Presented at:
Third Joint China/USA C hemical Engineering Conference (CUChE-3)
Beijing, China, September 25 - 28, 2000
Modeling the Complex Chemical Reactions and Mass Transfer in a Phosphoric
Acid Reactor
†
Paul M. Mathias†, Chau-Chyun Chen† and Marten Walters‡
‡
Aspen Technology, Inc.
KEMWorks Technology, Inc.
Ten Canal Park
5925 Imperial Parkway, Suite 105
Cambridge, MA 02141-2201
Mulberry FL 33860-7621
U.S.A.
U.S.A.
Introduction
The production of phosphoric acid by the “wet process” is a complex, large-scale industrial operation in
which phosphate rock is beneficiated, reacted with sulfuric acid and filtered to remove the by-product,
calcium sulfate. In this paper we demonstrate that valuable insight can be gained into this complex
chemical process through a fundamental model implemented in the Aspen Plus® process simulator.
Phosphoric acid is primarily produced by what is known in the industry as the wet process (Slack, 1968;
Becker, 1989). In the wet process, phosphate rock, which includes calcium, phosphate and a number of
impurities, is mined, beneficiated (concentrated) and then sometimes ground dry or wet through the use
of ball mills or rod mills. The rock is fed into an attack tank or reactor and reacted (digested) with sulfuric
acid (H2SO4). An extremely simple representation of the digestion is as follows:
Ca 3(PO4)2 + 3H2SO4 + 6H2O
> 2H3PO4 + 3CaSO4•2H2O
(1)
The reaction produces phosphoric acid (H3PO4) and calcium sulfate dihydrate or gypsum (CaSO4• 2H2O).
The gypsum precipitates and is filtered, giving phosphoric acid as the product. In a variation of the wet
process - the hemihydrate process - calcium sulfate hemihydrate (CaSO4• ½H2O) is produced as the
precipitate. The present phosphoric-acid discussion focuses on the production of phosphoric acid by the
dihydrate process.
The dihydrate process contains sections Figure 1. Production of Phosphoric Acid by the Dihydrate Process
such as attack and digestion reactors, flash
Sul furi c
HO
Aci d
coolers, filtration units, and phosphoric acid
Evap.
Water
concentration. The present simulation
Phosphate
Rock
focuses mainly on the sulfuric-acid-attack
reactor, which is the heart of the process.
We have used a rigorous description of the
thermodynamic and rate-based chemistry
occurring in the attack reactors to develop a
Slurry
steady-state model of the sections of the
dihydrate process containing the attack and
œ
œ
digestion reactors, the flash or vacuum
œœ
Return
œœ œ
Acid
coolers and the filtration units. Figure 1
presents a simple representation of the
Product Acid
Gypsum
process flow diagram. In general, the return
acid is mixed with the sulfuric acid in order to
dilute the sulfuric acid, as shown in Figure 1. But this is, of course, not necessary in the model.
2
Further details on the model and its application are available in Mathias and Mendez (1998) and Mathias
(1999).
Model Fundamentals – Thermodynamics, Kinetics and Mass Transfer
Phosphate rock mineralogy can be highly variable depending primarily on the origin of the rock
(sedimentary or igneous), formation and weathering. Most sedimentary deposits contain varieties of
carbonate-fluorapatite collectively known as francolite, which contains calcium, phosphate, fluoride,
carbonate and other species held together in a crystal lattice. When the rock is treated with a strong
mineral acid, such as sulfuric acid, the phosphate constituent is solubilized as phosphoric acid. In the
simulation we treat the phosphate compound in the rock as a mixture of fluorapatite (Ca 10(PO4)6F2) and
trical or calcium phosphate (Ca3(PO4)2). In most cases we expect fluorapatite to be the dominant
constituent, but we may also need small amounts of trical to quantitatively describe the measured rock
composition. We treat the carbonate component as calcium carbonate and use calcium fluoride to
describe any fluoride component in excess of that contained in the apatite. In order to obtain a realistic
description of the phosphate rock, we include the following major impurities: SiO2, Al 2O3, Fe 2O3, MgO and
Na 2O.
