Ind. Eng. Chem. Res. 1998, 37, 2203-2207
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Fused Chemical Reactions: The Use of Dispersion To Delay Reaction Time in Tubular Reactors Probjot Singh and H. Scott Fogler Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109
Fused chemical reactions are delayed exothermic reactions. An axial dispersion model is used to simulate the flow of alternately injected pulses of reactants separated by an inert. There is a delay in reaction and heat release because the reactants have to disperse through the inert spacer to react. The feasibility of this technique is described for the reaction between ammonium chloride and sodium nitrite catalyzed by acetic acid. This technique can be successfully applied to the effective dissolution of wax deposited in subsea pipelines. The delay in the reaction is required to supply heat to regions further down the pipeline that are more susceptible to wax deposition. Simulation results show that the delay in the heat release depends on the width of the inert spacer as well as the catalyst concentration. However, the amount of heat released depends on the inlet concentrations of the reactants. Simulations can successfully determine the inlet concentrations of the reactants and catalyst as well as the inert spacer width for a desired temperature profile inside the pipeline. Introduction Fused chemical reactions are reactions that have a delay in releasing heat from the time the reacting system enters the reactor. A technique for delaying an exothermic chemical reaction using dispersion inside a tubular reactor was investigated. An example of a fused chemical reaction is the aqueous exothermic reaction between ammonium chloride (NH4Cl) and sodium nitrite (NaNO2) catalyzed by an acid such as acetic acid separated by a spacer in a tubular reactor (Ashton et al., 1989). In the present work, the heat release is delayed by alternately pumping an inert spacer between pulses of different reactants in a pipeline. The heat generation will be delayed because the reactants have to disperse through the inert spacer to react, and the width of the inert pulse will determine the extent of the delay in the heat release. Effective dissolution of wax deposited in subsea pipelines is a potential application of this technique (see Figure 1). Wax precipitation and deposition from oil that is in transit from an off-shore oil well to the shore is a common phenomenon due to low deep-sea temperatures. Partial plugging of the transport pipelines due to the deposition of wax drastically reduces operating efficiency, and the removal of the deposited wax requires significant additional operating costs. Melting and redissolving the deposited wax is one of the solutions of this problem. The primary challenge in clearing these pipeline blockages is in supplying heat to regions farther down the pipeline that are more susceptible to wax deposition (Brown et al., 1993). If the exothermic reaction takes place just at the pipeline entrance, the resulting hot fluid will cool prior to reaching the wax deposit because of low subsea temperatures and lack of pipeline insulation. Hence, a delay in the heat release is needed if an exothermic reaction is to be efficiently used to melt wax deposits. Problem Statement An exothermic reaction between NH4Cl and NaNO2 that is catalyzed by H+ takes place inside a pipeline
Figure 1. A schematic of an offshore platform with a pipeline that is partially plugged by the wax deposition.
Figure 2. A schematic of a tubular reactor with system of pulses having the two reactants and the inert spacer denoted as A, B, and I, respectively.
