Temperature of Closed Feed Water Heater Outlets

13th International Symposium on Process Systems Engineering (PSE 2018)

Mahdi Mohammadi Ghaleni , ... Siamak Nejati , in Computer Aided Chemical Engineering, 2018

4 Comparison of experimental and computational results

Feed temperature is one of the most critical parameters in the MD process because it influences water partial pressure gradient existing across the membrane. Figure 3.a shows the effect of feed temperature on the permeate flux for two different hollow fiber membranes. The results indicate that the permeate flux increases with feed temperature. The modeling results were in good agreements with the experimental data when the tortuosity parameter was set to be equal to 2.5 and 8. The effect of tortuosity and feed temperature on the permeate flux of the system is also shown in Figure. 3b. The permeate flux increases with the increase in the feed temperature and the consequent increase in the temperature gradient across the membrane.

Figure 3. (a) Comparison between experimental results for the permeate flux of two hollow fiber membranes with low and high tortuosity and the prediction of the model for the membranes in a close-packed configuration[15]; (b) effect of feed temperature and tortuosity on the permeate flux.

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Gas permeation and supported liquid membranes

Patricia Luis , in Fundamental Modelling of Membrane Systems, 2018

Effect of feed temperature

The feed temperature is a key variable in the pervaporation process using SLMs for two reasons: (i) the vapor pressure of the feed solution increases with temperature, leading to a larger driving force that will enhance the transmembrane flux; and, (ii) the viscosity of the liquid membrane decreases with temperature, which will increase the diffusivity of the target compound through the SLM. However, higher temperature does not always produce an enhancement of flux. For example, in the separation of acetic acid/water studied by Qin et al. (2003), it was observed that the higher the temperature, the higher the acetic acid concentration in the permeate, and the higher the acetic acid selectivity. However, the permeation fluxes of both components (acetic acid and water) decreased sharply with an increase of temperature. Fig. 4.12 shows these results of transmembrane flux as a function of the temperature. Higher temperature increased the vapor pressures of acetic acid and water, which means higher driving forces for pervaporation, but it also reduced sharply the partition coefficient of acetic acid between the liquid membrane phase and the aqueous phase and the solubility of water in the liquid membrane phase. The solubility of water was more significantly influenced by the temperature increase than the acetic acid solubility; this explains why water permeation flux decreased more sharply than acetic acid. Nevertheless, the effect of the temperature should be also studied in terms of permeability, selectivity, and membrane stability.

Fig. 4.12. Effect of the temperature on the permeation fluxes of acetic acid and water using trioctylamine (TOA) as the liquid membrane.

Reproduced with permission from Qin, Y., Sheth, J.P., Sirkar, K.K., 2003. Pervaporation membranes that are highly selective for acetic acid over water. Ind. Eng. Chem. Res. 42, 582–595.

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Feedwater heating systems

British Electricity International, in Turbines, Generators and Associated Plant (Third Edition), 1991

2.2 System parameters

The final feed temperature (FFT) out of the ultimate HP heater is fixed within a few degrees by the bleed pressure and steam temperature available to the heater. On all current 660 and 500 MW units, the bleed point is the HP exhaust or 'cold reheat' pressure.

The feed temperature out of a heater is conditional on several factors. First, a bled-steam pipework temperature loss, usually 1.1 °C, which is subtracted from the saturation temperature equivalent of the bleed point pressure. The resultant temperature is the saturation temperature equivalent to the pressure of the steam entering the heater shell. The heater thermal performance and hence its heat transfer surface is determined by the values of the temperature terminal differences (TTDs) on the steam and drain sides.

The steam TTD is defined as the temperature difference between the saturated steam temperature at entry to the heater shell and the feed water leaving the heater. The drain TTD is the temperature difference between the feedwater entering the heater and the drains leaving the heater. To achieve optimum HP heater performance, it is usually necessary to partition each HP heater into three zones; namely, the desuperheating, condensing and drain cooling zones. The effect which TTDs have on the size of these zones is fully explained in Section 6 of this chapter.

By applying the line temperature drops to all HP heater bled-steam extraction pressures and the steam TTDs, the feed temperature out of each of the HP heaters is determined. Once the temperatures out of the heaters (and hence into the next heater) are known, the drain temperatures are found by applying the drain TTDs. However, it should be remembered that the smaller the TTDs, the greater will be the heat transfer surface to achieve the intended performance.

