5058
Ind. Eng. Chem. Res. 2001, 40, 5058-5065
Fused Chemical Reactions. 2. Encapsulation: Application to
Remediation of Paraffin Plugged Pipelines†
Duc A. Nguyen,‡ H. Scott Fogler,*,‡ and Sumaeth Chavadej§
Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, and
The Petroleum and Petrochemical College, Chulalongkorn University, Bangkok, Thailand 10330
Fused chemical reactions are reactions that undergo a delay before significant amounts of product
are produced. One class of fused chemical reactions is the class of reactions triggered by an
abrupt release of a catalyst. Fused chemical reactions have the potential of solving the problem
of organic deposition in sub-sea pipelines which is a problem with enormous economic
consequence (Singh, P.; Fogler, H. S. Ind. Eng. Chem. Res. 1998, 37 (6), 2203). The reaction
between ammonium chloride and sodium nitrite catalyzed by citric acid was chosen as an example
of a fused chemical reaction system where the acid was encapsulated in polymer-coated gelatin
capsules. The timed release of the acid catalyst was achieved by putting an additional polymeric
coating on the gelatin capsules. The reaction kinetics and the polymer dissolution kinetics were
investigated in an adiabatic batch reactor. An excellent agreement between simulation and
experimental results in the batch reactor was achieved. Experimental results in a flow-loop
reactor demonstrated that the fused chemical reaction could provide a substantial amount of
heat in situ. This amount of heat is sufficient to overcome the high heat loss to the surroundings
and to raise the temperature of the fluid above the effective temperature to soften and melt the
wax deposit. The delay in heat release was found to depend on the thickness of the polymeric
coating, while the amount and rate of heat release depended on the in situ reactant and acid
concentrations.
Introduction
Fused chemical reactions are reactions which can be
delayed from taking place by either physical or chemical
means. Fused chemical reactions have a wide range of
applications, such as in the pharmaceutical industry
(controlled release of drugs2), agricultural industry
(fertilizer management3), and oil industry (remediation
of paraffin, asphaltene, and hydrate deposits1 or reservoir stimulation4).
As oil wells are drilled further offshore in deeper
water, the phenomenon of paraffin, asphaltene, and
hydrate deposition becomes more severe and extensive
because of the extremely low ocean floor temperature.
Figure 1 shows a pipe section plugged by wax deposit
that was recovered from the pipeline on the ocean floor.
Removal of wax from wells and pipelines have accounted
for significant additional operating costs. The direct cost
of using deep-sea divers to cut and remove paraffin
blockage from a pipeline 40 000 ft in length and 6 in. in
diameter is about $6 000 000, while the production loss
during downtime is approximately $40 000 000 (as
reported by Elf Aquitaire). In some extreme cases such
as of the Lasmo field, U.K., the entire field was
abandoned with the cost of over $100 000 000 because
of recurrences of paraffin blockage.
† Submitted for the special issue of Ind. Eng. Chem. Res. to
be published in conjunction with the United Engineering
Foundation-CRE VIII conference to be held June 23-29, 2001
in Barga, Italy.
* To whom correspondence should be addressed. Phone:
(734) 763-1361. Fax: (734) 763-0459. E-mail: sfogler@
engin.umich.edu.
‡
University of Michigan.
§
Chulalongkorn University.
Figure 1. Paraffin plugging a pipeline.
One of the solutions to the paraffin deposition problem
is to melt and redissolve the deposit. The primary
challenge in clearing the pipeline blockages is in supplying heat to regions further down the pipeline that
are more susceptible to wax deposition.5 Because of the
characteristic delay time of the encapsulation technique,
a highly exothermic fused chemical reaction system
using encapsulation is very promising to provide a
substantial amount of heat at the desired location in
the pipeline.
10.1021/ie0009886 CCC: $20.00 © 2001 American Chemical Society
Published on Web 04/26/2001
Ind. Eng. Chem. Res., Vol. 40, No. 23, 2001 5059
Figure 3. Dissolution of paraffin deposits due to a separate feed
of reactant pulses.
Figure 2. Coiled tubing to control the location of the fused
chemical reaction.