It is necessary to include the ionic species that occur in the liquid phase of the attack tanks and much of
the process (Linkson, 1998; Liu and Watanasiri, 1999). Rigorous description of the chemical equilibrium
of the ionic and molecular species, and the nonideality of the resulting solution was often considered to
be extremely difficult, but this has changed due to significant advances in the theoretical framework
(Chen et al., 1982; Chen at al., 1984; Zemaitis et al., 1986; Chen, 1986) and the technological capability
of process simulators such as Aspen Plus (for further information, see Aspen Plus Getting Started
Manual: “Modeling Processe s with Electrolytes”). The Chen Electrolyte NRTL (ElecNRTL) model (Chen et
al., 1982; Chen at al., 1984; Chen, 1986) has been used in this work.
Details of the electrolyte-based thermodynamic model are presented elsewhere (Mathias and Mendez,
1998; Mathias, 1999). Here we only present some examples that demonstrate the concept.
H2SO4 + H2O <> H3O+ + HSO4HSO4- + H2O <> H3O+ + SO42Ca 2+ + SO42- + 2H2O <> CaSO4•2H2O
(2)
(3)
(4)
Eqns. (2) and (3) present the dissociation of sulfuric acid and Eqn. (4) shows the precipitation of gypsum.
Many of the parameters in the thermodynamic model can be estimated or derived from published values
of chemical thermodynamic properties, for example Wagman et al. (1982). The Aspen Plus databanks
provide many of the model parameters. Finally, the default values of the model parameters often provide
adequate accuracy. However, key model parameters must be obtained by fitting experimental data. The
Aspen Plus Data Regression System (DRS) has been used to obtain the optimum values of the model
parameters needed to accurately describe the important process conditions.
Figure 2
Vapor Pr essure of Phosphoric Acid Solutions
800
700
600
Vapor Pressure (mmHg)
Figure 2 presents a comparison between model and
data (Brown and Carlton, 1952) for the vapor
pressure of pure phosphoric acid solutions. These
data are important because accurate representation
of the vapor pressure is important for an accurate
simulation of the flash coolers. The good agreement
between model and data also indicates that the
model provides an accurate description of the
nonideality of phosphoric acid-water mixtures, the
two major components in the product acid.
500
100°C
400
90°C
300
80°C
200
An excellent source for solubility data relevant to
the phosphoric-acid process is the compilation by
Linke (1958). The solubility of gypsum in solutions
of phosphoric acid and sulfuric is extremely
70°C
100
60°C
50°C
0
0
10
20
30
Wt% P 2O5
40
50
60
The present thermodynamic model provides a
comprehensive description of the thermodynamic
properties of this system. Further details are
provided in Mathias and Mendez (1998).
Fi gure 3
Solubi li ty of Calcium Sul fate in P hosphori c Acid Sol uti ons
Comparison of ASPE N PLUS Model to Data of Taperova (1940) and Taperova
and Shul gina (1945)
1.6
1.4
Wt% CaSO 4 in Saturated Solution
important to the process. Figure 3 presents a
comparison between model and data for the
solubility of gypsum in phosphoric acid solutions.
The model provides an accurate correlation over a
wide range of conditions.
80 °C
1.2
6 0°C
1.0
4 0°C
0.8
2 5°C
0.6
0.4
0.2
The key reaction kinetics and mass transfer
phenomena in the reactor are rock dissolution and
Wt% P O in Solution
its tendency to coat, precipitation of gypsum (both
normal and nucleated) and co-precipitation of phosphate compounds in the gypsum (Slack, 1968; Becker,
1989). The plant losses are the undissolved or coated rock (known as citrate-insoluble or CI loss) and the
phosphate co-precipitation (known as the citrate-soluble or CS loss). These rate phenomena have been
captured with the following assumptions:
0.0
0
10
20
30
2
40
50
60
5
1. Rock dissolution, assumed to be proportional to the concentration of undissolved rock and inversely
proportional to the sulfate concentration.
2. Rock coating, assumed to be proportional to the concentration of undissolved rock, the gypsum
precipitation rate and the sulfate concentration.
3. Normal gypsum precipitation, assumed to be proportional to the calcium and sulfate concentrations
and the distance from equilibrium.
4. Nucleated gypsum precipitation, assumed to be negligible up to the supersaturated limit, and
extremely fast once this limit is reached.