HP heaters which are supplied with steam with a high degree of superheat can have negative TTDs, the higher feed temperatures out of the heaters being made possible by the total steam temperature as seen by the desuperheating zone. Figure 3.17 illustrates the principles explained above and shows typical TTDs for a 660 MW unit and the resultant heater inlet, outlet and drain temperatures. It should be noted that the second HP heater draws its steam from the BFP turbine which is relatively low in superheat, hence the steam TTD is larger than that of the ultimate heater which has more superheat in the bled-steam.

FIG. 3.17. Application of temperature terminal differences to heaters to find the temperature of feedwater and drains

The TTDs are determined by the economics of the cycle, the increase in cycle efficiency by use of smaller TTDs being weighed against the increased cost of heater surface.

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Arsenic Removal by Membrane Distillation

Parimal Pal , in Groundwater Arsenic Remediation, 2015

5.9.5.1 Effect of feed temperature on flux

The effect of feed temperature on water flux is illustrated in Figure 5.16. The changes of viscosity and density of water over the given range of temperature variation are not so strong and as a result the Reynolds number variation with the feed temperature does not significantly change at a given flow rate.

Figure 5.16. Effect of feed temperature on pure water flux [13].

Figure 5.16 illustrates that feed temperature has a remarkable influence on the permeate flux. For example, when the feed flow rate is 0.028   m/sec, an increase of temperature from 30 to 61   °C causes an increase in water vapor flux from all three different types of membranes. The fluxes of MS3220 and MS3020 increase exponentially with temperature, whereas the flux through the MS7020 increases linearly with temperature. The exponential increase of MD flux with temperature for commercial PTFE membranes is due to the exponential increase of vapor pressure with temperature as per the Antoine equation as described in the modeling section for vapor pressure of water. The permeate flux exhibits a linear dependence on the feed temperature for PP membrane since mass transfer resistance of the membrane is mainly governed by membrane thickness. In the reported system [31], membrane thickness of PP is substantially greater (2.6 times) than PTFE. Thus the effect of the membrane thickness at higher temperature overshadows the effect of the temperature on water flux. The reasons for the higher flux of PTFE membranes other than PP are higher porosity of PTFE membranes and rougher surfaces (especially the surface of the support layer) of PTFE membranes that help mixing at the membrane interfaces.

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Process Control

William A. Poe , Saeid Mokhatab , in Modeling, Control, and Optimization of Natural Gas Processing Plants, 2017

3.6.9.9.8 Feed Enthalpy Control

Feed enthalpy control is preferred to feed temperature control since feed quality has more impact on the operation of the tower. Feed enthalpy can be calculated by energy balance around the preheat train and feed quality will be kept constant.

Vapor–liquid circulation below the feed tray decreases relative to above the feed tray when the feed enthalpy is increased. Maximum feed preheat is preferred when the reboiler capacity is limiting or feed preheat is less costly than reboiler heat. When differential pressure above the feed tray or condenser capacity is the constraint, feed enthalpy should be decreased.

Nonlinear, predictive, multiinput/multioutput systems are quite valuable for distillation towers. Although the earlier discussion has presented some concepts for stabilizing and improving the profitability of distillation operations, maximum benefits are seldom obtained due to complications and interactions that most always arise. Model predictive methods have been developed and widely adopted for these operations. Model-based, multivariable control systems and neural net controllers, as well as rigorous optimization, are discussed in subsequent chapters of this work.

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27th European Symposium on Computer Aided Process Engineering

Marc Kalliski , ... Sebastian Engell , in Computer Aided Chemical Engineering, 2017

2 Data-based modeling

The evaporator set-up is similar for all evaporators; they differ only in the number of the evaporator stages (see Fig. (2)) and the processing capacities. The diluted spin bath is fed into the last evaporator stage and is blended with the spin bath that circulates through the circulation pump, the preheater and the evaporator stages. A defined share of the mixture of higher concentration is fed back to the spin bath cycle. The amount of water that is evaporated from the spin bath (evaporation capacity) depends on the flow rate F , the feed temperature T, and the temperature T_MK of the mixing condenser that creates a partial vacuum in the head of the evaporator.

Figure 2. Set-up of a single evaporator (left) and the operational window as a function of the feed temperature T and cycle flow F (right).

