Advances in Technology Innovation, vol. 3, no. 2, 2018, pp. 70 - 77 Energy-effective Predictive Temperature Control for Soy Mash Fermentation Based on Compartmental Pharmacokinetic Modelling Sophia Ferng 1 , Ching-Hua Ting 2,* , Chien-Ping Wu 2 , Yung-Tsong Lu 3 , Cheng-Kuang Hsu 1 , Robin Yih-Yuan Chiou 1 1 Department of Food Science, National Chiayi University, Chiayi, Taiwan, ROC. 2 Department of Mechanical and Energy Engineering, National Chiayi University, Chiayi, Taiwan, ROC. 3 Department of Biomechatronic Engineering, National Chiayi University, Chiayi, Taiwan, ROC. Received 07 June 2017; received in revised form 05 Sept ember 2017; accept ed 02 Oct ober 2017 Abstract Co mpart ment modelling has been successfully used in pharmacokinetics to describe the kinetics of drug distribution in body tissues. In this study, the technique is adopted to describe the dynamics of temperature response and energy exchange in a soy mash fermentation system. The object ive is to provide a prec ise temperature-controlled at mosphere for effect ive fermentation with the pre mise of energy saving. In analogy to pharmacokinetics, water and mash tanks are treated as compartments, energy flow as drug delivery, and the temperature as the drug concentration in a specific co mpart ment. The model allows us to estimate the time of injecting a certa in a mount of energy to a specific tank (co mpart ment) in a cost-effective way. Thus, model-based temperature control and energy management can be possible. Keywor ds: soy mash fermentation, temperature, predictive control, energy -effective, compartment model 1. Introduction Soy sauce was invented by the Chinese about 3500 years ago , and the modern producing technology was developed by the Japanese about 500 years ago. The production consists of solid -state fermentation, mash fermentation, and flavouring. The quality and cost of a soy sauce product are ma inly determined by the mash fermentation stage. In tradit ion, soy mash is placed in a pottery tank wh ich is e xposed to sunshine for 4~12 months. The duration of e xposure under the sun is season-dependent as the enzyme and the microbes in the mash are sensible to temperature variations [1-4]. Despite the cost raised by a longer fermentation time and more manpower, tradit ional soy sauces still deserve of popularity as their special flavours are superior to cheap, chemical ones . Because the mash fermentation is manipulated outdoors, the processes of fe rmentation are easily affected by the climate, and the mash is vulnerable to a lien contamination [5]. This may lead to a produce with unstable quality and a lien contamination. To overcome this proble m, we moved the fermentation fro m outdoors to indoors and controlled the fe rmentation c limate [5], as shown in Fig. 1. In the system, the pottery containing soy mash is bathed in a water tank and the temperature of the batching water is regulated to meet the require ments of various fermentation stages [5-6]. It has been demonstrated that a controlled fermentation climate can c reate a we ll environ ment fo r the enzy mes and microbes partic ipating in mash fermentation [7-8]. Thus, the produce can arrive at a better quality in a shorter time in comparison with the traditional approach [9]. * Corresponding author. E-mail address: cting@mail.ncyu.edu.tw Tel.: +886-5-2717642; Fax: +886-5-2717561 Advances in Technology Innovation, vol. 3, no. 2, 2018, pp. 70 - 77 Copyright ยฉ TAETI 71 Fig. 1 Setup of the energy-saving soy sauce fermentation system [5]. As Fig. 1 illustrates , the system consists of a heat pump which supplies hot water circulation fo r regulat ing the fermenter with desired