the results of both pilot plant and industrial applications, it can be concluded that the suggested model demonstrates good accuracy for the highly complex NOx absorption process. Improving column operation through design optimization and control. A similar example involves an industrial column that comprises 44 trays with an internal diameter of 3.6 m. Tray spacing is 0.9 m, except at the bottom of the column. The oxidation reaction (RR1) takes place mainly over the bottom six trays, where larger spacing is used for higher gas-phase hold-up to enhance the NO oxidation. Three independent water-cooling systems control the column temperature. In general, low column temperatures favor both the NO oxidation reaction and the absorption of NO2 in water. Empirical correlations were used for pressure drop, liquid-phase hold-up, film thickness, and stage interfacial area for sieve plate calculations (15). In the column configuration shown in Figure 6, a gas stream with a high concentration of NOx enters the bottom of the reactive absorption column, a liquid water stream enters at the top, and a weak solution of nitric acid enters as a side feed stream. The bottom liquid stream, an aqueous nitric acid solution, is partially recycled in the column 4.55 mol/s 293 K Side Feed Stream H2O HNO3 NO2 T 34.62 mol/s 6.02 mol/s 0.41 mol/s 306 K Recycle Stream Flowrate 4.55 mol/s for better control of the HNO3 concentration in the product stream, which is subject to quality constraints. Similarly, the concentration of NOx components in the gas stream at the top of the column is subject to composition constraints due to environmental regulations. Inlet stream data for the column are provided in Table 3. Applying the OCFE model formulation, the absorption column is partitioned into three sections with boundaries defined by the location of the side feed and draw streams attached to the column (15). Each column section is further partitioned into a number of finite elements. However, the six oxidation stages at the bottom of the column are treated as discrete stages. The resulting model is only one-third the size of the respective tray-by-tray model. Control of the total NOx composition in the fluegas stream is achieved by adjusting the temperature profile in the column. Three PID controllers use temperature measurements at selected stages, which act as inferential variables of NOx composition at H2 O the effluent gas AC Fluegas stream, to NOx Specifications manipulate the cooling water flowrate in the Cooling System stage coils. Another PID H2O, HNO3 TC controller directly controls TC the NOx composition at the fluegas stream TC through the manipulation of LC the solvent (water) flowrate Air, NOx at the top of the column. Dynamic simu- ■ Figure 6. A schematic representation of a NO absorption column with its lation runs using control x system. CEP January 2009 www.aiche.org/cep 71 Reactions and Separations NO2 Composition, Molar Fraction 0.015 Table 4. Column design configuration at different operating conditions. 0.0145 Case A (Operation Optimization) < 0.0125 > 0.32 < 0.0125 > 0.32 19 18 10 27 Liquid Feed Stream Flowrates Solvent (Top), mol/s Side Stream, mol/s 25 44.93 25 42.67 Cooling Water Flowrates Side Stream Feed Stage, mol/s Middle Section, mol/s Bottom Section, mol/s 10 247.47 100 10 247.09 100 Outlet Stream Concentrations NOx in Gas Outlet* HNO3 in Liquid Product* Total Cost, $/yr 0.0117 0.3222 72,634 0.0115 0.3216 69,074 0.0135 0.013 Column Specifications NOx in Gas Outlet* HNO3 in Liquid Product* 0.012 0.0125 0 0.5 1 1.5 Time, h 2.5 2 3 ■ Figure 7. Fluegas composition closed-loop response to a step change in the NOx composition of the inlet gas stream. gPROMS, shown in Figure 7, demonstrate the ability of the control system to successfully compensate for the effects of disturbances in the NOx concentration of the inlet gas stream. A viable alternative for improving the operation of the NOx absorption column (25) involves determining a suitable column configuration at different operating modes. Absorption columns are often equipped with piping to supply the feed streams at multiple locations. Design optimization determines the best location and distribution of the side feed and recycle streams at different operating conditions (e.g., variable feed gas composition and/or variable fluegas and product stream specifications). Table 4 shows that a 4.9% improvement in operating costs can be achieved through a suitable column configuration (calculation of the optimal position of the side feed streams to the column), solvent flowrates, and cooling policy in the entire column. Experimental design for improved parameter estimation. An experimental design was performed for the NOx absorption column described to estimate the kinetic parameters in reactions RR1 and RR3 (Table 1). Since the rates of reactions RR1 and RR3 are strongly affected by temperature, the cooling water flowrates at the column oxidation 1.1 Kinetic Parameter for RR3 Case B (Operation and Column Configuration Optimization) 0.014 Arbitrary Design Optimal Design 1.05 1 0.95 0.9 0.85 0.986 0.988 0.99 0.992 0.994 0.996 0.998 1 ■ Figure 8. Joint confidence region for the kinetic parameter estimates for RR1 and RR3. www.aiche.org/cep January 2009 CEP *molar fraction stages (the six stages from column bottom) were selected as input variables in order to obtain the necessary information for parameter estimation. Temperature and the composition of the liquid and gas bulk phases at the bottom oxidation stages were selected as feasible measured variables. The optimal steady-state experimental conditions (as dictated by the cooling water flowrates) were calculated by minimizing the volume of the joint confidence region for the kinetic parameter estimates (19). The experimental design capabilities of gPROMS were used to solve the resulting optimization problem using the rate-based/OCFE model of the absorption column. Figure 8 shows the surface reduction of the JCR for the two kinetic parameters. The dashed contour corresponds to the JCR of the kinetic parameter estimates for two arbitrarily selected steady-state experiments. The solid contour represents the JCR for the kinetic parameters achieved with the addition of an optimally designed experiment. In the optimally designed experimental run, the bottom three stages are operated at higher temperatures and stages four through six at lower temperatures. In both cases, model parameters have been scaled to unity at the nominal operating point to enable good numerical conditioning. 