Types of Fuses
Chemical Fuses. Chemical methods to fuse include
the following:
a. Series Reactions: A f B f C f D. The formation
of species D is delayed because of the slow reaction rate
of one of the series reactions.
b. Autocatalytic Reactions: A + B f 2B. Initially,
the concentration of B in the solution is very low; the
initial reaction rate, therefore, is slow. As the reaction
progresses, more B will be formed, leading to an everincreasing rate of the reaction.
c. Retardants: A + 2B f X (Slow); X + C f D
(Rapid); X + B f P (Moderate). Here a scavenger,
C, reacts with the intermediate, and the reaction will
not proceed to form the final product until C is consumed. As the initial concentration of C in the solution
increases, the delay time before a significant amount
of product P formed increases.
Physical Fuses. Physical means to fuse chemical
reactions are normally used for reactions in which the
reaction rate strongly depends on the concentration of
either one reactant or a catalyst:
catalyst
A + B 98 products + heat
The delay of the reaction can then be achieved by
physically separating either one of the reactants or the
catalyst from the reactive system. An example of a
chemical reaction which can be fused is the aqueous
exothermic reaction between ammonium chloride
(NH4Cl) and sodium nitrite (NaNO2) catalyzed by an
acid such as citric acid6 to produce a substantial amount
of heat:
H+
NH4Cl(aq) + NaNO2(aq) 98
NaCl(aq) + 2H2O + N2(g)
∆Hrx ) -79.95 kcal/mol at 25 °C
In the absence of the acid catalyst, this reaction proceeds
at an extremely slow rate.
Physical methods to fuse chemical reactions include
the following:
a. Physical Separation. The two reactants are
separated physically so that they only meet at the wax
deposition region. An example is the use of coiled tubing
which is shown in Figure 2. Essentially, a tube is
inserted into the pipeline up to the wax deposition
region. Reactant A is introduced to the tube, whereas
reactant B is flowed into the annulus. The two reactants
will only meet at the exit of the tube, where they react
and release heat to melt the paraffin deposit. This
technique works well for very short pipelines. However,
if the distance of the plug is more than 8 km from the
platform, one cannot effectively use coiled tubing.
Figure 4. Dissolution of paraffin deposits due to a reactive
mixture of water/oil emulsions.
b. Dispersion. Singh and Fogler1 developed an axial
dispersion model to simulate the flow of alternately
injected pulses of reactants separated by an inert
(Figure 3). There is a delay in reaction and heat release
because the reactants have to disperse through an inert
spacer to react. Simulation results show that the heat
released can be delayed for moderately long periods of
time. However, a large amount of inert is required for
a long delay time, which in turn lowers the maximum
temperature reached during reaction because the inert
slug acts as a heat sink. As a result, the temperature
will not be sufficiently high to melt and dissolve the wax
deposit.
c. Emulsification. Here an oil-in-water emulsion of
an aqueous-based fluid which contains the reactants
and an oil-based fluid which consists of aliphatic and/
or aromatic hydrocarbons is used to delay the reaction
(Figure 4).7 Each reactant was emulsified in the oil
separately in the oil base system, and the emulsion is
stabilized by the addition of a suitable surfactant. The
surfactant sterically stabilizes the drops, thereby retarding the coalescence of the individual A and B drops
and delaying the reaction. Several dewaxing operations
performed at the Campos Basin (Brazil) have reported
success using this process for short pipelines. However,
using this process for long pipelines is still a challenge,
because the heat release has to be delayed for a
considerably longer time.
d. Encapsulation. With this technique, either one
of the reactants or the catalyst is encapsulated. The
delay time is obtained from the controlled release of the
encapsulated substance to the bulk solution. Encapsulation is very widely used in the pharmaceutical,2,8
agricultural,3 and oil industries4 because it can provide
various types of release profiles (zero-order, first-order,
pulsed, and timed). Consequently, the encapsulation
technique was chosen in this work as the primary
method to delay the exothermic reaction between NaNO2
and NH4Cl by controlling the release of the encapsulated catalyst. The heat generation from the reaction
will be delayed because the polymeric coating has to
dissolve before the acid catalyst is released into solution.
This release mechanism is shown schematically in
Figure 5. The thickness of the polymeric coating will
determine the extent of the delay in the heat release.
The catalyst release parameters of dissolution time
and release time were determined for a variety of
experimental conditions and used in the mathematical
modeling phase of this work.