temperature settings . The system is controlled with a programmab le logic controller (PLC) and supervised with an industrial personal co mputer (IPC). The current principle of operation is to let the heat pu mp work at noontime for the benefit of a better operational efficiency and the hot water produce is stored in a storage tank for later use , usually in night time . The PLC man ipulates the solenoid valves and the circulation pump once the tempe rature of the mash is below a certain leve l. These two solenoid valves assure correct water flow directions. Hot water will c irculate for 3 min for adequate heat injection into the soy mash. The duration was determined through e xperimental studies via tria l-and-error. Fig. 2 de monstrates the temperature profiles of the soy mash, the at mosphere, and the circu lation wate r. Clea rly, the mash can ferment at an environ ment with a mo re stable te mperature regardless of a vary ing at mospheric climate. Though, the temperature variation in the fermenter has been imp roved to be with in 1ยฐC, much improved regardless of vary ing climate, it still fluctuates as a result of simple ON/OFF control using solenoid valves. (a) Temperature responses of the traditional procedure (b) Temperature responses of ON/OFF control Fig. 2 The temperature profiles of the soy mash, the atmosphere, and the water in the bathing tank The price of electric ity is diffe rent between peak and off-peak times . The heat pu mp has a ma ximu m efficiency at noontime . Ho wever, the demand of hot water circulation is usually in night time, several hours after the hot water preparation. The stored hot water will inevitably lose some heat to the space before being consumed. There should be an optimu m time of operat ing the heat pump in term of e lectric ity cost [10-12]. It would be possible to operate the heat pump at a most cost-effective way if we can determine when hot water circulation is demanded. The objective of this study is to develop a temperature and energy prediction model using the compartment modelling technique which has been successfully used in pharmacology for drug ad ministration [ 13]. As the system described in Fig. 1, we can partition the system into several unique co mpart ments and describe mathe matica lly the energy e xchanges among the Advances in Technology Innovation, vol. 3, no. 2, 2018, pp. 70 - 77 Copyright ยฉ TAETI 72 compart ments . In analogy to pharmacokinetics, the water storage tanks and the fermentation tanks are treated as compart ments, energy e xchange among tanks and the at mosphere as drug delivery, the te mperature as drug concentration, electrica l energy injected into the heat pump can be treated as a dose input. We can estimate energy flows, temperatures responses , and hence, electric ity consumption. Based on this, we can determine the best time of heat pu mp operation and control the time and duration of hot water circulat ion using simple and cheap solenoid valves . Hence, the profit can be promoted as a result of better and efficient fermentation without too much of energy consumption and therefore , secured environmental affect. Accordingly, a compromise can be arrived at among economy, ecology, and energy (3E). 