Investigation of scale formation in heat exchangers of phosphoric acid evaporator plants.
Le principal probleme dans la concentration de l'acide phosphorique est du a l'encrassement de la face cote tube des echangeurs de chaleur des unites d'evaporation. Les depots qui se forment sur les surfaces de transfert de chaleur sont dus a une sursaturation importante de la liqueur d'acide phosphorique par rapport au sulfate de calcium. Un examen de la litterature scientifique revele qu'aucune information n'est disponible sur le transfert de chaleur et sur l'encrassement par cristallisation des solutions d'acide phosphorique industrielles. Dans cette etude, on a etudie la solubilite de differents types de sulfate de calcium dans la solution d'acide phosphorique et sa dependance par rapport a la concentration en acide et a la temperature. Un grand nombre d'experiences d'encrassement ont ete menees dans un piquage d'une unite d'acide phosphorique a differentes vitesses d'ecoulement, temperatures de surface et concentrations, dans le but de determiner les mecanismes, qui controlent le processus de deposition. Apres avoir determine les effets des parametres operatoires sur le procede de deposition, on a mis au point un modele pour la prediction des resistances a l'encrassement. La reaction de cristallisation du sulfate de calcium suit une cinetique de second ordre par rapport a la sursaturation. On a trouve que l'energie d'activation evaluee pour la reaction de surface de la formation des depots etait de 57 kJ/mol. Les resistances a l'encrassement predites sont comparees aux donnees experimentales. Un bon accord quantitatif et qualitatif est trouve entre les vitesses d'encrassement predites et mesurees.
Keywords: phosphoric acid evaporators, calcium sulphate solubility, scale formation, modelling
Scale deposition in heat transfer equipment is known as a major engineering problem in many process industries, since deposits on heat transfer surfaces create a barrier to the transmission of heat, increase pressure drop and promote corrosion of tube material. These effects reduce the heat transfer equipment's performance significantly. Scales sometimes also limit or block pumps, tubing, casing, flow lines, heaters, tanks and other heat transfer or production equipment and facilities. Scale deposits are classified according to the physical and chemical processes that occur. Fouling occurring on the heat transfer surfaces of boilers and evaporators is usually a crystalline deposit caused by growth of mineral salt crystals on the surface.
In industrial phosphoric acid plants, the concentrated phosphoric acid solution is supersaturated with respect to calcium sulphate. As a result, part of the calcium sulphate in the liquor deposits on the heat exchanger tube walls. Since the thermal conductivity of these scales is very low (typically between 0.5-2 W/mK (Muller-Steinhagen, 1994)), thin deposits can already reduce the overall heat transfer coefficient significantly. Therefore, regular cleaning of heat exchangers is required, typically at bi-weekly intervals. The scaling problem can be particularly serious if the evaporator is incorrectly designed or operated. This may reduce the cleaning intervals to one week, which is a major drawback in the energy saving scheme.
Because of scaling and corrosion, wet-process acid concentration presents many problems, which have not been entirely solved, despite major efforts in the past decades. The problems of scaling are essentially economic. As scaling becomes more serious, maintenance costs and downtime increase, while the production rate decreases. After some time of operation, the internal surfaces of equipment in contact with acid are covered with scale, which is removed by washing out with hot dilute sulphuric acid at high velocity. This descaling action is partly by dissolution and partly by abrasion. The main equipment components that require regular washing are flash chamber, heat exchangers, and acid pipe work. In addition to reduced heat transfer rates, breakage of the fragile impregnated graphite heat exchanger tubes is a significant concern.
No information is available in the literature about crystallization fouling from phosphoric acid solutions and about the effect of operating parameters on this phenomenon. Hence, there is a lack of experimental evidence and physical understanding with respect to this subject. The mechanisms of crystallization fouling have been studied by many investigators. Numerous papers and patents have been published in the field of scale formation on heat exchanger surfaces under forced convective heat transfer. Detailed information can be found in the review books of Garrett-Price (1985), Melo et al. (1987), and Bott, (1995), and the review papers of Hasson (1979), Epstein (1983), Somerscales (1988) and Muller-Steinhagen (1994). However, hardly any research work on fouling of phosphoric acid solutions can be found in the literature. In what follows, some of the recent investigations on fouling of calcium sulphate are reviewed.