Experimental Section
Materials. Sodium nitrite (NaNO2) and ammonium
chloride (NH4Cl) were used as reactants. Hydrochloric
5060
Ind. Eng. Chem. Res., Vol. 40, No. 23, 2001
Figure 5. Encapsulation technique for the controlled release of
the acid catalyst.
acid (HCl) and sodium hydroxide (NaOH) were used as
pH-adjusting agents. Citric acid (C6H8O7) was used as
the catalyst. All chemicals used were of reagent grade
and were purchased from Aldrich. Hard gelatin capsules
size 4 (13 mm in length and 5 mm in diameter, natural/
transparent) were provided from Capsugel. A copolymer
of poly(methylmethacrylic acid) and poly(methyl methacrylate) with the trade name Eudragit S100 (Rhöm
Pharm, Darmstadt, Germany) provided by RohmAmerica was used as the coating polymer. This polymer
is soluble in the reactive system (aqueous medium) in
the working pH range (5-8). Ethanol and acetone used
as solvents to prepare the polymer solution were purchased from Aldrich.
Reaction Kinetics Studies. The kinetics of this
reaction were investigated using an adiabatic batch
reactor (Dewar flask, Fisher Scientific, Pittsburgh, PA).
The temperature and pH of the solution were monitored
using a digital thermometer with a type J thermocouple
and a pH meter purchased from Cole Parmer Instruments, Chicago, IL. An initial rate method was applied
to find the order of the reaction as well as the specific
reaction rate constant, k.
Preparation of Acid-Filled Capsules. The 18 wt
% polymer solution used for coating capsules was
prepared by stirring 17.27 g of Eudragit S100 pellets
in a mixture of 60 mL of ethanol and 40 mL of acetone
for at least 1 h until a clear solution was obtained. Hard
gelatin capsules were filled with approximately 0.001
mol (0.192 g) of citric acid. After the capsules were filled
and the halves were locked back together, the core
capsules were coated with the polymer solution by
means of alternately dipping half of the capsule into the
polymer solution and then drying it for about half a day.
The procedure was then repeated for the other half of
the capsule. The thickness of the polymeric coating was
controlled by varying the number of dips and the drying
time.
Measurement of the Coating Thickness. The
thicknesses of each capsule before and after coating
were measured using a dial gauge (SIS-6 from Peacock,
Japan). The dial gauge can measure a thickness to an
accuracy of (0.03 mm. The thickness of the Eudragit
S100-coated layer was then deduced from the difference
of the two thicknesses. Four different positions were
measured for each capsule to calculate the least thickness difference.
Batch Experiments. To determine the kinetics of
polymer dissolution as well as to obtain parameters for
evaluating the efficiency of the encapsulation technique
Figure 6. Definition of parameters deduced from the temperature-time and pH-time trajectories.
to delay the fused chemical reaction, experiments were
conducted in a batch reactor. Temperature-time and
pH-time trajectories were recorded for each experiment. The effects of stirring speed, thickness of the
polymeric coating, initial temperature, initial pH of the
solution, and number of capsules used per unit volume
of the reactive solution were studied.
From the pH-time trajectories monitored, values of
the dissolution time and the release time were deduced
and used in the polymer dissolution kinetics study.
From the temperature-time trajectories, values of the
delay time and the rate of temperature increase were
computed and compared with simulation results. The
temperature-time and pH-time trajectories are shown
in Figure 6. Essentially, the dissolution time is the time
when the pH of the solution begins to drop because of
the release of the catalyst inside the capsules (the time
when the polymeric coating and the gelatin capsule have
been dissolved). The release time is computed from the
dissolution time to the time when the pH of the solution
does not change significantly. Regarding the parameters
obtained from temperature-time trajectories, the delay
time gives us an idea as to when the temperature starts
increasing significantly while the rate of increasing
temperature describes how rapidly the temperature
rises after the delay time.
In all batch experiments, the concentrations of the
two reactants NaNO2 and NH4Cl were fixed at 2.5 M.
The concentration of capsules is normally 2 capsules/
100 mL of reactive solution unless specified otherwise.
Results and Discussion
Reaction Kinetics. a. Method of Initial Rates.