2.1 Model structure for a single evaporator

The cycle flow rate F and the feed temperature T are the manipulated variables that are used to operate the evaporator within the operational window shown in Fig. (2) on the right hand side. The specific steam consumption as well as the evaporation capacity exhibit a linear correlation. The rhombus is shifted as a result of a changing condenser temperature T_MK and fouling processes during the production. Experimental data indicated that the effect of the disturbance on T_MK can also be approximated by a linear dependency.

Eq. (2 – 3) describe the evaporation capacity (EC) and the specific steam consumption (SC) as a linear function of the inputs (T, F), the disturbance (T_MK ), and the fouling state f _fouling,i . The absolute steam consumption (AS) results from Eq. (4).

(2) $EC=a_{1}T+a_{2}F+a_3{T}_{MK}+b_0+f_{\mathit{fouling},1}$

(3) $SC=c_{1}T+c_{2}F+c_3{T}_{MK}+d_0+f_{\mathit{fouling},2}$

(4) $\mathit{AC}=EC·SC$

2.2 Optimal control of a single evaporator

The analysis of the right side of Fig. (2) reveals that the most efficient operating point for any feasible evaporation capacity lies on the lower boundary of the operating window where the specific steam consumption is the lowest. Until recently, the operators were allowed to choose any combination of the manipulated variables that results in the same evaporation capacity, possibly at sub-optimal efficiency. Within the EU funded project MORE (www.more-nmp.eu), a control structure was implemented that keeps the cycle flow rate F at the minimum as long as the specified evaporation capacity can be achieved by increasing the feed temperature. Only if the feed temperature is at the upper limit, the cycle flow rate F is increased to meet the evaporation capacity requirement.

2.3 Automatic model generation for data-based models

A modeling tool was implemented in MATLAB® to automatize the modeling process based on historical production data. The tool performs a data pretreatment to remove inconsistent data and fouling influences from the data. The remaining data is screened for step changes in the evaporation capacity and a set of steady-state operating points before and after changes is obtained. Based on this information linear regression models for SC and EC are fitted to the data and validated. The fouling parameter in the model is adapted online according to the observed behavior of the evaporators.

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Single Effect Evaporation – Vapor Compression

Hisham T. El-Dessouky , Hisham M. Ettouney , in Fundamentals of Salt Water Desalination, 2002

Evaporator and Feed Preheaters Energy Balances

Two preheaters are used to increase the feed temperature from the intake seawater temperature T _cw to T_f. The intake seawater is divided into two portions, αM_f and (1-α)M_f. In the first preheater, heat is exchanged between αM_f and the condensed vapors, and in the second preheater, heat is exchanged between (1-α)M_f and the rejected brine. The thermal load of the two heat exchangers is given in terms of the intake seawater

(21) ${\text{Q}}_{\text{h}}={\text{M}}_{\text{f}}{\text{C}}_{\text{p}}{(\text{T}}_{\text{f}}-{\text{T}}_{\text{cw}})$

The seawater feed flow rate given by Eq. (20) is substitute in Eq. (21). This gives

(22) ${\text{Q}}_{\text{h}}={\text{M}}_{\text{d}}{\text{\hspace{0.17em}C}}_{\text{p}}{(\text{X}}_{\text{b}}{/(\text{X}}_{\text{b}}-{\text{X}}_{\text{f}}{\left)\right)(\text{T}}_{\text{f}}-{\text{T}}_{\text{cw}})$

Equation (21) can be also written in terms of the heat load of the condensed vapor and the rejected brine, which gives

(23) ${\text{Q}}_{\text{h}}={\text{M}}_{\text{d}}{\text{\hspace{0.17em}C}}_{\text{p}}{(\text{T}}_{\text{d}}-{\text{T}}_{\text{o}})+{\text{M}}_{\text{b}}{\text{\hspace{0.17em}C}}_{\text{p}}{(\text{T}}_{\text{b}}-{\text{T}}_{\text{o}})$

The brine flow rate, M_b, given by Eq. (19) is substituted in Eq. (23). This reduces Eq. (23) into

(24) ${\text{Q}}_{\text{h}}={\text{M}}_{\text{d}}{\text{\hspace{0.17em}C}}_{\text{p}}{(\text{T}}_{\text{d}}-{\text{T}}_{\text{o}})+{\text{M}}_{\text{d}}{(\text{X}}_{\text{f}}{/(\text{X}}_{\text{b}}-{\text{X}}_{\text{f}}{\left)\right)\text{C}}_{\text{p}}{(\text{T}}_{\text{b}}-{\text{T}}_{\text{o}})$