modeled as a tubular reactor with dispersion. Because the ocean floor is at 5 °C, the reaction mixture is cooled as it flows through the pipeline. To deliver the heat release at long distances from the pipeline entrance, pulses of the reactants separated by an inert may be injected, as shown in Figure 2. The objective is to compute the average temperature of one set of pulses as a function of the location inside the pipeline and to investigate the effect of pulse width on the extent of delay in the reaction. The reaction system is as shown below:
A + B f Products + Heat An example is the aqueous exothermic reaction between NH4Cl (or NH4NO3) and NaNO2 that can be catalyzed by acids, such as acetic acid, as shown here
S0888-5885(97)00602-7 CCC: $15.00 © 1998 American Chemical Society Published on Web 03/20/1998
2204 Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998
(Ashton et al., 1989):
DC* ∂2C* L i i (r ) ) Pem 2 + Dθ uCio i ∂z
H+
NH4Cl(aq) + NaNO2(aq) 98 2H2O + NaCl(aq) + N2(g) ∆HR ) -334.47 kJ/mol
(1)
The kinetics of this exothermic reaction were investigated in the laboratory whereby a temperature-time profile was recorded as the reaction proceeded adiabatically in a well-mixed batch reactor. Results show that the reaction kinetics can be expressed by the following power law rate equation:
-rNH4Cl ) -rNaNO2 ) k[NH4Cl]1.2[NaNO2]1.5[H+]1.6 (2) The rate constant k can be expressed in an Arrhenius form as follows:
[(
k ) k1 exp
)]
1 E 1 R T1 T
(3)
where k1 ) 2.1 (dm3/mol)3.3 s-1, E/R ) 8000 K, and T1 ) 298 K. If acetic acid is used as a catalyst, then H+ concentration can be expressed as follows:
H+ ) (1.76 × 10-5[CH3COOH])1/2 mol/dm3 Other parameters (typical for subsea pipelines) are as follows:
diameter of the pipeline, dt ) 0.3 m
L(∆HA × rA) ∂2T* DT* 4UL ) Pet + T* 2 Dθ FCpu(To - Toc) FCpudt ∂z
De De dt De ) ) 0.21 w Pem ) × ) 2.1 × 10-6 udt uL udt L In the case of turbulent flow, the Peclet number for thermal dispersion is assumed equal to that for material dispersion (Bird et al., 1960).
Pet )
CP ) 4.18 kJ/kg inlet temperature, To ) 25 °C surrounding temperature, Toc ) 5 °C average overall heat transfer coefficient, U ) 20 W/m2 K Reynolds number, Re )
dtuF ) 3 × 105 µ
Sodium nitrite also reacts with acetic acid; however the rate of this side reaction is negligible compared with the reaction between NH4Cl and NaNO2. To minimize the reaction between NaNO2 and acetic acid, acetic acid is mixed in the pulse of NH4Cl. Governing Differential Equations A dispersed plug flow model (Fogler, 1992) is used to solve this problem. The simplified governing equations of mass and energy balance in Lagrangian coordinates are expressed as follows by the dimensionless mass balance equation (eq 4) and the dimensionless energy balance equation (eq 5):
(5)
where T* ) (T - Toc)/(To - Toc), is a dimensionless temperature having To and Toc as the inlet temperature and ocean temperature respectively; F is the density of the liquid; CP is the heat capacity of the liquid; dt is the diameter of the pipeline; U is the overall heat transfer coefficient for the heat transfer through the pipe wall; ∆HA is the heat of reaction per mole of A reacted; rA is the rate of reaction of A; Pet ) Rt/uL is the Peclet number for heat transfer and Rt is the thermal dispersion coefficient. For a Reynolds number (Re) ) 3 × 105 (turbulent flow), the Peclet number (for material dispersion) is given as follows (Levenspiel, 1958):
average velocity, u ) 1 m/s
fluid viscosity, µ ) 0.001 Pa s
(4)
where i ) 1 represents NH4Cl; i ) 2 represents NaNO2; i ) 3 represents CH3COOH; C*i ) Ci/Cio is the dimensionless concentration and Cio is the concentration at the entrance; L is the total length of the pipeline; u is the average velocity inside the pipeline; θ ) tu/L, is the dimensionless time; z ) x/L, is the dimensionless distance; ri is the rate of reaction with respect to the species i; because CH3COOH is a catalyst, r3 ) 0; Pem ) De/uL, is the Peclet number for mass transfer and De is the material dispersion coefficient; D/Dθ ) (∂/∂θ + ∂/∂z) is the time derivative in Lagrangian coordinates.