The combined mole balance on species A, rate law, and
energy balance for an adiabatic batch reactor is9
( )
R β
dT -∆Hrx(T0) kCACB
)
dt
Cps
CA0
(1)
Here, changes in the overall heat capacity of the solution
have been neglected. The initial rate of the temperature
rise which can be calculated from experimental temperature-time trajectories can be related to the rate
parameters as follows:
β
kt)0[-∆Hrx(T0)]CB0 R-1
dT
)
CA0
dt t)0
Cps
( )
(2)
Consequently, a log-log graph of the slope calculated
Ind. Eng. Chem. Res., Vol. 40, No. 23, 2001 5061
Figure 7. Effect of [NaNO2] on the reaction rate.
versus the initial concentration revealed the coefficient
R - 1 following eq 2. Here, Figure 7 gives the reaction
order with respect to sodium nitrite, R, to be approximately 3.1.
The order with respect to ammonium chloride was
analyzed in a similar manner and found to be 2.5.
b. Effects of pH and Temperature of the Solution. The rate constant, k, for oxidation-reduction
reactions is typically expressed as
k ) k1 + k2[H+]m + k3/[H+]n
(3)
where [H+] is the concentration of proton in the solution
and k1, k2, and k3 are the rate constants in the medium,
high, and low pH regions, respectively. The rate constant ki can be expressed by the Arrhenius equation:
ki ) k0ie
-Ei/RT
Figure 8. Reaction rate constant as a function of pH.
Figure 9. Typical temperature trajectories for batch reactors for
a delay time of up to 12 h.
(4)
The rate constants and activation energies were then
obtained by using nonlinear regression for values of kt)0
at different initial pH values and initial temperatures
following the model specified in eqs 3 and 4.
The complete equation for the specific reaction rate
constant was found to be
k ) k1 + k2[H+]1.8 + k3/[H+]0.7
(5)
k1 ) 8 × 109e-12000/T
(6a)
where
13 -7000/T
k2 ) 5 × 10 e
k3 ) -8 × 105e-13000/T
(6b)
(6c)
c. Summary of Reaction Kinetics. The reaction
rate is basically third-order with respect to sodium
nitrite and second-order with respect to ammonium
chloride:
3.1
C2.5
-γNaNO2 ) kCNaNO
2 NH4Cl
Figure 10. Typical temperature trajectories in batch reactors for
a delay time of up to 20 h.
(7)
Such a fifth-order reaction usually is comprised of
several intermediate steps. This equation also reveals
that the reaction rate strongly depends on the concentration of both reactants.
Figure 8 plotting the reaction rate constant as a
function of the solution pH, calculated from eq 5, clearly
shows that the reaction rate is a strong function of the
pH in the solution. The reaction rate is very slow at high
pH and very rapid at low pH. Therefore, we can control
the rate of reaction by controlling the acid concentration
in the solution.
Batch Experiments. Typical temperature-time trajectories from batch experiments are shown in Figures
9 and 10. When no coating was applied, the temperature
rose after a very short delay of only about 6 min.
However, with only a 0.04 mm coating, the reaction was
delayed for 2 h. The delay time increased as the
thickness of the coating increased. For a coating thickness of 0.4 mm, a delay of approximately 20 h was
achieved before the reaction occurred. This 20-h delay
time corresponds to a flow distance in a pipeline of
approximately 70 km under normal operating conditions! In other words, results from batch experiments
show that the encapsulation technique can definitely
provide a desired and significant delay time!
d. Polymer Dissolution Process. Because the
polymer used [a copolymer of poly(methyl methacrylate)
and poly(methylmethacrylic acid)] can be considered as
5062
Ind. Eng. Chem. Res., Vol. 40, No. 23, 2001
Figure 12. Effect of stirring speed on the dissolution rate.
Figure 11. Effect of thickness of the coating on the dissolution
time.
a polyacid, the dissolution of the polymeric coating on
the capsules’ surface essentially consists of three steps:
1. Ionization of the polymer chain:
2. Detachment of the ionized polymer chain from the
polymer matrix.
3. Diffusion of the ionized polymer chain from the
polymer surface to the bulk solution.