Equating Eqs. (22) and (24) gives

(25) $\begin{array}{l}({\text{M}}_{\text{d}}{\text{\hspace{0.17em}C}}_{\text{p}}({\text{T}}_{\text{d}}-{\text{T}}_{\text{o}})+{\text{M}}_{\text{d}}({\text{X}}_{\text{f}}/({\text{X}}_{\text{b}}-{\text{X}}_{\text{f}})\left){\text{C}}_{\text{p}}\right({\text{T}}_{\text{b}}-{\text{T}}_{\text{o}}\left)\right)\\ ={\text{\hspace{0.17em}M}}_{\text{d}}{\text{\hspace{0.17em}C}}_{\text{p}}({\text{X}}_{\text{b}}/({\text{X}}_{\text{b}}-{\text{X}}_{\text{f}}\left)\right)({\text{T}}_{\text{f}}-{\text{T}}_{\text{cw}})\end{array}$

Equation (25) is simplified to determine the outlet temperature of the heating streams, T_o, which gives

(26) ${\text{T}}_{\text{o}}={(\text{T}}_{\text{cw}}-{\text{T}}_{\text{f}})+{(\text{X}}_{\text{f}}/{\text{X}}_{\text{b}}{)\text{T}}_{\text{b}}+({(\text{X}}_{\text{b}}-{\text{X}}_{\text{f}}{)/\text{X}}_{\text{b}}{)\text{T}}_{\text{d}}$

In the evaporator, heat is supplied to the feed seawater, where its temperature increases from T_f to T_b. Also, latent heat is consumed by the formed vapor at a temperature of T_b. This energy is supplied by the latent heat of condensation for the compressed vapors at T_d and by the superheat of the compressed vapors, T_s-T_d. The evaporator thermal load is given by

(27) ${\text{Q}}_{\text{e}}={\text{M}}_{\text{f}}{\text{\hspace{0.17em}C}}_{\text{p}}{(\text{T}}_{\text{b}}-{\text{T}}_{\text{f}})+{\text{M}}_{\text{d}}{\text{λ}}_{\text{b}}={\text{M}}_{\text{d}}{\text{λ}}_{\text{d}}+{\text{M}}_{\text{d}}{\text{\hspace{0.17em}C}}_{{\text{p}}_{\text{v}}}{(\text{T}}_{\text{s}}-{\text{T}}_{\text{d}})$

In the above equation λ_b and λ_d are the latent heat of formed vapor at T_b and condensing vapor at T_d. The feed flow rate given by Eq. (20) is substituted in Eq. (27). The resulting equation is

(28) ${\text{M}}_{\text{d}}{(\text{X}}_{\text{b}}{/(\text{X}}_{\text{b}}-{\text{X}}_{\text{f}}{\left)\right)\text{C}}_{\text{p}}{(\text{T}}_{\text{b}}-{\text{T}}_{\text{f}})+{\text{M}}_{\text{d}}{\text{λ}}_{\text{b}}={\text{M}}_{\text{d}}{\text{λ}}_{\text{d}}+{\text{M}}_{\text{d}}{\text{\hspace{0.17em}C}}_{{\text{p}}_{\text{v}}}{(\text{T}}_{\text{s}}-{\text{T}}_{\text{d}})$

Equation (28) is then simplified to determine the seawater feed temperature, T_f. This is given by

(29) ${\text{T}}_{\text{f}}=\left(\right({\text{X}}_{\text{b}}-{\text{X}}_{\text{f}}{)/\text{X}}_{\text{b}}\left)\right(({\text{λ}}_{\text{b}}-{\text{λ}}_{\text{d}})/{\text{C}}_{\text{p}}-{(\text{Cp}}_{\text{v}}{/\text{C}}_{\text{p}}{\left)\right(\text{T}}_{\text{s}}-{\text{T}}_{\text{d}}\left)\right)+{\text{T}}_{\text{b}}$

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Membrane distillation—Principles, applications, configurations, design, and implementation

Abdullah Alkhudhiri , Nidal Hilal , in Emerging Technologies for Sustainable Desalination Handbook, 2018

3.11.1 Feed temperature

As can be seen in Table 3.9 , the feed temperature has a strong influence on the distilled flux. According to the Antoine equation, the vapor pressure increases exponentially with temperature. Therefore, the operating temperature has an exponential effect on the permeate flux [33,69]. At constant temperature difference between the hot and the cold fluid, the permeate flux increases when the temperature of the hot fluid rises, which means the permeate flux is more independent of the hot fluid temperature. Alkhudhiri et al. [10], Qtaishat et al. [109], Gunko et al. [26], and Chen et al. [168] pointed out that increasing the temperature gradient between the membrane surfaces will affect the diffusion coefficient positively, which leads to increased vapor flux. Similarly, Srisurichan et al. [83] believed that there is a direct relation between diffusivity and temperature, so that working at high temperature will increase the mass transfer coefficient across the membrane. Moreover, temperature polarization decreases with increasing feed temperature [84,108].