Jamialahmadi and Muller-Steinhagen (1993) studied the effects of scale deposition on nucleate pool boiling heat transfer over a wide range of heat fluxes for various solution concentrations. The general shape of the heat transfer coefficient versus time curves was characterized by an initially sharp decrease to a secondary minimum, followed by an increase to a secondary maximum and a subsequent gradual decrease towards an asymptotic value. However, a strong effect of the adjusted process conditions on the transient heat transfer coefficient was observed.
Najibi et al. (1997) performed many experiments on calcium sulphate scale deposition during sub-cooled flow boiling in a vertical annulus. They have shown that the deposition rate is controlled by different mechanisms, depending on flow velocity and surface temperature. They also observed different trends for conditions where convective heat transfer or nucleate boiling prevails. For flow velocities up to 2 m/s, a linear increase in fouling resistance with time was observed, which is indicative of pure crystallization fouling without any suspended particulate matter.
Sudmalis and Sheikholeslami (2000) investigated the co-precipitation of calcium sulphate and calcium carbonate under various operating conditions. The results have been compared with crystallization results of single salts. They pointed out that induction period and kinetics of co-precipitation of these salts follow those of pure calcium carbonate. Calcium sulphate was precipitated in form of dihydrate and had a needle-shape structure, while calcium carbonate had a spiral growth and was precipitated in form of calcite. They concluded that the relationship between the thermodynamic concentrations of [Ca.sup.2+] for pure calcium sulphate and calcium carbonate solutions depended on the pH of the solution. The precipitate structure was affected by co-existence of the salts.
More recently, Helalizadeh et al. (2000) performed many experiments to investigate scale formation from solutions of calcium sulphate/calcium carbonate mixtures. Depending on flow velocity and surface temperature, the deposition rate was found to be controlled by both mass transfer and chemical reaction. Scanning Electron Microscopy and X-ray analyses showed that deposits included a mixture of crystals of the two dissolved salts and had an adhesion strength that was approximately between that of CaS[O.sub.4] and CaC[O.sub.3]. The results of the measurements at different conditions were used to develop a mechanistic model for deposition from salt mixtures (Helalizadeh et al., 2005). It was assumed that the deposition of calcium sulphate/calcium carbonate mixtures on the heat transfer surface during convective heat transfer and sub-cooled flow boiling takes place in two successive steps. Hence, the proposed model includes transport and reaction processes and was developed based on forced convection data. The boiling effect was considered by inclusion of an enhancement factor, E. The advantage of this correlation is the simplicity in form and the need for less parameters in comparison to other correlations. In addition, experiments were performed to study the effect of surface energy on fouling behaviour.
Coated heat transfer surfaces were tested successfully to reduce calcium sulphate, calcium carbonate and calcium sulphate/calcium carbonate mixture fouling. The fouling runs on surfaces modified by Muller-Steinhagen and Zhao (1997) demonstrated that magnetron sputtering, ion implantation or autocatalytic Ni-P-PTFE coating of heat transfer surfaces may lead to a reduction of scale formation at otherwise identical operating conditions, due to a reduction of the surface energy. It was also observed that deposits formed on low energy surfaces were less adherent and less dense than for untreated surfaces.
SOLUBILITY OF CALCIUM SULPHATE IN PHOSPHORIC ACID SOLUTIONS
While there are numerous data on the solubility of calcium sulphate in pure water, data on the solubility of this compound in phosphoric acid solutions are limited. Some data have been provided by Slack (1968), Linke (1965) and White and Mukhopadhyay (1990).
The solubility of the various hydrate forms in phosphoric acid solutions has been reported by Slack (1968) at a series of temperatures between 25 and 90[degrees]C. The curves in Figure 1, prepared from solubility data reported by Slack (1968), show that at temperatures higher than the equilibrium temperature the dihydrate and hemihydrate curves diverge more sharply at 32% [P.sub.2][O.sub.5] than at the two higher concentrations, and that the least divergence is obtained at the highest concentration. This means that at low phosphoric acid concentrations the nucleation threshold value is reached with less increase in temperature over the equilibrium temperature than at higher concentrations. Within the transition region on both sides of the limiting temperature, dihydrate nucleation will decrease with increasing temperature. At a certain temperature the supersaturation relative to dihydrate will not reach the threshold value for dihydrate nucleation, and only hemihydrate will form. In analogy with the above, it follows that the lowest possible working temperature for a hemihydrate process depends on the highest supersaturation in the reaction system.
