Energy Conversion and Management 62 (2012) 40–46
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
A design algorithm for batch stirred tank transesteriﬁcation reactors C.N. Anyanwu a,⇑, C.C. Mbajiorgu b, O.U. Oparaku a, E.U. Odigboh b, U.N. Emmanuel c a
National Centre for Energy Research and Development, University of Nigeria Nsukka, Nigeria Dept. of Agricultural and Bioresources Engineering, University of Nigeria Nsukka, Nigeria c Dept. of Electronic Engineering, University of Nigeria Nsukka, Nigeria b
a r t i c l e
i n f o
Article history: Received 20 December 2011 Received in revised form 30 March 2012 Accepted 30 March 2012 Available online 25 June 2012 Keywords: Biodiesel Computer software Reactor Vegetable oil Design CI engine
a b s t r a c t A 50 L per batch, stirred tank reactor, suitable for carrying out transesteriﬁcation of vegetable oils was designed and constructed. The major design assumptions included stainless steel plate thickness of 2 mm, reaction temperature of 60–65 °C and an initial/ﬁnal ﬂuid temperature of 25/70 °C. The calculated impeller Reynolds number was in the mixed regime zone of 10–104; the power number was varied between 1 and 5, while a typical propeller speed of 22.5 rev/s (or 1350 rev/min) was adopted. The limiting design conditions were maximum reactor diameter of 1.80 m, straight side height-to-diameter ratio in the range of 0.75–1.5 and minimum agitator motor power of 746 W (1 Hp). Based upon the design, a simple algorithm was developed and interpreted into Microsoft C Sharp computer programming language to enable scale up of the reactor. Performance testing of the realized reactor was carried out while using it to produce Neem oil biodiesel via base – catalyzed methanolysis, which yielded high quality fuel product. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction With global carbon emissions already in excess of the dangerously high level of 450 ppm , concerted efforts are now geared towards reducing the use of fossil fuels by increasing the application of renewable energy derived fuels, especially in the transport sector. Biodiesel derived from vegetable oils and fats has been demonstrated as the best suited alternative fuel for compression ignition engines. The biodiesel manufacturing process converts oils and fats into long chain mono alkyl esters, or fatty acid methyl esters (FAMEs), which are utilized as biodiesel fuel after some puriﬁcation processes. Straight vegetable oils (SVOs) have been used in compression ignition (CI) engines as alternative fuels, starting with Rudolph Diesel’s successful trials in the early 19th century when he used peanut oil to power his CI engine. Research has, however shown that raw vegetable oils are capable of causing problems to the engine in the long term, owing to their high viscosity [2,3]. Transesteriﬁcation of vegetable oils into biodiesel has, therefore, become a standard way of producing fuel grade products from them by reducing their viscosity to acceptable values of about 3.2 cSt. Although biodiesel has numerous advantages over fossilderived diesel fuel such as safety (high ﬂash point, usually above 140 °C), environmental friendliness (low greenhouse gas emissions), and bio-degradability (low trace metal and sulfur contents); the major factor limiting its widespread utilization is high cost of ⇑ Corresponding author. Tel.: +234 805 1980070. E-mail address: cnasoﬁ[email protected]
(C.N. Anyanwu). 0196-8904/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2012.03.027
production. The production cost of biodiesel is still higher than the pump price of diesel in most countries, thereby making it less attractive to the public, except with government incentives. The high production cost of biodiesel is a direct consequence of the high price of vegetable oil raw materials, most of which are edible (ﬁrst generation biofuel sources) and serve as food for man. For this reason, it has been adduced that a sustainable biodiesel industry with vegetable oil starting raw material ought to be based on non-edible oils , often referred to as second generation biofuel sources; or even third generation biofuel resources such as algae. In addition, second generation biofuel resources such as jatropha, castor, rubber seed, and neem oils offer great potentials for the development of agriculture and light industries. Apart from high vegetable oil prices, the processing cost of biodiesel is also high, constituting 20–25% of the total production cost . Arising from the need to continue research work aimed at reducing processing costs, it is necessary to study the transesteriﬁcation of oils using uniform bench-scale processors to enable proper application of obtained optimal results to commercial scale plants. The main objective of the present work is to develop a computer program based on the design algorithm of a batch biodiesel reactor. Speciﬁcally, it describes the development of a C Sharp computer program for design of batch stirred tank transesteriﬁcation reactors. 2. Technology and kinetics of transesteriﬁcation There are ﬁve major technological means used to obtain fuel grade products from vegetable oils, namely dilution, pyrolysis,
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Fig. 1. Schematic of acid/base transesteriﬁcation process. Source: .