Table 3.9. Effect of temperature on permeate flux

Ref.	MD type	Membrane type	Pore size	Solution	Feed velocity (m/s)	T in (°C)	Permeate (kg/m2  h)
[11]	AGMD	PVDF	0.45	Artificial seawater	5.5   L/min	40–70	≈   1–7
[84]	DCMD	PVDF	0.22	Pure water	0.1	40–70	≈   3.6–16.2
[167]	DCMD	PTFE	0.2	NaCl (2   mol/L)	16   cm3/s	17.5–31	≈   2.88–25.2
[79]	DCMD	PTFE	0.2	Pure water	–	40–70	≈   5.8–18.7
[155]	DCMD	PVDF	0.4	Sugar	0.45	61–81	≈   18–38
[110]	DCMD	PVDF	0.4	Pure water	0.145	36–66	≈   5.4–36
				NaCl (24.6   wt%)	0.145	43–68	≈   6.1–28.8
[42]	VND	3MC	0.51	Pure water	–	30–75	≈   0.8–8.8   mol/m2  s
[83]	DCMD	PVDF	0.22	Pure water	0.23	40–70	≈   7–33   L/m2  h
[158]	SGMD	PTFE	0.45	Pure water	0.15	40–70	≈   4.3–16.2
[29]	DCMD	PVDF	0.11	Orange juice	2.5   kg/min	25–45	30   ×   103–108   ×   103
[28]	DCMD	PTFE	0.2	NaCl (5%)	3.3   L/min	5–45	1–42
[28]	AGMD	PTFE	0.2	NaCl (3%)	3.3   L/min	5–45	0.5–6

In terms of coolant temperature, a noticeable change takes place in the permeate flux when the cold side temperature decreases [26,29,33]. In addition, more than double permeate flux can be achieved compared to a solution, at the same temperature difference [69]. Banat and Simandl [11] and Matheswaran et al. [169], however, found that the effect of the cold side temperature on the permeate flux is neglected at fixed hot side temperature, because of low variation of vapor pressure at low temperatures.

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Process Systems Engineering for Pharmaceutical Manufacturing

Paul Brodbeck , in Computer Aided Chemical Engineering, 2018

4.2.5 S88 batch standard fixed software/hardware link

Implementations of S88 in the batch industry typically have a way to assign a software unit to an equipment unit operation that fixes the software to the hardware. This is referred as binding, when you assign a specific software object to a physical piece of equipment they are bound together. For a typical control loop, there would be a control module specifically assigned to a piece of hardware in the field. So a PID control module for flow would be assigned to a flow transmitter and a flow valve. This is typical the way regulatory controls are configured. The PID block is based on a software object, but there is typically a single instance of the control module class for each field element. A one-to-one correspondence between the control module and the field element. Every element on the field is assigned to a control module and every control module is assigned to an element in the field. Control modules are objects that instances of the class, which makes them object oriented. This type of configuration works because the number of field elements and their locations in the field are known in advance and can be directly wired and configured.

In the batch world, you may not know which field elements are required when you are programming. In addition and possible more importantly, you may want to write a program that can be used over and over on multiple unit operations. Many times, in batch, there may be multiple units that are similar and perform the same function. In this case, it would not make sense to write a separate program or Phase (S88 terminology) for each unit. Even if you could copy and paste the Phase into 12 separate units, you would have to modify each Phase to write to the specific devices assigned to that unit. The big problem comes when you want to modify a Phase on a specific unit type. You would need to modify the Phase on each unit individually. So you have to modify all 12 Phases. This can be a challenge to make sure that all the Phases are identical. Also, you would have to test all 12 Phases individually.