[FIGURE 1 OMITTED]
EXPERIMENTAL EQUIPMENT AND PROCEDURE
Figure 2 shows the schematic diagram of the test rig used for the present investigations. All components in contact with the test liquid have been made from stainless steel. The test rig was installed in a side-stream of the phosphoric acid plant of the Razi Petrochemical Complex (RPC) in Iran, connected to the main stream at the discharge of the transfer pump that transfers product acid from the first stage to the second stage evaporation unit. The piping of the pilot plant was well insulated to prevent heat losses from the system. Phosphoric acid liquor entered the apparatus, passed through the heating section and returned to the main stream. The flow velocity of the liquid was measured with a calibrated magnetic flow meter. The fluid temperature was measured with thermocouples located in two mixing chambers, before and after the test section. The pressure in the test section was measured with a suitable pressure gage. Two 2" valves were installed in the pilot plant to allow flushing the whole system with water after each experimental run, to reduce corrosion effects of the crude phosphoric acid that is highly corrosive due to its high content of chloride and fluoride ions.
[FIGURE 2 OMITTED]
The test section shown in Figure 2 consists of an electrically heated cylindrical heating rod, which is mounted concentrically within the surrounding pipe. The test heater used in fouling measurements was manufactured by Ashland Chemicals according to specifications by Heat Transfer Research Inc. (HTRI). It is a cylindrical, electrically heated stainless steel rod that was located concentrically within the surrounding vertical pipe and the test liquor was flowing through the resulting annulus in upward direction. The dimensions of the test section are:
Outer diameter of annulus 50.80 mm Inner diameter of annulus or heating rod diameter 10.67 mm Total length of annular section 380.0 mm Length of heated section 99.10 mm Entrance length to heated section 216.0 mm Entrance length to thermocouple location 298.6 mm
The test heater was equipped with four E type thermocouples located in one plane, 82.6 mm after the beginning of the heated section. One thermocouple was connected to a temperature controller to avoid overheating of the test heater. For safety reasons the fouling runs were terminated once the surface temperature of the heater exceeded 220[degrees]C.
The local wall temperature of the heater was measured with the three remaining thermocouples. The thermocouples were calibrated to give the surface temperature according to the following equation:
[T.sub.s] = [T.sub.tc] - q/[lambda]/s (1)
The ratio of [lambda]/s was determined with a Wilson plot technique. The average surface temperature of the heater is then calculated as:
[T.sub.s] = 1/3 x [3.summation over (i=1)] ([T.sub.tc,i] - [??]/[[lambda].sub.i]/[s.sub.i]) (2)
using the readings of all three thermocouples.
All temperatures, flow velocity, heat flux, and heat transfer coefficient were recorded every 10 min with a desktop computer, in connection with an Axiom 16-channel high-speed A/D converter board (AX5411: multifunction analogue/digital input/output board, 16 single-ended analogue input with 12-bit resolution) and an Axiom 16-channel amplifier/multiplexer panel (AX752: 16-channel signal conditioning/multiplexer panel designed to accommodate thermocouples). The power supplied to the test heater could be calculated from the measured current and voltage. A menu driven program was written in Quick Basic for real-time data acquisition, display and analysis on computer.
The heat transfer coefficient was defined as:
[alpha] = q/[T.sub.s] - [T.sub.b] (3)
The local bulk temperature at the wall thermocouple plane was calculated assuming that the bulk temperature increases linearly from [T.sub.b1], in mixing chamber 1, to [T.sub.b2], in mixing chamber 2, which is a valid assumption for a constant heat flux boundary condition:
[T.sub.b] = [T.sub.b1] + 82.6/99.1 x ([T.sub.b2] - [T.sub.b1]) (4)
Power regulator, ampere meter, voltmeter, and temperature indicators were calibrated and tested after installation for proper operating conditions. The magnetic flow meter was calibrated frequently because the detector electrodes suffered from scale formation and the subsequent cleaning.