micro-emulsiﬁcation, catalytic cracking and transesteriﬁcation . Among these, transesteriﬁcation is the most commonly applied technique in view of its comparative cost advantage and convenience [7,8]. Among other methods of transesteriﬁcation, such as the acid [9,10] and enzyme catalyzed processes, and (non-catalytic) supercritical methanol process [11–14]; base catalysis has found widespread industrial application owing to the fact that it produces greater yield, is simple and can be scaled up easily being a more ﬂexible process. However, a major requirement towards the feedstock for the base catalyzed process is that it should contain less than 0.05 wt.% of water and less than 0.5 wt.% free fatty acid . According to Canakci and Van Gerpen , transesteriﬁcation will not occur when the FFA content is above 3%. A schematic ﬂow diagram of the transesteriﬁcation process is presented in Fig. 1. In the batch-scale base process, most of the steps are usually undertaken separately. The catalyst promotes an increase in solubility to allow the reaction to proceed at a reasonable rate , and is required because the alcohol is sparingly soluble in the oil phase. The most common catalysts used are strong mineral bases such as sodium hydroxide and potassium hydroxide. Firstly, the catalyst (usually 0.5–1.5% w/w) is mixed with the methanol (6:1 ratio to the oil, i.e. 100% excess) in a smaller container (the actual catalyst sodium or potassium methoxide is produced during this step). This mixture is then transferred into the transesteriﬁcation reactor, where the vegetable oil has been charged and preheated. The reactor is covered tightly and heated to 60–65 °C for duration ranging from 30 to 120 min with agitation for optimal results. The mixture is then transfered into a settling tank (separator) with a high height-to-diameter ratio. Two phases of glycerol (lower) and biodiesel (upper) begin to emerge after a few minutes, but complete phase separation is only possible after a period of 2–8 h. The glycerol phase with a speciﬁc gravity of about 1.25 settles at the bottom, whereas the biodiesel remains on top.
3. Reactors for transesteriﬁcation Both batch and ﬂow reactors are used for transesteriﬁcation of vegetable oils, but batch reactors are usually more adapted for research and testing activities, since they are more ﬂexible and easy to control. Stirred, batch reactors for the purpose are often unbafﬂed tank vessels made of stainless steel plates and mounted on a suitable stand.