The mechanism of polymer dissolution is currently
being studied in great depth using a rotating-disk
apparatus, and the results will be presented at a later
date.
e. Effect of the Coating Thickness. To examine the
effect of the thickness of the Eudragit S100 layer on the
dissolution time, citric acid-filled capsules were coated
with a 18 wt % solution of Eudragit S100 in various
coating thicknesses from 0 to 0.37 mm. The temperatures were kept at 24 °C, while other parameters such
as concentrations of the two reactants, size and number
of the capsules, volume of the reactive solution, stirring
speed, and the pH of the solution were maintained
constant throughout the experiments.
Figure 11 reveals an excellent linear relationship
between the coating thickness and the dissolution time.
Therefore, the rate of dissolution of the polymer can be
described by the ratio between the thickness of the
coating and the dissolution time:
dL
)
dt
thickness of the coating
) γ(T,pH,Re) (8)
dissolution time
dissolution rate (γ) ) -
where L is the thickness of the coating. This dissolution
rate is independent of the coating thickness. Hence,
hereafter, the dissolution rate calculated from the above
equation will be used to derive the rate expression of
the polymer dissolution instead of the dissolution time.
f. Effect of the Mixing Degree. The effect of the
mixing degree on the dissolution rate was studied in
order to investigate the mechanism of the polymer
dissolution. Experimental results (Figure 12) showed
that the dissolution is reaction-limited and that the
polymer dissolution rate is independent of the flow
regime of the surrounding solution. The dissolution of
the polymeric coating is therefore limited by the ioniza-
tion reaction at the polymer surface which can be
expressed as
γ ) -dL/dt ) kp[OH-]a
(9)
where kp is the specific reaction rate and a is the
reaction order with respect to the hydroxide ion concentration.
g. Effect of the Solution pH on Polymer Dissolution. To determine the reaction order with respect to
the concentration of proton in the solution, the pH of
the solution was varied from 6.19 to 8.06 by adding a
prescribed amount of sodium hydroxide (from 0 to 0.01
mol/L of the reactive solution).
h. Summary for Polymer Dissolution Kinetics.
On the basis of the preliminary results, it can be
concluded that the polymer dissolution is limited by the
ionization of the polymer at the surface; its rate is a
function of temperature and the pH of the reactive
solution as follows:
γ ) -dL/dt ) 570.4e-1158/T[OH-]0.411 (mm/h)
(10)
Simulation Results
Assumptions.
1. The dissolution of a particular capsule is not
affected by the presence of other capsules; i.e., the
capsules behave independently. However, a capsule,
once completely dissolved, decreases the solution pH
and thereby affects the dissolution of other capsules.
2. Once the coating dissolves to the point where there
is a breakthrough in the capsule coating, the catalyst
is released linearly from the capsule. The released
catalyst is immediately dissolved in the solution.
Methodology. For a well-mixed batch reactor, the
following apply:
(a) Mole balance:9
rA
dX
)dt
CA0
(11)
where CA0 is the initial concentration of reactant A, rA
the rate of appearance of A, X the conversion of reactant
A, and t the time.
(b) Energy balance:9
dT UA(Ta - T) + (rAV)[∆Hrx(T)]
)
dt
NA0Cps
(12)
where A is the heat-transfer area of the reactor and U
is the overall heat-transfer coefficient of the reactor.
Ind. Eng. Chem. Res., Vol. 40, No. 23, 2001 5063
Figure 13. Comparison between simulation and experimental
delay times at 24 °C.
Figure 14. Comparison between simulation and experimental
temperature profiles.
(c) Reaction kinetics: eqs 5, 6a-c, and 7.
(d) Polymer dissolution kinetics: eq 10.
(e) Catalyst concentration:
{
0
if t e tl
ncN0 t - tl
if tl < t < tl + tr
Ccatalyst )
V
tr
ncN0
if t g tl + tr
V
(13)
where L is the thickness of the polymeric coating, nc
the number of capsules introduced into the reactive
solution, N0 the number of moles of catalyst encapsulated in one capsule, tl the dissolution time, and tr the
release time.
(f) pH of the solution:
pH ) f(CNaNO2,CNH4Cl,CNaOH,Ccatalyst)
Figure 15. Experimental setup for flow conditions.
(14)
where CNaNO2, CNH4Cl, CNaCl, CNaOH, and Ccatalyst are the
concentrations.