Liquor samples were analyzed using the facilities of the industrial laboratory of the Razi Petrochemical Complex (RPC). The solution composition was 57 wt% [H.sub.3]P[O.sub.4] and the concentration of CaS[O.sub.4] was varied from 1.4 wt% to 1.85 wt%. Scale samples were analyzed in the RPC laboratory and also in the Bandar Imam Petrochemical Complex laboratory. The range of the experimental operating conditions is shown in Table 1.
ERROR ANALYSIS OF EXPERIMENTAL DATA
Experimental error may be introduced in the measured heat transfer coefficients or fouling resistances due to heat losses from the test section to the ambient air and measurement errors of heat flux, bulk temperature, flow velocity, solution concentration and surface temperature of the heaters. The heat transfer coefficient also depends to a minor extent on the surface texture of the heat transfer surfaces. It was assumed that the cleaning of the heaters after each fouling experiment restored the surfaces to a comparable initial roughness. Repeating some fouling runs confirmed this assumption, as similar fouling curves were obtained. Even though the heat transfer surface of the test section has been made from a different material (i.e., stainless steel) than those of the comparative plant heat exchanger (i.e., graphite), good agreement between plant and pilot unit fouling rates has been found, once the heat transfer surfaces had been fouled and cleaned several times.
The error of the adjusted heat flux is due to errors in the measurements of electrical current and voltage. It was observed that the power delivered by the heater boxes showed small fluctuations depending on the time of the day. While this phenomenon does not affect the convective heat transfer coefficient, the related variation in heat transfer surface temperature will have some effect on the rate of fouling. Since the heat flux fluctuations have been relatively small and around an average value that was used in subsequent calculations, this effect is considered as negligible.
The flow velocity was measured with a magnetic flow meter with a measurement accuracy of 3% of reading. The fluid pressure was measured with strain-gauge sensors having a factory calibrated accuracy of about 0.8% of the operating range, which was adequate for the present fouling experiments.
Heat losses through the insulation of the test section affect the bulk temperature of the liquid. However, since both inlet and outlet temperatures of the liquid have been measured to determine the bulk temperature at the wall thermocouple level, there is no relevant effect of heat losses. The bulk liquid temperatures were measured with K-type thermocouples located in mixing chambers before and after the test sections. These thermocouples were initially checked against a quartz thermometer with an accuracy of 0.02 K. The inaccuracy in temperature measurements is due to the calibration of the thermocouples that leads to a deviation of approximately [+ or -]0.2 K.
The largest experimental errors for the heat transfer coefficients and fouling resistances would hence be expected at high heat fluxes with a small temperature difference between heat transfer surface and liquid bulk temperature, i.e., at high flow velocities. For fouling resistance measurements, the inaccuracy changes during the test run due to the change in temperature differences between heater surface and fluid bulk. In this investigation, the maximum temperature differences for heat transfer coefficient measurements were 18[degrees]C. Thus a minimum error of 3.4% is expected for the evaluated heat transfer coefficients:
+ [square root of ([(0.01).sup.2] + [(0.2/18).sup.2] + [(0.03).sup.2])] = [+ or -]0.0335
Errors are higher when the temperature differences are lower. For the smallest initial temperature difference of 3[degrees]C, the estimated error in the evaluated heat transfer coefficient is equal to 7.4%:
+ [square root of ([(0.01).sup.2] + [(0.2/3).sup.2] + [(0.03).sup.2])] = [+ or -]0.0738
Even for the thin deposits found in the present study, the heater surface area is slightly increased and the cross-sectional area for flow decreased. Furthermore, the changing surface roughness associated with deposit formation may have some effect on the heat transfer coefficient. However, these effects are small enough to be neglected. Since the power supplied by the electrical heater is almost constant with time, the temperature at the deposit/ liquor interface is hence constant at the value of the initially clean heat transfer surface.