3.1. Chemical design of the reactor The relationship between reaction time and reactor volume (V) in the case of batch reactors is given by the equation :
t ¼ NA0
dx rA V
where t is the time (s), NA0 the initial number of moles of reactant A, rA the reaction rate, and x is the conversion. According to some authors [19,20], the acid- and base-catalyzed transesteriﬁcation of vegetable oils follow a pseudo second order chemical reaction mechanism, combined with a shunt reaction scheme at lower alcohol-to-oil ratios such as 6:1. Since the reaction time is a function of the desired conversion (x), it is possible to link a given reactor volume to degree of conversion once the reaction time is speciﬁed. A typical value of k is of the order of 0.001–0.01 d m3 mol1 s1. However, since the reactor is intended for transesteriﬁcation studies at different temperatures and reaction durations, greater emphasis has been placed on the mechanical design aspects. 3.2. Mechanical design of the reactor 3.2.1. Description of the reactor The reactor for the present work was a Batch Stirred Tank (BSTR), unbafﬂed cylindrical vessel with conical bottom. It was heated with an electrical coil and agitated by means of a straight entering stirrer, powered by a single phase AC motor. The choice of a batch reactor is supported by literature , which indicates that they are more ﬂexible and produce higher yield of product in comparison with continuous ﬂow reactors, although the latter are often associated with lower operating costs and high throughputs. A batch reactor is often preferred for research work and in situations where the down-time is much less than the reaction time, especially for slow reactions like transesteriﬁcation, which require up to 1 h. A ﬂexible thermo-regulator capable of maintaining the temperature of a given medium within ±0.5 °C was fabricated based on the LM35 integrated circuit to enhance accurate temperature control during the transesteriﬁcation process. 3.2.2. Sizing of the reactor Preliminary experiments carried out using conventional laboratory equipment (hot plate, equipped with magnetic stirrer and temperature sensor) corroborated literature data [22–24], which
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show that the expected reaction time for the transesteriﬁcation of Neem oil ranges between 0.5 and 2.0 h, depending on other reaction conditions such as temperature, alcohol-to-oil ratio and catalyst amount. In the present work, 1 h was taken as the design reaction time, whereas the reactor was assumed to work for 10 h per day.
to enable its use even in scaled-up versions of the equipment. According to Priday et al. , slanting propellers are not suitable for agitators requiring more than 3 Hp (2.24 kW). The design requirement is that the straight entering paddle should be mounted at a distance of DT/4 from the bottom of the reactor for effective mixing.
3.2.3. Reactor batch size A 500 L per day batch reactor operating for 10 h each day with an average reaction time (including down-time) of 1 h would have a batch volume given by the expression
18.104.22.168. Length of propeller. A distance of 10 cm was allowed between the agitator motor mounting and the top of the reactor for ease of maintenance. Therefore, the total length of the propeller shaft (Lp) was calculated as per the expression:
V bt ¼
¼ 0:05 ½m3
where Vbt is the batch volume, and Rcp is the capacity of the reactor, liters per day. 3.2.4. Diameter and height of reactor The reactor would not be ﬁlled to the brim due to safety considerations. It was assumed that the volume of conical section of the vessel is equal to the difference between the total volume and the effective volume. Thus,
pDT H ¼ 4V bt
where DT is the diameter of vessel, m and H is the straight side height, m. According to Knudsen et al. , the height to diameter ratio of an unbafﬂed reactor should lie between 0.75 and 1.5. Therefore we assumed 1.3 times the diameter as height
Lp ¼ H þ hc 0:25DT þ 0:10 ½m
Since hc = 0.5DT the conical section was welded to the base at an angle of 135° with respect to the straight side. The outlet tap diameter was 2.5 cm (but could be up to 5.0 cm in larger tanks, such that hc was taken to be equal to the reactor radius).
Lp ¼ H þ 0:25DT þ 0:1 ½m 22.214.171.124. Diameter of propeller (Da). Tilton  recommended that the propeller diameter should be within (0.3–0.6)DT. In order to save materials and also operating costs since power, P = f(Da); Da was chosen as 0.4DT in the present work, such that Da = 0.148 m. 3.2.7. Power requirement of agitator motor The degree of laminarity or turbulence within the reactor was deﬁned by the impeller Reynolds number, given by the expression :
H ¼ 1:3DT Then 1:3p
¼ 4V Bt
rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 3 4V Bt 3 4 0:05 ¼ ¼ 0:37 m 1:3p 1:3p
and H = 1.3DT = 0.48 m. 3.2.5. Volume of conical section, Vc The volume of conical section (Vc) of the cylindrical vessel (where r1 and r2 are the radii of the reactor and outlet tap, respectively) was given by the expression:
Vc ¼ p
hc 2 r 1 þ r 1 r 2 þ r 22 3
V c ¼ 0:17DT p 0:25D2T þ 0:0125DT þ 0:000625 ¼ 0:0078 m3
With an effective volume of 50 L, the reactor should therefore be ﬁlled up to the 40 cm mark on the straight height. 3.2.6. The propeller shaft and paddle A straight-entering propeller, which is recommended for vessels with diameters less than 6 ft (1.80 m) or 1000 gallons (4 m3), was chosen for the unbafﬂed stainless steel tank. This was done
r1 hc r2 Fig. 2. Conical section of the reactor.
