analise dinâmica de um chiller de absorção de brometo de lítio ...

99fermentation heat exchanger is made of stainless steelAISI 304. The overall thermal conductances UA of heatexchangers are shown in Table 2.Table 2. Overall Heat Transfer Coefficients of Heat Exchangers.ComponentUA( kW K −1 )Generator 165.0Absorber 297.0Condenser 198.0Evaporator 371.3Solution heat exchanger 31.6Fermentation heat exchanger 966.42.2 Mathematical Modeling2.2.1 Absorption Chiller The modeling of the absorptionchiller is performed based on energy, massand species balances, considering a quasi-steady stateregime (the system moves quickly through a sequence ofsteady states, even while subjected to varying conditionsover time), according to the theoretical fundamentals ofHerold et al. (1996).Themassflowratebalanceofthegeneratoriscalculatedusing the expressionṁ 3 = ṁ 4 + ṁ 7 (1)Considering that there is no lithium bromide in thesuperheated steam (point 7), the lithium bromide balancein the generator is given byṁ 3 ·ξ 3 = ṁ 4 ·ξ 4 (2)where ξ 3 is the lithium bromide mass fraction of theweak solution and ξ 4 is the lithium bromide mass fractionof the strong solution.The solution pump reaches the steady state flow ratequickly and maintains a constant rate. The expressionfor the work input of the solution pump is obtained as][ṁ1 · (PẆ p = 100· 2 − P 1)(3)η p ·ρ 1where η p is the solution pump efficiency and its valueis 72 % and ρ 1 is the density of the aqueous lithiumbromide solution at point 1 in Figure 1.The modeling of the heat exchanger-cycle cooling systemof the absorption chiller is carried out using the energybalance and the Logarithmic Mean TemperatureDifference (LMTD).The coefficient of performance (COP) oftherefrigerationmachine is defined as follows˙Q eCOP =(4)˙Q g +Ẇ pwhere ˙Q e is the cooling capacity, ˙Q g is the heat flowinput in the generator and Ẇ p is the work input of thesolution pump.2.2.2 Fermentation The mathematical model forthe ethanol fermentation is an unstructured model andthe modeling is performed based on kinetic rate modelscoupled with mass balance equations for the cell, substrateand ethanol and the energy balance, for an industrialfed-batch fermentation process. It is assumed thatthe feed is sterile (X in =0).The global mass balance is described asdV= Ḟ (5)dtwhere Ḟ is the substrate feed volume flow rate and dV/dtrepresents the variation in the volume during the fermentationprocess.TherateofcellgrowthisdefinedasfollowsdX= μ ·X − Ḟ ·X(6)dtVwhere μ is the specific growth rate and the factor Ḟ/Vis the dilution rate as the feed is added during the fermentationprocess.The substrate consumption is modeled by the equationdSdt = − μ ·X − m X ·X + Ḟ · (Sin − S) (7)Y X/S Vwhere Y X/S is the yield factor of the cell based on thesubstrate consumption and m X is the maintenance coefficient.The ethanol formation is written asdE= Y E/S · μ ·X+ m E ·X − Ḟ ·Edt Y X/S V(8)where Y E/S represents the yield factor of ethanol basedon substrate consumption and m E is the ethanol productionassociatedwithgrowth.The variation in fermentation temperature T 21 duringthe process is described by Eqn (9) and it is determinedthrough the energy balance of the fermentation system.dT 21= Ḟdt V · (Tin − T21) − ˙V 21 · (T21 − T22)V( ) ()ΔHS μ ·X+· + m X ·Xρ in ·Cp in Y X/S(9)where ΔH S is the heat released during the fermentationprocess and its value is 697.7kJper kilogram of substrateconsumed (Albers et al. 2002), the inlet temperature T inand the volume flow rate ˙V 21 areshowninTable4.In the model shown, the specific growth rate is expressedas a function of limiting substrate concentrationS (Monod equation) and of the inhibitory effects ofsubstrate and ethanol concentration (Ghose and Tyagi1979), as represented by the following equation( )(Sμ = μ max · · exp(−K i ·S)· 1 − E ) n(10)K S + SE maxwhere μ max is the maximum specific growth rate, K Sis the substrate saturation constant, K i is the substrateInt. J. of Thermodynamics (IJoT) Vol. 13 (No. 3) / 113