EXPERIMENTAL RESULTS AND DISCUSSION
The effect of operating conditions such as fluid velocity, surface temperature, and bulk concentration on the rate of fouling must be determined by isolating one parameter at a time. Therefore, it was necessary to conduct experiments under controlled conditions, where certain parameters can either be constant or where the effects of these parameters are minimized. It should be noted that conducting such experiments was not a straightforward task since they had to be synchronized with the parallel operation of the actual processing plant. In the present investigation, it took considerably longer than one year after installation and commissioning of the test rig to perform enough suitable experiments from which those, where the desired parameters were constant, could be extracted.
A fouling curve represents the relationship between fouling resistance and time. In the present investigation, the fouling resistances were calculated from the measured heat transfer coefficients at the beginning of each experiment and the actual heat transfer coefficients after a certain time, according to the following equation:
[R.sub.f] = 1/[[alpha].sub.foul](t) - 1/[[alpha].sub.clean](t = 0) (5)
The shape of fouling curves may be linear, falling rate, asymptotic or saw-tooth. It is indicative of the phenomena occurring during the fouling process. In this investigation, measured fouling curves showed an almost linear increase in fouling resistance with time. A linear relationship is generally characteristic of hard and adherent deposits and indicates that the deposition rate is either constant and there is no removal, or that the difference between deposition rate and removal rate is constant (Bott, 1995).
Effect of Flow Velocity
As the velocity is increased, the heat transfer coefficient is also increased. Thus, for a given temperature difference, the required heat transfer area and hence the capital cost reduce with increasing flow velocity. On the other hand as the velocity is increased, the pressure drop is also increased. However, the optimum velocity for acceptable pressure drop may not be the same as that required for minimizing the occurrence of fouling.
Many investigations have been accomplished to determine the effect of flow velocity on deposit formation during forced convective heat transfer. Different effects of the fluid velocity have been reported in the literature. Increasing the flow velocity frequently reduces fouling (Hasson and Zahavi, 1970); in some cases, however, also an increase in fouling has been reported (Hatch, 1973). The deposition process generally depends on mass transfer of the precursors and a formation/attachment reaction to/at the heat transfer surface. These two processes are thought to act in sequence, involving a mass transfer coefficient, ?, and a reaction rate constant [k.sub.r]. If the formation/attachment reaction is assumed to be a first order reaction, the rate of deposit formation, [[??].sub.d] is defined by the following equation:
[[??].sub.d] = [beta] [1/2([beta]/[k.sub.r]) + ([C.sub.b] - [C.sup.*]) - [square root of (1/4 [([beta]/[k.sub.r]).sup.2] + ([beta]/[k.sub.r])([C.sub.b] - [C.sup.*]))]] (6)
where [C.sub.b] and [C.sup.*] are the concentration of foulant in the bulk of the liquor and the saturation concentration at the surface temperature, respectively.
Obviously, the relative magnitude of the mass transfer coefficient and reaction rate constant will determine whether one or both of these processes will control the rate of deposition. Since the mass transfer coefficient depends on the fluid velocity, then the rate of fouling will be affected by fluid velocity when mass transfer is slower than the formation/attachment reaction. If the formation/attachment reaction is slower than the transport processes, then the rate of formation will be susceptible to a variable other than fluid velocity, i.e., the surface temperature. Therefore, if the fouling process is not mass transfer-controlled, the fouling rate should be independent of the flow velocity as long as the surface temperature remains constant. In certain circumstances this prevalence of one process over the other may change with time and/or operating parameters. For example, Ritter (1983) proposed that crystallization fouling of calcium sulphate under forced convective conditions is mass transfer-controlled, while Hasson and Zahavi (1970) claimed that it is reaction-controlled.
Increasing the fluid velocity also increases the wall shear stress, which may cause the removal of part or all of the deposits. This may yield lower ultimate values of the fouling resistance; for weakly adhering deposits, increasing the flow velocity may even completely eliminate fouling. If the deposits are tenacious, increasing the flow velocity may, up to a certain point, not decrease fouling significantly. For very hard and strongly adhering deposits like CaS[O.sub.4] and CaC[O.sub.3], therefore, increasing the flow velocity has only a small effect on the fouling process. For several industrial processes involving calcium and silica scales, no reduction of deposition was found for flow velocities up to 5 m/s (Ritter, 1983).