where NRe is the Reynolds number (which is less than 10 for laminar and above 104 for turbulent ﬂow regimes), Da the propeller diameter (0.15 m), N the rotational speed (22.5 rev/s), q the ﬂuid density (900 kg/m3), and M is the ﬂuid viscosity (0.2 Pa s). A typical value of N in single phase motors is 1350 rpm (22.5 rev/s) and was taken as design value for the agitator motor. For most vegetable oils, the density and viscosity are in the range 900 kg/m3 and 0.2 Pa s, respectively. These values were adopted in the design, leading to a Reynolds number of 2278. The power requirement of the agitator motor, P in watts was obtained from the expression :
P ¼ Np qDa5 N3 In Eq. (5), hc is the height of the conical section of the reactor as shown in Fig. 2. Hence,
where Np is the power number, which depends on the Reynolds number and was obtained from Nomographs as given in . Other symbols have the same meaning as in Eq. (8). The relationship expressed in Eq. (9) is given by plots of power number versus Reynolds as presented for different types of propellers in . The Power number corresponding to a Reynolds number of 2278 for a propeller with few blades varies between 1 and 5, hence the power requirement could vary between 746.4 W and 3112 W. A 1 Hp motor was chosen for the present work as this would reduce initial and running costs. 3.2.8. Power requirement of heating coil The heat supplied by the electrical coil (Qcoil) is absorbed by the reactants, the stainless steel tank and the agitator. The balance is lost heat. Thus
Q coil ¼ Q oil þ Q steel þ Q ag þ losses
where Qoil is the heat absorbed by oil; Qsteel the heat absorbed by the stainless steel vessel; Qag the heat absorbed by the agitator; and Losses is the heat losses.
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These heat losses are often within 5–7% of the heat supplied. For the present design, a worst-case value of 10% was adopted, whereas initial and reaction temperatures of 25 °C and 70 °C, respectively for all the ﬂuid reactants were used. Thus
0:9Q coil ¼ 45½ðC p V qÞoil þ ðC p V qÞsteel þ ðC p V qÞag
Q coil ¼ 50½ðC p V qÞoil þ ðC p V qÞsteel þ ðC p V qÞag
where Voil = Vbt is the volume of oil (reactants) = 0.05 m3, Vsteel the volume of stainless steel vessel, Vag the volume of agitator; C p oil the heat capacity of reactants (oil), C p steel the heat capacity of stainless steel = 0.5 kJ/kg K, C p ag the heat capacity of cast iron agitator = 0.6 kJ/kg K, qoil the density of oil = 900 kg/m3, qsteel the density of steel = 7800 kg/m3, and qag is the density of cast iron (agitator) = 7200 kg/m3. According to Liley et al. , the speciﬁc heat capacity of vegetable oils may be obtained from the expression
0:5 C p ¼ qﬃﬃﬃﬃﬃﬃﬃ þ 0:007ðt 15Þ; 15 d4
where d is the density (g/cm3), Cp the Speciﬁc heat capacity (Cal/g °C), and t is the temperature (°C). 126.96.36.199. Volume of stainless steel material. The volume of material used to construct the conical section of the cylinder was taken as 5% of the entire material (as conﬁrmed through practical calculations). Therefore, the volume of the steel material was calculated as follows:
V steel ¼ 1:05pDT Hd
where DT is the reactor diameter; H the straight side height of the reactor; and d is the thickness of the steel plate (m). 188.8.131.52. Volume of cast iron agitator. The volume of material needed to fabricate the padle was taken as 10% of the volume of cast iron needed to fabricate the entire propeller. Therefore,
V CastIron ¼ 0:275pDa2 LP
Q coil ¼ 50½ð900 2:15V Bt Þ þ ð7800 0:5V steel Þ þð7200 0:6V CastIron Þ Q coil ¼ 5 104 ½1:935V Bt þ 4:095pDT Hd þ 1:188pDa2 LP ; kJ
