Chemical and Petroleum Engineering, Vol. 42, Nos. 7–8, 2006

ANALYSIS AND DESIGN OF PHOSPHORIC-ACID EVAPORATORS OPERATING ON ENERGY OF SUPER-HIGH-FREQUENCY FIELD

F. E. Mogilevskii and A. L. Shatalov

An industrial evaporator is analyzed with consideration given to the promising nature of the technology of evaporating phosphoric to metaphosphoric acid using the energy of a super-high-frequency electromagnetic field, and a design is proposed for such an evaporator.

Shatalov and Mogilevskii [1] demonstrate the promising nature of the technology whereby orthophosphoric acid (OPA) is evaporated to metaphosphoric acid (MPA) by the energy of a super-high frequency (SHF) electromagnetic field (EMF), and the feasibility the radial method [2] to determine the structure of the SHF field in waveguide constructions of an evaporator system, and the temperature distribution in the medium being heated. To analyze industrial equipment for the evaporation of OPA by the energy of an SHF field with respect to an assigned output, it is necessary to determine the following basic characteristics: the geometry of the effective volume of the vessel, the distribution of EMF sources, and the total power output of the SHF field. Studies of the kinetics of OPA evaporation [1] have indicated that a greater part of the time (more than 70%) required for the process elapses with the solution at a virtually constant volume and temperature; it is therefore expedient to employ a batch-action evaporator. Selection of the source of the SHF field – magnetrons – will exert a significant influence on the geometric form of the effective volume of the equipment. Industrial magnetrons are manufactured with a power output of 2.5–100 kW and are effectively used in highly productive industrial equipment to heat media, the electrophysical properties of which vary negligibly here. It should be pointed out that the power sources must be particularly carefully matched to the effective volume, and this matching should not be altered in the production process [3]. The unit (as applies to 1 kW of power output) cost of the indicated sources of SHF fields exceeds 30000 rubles/kW. The unit cost of low-output magnetrons (up to 0.9 kW) does not exceed 3000 rubles/kW; they are therefore more acceptable for equipment with an output of 10–30 kW. Quartz or heat-resistant glass, which makes it possible to heat acid to 500–600°C, is the material most suitable for the walls of the effective container of the evaporator (owing to its radioparency and thermal stability). Tubing is the most widespread product formed from this material; it is therefore expedient to use it as a base for the design of the evaporator. A tubular container design will determine the geometry of the effective volume of the evaporator. Figure 1 shows the general design scheme of the evaporator. The evaporator consists of a metallic housing, a vessel containing the acid to be evaporated, which is fitted with a branch pipe for the discharge of vapor for condensation (which is also used for delivery of the initial solution), and a branch pipe for the overflow of concentrated (by evaporation) acid. The antennas of the SHF-field sources (magnetrons), determination of the required number of which (for the required output), and their arrangement on the wall of the effective volume is a problem basic to analysis of the evaporator, are introduced to the effective volume through the wall of the housing. Moscow State University of Engineering Ecology (MGUIÉ). Translated from Khimicheskoe i Neftegazovoe Mashinostroenie, No. 8, pp. 10–12, August, 2006. 0009-2355/06/0708-0427 ©2006 Springer Science+Business Media, Inc.

427

3

1

2

4

5

Fig. 1. Model of effective volume of evaporator: 1) metallic housing of evaporator; 2) vessel formed from heat-resistant glass and containing acid subject to evaporation; 3) branch pipe for discharge of water vapor and delivery of initial solution; 4) antennas of SHF-field sources; 5) drain pipe.

T, °C III

300 II

200

100

I

0

10

20

30

40

τ, min

50

Fig. 2. Simplified curve of kinetics of OPA evaporation to MPA.

The low-output sources operate, as a rule, at a frequency of 2.45 GHz. In the evaporator, it is expedient to use magnetrons with a power output of 0.9 kW. Industry is manufacturing primarily a modification of these magnetrons with an antenna matched to a rectangular waveguide with a 90 × 45-mm cross section. This waveguide can be used as a transmission line for power from the magnetron to the working chamber. Determination of Power Consumption of Process The amount of power required for OPA evaporation by the energy of the SHF field is determined by the assigned productivity of the evaporator, and also by the thermal and electrophysical properties of the solution. Analysis of the literature [4–6] has indicated that these properties are undefined at temperatures above 100°C; we can therefore use experimental results cited in [1] for the analysis. Three stages were established from investigation of the kinetics of OPA evaporation [1] (Fig. 2): I – heating from the initial temperature to the boiling point; II – boiling with heating to 325°C; and III – heating with no marked increase in temperature, and evaporation of moisture to the moment when the temperature rises above 325°C (molecular restructuring). To simplify power-consumption analyses, therefore, the curve of the evaporation kinetics can be divided into three corresponding segments, which are clearly distinguished with respect to specific power consumption. Let us assume that the first two stages are represented by linear relationships. Such a representation of the entire process transforms the actual curve of the evaporation kinetics into a schematic diagram (see Fig. 2). Thermophysical characteristics are determined, and the power consumed in each stage of the process and overall power outlays for the industrial evaporator calculated for each of the stages are indicated. 428