2. Materials and Methods 2.1. Compartment modelling Fig. 3 illustrates the proposed compartment mode l. The heat pu mp is identified as an energy supply to the hot water circulat ion system. The soy mash pot (Co mpart ment 2) is bathed in hot water ( Co mpart ment 1). There is heat e xchange in between. Co mpa rt ment 1 will inevitably loss heat to the atmosphere. Co mpart ment 3 stores hot water p roduce fro m the heat pump. Heat energy is supplied fro m Co mpart ment 3 to Co mpart ment 1 via water circulation. Coo led water is to be circulated back to Co mpart ment 3 fro m Co mpart ment 1. Co mpart ment 1 is equipped with a well-designed stirrer that mixes incoming hot water and the e xisting cool water efficiently. In other word, energy is in jected into Co mpart ment 1 as a dose bolus rather than via heat transfer. Thus, there is no ๐‘˜31 and ๐‘˜13 corre lation in between. To simplify the proble m, the storage tank (Co mpart ment 3) is treated as an infinite tank comparing to Compart ment 1. Since the hot water storage tank is well insulated, no-heat-loss is assumed, ie. ๐‘˜30 = 0 . Eq. (1) describes the dynamics of energy transfer based on the compart mental model; where ๐‘‡1 is the temperature o f Co mpart ment 1, ๐‘‡2 is the te mperature of Co mpart ment 2, and r(t) is the injected energy dose: ๏€จ ๏€ฉ ๏€จ ๏€ฉ1 10 12 1 21 2 2 12 1 21 2 dT r t k k T k T dx dT k T k T dx ๏ƒฌ ๏€ฝ ๏€ญ ๏€ซ ๏ƒ— ๏€ซ ๏ƒ— ๏ƒฏ๏ƒฏ ๏ƒญ ๏ƒฏ ๏€ฝ ๏ƒ— ๏€ญ ๏ƒ— ๏ƒฏ๏ƒฎ (1) ๐‘˜12๏ผšThe transfer constant of heat in circulation water transfer to soy mash (๐‘  โˆ’1 ) ๐‘˜21 ๏ผšThe transfer constant of heat in soy mash transfer to circulation water (๐‘  โˆ’1 ) ๐‘˜10๏ผšThe transfer constant of heat in circulation water dissipate into the air (๐‘  โˆ’1 ) ๐‘˜30 ๏ผšThe transfer constant of heat in storage water dissipate into the air (๐‘  โˆ’1 ) Fig. 3 The proposed compartment model 2.2. Determination of system parameters Fig. 4 shows the experimental setup for determin ing the k coefficients. Tanks were filled with water of different temperatures and hence, energy flowed fro m high te mperature to low te mperature sites. Te mperature responses were recorded every 10 min till thermodynamic equilibriu m. Acquired data were fitted to first-order equations using the MATLAB curve fitting toolbox. Advances in Technology Innovation, vol. 3, no. 2, 2018, pp. 70 - 77 Copyright ยฉ TAETI 73 (a) for ๐‘˜12 (b) for ๐‘˜21 (c) for ๐‘˜10 Fig. 4 Experimental setups for determining the k coefficients Other para meters to be determined are the volume of the circulat ion water, the volu me of the soy mash and the hot water circulation time. 2.3. Energy consumption cost function The heat pump e xtracts energy from the air to heat up water. The ambient te mperature is the key factor that influences the effic iency of heat pump operation [11]. The higher the a mb ient temperature is, the higher the heat pump effic iency. Hence to operate the heat pu mp at noontime will have the ma ximu m operational e fficiency. Ho wever, the noontime is categorized as a peak t ime in e lectric ity pricing, ie. the p rice of electric ity is h igher than other times. The mash fermentation tank will have a lower te mperature at n ight time and therefore, the hot water prepared at noontime is not used for several hours . In other word, the hot water produced by the heat pump at noontime will loss a big amount of energy to the atmosphere. Thus, it may be more profitable by operating the heat pump away fro m noontime as a co mpro mise among electric ity price, heat pu mp effic iency, and energy loss. Accordingly, an energy consumption cost function is to be developed to account for the efficiency of the heat pump, the electricity pricing policy, and the heat loss of the hot water storage tank. 3. Results and Discussion 3.1. System parameters Te mperature responses were acquired with a sampling period of 10 min for 6 h wh ich is long enough for the system to reach thermodynamic equilibriu m. The acquired data are fitted to a first-order equation using the MATLAB curve fitting toolbox. Fig. 5 shows the temperature responses. (a) for ๐‘˜12 (b) for ๐‘˜21 (c) for ๐‘˜10 Fig. 5 Temperature responses for determining the compartment -model coefficients Fig. 5(a) is the temperature profile for ๐‘˜12 and can be described as: ๐‘‡ = 5.727๐‘’ โˆ’๐‘ก 7.143 โ„ + 39.37 ยฐC (2) with a t ime resolution of 10 min (600 s ). The t ime constant is 7.143 ร— 600 = 4285.8 s and its reciprocal gives ๐‘˜12 = 2.33 ร— 10 โˆ’4 ๐‘  โˆ’1. Advances in Technology Innovation, vol. 3, no. 2, 2018, pp. 70 - 77 Copyright ยฉ TAETI 74 Fig. 5(b) is the temperature profile for ๐‘˜21 and can be described as: ๐‘‡ = 9.86๐‘’โˆ’๐‘ก 5 .821 โ„ + 36.52 ยฐC (3) The time constant is 5.821 ร— 600 = 3492.6 s and its reciprocal gives ๐‘˜12 = 2.86 ร— 10 โˆ’4 ๐‘  โˆ’1 . Fig. 5(c ) is the temperature profile for k 10 . The bathing tank is cladded with a good insulation materia l. Hence as the profile shows, this is a very slow heat transfer s ystem. It took 11 days to reach thermodynamic equilibriu m and resulted in 1716 record ings . These data are down-sampled with a factor of 50. The profile can be described with first -order dynamics, as: ๐‘‡ = 18.85๐‘’ โˆ’๐‘ก 8.523 โ„ + 28.81 ยฐC (4) The new sampling period is 60 ร— 10 ร— 50 = 3 ร— 104 s , the time constant is 8.523 ร— 30000 = 255690 s , and the coefficient is ๐‘˜10 = 3.91 ร— 10 โˆ’6 ๐‘  โˆ’1. 3.1.1. Other constants Co mpart ment 1 has a space of 220 litres for circulat ion water and Co mpart ment 2 acco mmodates 160 litres of soy mash. 3.1.2. Thermodynamics of the circulation water The purpose of water c irculat ion control is to regulate the temperature of the soy mash in Co mpart ment 2 through controlling the heat in jected into Co mpart ment 1. Fig. 6 illustrates the conceptual thermodynamics of the two co mpart ments. Co mpart ment 1 has a water d istributor designed to mix the inco ming water with the e xisting one in an effective way. Hence the two med ia a re assumed to mix instantaneously. The first la w of thermodyna mics describes the heat balance of the thermodynamic system, as: ๐‘„๐‘–๐‘› + ๐‘„๐‘œ๐‘Ÿ๐‘–๐‘”๐‘–๐‘› โˆ’ ๐‘„๐‘œ๐‘ข๐‘ก = ๐‘„๐‘“๐‘–๐‘›๐‘Ž๐‘™ (5) Fig. 6 Heat balance in the batching tank Substituting ๐‘„ = ๐‘š ร— โ„Ž๐‘“ to Eq. (4) and discretizing give, ๏ฟฝฬ‡๏ฟฝ โ„Ž ร— โˆ†๐‘ก ร— โ„Ž๐‘“ (๐‘‡โ„Ž ) + ๐‘š๐‘ ร— โ„Ž๐‘“ (๐‘‡๐‘ ,๐‘˜โˆ’1 ) โˆ’ ๏ฟฝฬ‡๏ฟฝ โ„Ž ร— โˆ†๐‘ก ร— โ„Ž๐‘“ (๐‘‡๐‘ ,๐‘˜โˆ’1 ) = ๐‘š๐‘ ร— โ„Ž๐‘“ (๐‘‡๐‘ ,๐‘˜ ) (6) with ๏ฟฝฬ‡๏ฟฝ โ„Ž the circulating water flow rate, โ„Ž๐‘“ the enthalpy of water at a specific te mperature, ๐‘š๐‘ the mass of the bathing water, ๐‘‡โ„Ž the temperature of the incoming hot water, ๐‘‡๐‘ the temperature of the bathing water, โˆ†๐‘ก the heating duration, and k the time stamp. The enthalpy can be approximated with the specific heat, ie. โ„Ž๐‘“ โ‰… ๐ถ๐‘ ร— ๐‘‡ , hence Eq. (6) can be rewritten as : ๏ฟฝฬ‡๏ฟฝ โ„Ž ร— โˆ†๐‘ก ร— ๐ถ๐‘ ร— ๐‘‡โ„Ž + ๐‘š๐‘ ร— ๐ถ๐‘ ร— ๐‘‡๐‘ ,๐‘˜โˆ’1 โˆ’ ๏ฟฝฬ‡๏ฟฝโ„Ž ร— โˆ†๐‘ก ร— ๐ถ๐‘ ร— ๐‘‡๐‘ ,๐‘˜โˆ’1 = ๐‘š๐‘ ร— ๐ถ๐‘ ร— ๐‘‡๐‘ ,๐‘˜ (7) Rearranging the above gives the temperature response: ๐‘‡๐‘ ,๐‘˜ โˆ’ ๐‘‡๐‘ ,๐‘˜โˆ’1 = โˆ†๐‘‡๐‘ = ๏ฟฝฬ‡๏ฟฝ โ„Ž ร—โˆ†๐‘ก ๐‘š๐‘ (๐‘‡โ„Ž โˆ’ ๐‘‡๐‘ ,๐‘˜โˆ’1 ) (8) The follo wing values are used for simu lation validation: ๏ฟฝฬ‡๏ฟฝโ„Ž = 10kg/min, โˆ†๐‘ก = 3 min, ๐‘š๐‘ = 220 kg, ๐‘‡โ„Ž = 47โ„ƒ. The water storage tank (Co mpart ment 3) has a capacity of 1500 lit res and only 30 litres are de manded for the c irculat ion. Advances in Technology Innovation, vol. 3, no. 2, 2018, pp. 70 - 77 Copyright ยฉ TAETI 75 Hence it is reasonable to assume a constant ๐‘‡โ„Ž . The initia l te mperature of the bathing water ๐‘‡๐‘,k โˆ’1 is assumed as 36.8ยฐC. Substituting the above values into Eq. ( 8) results in โˆ†๐‘‡๐‘ = 1.39ยฐC , ie. a 3-min heat in jection heats up the bathing water by 1.39ยฐC . This information will be used in compartment modelling. 