1.002 1.004 Kinetic Parameter for RR1 72 Number of Stages Top Section Middle Section Final thoughts Detailed and accurate models are essential for numerous online and offline reactive absorption column applications, including control performance evaluation, operator training, design optimization, and steady-state operation optimization. Rate-based models using the two-film theory and adapted to the particular features of reactive absorption units provide a reliable modeling framework. OCFE techniques allow for significant reduction of model size (in terms of the number of modeling equations) without compromising the accuracy of the model predictions. Hence, the predictive power of rate-based models has been efficiently combined with the systematic and adaptable approximating properties of the OCFE technique. Examples given in this article demonstrate the accuracy of the models and the successful implementation in design and control applications. C EP Acknowledgements The experimental data for industrial-scale one-pass sieve tray column in the NOx absorption example were provided in the context of research funded by the European Commission, Project OPT-ABSO (G1RD-CT-2001-00649). EUGENY KENIG, PhD, is professor and chair of the Fluid Process Engineering in the Mechanical Engineering Dept. at the Univ. of Paderborn (Pohlweg 55, 33098 Paderborn, Germany; Phone: +49 5251 60 2408; E-mail: eugeny.kenig@upb.de). He worked for the Russian Academy of Sciences, and later became a postdoctoral fellow at the Univ. of Dortmund. He also worked for BASF AG in Ludwigshafen, Germany, before returning to Dortmund as a professor. His main expertise is in the mathematical modeling and simulation of complex process systems (reactive and hybrid separations, microseparations, design and optimization of column internals). He has authored more than 200 publications and has participated in the research and coordination activities of several large European and joint national projects. A member of DECHEMA, Kenig holds an MS in applied mathematics from the Moscow Univ. of Oil and Gas, a PhD in chemical engineering from the Russian Academy of Sciences, and a DSci and a Venia Legendi from the Univ. of Dortmund. PANOS SEFERLIS, PhD, is an assistant professor in the Dept. of Mechanical Engineering at Aristotle Univ. of Thessaloniki (AUTh) and a collaborating researcher in the Chemical Process Engineering Research Institute (CPERI) at the Centre for Research and Technology – Hellas (CERTH) (P.O. Box 484, 54124, Thessaloniki, Greece; Phone: +30 2310 99 4229; E-mail: seferlis@auth.gr). His interests are in the areas of automatic control of process and mechanical systems, integrated process design and control, and optimization. Prior to coming to AUTh in 2006, he worked for CPERI for six years, he was a postdoctoral fellow at Delft Univ. of Technology, the Netherlands, and he worked for Honeywell Hi-Spec Solutions in Canada. He has authored more than 50 publications and is a member of AIChE and the Society for Industrial and Applied Mathematics (SIAM). He has a BS in chemical engineering from AUTh and a PhD in chemical engineering from McMaster Univ. in Canada. Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. Taylor, R., and R. Krishna, “Multicomponent Mass Transfer,” Wiley, Hoboken, NJ (1993). Doraiswamy, L. L., and M. M. Sharma, “Heterogeneous Reactions: Analysis, Examples and Reactor Design,” Wiley, Hoboken, NJ (1984). Danckwerts, P. V., “Gas-Liquid Reactions,” McGraw-Hill, New York, NY (1970). Seader, J. 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Schultes, “Prediction of Mass Transfer Columns with Dumped and Arranged Packings,” Trans. IChemE, 77 A, pp. 498–504 (1999). 19. Atkinson A. C., and A. N. Donev, “Optimum Experimental Designs,” Oxford Univ. Press, Oxford, U.K. (1992). 20. Joshi, J. B., et al., “Absorption of NOx Gases.” Chem. Eng. Comm., 33, pp. 1–92 (1985). 21. Emig, G., et al., “Absorption with Simultaneous Complex Reactions in Both Phases, Demonstrated by the Modeling and Calculation of a Counter-Current Flow Column for the Production of Nitric Acid,” Comput. Chem Eng., 3, pp. 143–150 (1979). 22. Suchak, N. J., et al., “Modeling and Simulation of NOx Absorption in Pilot-Scale Packed Columns,” AIChE J., 37, pp. 323–339 (1991). 23. Siddiqi, M. A., and K. Lucas, “Correlations for Prediction of Diffusion in Liquids,” Canad. J. Chem. Eng., 64 (5), pp. 839–843 (1986). 24. Hüpen, B., and E. Y. Kenig, “Rigorous Modelling of NOx Absorption in Tray and Packed Columns,” Chem. Eng. Sci., 60, pp. 6462–6471 (2005). 25. Dalaouti, N., and P. Seferlis, “Design Sensitivity of Reactive Absorption Units for Improved Dynamic Performance and Cleaner Production: The NOx Removal Process,” J. of Cleaner Production, 13, pp. 1461–1470 (2005). CEP January 2009 www.aiche.org/cep 73 ...
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