length of the pipeline, L ) 30000 m
fluid density, F ) 1000 kg/m3
i ) 1, 2, 3
Rt ) Pem ) 2.1 × 10-6 uL
Boundary Conditions The boundary conditions are as follows:
C* 1 ) C* 3 ) 1, at z ) 0, for nτ ×
(Lu) e θ < (n + 0.25)τ × (Lu)
C* 1 ) C* 3 ) 0, at z ) 0, for (n + 0.25)τ ×
(Lu) e θ < (n + 1)τ × (Lu)
C* 2 ) 1, at z ) 0,
(Lu) e θ < (n + 0.75)τ × (Lu) u C* ) 0, at z ) 0, for nτ × ( ) e θ < (n + 0.5)τ × L (Lu) and (n + 0.75)τ × (Lu) e θ < (n + 1)τ × (Lu) for (n + 0.5)τ ×
2
T* ) 1, at z ) 0, for all θ where τ is the injection time period for one set of pulses (e.g., AIBI) and n ) 0, 1, 2,..., N represents the count
Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2205
Figure 3. Local dimensionless concentration and temperature profiles at the entrance of the pipeline for a pulse width 30 m, C1o ) C20 ) 7 mol/dm3, and C3o ) 1 mol/dm3.
Figure 4. Local dimensionless concentration and temperature profiles at a location of 3 km from the entrance of the pipeline for a pulse size 30 m, C1o ) C2o ) 7 mol/dm3, and C3o ) 1 mol/dm3.
on the set of pulses being injected in the pipeline. The widths of all pulses of the different materials, w, are assumed to be the same and are directly related to the injection time period for one set of pulses, τ, as follows:
w)
τ×u 4
The governing equations are four simultaneous coupled nonlinear partial differential equations for the dependent variables C*1, C*2, C* 3, and T* as a function of independent variables θ and z. These partial differential equations are discretized in the finite difference equations (as shown in the Appendix) and solved using an implicit technique. Results and Discussion The movement of the system of pulses inside the pipeline can be visualized as the propagation of a temperature wave whose maxima and minima can be expected to occur respectively at the maximum and minimum overlap of the concentration waves of the reactants inside the pipeline. To describe the propagation of reactant concentration waves and temperature wave inside the pipeline, let us consider a particular case of the pulse flow having C1o ) C2o ) 7 mol/dm3, C3o ) 1 mol/dm3, and a pulse size of 30 m. Figures 3 through 7 show the local concentration and temperature profiles when the center of the inert spacer reaches 0, 3, 5, 10, and 20 km, respectively, from the entrance of the pipeline. All sets of pulses (e.g., BIAIB) are identical as far as the temperature and concentration waves are concerned. Hence, the control volume for these concentration and temperature waves (in Figures 3-7) consists of half pulse width of A (NH4Cl and CH3COOH), one pulse width of inert, and half pulse width of B (NaNO2). Hence, only one-half of the concentration wave (i.e., between adjacent maxima and minima) are shown in these figures. Figure 3 shows dimensionless concentration profiles for NH4Cl, NaNO2, and CH3COOH and the temperature profile at the entrance of the pipeline. Two distinct nonoverlapping half pulses of the reactants separated by an inert spacer can be seen in this figure showing a constant temperature profile of 25 °C. Figure 4 shows dimensionless concentration and temperature profiles when the center of the inert spacer is at 3 km. The reaction zone where the two reactants are mixed is primarily between 2.98 and 3.02 km. The maxima in the temperature profile shows the extent of heat release in the reaction zone. The dimensionless concentration
Figure 5. Local dimensionless concentration and temperature profiles at a location of 5 km from the entrance of the pipeline for a pulse size 30 m, C1o ) C2o ) 7 mol/dm3, and C3o ) 1 mol/dm3.