The value obtained for coil energy using Eq. (16) was 5279 kJ. This quantity of heat energy must be supplied during the pre-heating period. Assuming a pre-heating period of 30 min, then the coil power amounts to 2.93 kW, including losses. The actual power rating of the heating coil used in the present design was 2.5 kW. 3.2.9. The thermoregulator A thermoregulator is a feedback mechanism used to monitor the reactor temperature and control it within a pre-set range or point. A linear type thermoregulator was fabricated based on the LM35 integrated circuit and used to control the heating element. Since the sensor circuit cannot be immersed in the liquid reactant phase, it was encased in a water-tight aluminum container and calibrated against the readings obtained from a K-type thermocouple (BK Precision), made in Taiwan. 3.2.10. Thickness and type of insulation To reduce heat losses from the reactor, it was necessary to insulate the vessel with properly selected and sized material. The insulation material was glass wool with thermal conductivity
Fig. 3. Temperature proﬁle of the wall of the reactor.
k = 0.03 W/mK. Assuming the average temperature of the reactor to be 70 °C, whereas the outer wall temperature should not exceed 25 °C; then, applying Fourier’s conduction heat transfer equation  to Fig. 3:
dQ dt ¼ kA dh dx
x1 k1 A1
h1 h4 þ k2xA2 2 þ k3xA3 3
where dQ/dh = q is the heat power (ﬂux) (W), x1 = x3 the thickness of steel plate (0.002 m), x2 the thickness of insulator, m, x3 the thickness of leather covering (0.001 m), k1 the heat transfer coefﬁcient of steel (45 w/mK), k2 the heat transfer coefﬁcient of glass wool (0.03 W/mK), k3 the heat transfer coefﬁcient of leather (0.03 W/ mK), A1 the Area of steel plate (m2), A2 (A3) the area of glass wool insulator (leather material) (m2), h1 the reactor temperature (70 °C), h2 the temperature at the inner metal/insulator boundary (°C), h3 the temperature at the leather/insulator boundary (°C), and h4 the outer wall temperature (25 °C). Obviously,
x2 ¼ k2 A2
h1 h4 2x1 q k 1 A1
The heat ﬂux (power), q was obtained from the initial considerations and substituted in Eq. (17) such that x2 = 0.3 mm was found to be adequate glass wool insulation for the present design. The actual thickness of insulation used was 5.0 mm, considering availability of construction materials. The front and top views of the realized reactor are presented in Figs. 4 and 5, respectively. 4. Performance evaluation 4.1. Testing of the reactor This was carried out by using the reactor to produce biodiesel from 50 L of Neem oil. The temperature was maintained at 50 °C, using the fabricated thermoregulator. Alcohol to oil ratio of 6:1 was applied, while using 1% w/w NaOH as the catalyst. Neem oil purchased from a farm in Katsina State of Nigeria was degummed at 60 °C using 10% v/v (i.e. 5 L) of water heated to 70 °C. The mixture was then allowed to separate by gravity and the top (oil) phase was collected and subjected to acid esteriﬁcation in order to reduce its FFA content. Acid esteriﬁcation was carried out by heating the oil to 50 °C and adding 20% v/v (i.e. 10 L) of methanol slowly into the oil with agitation. The agitation was continued for a few minutes, after which 5% (i.e. 2.5 L) of concentrated sulfuric acid was added. Stirring was continued for another 30 min, after which the mixture was transferred into a settling tank and allowed to separate. The bottom (oil) phase was then collected into in a clean container and the free fatty acid content tested. The oil (with
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Fig. 4. Front view of the reactor.