For scale formation in the phosphoric acid plant, the effect of fluid velocity on the fouling resistance is shown in Figure 3 for constant solution concentration, initial surface temperature and bulk temperature. Since the surface temperature has a significant effect on the fouling rate, it was decided to start all tests with an initial surface temperature of 107[degrees]C to allow a better comparability. The liquor velocity ranged from 1.3 m/s up to 1.8 m/s. Due to the process plant operating conditions, it was not possible to conduct reliable experiments at lower velocities .
[FIGURE 3 OMITTED]
Effect of Surface Temperature
The variation in fouling resistance with initial surface temperature for phosphoric acid solutions at constant flow velocity, bulk temperature and solution concentration is shown in Figure 4. As was expected, the fouling resistance depends strongly on the heat transfer surface temperature. As the temperature of the heat transfer surface increases, the reaction rate constant increases according to an Arrhenius relationship.
[FIGURE 4 OMITTED]
As discussed earlier, the mechanism of fouling on the heat transfer surface can be controlled either by molecular diffusion or by chemical reaction at the heat transfer surface or by both mechanisms. The dominant effect of the surface temperature indicates that the controlling mechanism in this case is the chemical reaction at the heat transfer surface.
Effect of Solution Concentration
The effect of solution concentration on the fouling resistance at constant bulk temperature, surface temperature and fluid velocity is shown in Figure 5. The fouling curves for all concentrations show an almost linear trend, with fouling for the higher concentrations being considerably more severe than for the lower concentration.
[FIGURE 5 OMITTED]
The important factor relevant to crystallization fouling is the degree of supersaturation of the deposit forming species, rather than the molar concentration. Hence, the extent of supersaturation will generally determine the rate of the crystallization or scale formation. Here, supersaturation is defined as the difference between the actual concentration of calcium sulphate and the solubility of calcium sulphate in the phosphoric acid solution. It should be noted that, for the present case, the deposition rate, i.e., the slope of the fouling curves, is approximately proportional to the square of the supersaturation.
MODELLING OF DEPOSITION PROCESS
Since fouling is a time-dependent phenomenon, the use of constant design values for the fouling resistance, which is common practice in designing heat exchangers, at best allows estimation of what may happen to the heat exchanger performance, but not when this will happen. In order to provide a satisfactory surface area for an acceptable period of operation it is, therefore, necessary to be able to predict the dependence of fouling resistance on both time and operational parameters. A reliable scale prediction model would also be very desirable to predict the possibility and severity of scale deposition for the various heating or cooling processes in the phosphoric acid plant; and it would be an effective tool for decisions about the types of treatment that may be applied to prevent scaling problems and for scheduling of cleaning cycles.
Development of the Deposition Model
This section presents the derivation of a model for predicting the formation of calcium sulphate scales, which are the dominant cause of fouling in phosphoric acid concentration plants. In this model, the effects of the main parameters for scale formation, such as surface temperature and concentration have been considered. The following assumptions have been made due to the lack of more comprehensive, detailed information and to simplify the modelling approach:
1. Only a negligible amount of deposit is re-dissolved in the process acid, since the solution is supersaturated.
2. The bulk fluid concentration remains constant and equal to the initial value during the course of an experiment. This is a valid assumption, since phosphoric acid from the main plant enters and leaves the test rig continuously. Contrary to experiments with closed test loops, the composition of the investigated fluid does not change significantly due to the formation of deposits.