Figure 6. Local dimensionless concentration and temperature profiles at a location of 10 km from the entrance of the pipeline for a pulse size 30 m, C1o ) C2o ) 7 mol/dm3, and C3o ) 1 mol/ dm3.
profile for the catalyst CH3COOH (i.e., C3) is higher than that of the reactant NH4Cl (i.e., C1) because of the consumption of the reactants during the reaction. Figures 5 and 6 show dimensionless concentration and temperature profiles when the centers of the inert spacers are at 5 and 10 km, respectively. There is a smaller degree of overlap between the two reactant concentration profiles at these locations compared with that at 3 km (i.e., Figure 4). The reason for this difference is that the temperature at these locations is relatively higher than that at 3 km, which increases the reaction rate such that it becomes almost instantaneous. An overlap of the reactant concentration profiles is not possible for an instantaneous reaction. Also seen in Figures 5 and 6 is that the amplitude of the temperature
2206 Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998
Figure 7. Local dimensionless concentration and temperature profiles at a location of 20 km from the entrance of the pipeline for a pulse size 30 m, C1o ) C2o ) 7 mol/dm3, and C3o ) 1 mol/ dm3.
Figure 8. Volume average temperature as a function of location down the pipeline for various pulse sizes keeping C1o ) C2o ) 7 mol/dm3, and C3o ) 1 mol/dm3.
wave decreases as the system moves from 5 to 10 km, which indicates the existence of thermal dispersion. Figure 7 shows dimensionless concentration and temperature profiles at a time when the center of the inert spacer is at 20 km. The flat temperature profile indicates that the system is in the state of complete thermal mixing. However, the reactant concentration profiles are distinct from each other and their magnitude is j g N/5 ) 0 for other grid points C* 2 ) 1 for 4N/5 > j g 3N/5
Notation C*i ) dimensionless concentration of i-component, i ) 1 means NH4Cl, i ) 2 means NaNO2, and i ) 3 means CH3COOH Cio ) initial concentration of ith component CP ) heat capacity of the fluid dt ) pipe diameter De ) dispersion coefficient E ) activation energy k ) rate constant Pet ) Peclet number for thermal dispersion Pem) Peclet number for material dispersion ri ) reaction rate with respect to species i rA ) reaction rate of reactant A R ) universal gas constant Re ) Reynolds number t ) time τ ) injection time period for one set of pulses To ) initial temperature of the fluid Toc ) temperature of the surroundings (ocean) Tav ) average temperature of a single set of pulses u ) average velocity U ) overall heat transfer coefficient L ) length of the pipeline Rt ) thermal dispersion coefficient F ) density of the fluid w ) pulse width
Appendix. Solution Technique The governing conservation equations of mass and energy are four simultaneous nonlinear partial differential equations describing the dependent variables C*1, C*2, C*3, and T* as a function of independent variables θ and z. These partial differential equations are discretized in the following finite difference equations and solved using an implicit technique.
) 0 for other grid points T* ) 1 for all grid points Boundary Conditions (identical wave front):
C*′ i (0) ) C* i(4N/5) for i ) 1, 2, 3 T*′(0) ) T*(4N/5) and
C*′ i (N) ) C* i(N/5) for i ) 1, 2, 3 T*′(N) ) T*(N/5) At the end of the time-step, C*′ i and T*′ at all grid points may be obtained. This process is repeated in time until θ ) 1, which represents the exit of the pipeline. Literature Cited Ashton, J. P.; Klrspel, L. J.; Nguyen, H. T.; Credure, D. J. In-Situ Heat System Stimulates Paraffinic-Crude Producers in Gulf of Mexico. SPE 15660, 1989, SPEPE. Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; Wiley: New York, 1960; p 629. Brown, T. S.; Niesen, V. G.; Erickson, D. D. Measurement and Prediction of the Kinetics of Paraffin Deposition. SPE 26548, 1993, SPE. Fogler, H. S. Elements of Chemical Reaction Engineering, 2nd ed.; Prentice Hall, New Jersey, 1992; p 765. Levenspiel, O. Longitudinal Mixing of Fluids Flowing in Circular Pipes. Ind. Eng. Chem. 1958, 50, 343.
Received for review August 29, 1997 Revised manuscript received January 13, 1998 Accepted January 14, 1998 IE9706020