Fig. 5. Top view of the reactor.
a water content of 0.2%), was charged into the reactor and preheated to 50 °C (Optimum reaction temperature was determined based on reactions conducted using conventional laboratory hotplate equipped with thermoregulator.) The pre-determined quantity of NaOH was dissolved in the methanol and transferred into the reactor and the reactor was closed and maintained at 50 °C with agitation. At the end of 1 h, heating and stirring were stopped and the mixture transferred into a separating column, where it was allowed to stand for about 4 h for complete gravity separation of the biodiesel and glycerol. Thereafter, the supernatant (biodiesel) phase was decanted, washed several times with tap water until a pH value of 7.0 was obtained. The product was then subjected to quality control characterization tests, results of which are presented in Table 2. Flash point was determined using the Pensky Martens Closed cup method as per ASTM D-93 A. Kinematic viscosity was measured using the Canon Fenske Viscometer according to
ASTM ASTM D 445-04, while Acid number was determined according to ASTM D 664 method. 4.2. Testing of the C Sharp software The software was tested while using it to carry out design calculations for different sizes of batch stirred tank reactors with similar features to the one already constructed. Reactors with batch size of between 2 L and 10,000 L were sized using the programme. These results are presented in Appendices A–E. 5. Results and discussion The fabricated 50 L batch, stirred tank, reactor was used to process neem oil biodiesel, after acid esteriﬁcation of the feedstock to
C.N. Anyanwu et al. / Energy Conversion and Management 62 (2012) 40–46 Table 1 Properties of the pretreated neem oil. S/No
1 2 3
Water content Density Free fatty acid
0.20 881 0.13
% kg/m3 %
Nsukka for funding support provided for this research work. Contributions made by Prof. C.A. Nwadinigwe, technical staff of N.C.E.R.D. and colleagues in the Department of Agricultural and Bioresources Engineering are highly acknowledged.
Appendix A A.1. Computation details Table 2 Determined properties of the biodiesel.
1 2 3 4 5 6
Flash point Kinematic viscosity Water and sediments Acid number Free glycerol Total glycerol
168 3.7 0.03 0.24 0.012 0.016
>130 1.9–6.0 <0.05 0.50 max 0.020 0.024
°C mm2/s % mg KOH/g wt.% wt.%
As per ASTM D6751 requirements. Source: .
reduce its FFA content to 0.13%. The methyl ester yield obtained at the end of washing was 84.6%, which is comparable with results reported elsewhere . The properties of the pretreated neem oil are presented in Table 1. Values obtained for all the parameters of the produced methyl ester (Table 2) were within ASTM D6751 standard stipulated limits, an indication that the product can be used as fuel grade biodiesel. It was observed that agitation alone required 0.75 kW h during the reaction, compared to heating that consumed about 1.96 kW h since the total heating power was for pre-heating (which lasted for 22.5 min) and reaction (24.6 min). Although the energy required for agitation was only 27.6% of the processing costs (excluding pre-treatment), it could be reduced further if a 0.5 Hp (374 W) centrifugal pump had been employed to circulate the reactants through the reactor. Using the developed C Sharp software for reactor design is a time-saving measure, which also reduces the incidence of human errors in the design calculations. Tests carried out using the software also indicated that it can be used by professionals who have little or no in-depth knowledge of reactor design practice. Nonetheless, it is clear that reactor scale-up is not a purely mechanical design problem, considering the fact that the mechanical aspects have a great inﬂuence on diffusion, heat transfer and chemical kinetics; which determine the reactor’s overall performance. Adeyemi et al. , who studied the effect of certain variables on FAME yield concluded that there is high correlation between FAME yield, peak time and reaction temperature; although wide impeller speed variations for Rushton and Elephant ear types gave rise to only little difference in FAME yield between 89% and 94%. Future research work would investigate the inﬂuence of reactor size and degree of agitation on transesteriﬁcation kinetics and quality of ﬁnal biodiesel product. 