The above system of coupled ordinary differential
equations was solved using the fourth-order RungeKutta method.10
Comparison between Simulation and
Experimental Results for a Batch Reactor
The delay time, which is the time when the temperature of the reactive solution starts to rise rapidly, was
chosen as the main parameter to compare simulation
results to experimental results. In addition, some temperature-time trajectories were also used to evaluate
the similarities between the experimental and simulation results.
As shown in Figures 13 and 14, excellent agreement
in the delay time and temperature-time trajectories
was achieved. The simulated temperature-time trajectories have virtually identical delay times and rates of
increasing temperature with the experimental trajectories. Because the exothermic reaction is very rapid at
low pH and slow at high pH, it was necessary to study
the reaction at low temperature for low pH and at high
temperature for high pH in order to obtain good
experimental results using the method of initial rates.
Therefore, for extrapolation for medium pH and room
temperature using the kinetic model, there were some
deviations which resulted in the early temperature rises
in the simulated temperature-time trajectories. The
Figure 16. Typical temperature profiles in flow conditions.
reaction mechanism and kinetics are being studied
further to reduce this deviation.
Demonstration of the Fused Chemical
Reactions in a Flowloop System
The ability of encapsulated fused chemical reactions
to deliver a substantial amount of heat at the desired
location, a location far from the entrance of the pipe was
also examined in a flow-loop system. The system is a
300 m, 1 in. PVC pipe flow system built at Conoco,
Production Research Division, and is shown in Figure
15.
The temperature profiles at different times in the
pipeline of a typical experiment are shown in Figure
16. The temperature profiles show that the reaction was
delayed until the chemical slug reached the point
approximately 750 m from the injection point. The
5064
Ind. Eng. Chem. Res., Vol. 40, No. 23, 2001
reaction generated a substantial amount of heat that
raised the temperature to 82 °C, which is higher than
the melting point of the wax deposit. The hot fluid was
then redirected through the dewax observation pipe
section where some candle wax had been deposited. The
combined effect of high temperature and high shear
stress was observed to sweep the wax deposit off the
pipe wall as large particles. The addition of dispersant
is desirable to disperse the melted wax in the solution,
preventing it from redepositing on the pipe wall.
More flow experiments are being conducted to achieve
a complete understanding of the controlled release of
the encapsulated acid catalyst as well as to address
some other aspects such as neutral buoyancy of the
capsule and the dispersion of the reactants in flow
conditions.
Conclusions
The reaction kinetics was found to be a strong
function of the pH of the solution, which is typical for
oxidation-reduction reactions. This important characteristic provides great flexibility to control the rate of
reaction and the release of heat by simply changing the
pH of the solution. The release of the catalyst encapsulated in Eudragit S100-coated hard gelatin capsules
is controlled by the dissolution of the polymeric coating.
The polymer dissolution is limited by the ionization of
the polymer at the surface. Encapsulation of the catalyst
by a soluble polymer such as Eudragit S100 is a very
promising technique to delay the release of heat from
exothermic reactions. Experimental results clearly show
that the release of heat can be delayed as long as 20 h
which, in normal operating conditions of the pipeline,
is equivalent to a distance from the platform of approximately 70 km. More importantly, both the delay
time and the rate of heat release are controllable so that
a desired temperature-length profile in the pipeline can
be achieved easily. The feasibility of the fused chemical
reaction to remove wax deposit in pipelines was demonstrated in a laboratory flow loop. The release of heat
was delayed to the desired location in the pipeline. The
in situ release of heat was sufficient to raise the
temperature of the fluid sufficiently so that the removal
of wax was observed.
Acknowledgment
The authors acknowledge Capsugel and RohmAmerica for providing the capsules and coating materials. We also thank Dr. Steve C. K. Tsai and the staff at
the Conoco, Production Research Division, Ponca City,
for their advice and laboratory support in building the
flowloop. We also gratefully acknowledge the financial
support from Petrovietnam and the continuous support
of our affiliate companies: Baker Petrolite, Chevron,
Conoco, PDVSA-Intevep, Halliburton, Phillips Petroleum, and Schlumberger.