Material- and Energy-Balance Equations. Transformation of OPA in a water-evaporation process reduces to the following conservation equation for the mass of the substance: MOPA = MMPA + Ms,

(1)

where MOPA is the mass of the initial OPA; MMPA is the mass of the MPA obtained; and Ms is the mass of the steam. For the industrial evaporator, the value of MMPA is given by the productivity required multiplied by the time assigned for the process. The energy of the SHF field, which is absorbed by the acid, is consumed in the three above-mentioned sequential stages of the process. Moreover, thermal energy losses to the surrounding space must be considered. In this connection, the energy-balance equation can be written as QSHF = QI + QII + QIII + Ql,

(2)

where QSHF is the SHF power absorbed; QI, QII, and QIII are the power consumed, respectively, in stages I, II, and III of the process; and Ql is the power of the heat lost to the surrounding environment through the walls of the evaporator. The measures taken to match the experimental device [1] enable us to assume that no less then 90% of the field energy was transformed into thermal energy. The power output of the source of the SHF field in the experimental device was 600 W (according to rated values for the magnetron), and, consequently, the power of the heat released in the acid was no less than 540 W. Determination of Power Consumption for Individual Stages of Process Stage of Heating to Boil. Heating of the solution is begun at a temperature Ti = 25°C, and is continued until the acid starts to boil at Tboil = 153°C. The time required for this stage of the experiment t1 = 120 sec. The power consumed in this stage was determined from the equation QI = c1 ρV

∆T ∂T ≈ c1M OPA 1 , ∂t ∆t1

(3)

where c1 is the specific heat of the solution in stage I, and V is the volume of the initial OPA. Equation (3) is derived from the general equation of heat conduction in a medium with a source of internal heat liberation q: ∂T cρ = λ∇ 2 T + q ∂t by integrating over the entire volume V. Here, it was assumed that the temperature distribution is uniform in the volume, and heat exchange within the acid can be neglected, since convective mixing is rather vigorous within the solution and will contribute to more rapid temperature equalization in the heated volume than that induced by temperature gradients. From Eq. (3), we can find the heat capacity of the acid in the heating stage: c1 =

Q∆t1 , M OPA∆T1

where Q = 540 W is the power of the thermal-energy source. According to the calculation, c1 = 2.52 kJ/(kg⋅°C); this corresponds to the value c = 2.53 kJ/(kg⋅°C), which is the heat capacity of OPA with a mass concentration of 62% at 21°C [4]. This correspondence is explained by rather good matching attained on the experimental device. Boiling Stage. Boiling initiates at T2 = 153°C, and continues to T3 = 325°C. The second stage required a time ∆t2 = 840 sec, during the course of which water was evaporated in the amount ∆Ms = 0.050 kg, and the temperature was raised 429

by 172°C. This stage of the process is most difficult to analyze, since the boiling point rises as evaporation proceeds owing to an increase in the concentration of the solution. The power consumed in this stage was analyzed in the following manner. All power consumed in this stage can be separated into two parts – for the vaporization of water Pv and heating of the solution Ph to 325°C. Each part can be assumed proportional to a weighting factor equal to the fraction of the corresponding mass in the overall mass of boiling acid: QII = Pv + Ph = 0.2QSHF + 0.8QSHF. The power consumed for vaporization of the water can be determined from the relationship Pv = 0.2QII = r

dM v ∆M v ≈r , dt ∆t2

(4)

from which we obtain the heat of vaporization r = 1814 kJ/kg of water from the solution. The specific heat of the OPA varies from 2.35 to 1.76 kJ/(kg⋅°C) [4] as its concentration changes from 62.10 to 89.72% (within the range obtained in [1]). If we adopt its average value as the heat capacity of the solution being heated in the second stage (c2 = 2.06 kJ/(kg⋅°C)), the power Ph can be defined by expression (4); as a result, we obtain Ph = 428 W. State of Molecular Restructuring. After reaching a temperature of 325°C, the OPA begins to transform into MPA at virtually constant temperature. In the experimental device, this stage was continued for a period of 1800 sec. All energy absorbed by the solution was expended in separating water chemically bound to the OPA from the latter, and the power consumed in this stage was maximum. The amount of vapor that is formed here is very small; it was therefore not recorded experimentally in [1]. The power consumed in this stage can be represented by the following relationship: QIII = kMMPA,