6. Conclusion A design algorithm for batch stirred tank transesteriﬁcation reactors was developed. On the basis of the algorithm, a generic MS C Sharp programme was developed and tested by using it to scale up the designed reactor. Performance evaluation of the constructed reactor, which was also carried out, showed good results. Acknowledgments The authors are grateful to the Management of the National Centre for Energy Research and Development, University of Nigeria
Reactor capacity, Rcp: 20 L. Batch size of reactor, Vbt: 0.002 m3. Diameter of vessel, DT: 0.1221 m. Straight side height, H: 0.1587 m. Volume of conical section, Vc: 0.0004 m3. Safe loading mark, h: 0.0342 m. Length of propeller: 0.3892 m. Reynolds number, NRe: 241.1208. Power requirement of the agitator motor: 2.8368 W. Thickness of stainless steel sheet: 0.002 m. Diameter of propeller, Da: 0.0366 m. Length of propeller, Lp: 0.3892 m. Pre-heating time, t: 30 min. Qcoil: 195.9459 J. Power requirement of heating coil: 0.1089 kW. Appendix B B.1. Computation details Reactor capacity, Rcp: 500 L. Batch size of reactor, Vbt: 0.05 m3. Diameter of vessel, DT: 0.3569 m. Straight side height, H: 0.464 m. Volume of conical section, Vc: 0.007 m3. Safe loading mark, h: 0.07 m. Length of propeller: 0.7532 m. Reynolds number, NRe: 2064.6738. Power requirement of the agitator motor: 608.6462 W. Thickness of stainless steel sheet: 0.002 m. Diameter of propeller, Da: 0.1071 m. Length of propeller, Lp: 0.7532 m. Pre-heating time, t: 30 min. Qcoil: 4874.0195 J. Power requirement of heating coil: 2.7078 kW. Appendix C C.1. Computation details Reactor capacity, Rcp: 5000 L. Batch size of reactor, Vbt: 0.5 m3. Diameter of vessel DT: 0.769 m. Straight side height, H: 0.9997 m. Volume of conical section, Vc: 0.0649 m3. Safe loading mark, h: 0.1397 m. Length of propeller: 1.392 m. Reynolds number, NRe: 9580.0482. Power requirement of the agitator motor: 28226.4019 W. Thickness of stainless steel sheet: 0.002 m. Diameter of propeller, Da: 0.2307 m. Length of propeller, Lp: 1.392 m. Pre-heating time, t: 30 min. Qcoil: 48671.3591 J. Power requirement of heating coil: 27.0396 kW.
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Appendix D D.1. Computation details Reactor capacity, Rcp: 10,000 L. Batch size of reactor, Vbt: 1 m3. Diameter of vessel, DT: 0.9689 m. Straight side height, H: 1.2596 m. Volume of conical section, Vc: 0.128 m3. Safe loading mark, h: 0.1736. Length of propeller: 1.7018 m. Reynolds number, NRe: 15211.1682. Power requirement of the agitator motor: 89669.0786 W. Thickness of stainless steel sheet: 0.020 m. Diameter of propeller, Da: 0.2907 m. Length of propeller, Lp: 1.7018 m. Pre-heating time, t: 30 min. Qcoil: 97318.2696 J. Power requirement of heating coil: 54.0657 kW. Appendix E E.1. Computation details Reactor capacity, Rcp: 20,000 L. Batch size of reactor, Vbt: 2 m3. Diameter of vessel, DT: 1.2207 m. Straight side height, H: 1.5869 m. Volume of conical section, Vc: 0.2532 m3. Safe loading mark, h: 0.2163 m. Length of propeller: 2.0921 m. Reynolds number, NRe: 24141.7351. Power requirement of the agitator motor: 284549.2772 W. Thickness of stainless steel sheet: 0.020 m. Diameter of propeller, Da: 0.3662 m. Length of propeller, Lp: 2.0921 m. Pre-heating time, t: 30 min. Qcoil: 194597.1521 J. Power requirement of heating coil: 108.1095 kW.
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