Nomenclature
R, β )reaction orders
γ ) dissolution rate (mm/h)
∆Cp ) overall change in the heat capacity with respect to
the limiting reactant (J mol-1 K-1)
∆Hrx(T) ) heat of reaction at temperature T with respect
to the limiting reactant (J mol-1)
a ) polymer dissolution rate order with respect to the
hydroxide ion concentration
A ) heat-transfer area of the reactor (m2)
CA ) concentration of reactant A in the solution (mol dm-3)
CA0 ) initial concentration of reactant A in the solution
(mol dm-3)
CB ) concentration of reactant B in the solution (mol dm-3)
CB0 ) initial concentration of reactant B in the solution
(mol dm-3)
CNaNO2 ) concentration of NaNO2 in the solution (mol dm-3)
CNH4Cl ) concentration of NH4Cl in the solution (mol dm-3)
CNaCl ) concentration of NaCl in the solution (mol dm-3)
CNaOH )concentration of NaOH in the solution (mol dm-3)
Ccatalyst ) concentration of acid catalyst in the solution (mol
dm-3)
Cps ) heat capacity of the solution with respect to the
limiting reactant (J mol-1 K-1)
E1 ) activation energy of the medium-pH region (J mol-1)
E2 ) activation energy of the low-pH region (J mol-1)
E3 ) activation energy of the high-pH region (J mol-1)
Ep ) activation energy for the polymer dissolution (J mol-1)
k ) rate constant of the exothermic reaction (mol-4.6 dm-13.8
s-1)
k1 ) rate constant in the medium-pH region (mol-4.6 dm-13.8
s-1)
k2 ) rate constant in the low-pH region (mol-6.4 dm-15.6
s-1)
k3 ) rate constant in the high-pH region (mol-3.9 m-13.1 s-1)
kp ) rate constant of the polymer dissolution (mm/h)
L ) thickness of the polymeric coat (mm)
nc ) number of capsules introduced into the reactive
solution
N0 ) number of moles of catalyst encapsulated in one
capsule (mol)
NA0 ) initial number of moles of the limiting reactant in
the solution (mol)
pH ) pH of the solution at the given condition
rA ) rate of appearance of the reactant A (mol dm-3 s-1)
T ) temperature of the solution (K)
Ta ) temperature of the surrounding area (K)
t ) time (h or s)
tl ) lag time (h)
tr ) release time (h)
U ) overall heat-transfer coefficient of the reactor (J s-1
K-1 m-2)
[OH-] ) concentration of OH- in the solution (mol dm-3)
[H+] ) concentration of proton in the solution (mol dm-3)
X ) conversion of the limiting reactant
Literature Cited
(1) Singh, P.; Fogler, H. S. Fused Chemical Reactions: 1. The
Use of Dispersion to Delay Reaction Time in Tubular Reactors.
Ind. Eng. Chem. Res. 1998, 37 (6), 2203.
(2) Hirayama, F.; Uekama, K. Cyclodextrin-based controlled
drug release system. Adv. Drug Delivery Rev. 1999, 36 (1), 125.
(3) Akelah A. Novel utilizations of conventional agrochemicals
by controlled release formulations. Mater. Sci. Eng. C 1996, 4 (2),
83.
(4) Economides, J. M.; Nolte, G. K. Reservoir stimulation, 3rd
ed.; Wiley: New York, 2000.
(5) Brown, T. S.; Niesen, V. G.; Erickson, D. D. Measurement
and Prediction of the Kinetics of Paraffin Deposition. SPE 1993,
26548.
Ind. Eng. Chem. Res., Vol. 40, No. 23, 2001 5065
(6) Ashton, J. P.; McSpadden, H. W.; Velasco, T. T.; Nguyen,
H. T. Method of and Composition for Removing Paraffin Deposits
from Hydrocarbon Transmission Conduits. U.S. Patent 4,755,230,
1988.
(7) Khalil, C. N. Process for the thermo-chemical dewaxing of
hydrocarbon transmission conduits. U.S. Patent 5,639,313, 1997.
(8) Langer, R. S.; Wise, D. L. Medical Applications of Controlled
Release; CRC Press: Boca Raton, 1984; Vols. I and II.
(9) Fogler, H. S. Elements of Chemical Reaction Engineering,
3rd ed.; Prentice-Hall: Englewood Cliffs, NJ, 1999.
(10) Carnahan, B.; Luther, H. A.; Wilkes, J. O. Applied Numerical Methods, Reprint; Wiley: New York, 1990.
Received for review November 27, 2000
Revised manuscript received February 22, 2001
Accepted March 12, 2001
IE0009886