(5)

where k is the heat of transformation of the OPA to MPA. From experimental data and relationship (5), we obtain k = 4611.429 kJ/kg. The results obtained can be used to analyze both batch-action and continuous-action industrial vessels. Analysis of Periodic-Action Evaporator Modeling and Analysis of Single Section. Let us assume the required MPA output of the evaporator to be 2 kg/h. A computer analysis of various alternate schemes of the effective volume was performed to select the optimal diameter of the effective volume containing the acid. The analysis was conducted by the radial method [2]. A 3-D model of a single section (Fig. 3) in which it is possible to vary the following dimensions is created by the program Autodesk AutoCAD: the inside diameter of the tubular housing of the evaporator, the diameter of the quartz tube, and the length of the section along its axis. For each alternate scheme, we calculated the distribution of the electric field, and analyzed the temperature distribution within the volume of the evaporator. A scheme that provides for maximum heat liberation and uniformity of heat liberation within the volume of acid was selected from results of the analysis. Some of these results are shown in Fig. 4. It is apparent from Fig. 4a that the heat-release field essentially does not extend beyond the partitions separating the effective chamber, and all energy is concentrated in that half of the tube containing the acid, which is closer to the source. This half is heated uniformly – heating is maximum in the sector exposed to the source of radiation. As is apparent from Fig. 4b, two heat-release maxima develop under the action of the EMF: near the wall of the quartz tube, and within the volume of acid. The heat-release zones are oriented along the axis of the tube and are displaced in the direction of the partitions separating the effective chamber. Virtually no heat release occurs in the section of the effec430

4

1 2 3

Fig. 3. General appearance of individual section of evaporator: 1) supply waveguide with SHF power source (conventionally shown); 2) metallic tube of evaporator housing; 3) quartz tube half-filled with phosphoric acid; 4) metallic partition.

a

b

Fig. 4. Field of heat release in effective volume: a) section on XY plane; b) section on YZ plane. Section of evaporator segment is isolated (darkened zone represents heat release within tube containing acid, and degree of darkening is proportional to amount of heat released).

tive chamber, which is situated beyond the partitions. Comparison of all alternate design schemes indicated that maximum heat release is achieved when the diameter of the quartz tube d ≈ 100 mm (one of the dimensions available in manufacturers’ lists of products) and the diameter of the effective volume (housing) D = 180 mm. For a batch-action evaporator, it is expedient to select the volume of the effective chamber such that the mass of acid placed in it would be sufficient for a single production shift (7 h). For an assigned output of 2 kg/h, the volume of MPA obtained will then be 6.7 liters considering that its density is 2100 kg/m3. The volume of water evaporated will amount to approximately a third of the initial volume of the MPA [1]; this will yield an additional volume at V ≈ 2.22 liters, and, consequently, the total volume of the OPA charge VOPA = 8.9 liters. For an OPA density of 1670 kg/m3, the mass of the initial OPA charge MOPA = 15.4 kg. Since the acid should occupy half of the total volume of the quartz tube (to obtain the maximum evaporation surface), the volume of the quartz tube should be no less than 17.8 liters. When d = 100 mm, the computed minimum length of the effective vessel l = 2.27 m. Calculation of Required Power. Knowing the amount of acid that should be evaporated in the vessel and specific power consumption of the stages, the power required for the sources of the SHF field can be readily calculated. The specific power consumption for the above-mentioned three stages of the process can be set at wI = 0.5, wII = 0.7, and wIII = 0.8 kW/kg, respectively. The average specific power consumption w = 0.67 kW/kg. Based on the total mass of the evaporator charge and the average specific power consumption, the power demand of the SHF sources will be: W = wMPA = 10.3 kW. 431

2

1

3

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Fig. 5. General appearance of evaporator with SHF-energy sources: 1) tubular housing; 2) flange packing at ends; 3) waveguide; 4) magnetron (n = 12).

Losses to the ambient medium through the walls of the evaporator will not exceed 50 W, and, consequently, will have no noticeable effect on the overall energy consumption of the evaporator. If magnetrons with an SHF power output of 0.9 kW are used, their required number n = 12. Evaluation of Mutual Effect of Magnetrons. In addition to calculating the EMF within a single section of the industrial device, we analyzed the flow of electromagnetic energy through the cross section of the industrial evaporator. Since the ingress of one magnetron into the EMF created by another is undesirable (because the power output and service life will be reduced), it is necessary to arrange the sources of the SHF field so that their mutual effect would be minimal. A one-order reduction in power is sufficient. Analysis of the field within that section of the evaporator containing one magnetron indicates that the EMF flux is diminished by a factor of 10 at a distance of 60 mm from the magnetron. Since it is required to establish 12 magnetrons uniformly over a length of no more than 2 m, the distance between them will, of course, exceed 60 mm. Based on results of our analysis, a vessel, which operates in the following manner, was designed for evaporation of OPA to MPA (Fig. 5). The initial OPA is flushed into the device via a feed pipe. After the device has been filled, all magnetrons, the SHF field of which is absorbed in the acid, are activated, as a result of which heating and evaporation are initiated. On completion of the evaporation process, the acid obtained should be removed from the evaporator before cooling to T = 100–120°C. In the opposite case, an increase in the viscosity of the acid will render its draining difficult.

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3. 4. 5. 6. 7. 432

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