To get around the issue of creating a separate Phase for every unit, the concept of a Unit Alias was created. An Alias is a placeholder that allows you to write a Phase without knowing the actual element or piece of equipment you are writing to. For instance, if there were 12 units and each unit had a Flow Valve, then you could create an Alias called FlowValve. Now each Unit has its own Flow Valve, for instance, FCV-101, FCV-102, to FCV-112, etc. See Table 1 below.

Table 1. Example unit alias table

	Alias names
Unit #	FLOWVALVE	FLOWRATE	FEEDTEMP
U1	FCV-101	FI-101	TI-101
U2	FCV-102	FI-102	TI-102
U3	FCV-103	FI-103	TI-103
U4	FCV-104	FI-104	TI-104
U5	FCV-105	FI-105	TI-105
U6	FCV-106	FI-106	TI-106
U7	FCV-107	FI-107	TI-107
U8	FCV-108	FI-108	TI-108
U9	FCV-109	FI-109	TI-109
U10	FCV-110	FI-110	TI-110
U11	FCV-111	FI-111	TI-111
U12	FCV-112	FI-112	TI-112

Also there are two other Aliases in Table 1 defined as FLOWRATE and FEEDTEMP. The idea is that when the sequential code for the Phase is written you refer to the Alias not the actual tag name. For instance, a line of code in a Phase might look like this.

If FEEDTEMP > 100 then

OPEN FLOWVALVE

WAITUNTIL FLOWRATE > 50

In this simple code, the Phase waits until the feed temperature (FEEDTEMP) is greater than 100°C and then opens the flow control valve (FLOWVALVE). It waits until the feed rate (FLOWRATE) is greater than 50  kg/h. and then continues to the next action in the sequence. So when the Phase is being run on one of the Units, it substitutes the Alias with the real piece of equipment. So for Unit #3 the code would be:

If TI-103 > 100 then

OPEN FCV-103

WAITUNTIL FI-103 > 50

The concept of an Alias is very common for batch processes in the pharmaceutical and specialty chemical industries. It allows a Phase to be written once and run on any number of Units that are similar enough. The Phase program is referred to as a Phase Class and can run against any Unit that is validated for it. Fig. 7 below shows 5 Units in a process that is using Phase Classes. For a typical S88 batch plant, the Units are assigned during the configuration phase of a project. At this point, the software Unit is assigned to the physical Unit by filling out the Unit Alias Table depicted in Table 1 above. Once the Unit Alias Table is configured, it is tested and validated. From that point on, the software Unit is fixed or "bound" to the unit equipment and cannot be changed during normal operations. Any change would need to be made when the Unit is down and under change control and would require extensive testing to prove that it functions as required.

Fig. 7. Fixed software/hardware link.

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Reaction Kinetics and the Development of Catalytic Processes

Noemi S. Schbib , ... José A. Porras , in Studies in Surface Science and Catalysis, 1999

3.1.1. Disturbance in the feed temperature for the first bed (R1)

The first bed was simulated under a +8% step in the feed temperature. The axial profiles for the temperature and concentrations of C ₂H₂ and C₂H₄, at six different times are shown in figs. 2 to 4. The axial temperature profile in the final steady-state (t=∞) is higher than the initial one (t=0) (Fig. 2). Due to the higher reaction rate, this evolution is accompanied by a drop in the acetylene concentration profile (Fig. 3). At the same time, a maximum appears at the final ethylene concentration profile (t=∞) (fig. 4) because this is an intermediate compound in the following series of reactions: $C_2{H}_2\stackrel{r_A}{\to }{C}_2{H}_4\stackrel{r_E}{\to }{C}_2{H}_6$ .

Figure 2. Axial temperature profiles in R1. Disturbance in the feed to R1 (T_e = 69.5 → 75°C)

Figure 3. Axial profiles for C₂H₂ in R1 Disturbance in the feed to R1 (T_e = 69.5 → 75°C)

Figure 4. Axial profiles for C₂H₄ in R1. Disturbance in the feed to R1 (T_e = 69.5 → 75°C)

The temperature profile changes gradually since it is related to the slow propagation rate of the "thermal wave". A quick change of the concentration profiles simultaneously occurs (figs. 3 and 4). These different propagation rates cause the inverse response exhibited by the outlet temperature (Fig. 5). This effect, called "wrong-way behavior", has been observed before by other authors [9, 10]

Figure 5. Outlet temp. for bed R1 (z= 180cm). Disturbance in the feed to R1 (T_e = 69.5 → 75°C)

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