3. The deposit layer is homogeneous across its thickness, in terms of thermal conductivity and density.
4. The average bulk temperature is constant.
5. The possibility of aging effects on the deposit structure and properties is not considered.
6. The reaction of calcium sulphate crystallization follows a second order rate with respect to the supersaturation.
A segment of the heated section of the test rig is depicted in Figure 6. The thermal resistance for heat conduction through a cylindrical layer of deposit, which in this case is identical to the fouling resistance, can be written as:
[R.sub.f] = [r.sub.i]ln([r.sub.d]/[r.sub.i])/[[lambda].sub.d] = [d.sub.i]ln([d.sub.d]/[d.sub.i])/2[[lambda].sub.d] (7)
[FIGURE 6 OMITTED]
The thickness of scale deposited can be predicted from the following calcium sulphate mass balance for an incremental cross-sectional volume of the heated section:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the mass of calcium sulphate precipitated, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the calcium sulphate concentration of the liquor, and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the saturation calcium sulphate concentration. Precipitation may occur due to supersaturation conditions at the heat transfer surface and in parallel due to supersaturation conditions in the fluid bulk. The saturation calcium sulphate solubility at different temperatures and phosphoric acid concentrations is calculated from appropriate correlations derived from solubility data. As already indicated in Figure 5, the reaction rate of calcium sulphate crystallization is of second order with respect to supersaturation. This has also been found by White and Mukhopadhyay (1990).
[K.sub.w] is the rate constant for surface deposition and is evaluated at surface temperature, [T.sub.s]. All calcium sulphate precipitation described by the first term of Equation (9) is assumed to adhere onto the tube wall. Only calcium sulphate precipitation contributed from this term results in fouling on the heater surface. The second rate constant, [K.sub.b], is the volumetric rate constant for the bulk reaction, and is evaluated at [T.sub.b]. All calcium sulphate precipitation predicted by the second term in Equation (9) is assumed to nucleate in the bulk and remain suspended in the liquor. The change of scaled diameter with time is described by the following equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
where [fr.sub.d] is the average value for the mass fraction of calcium sulphate in the actual deposit, which was obtained from analyses of the scale samples.
Solving Equation (10) with initial boundary conditions ([d.sub.d](0) = [d.sub.i]) gives the scaled diameter as a function of time as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
Substitution of Equation (11) into Equation (7) gives the time-dependent fouling resistance:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)
The surface reaction rate constant [K.sub.w] is assumed to obey the Arrhenius equation:
[K.sub.w] = [k.sub.0].exp(-[E.sub.act]/R[T.sub.s]) (13)
Fouling resistance data for all measurements were regressed to fit the model given by Equation (12). Appropriate values of scale thermal conductivity, scale density, and calcium sulphate fraction were used ([[lambda].sub.d] = 0.79 W/m.K, [fr.sub.d] = 0.87, [[rho].sub.d] = 2650 kg/[m.sup.3]). The value of thermal conductivity has been obtained from measurements using a thermal conductivity apparatus in the Bandar Imam Petrochemical Complex (BIPC) laboratory. An average value for [fr.sub.d] was obtained using the results of the analyses of the scale samples in the Razi Petrochemical Complex (RPC) laboratory. The density of the scale was taken from published data (Muller-Steinhagen, 1994; Garret-Price, 1985; Najibi et al., 1997).
The results of the regression analyses of all measurements with different surface temperatures were plotted in Figure 7 as a function of 1/[T.sub.s]. The predicted [K.sub.w] values collapsed into a single function of [T.sub.s]. This confirms the assumed dependence of the reaction rate constant on the square of the calcium sulphate supersaturation. The natural logarithm of the rate constant was regressed and the Arrhenius temperature dependency determined. The activation energy evaluated for the surface reaction of the deposit formation is found to be 57 kJ/mol. The frequency factor ([k.sub.0]) is determined to be 35 400 (kg/[m.sup.2].min.[wt%.sup.2]).
[FIGURE 7 OMITTED]
Validation of the Proposed Model
To consider the effect of surface temperature, the fouling model was used to predict the fouling resistance at different surface temperatures. Because of the small effects of fluid velocity and bulk temperature, only results at fluid velocity of 1.5 m/s and bulk temperature of 75[degrees]C are shown in Figure 8. It is obvious that there are significant changes in the fouling resistances as the surface temperature is increased from 103[degrees]C to 114[degrees]C. Figure 8 also includes experimental data for corresponding operating conditions. Obviously, the fouling trends are predicted with reasonable accuracy.
[FIGURE 8 OMITTED]
The model predictions and experimental data shown in Figure 9 represent the effect of liquor concentration on the fouling resistance. The remaining parameters fluid velocity, surface and bulk temperature were kept constant at predetermined values. According to the proposed model, the effects of liquor concentration are reflected by supersaturation and reaction processes. This diagram confirms the strong effect of liquor concentration on the fouling resistance in the present case. The predicted and the measured fouling resistances of all experimental runs are compared in Figure 10. Good agreement exists between the experimental data and the model predictions.