5. Co-precipitation losses, assumed to be proportional to the total gypsum precipitation rate and ratio of
the phosphate and sulfate concentrations.
All these effects have been incorporated into a user subroutine for the stirred-tank reactor (RCSTR) in
Aspen Plus.
Aspen Plus Implementation and Results
The key building blocks for the Aspen Plus
®
simulation model are the thermodynamic model Figure 4. Aspen Plus Simulation of the D ihydrate Process
S ulfuric Acid Phosphate Rock
and the RCSTR model. Each tank of the reactor
0.0 1
0.01
0.01
is an RCSTR block and the other pieces of
Water
0.98
equipment in the plant are represented by
0.01
blocks such as HEATER, FLASH2 (2-phase
0.01
Rx 1
Rx 2
flash), SEP2 (two-outlet component splitter) etc.
0 .01
Gases
P roduct
Acid
The filtration system is treated as a series of
H 2O
Evap.
0.98
Rx
9
Rx
3
SEP2 blocks. A schematic representation of a
Filter
0.98
particular Aspen Plus flowsheet is presented in
Gypsum
Figure 4. It is assumed that most of the rock is
Ret
urn
Rx 8
Rx 4
Acid
fed to Rx2, and that most of the sulfuric acid
and return acid are fed to Rx3. The sulfuric acid
and return acid are assumed to be piped
Rx 6/7
Rx 5
independently, but, as noted earlier, in current
Slurry
practice recycle acid and sulfuric acid are
generally mixed prior to addition to the reactor. Other plant configurations can easily be modeled.
The Aspen Plus model has many uses, including gaining insight into the process, trouble-shooting plant
problems and anticipating the effect of design changes. Here we only briefly describe three studies of the
effect of plant operation on CI and CS losses.
A. Plant throughput
B. Sulfate level
C. Sulfuric acid split between Reactors 2 and 3 (see Figure 4)
In all the studies presented below, the acid strength was held constant at 26% P 2O5.
A. Plant throughput. The model predicts that the effect of increased production with the same equipment
is to increase CI losse s, while keeping the CS losses approximately constant. This effect results
because the reactors have less residence time to dissolve the rock, and the result is in agreement
with plant experience.
Figur e 5. Lo sses as a F un ctio n of SO4
Weight % CS and CI Losses
B. Sulfate level. Figure 5 shows the effect of
6
increasing the sulfuric acid flow to the plant,
which will result in an increase in the residual
5
CSL+CI L
sulfate level of the product acid. The CS losses
4
go through a weak maximum at a sulfate level of
about 2.5%. This is a complicated effect
CSL
3
resulting from the direct beneficial effects of
increasing the sulfate level (lower CS losse s)
2
and the negative secondary effect where
CIL
1
increased sulfate level shifts more of the
gypsum precipitation to Compartment #2 where
0
the sulfate levels are lower (higher CS loss).
1. 5
2. 0
2. 5
3.0
This kind of insight into the interaction of effects
Weight % SO4 in Product Acid
can only be gained through a complete plant
model like the present one. It should be noted that the present model suggests operating at the
lowest possible sulfate levels in order to minimize the total phosphate loss. However, it is well known
that the gypsum crystals that form at low sulfate levels are difficult to filter. In future versions of the
model we plan to include the description of the particle-size distribution of the gypsum crystals.
The above examples indicate the value that can be
gained from a fundamentally based process model
incorporated into a process simulator.
F ig ure 6. Effect of Su lfu ric Acid Sp lit o n Los ses
6
CSL+CIL
5
WQeight % CS and CI Losses
C. Sulfuric acid split. Figure 6 predicts the effect of
feeding the sulfuric acid to the rock compartment
(Rx 2 in Figure 4) rather than Compartment #3.
The CS losse s come down because sulfate level
in the rock compartment rises, but unfortunately
the CI losse s rise faster because the higher
sulfate level significantly increases the rate of
rock coating.
3.5
CSL
4
3
2
CIL
1
0
0
5
10
15
% of Sul furi c Acid Fed to Com partment 2
Conclusions
Phosphoric acid reactors have been considered to be too complex to be modeled on a fundamental
basis. This work demonstrates that these kinds of chemical processe s can indeed be modeled and that
the benefits in terms of process understanding and rational process improvement are considerable.
20
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