3.1.3. Validation The compart ment model of Fig. 3 was validated using the MATLAB SimBiology toolbo x using the para meters identified in Section 3. Fig. 7 shows simu lation and actual responses . There is a strong degree of coherence in between. This promising result indicates that the proposed compartment mode l can e ffective ly describes the energy fl ows of the fermentation system. Fig. 7 Simulation and actual responses It is clea r that the t iming of operating the heat pu mp is the key issue of saving energy cost for the fermentation system. The timing should account for the operational effic iency, electricity pricing, and heat losses from tanks. Thus, the above three factors are transcribed as an energy cost function : minimis ing the function for the least energy bill. In this study, the heat pump was set to produce hot water at 47โ„ƒ. The energy for 1 litre of hot water produce is: ๐‘„ = ๐‘š ร— ๐ถ๐‘ ร— โˆ†๐‘‡ = 1 ร— 4.2 ร— (47 โˆ’ ๐‘‡๐‘ก ) = 197.4 โˆ’ 4.2 ๐‘‡๐‘ก (9) with ๐‘‡๐‘ก the temperature of the water in the storage tank, which can be estimated using the compartment model . The performance of a heat pump is described with the so-called Coeffic ient of Pe rformance (COP). It is a ratio of the heat generated, Q, by the heat pump to the energy consumed, W, by the heat pump [14], as: ๐ถ๐‘‚๐‘ƒ = ๐‘„ ๐‘Š (10) The work done by the heat-pump compressor is: ๐‘Š = ๐‘„ ๐ถ๐‘‚๐‘ƒ = 197 .4โˆ’4.2 ๐‘‡๐‘ก ๐ถ๐‘‚๐‘ƒ ๐‘˜๐ฝ (11) The COP coefficient is sensitive to the amb ient temperature ๐‘‡๐‘Ž . Table 1 lists the COPs of the heat pump (CHP -80Y, SUN TECH, Taiwan). The hotter the ambient is, the larger the COP. Table 1 COPs of the heat pump at different ambient temperatures Ambient (ยฐm) -20 -15 -10 -5 0 2 7 10 16 20 25 30 35 43 COP 2.2 2.4 2.6 2.5 2.6 2.8 3.7 4.0 4.2 4.3 4.4 4.5 4.4 4.3 Advances in Technology Innovation, vol. 3, no. 2, 2018, pp. 70 - 77 Copyright ยฉ TAETI 76 The comp ressor of the heat pump is assumed to have an effic iency ฮท=0.9. The work de manded by the heat pump to produce 1 litre of hot water is: ๐‘Š๐‘– = ๐‘Š ๐œ‚ = 197.4 โˆ’ 4.2 ๐‘‡๐‘ก ๐ถ๐‘‚๐‘ƒ รท 0.9 = 219.33 โˆ’ 4.67 ๐‘‡๐‘ก ๐ถ๐‘‚๐‘ƒ kJ (12) or in KWH, as: ๐‘Š๐‘– = 219.33 โˆ’ 4.67 ๐‘‡๐‘ก ๐ถ๐‘‚๐‘ƒ รท (3.6 ร— 103 ) = 0.060925 โˆ’ 0.001297 ๐‘‡๐‘ก ๐ถ๐‘‚๐‘ƒ ๐พ๐‘Š๐ป (13) The cost C, in NTD, that the heat pump take to produce 1 litre of hot water is: ๐ถ = ๐ธ ๐ถ๐‘‚๐‘ƒ (0.060925 โˆ’ 0.001297 ๐‘‡๐‘ก ) (14) where E is the price of unit KWH in NT D/KW H, a value varies at peak and off-peak times. Table 2 shows the pricing policy of Taiwan Power Co mpany (TPC). The above cost function is a function of the time of heat pump operation (transcribed as COP and E) and heat losses from the storage tanks (transcribed as ๐‘‡๐‘ก ). Table 2 Pricing policy of Taiwan Power Company 4. Conclusions We have built a co mpart ment model for describing te mperature response, heat exchange, and energy demand of a soy mash fermentation system. There is a strong coherence between simulat ion and actual results . Simu lation results show that the model can accurate ly predict the trend of te mperature response. Thus, our ne xt work is to imp le ment model -based predictive temperature control based on the developed compart ment model. This will g ive a more precise te mperature control. The model a lso describes the heat exchange, or energy flow, between tanks (compart ments). This feature allows us to estimate the optimu m t ime of running the heat pump. Hence we can arrive at a p ro mising te mperature control with an economic electricity bill. 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