[FIGURES 9-10 OMITTED]
The primary problem in concentrating phosphoric acid is due to fouling on the tube-side of the heat exchangers of the evaporators. Scaling on the heat transfer surfaces occurs because of high supersaturation of phosphoric acid liquor with respect to calcium sulphate. Since there is basically no published information on this specific, but highly relevant problem of heat exchanger operation, a detailed investigation has been performed with a test rig installed in the side-stream of a producing phosphoric acid plant.
Initially, the solubility of different calcium sulphate types in phosphoric acid solution was studied and their dependency on acid concentration and temperature were investigated.
Subsequently, a large number of fouling experiments were carried out at different flow velocities, surface temperatures and concentrations to determine the mechanisms, which control deposition process. For the investigated range of operational parameters, an almost linear rate of fouling resistance with time has been observed in most experiments. The results proved that the controlling mechanism was chemical reaction at the heat transfer surface and that erosion of the deposit is negligible.
Finally, a mechanistic model for prediction of CaS[O.sub.4] fouling resistances from pure solution was adapted to the case of CaS[O.sub.4] from the process liquor in phosphoric acid plants. Laboratory analyses of the physical properties of the deposited scales could be used to reduce the number of fitting parameters to 2. The activation energy evaluated for the surface reaction of the deposit formation was found to be 57 kJ/mol. This agrees very well with the activation energy that was found by analyzing operating data of the actual plant heat exchanger (Behbahani et al., 2003). The predicted fouling resistances were compared with the experimental data. Quantitative and qualitative agreement between measured and predicted fouling rates is good.
The support of the presented investigations by Razi Petrochemical Complex is gratefully acknowledged.
A heat transfer area ([m.sup.2])
C concentration (kg/[m.sup.3])
d diameter (m)
[E.sub.act] activation energy (J/mol)
[fr.sub.d] mass fraction of calcium sulphate in the deposit
[k.sub.0] frequency factor (kg/([m.sup.2].min.[wt%.sup.2]))
[K.sub.b] bulk reaction rate constant ([m.sup.3]/kg.s)
Kw surface scaling reaction rate constant ([m.sup.4]/kg.s)
L length (m)
[??] mass flow rate (kg/s)
m mass (kg)
[[??].sub.d] rate of mass deposited (kg/[m.sup.2].s)
q heat transfer rate (W)
[??] heat flux (W/[m.sup.2])
r radius (m)
R universal gas constant (J/mol.K)
[R.sub.f] fouling resistance ([m.sup.2].K/W)
s distance between thermocouple location and heat transfer surface (m)
T temperature ([degrees]C or K)
t time (s)
V volume ([m.sup.3])
[alpha] heat transfer coefficient (W/[m.sup.2].K)
[beta] mass transfer coefficient (m/s)
[lambda] thermal conductivity (W/m.K)
[rho] density (kg/[m.sup.3])
Subscripts and Superscripts
CaS[O.sub.4] calcium sulphate
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Manuscript received May 30, 2005; revised manuscript received January 2, 2006; accepted for publication January 4, 2006.
R. M. Behbahani (1), H. Muller-Steinhagen (2) * and M. Jamialahmadi (1)
(1.) Research Department, Petroleum University of Technology, Ahwaz, Iran
(2.) Institute for Thermodynamics and Thermal Engineering, University of Stuttgart, Germany, Institute of Technical Thermodynamics, German Aerospace Centre, Stuttgart, Germany
* Author to whom correspondence may be addressed. E-mail address: email@example.com
Table 1. Operating conditions in the side-stream test rig Flow velocity (m/s) 1.3-1.8 Bulk temperature ([degrees]C) 73-78 Surface temperature ([degrees]C) 102-129 Concentration (wt%) 56-59 [H.sub.3]P[O.sub.4] Concentration (wt%) CaS[O.sub.4] Concentration (wt%) 1.4-1.85
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|Author:||Behbahani, R.M.; Muller-Steinhagen, H.; Jamialahmadi, M.|
|Publication:||Canadian Journal of Chemical Engineering|
|Date:||Apr 1, 2006|
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