N. L Larrea tridentata
5.9 Pruebas de actividad biológica (Mata-Cárdenas et al , 2008):
Two methods of monitoring fouling in situ are described in this section. They both
rely on using the heat transfer coefficient to estimate the heat transfer resistance which is linked to the mass of fouling deposit. The first method measures the global amount of fouling in the equipment. The second measures local fouling development over a small surface area of the heated surface.
3.3.2.1 Theory
The heat transfer flux, q, is given by:
hm p
q U ( )
A φ
= = θ − θ (3.4)
where φ = rate of heat transfer
A = surface area
U = overall heat transfer coefficient
θhm θ
= temperature of the heating medium
p = temperature of the process fluid
The overall heat transfer coefficient is defined as the inverse of the total heat transfer resistance, R. In our case, heat is transferred from the heating medium through the heat exchanger wall to the process fluid as shown in Figure 3.11. The total heat transfer resistance is made up of several components: the resistance
contributed by the process fluid, Rp; the resistance contributed by the fouling layer,
Rf; the resistance contributed by the stainless steel wall and its attachment, Rw; and
the resistance contributed by the heating medium, Rhm. The overall heat transfer
coefficient at a given time is therefore represented by:
p f w hm 1 1 U R R R R R = = + + + (3.5)
Figure 3.11 Schematic drawing of the sectional view of a fouled surface showing the thermal resistances across the heat exchanger.
With a constant flow of heating medium and product, the sum of resistances, Rp, Rw
and Rhm may be approximated by the inverse of the initial overall heat transfer
coefficient, U0, measured at the beginning of the run when the surface is clean.
Therefore the resistance of the fouling layer can be estimated from calculations of the overall heat transfer coefficient:
f 0 1 1 R U U = − (3.6)
Rearranging equation (3.6) gives a normalised overall heat transfer coefficient, Nf:
f 0 f 0 U 1 N U 1 R U = = + (3.7)
In theory, Nf values range from 0 to 1. At the start of a run Rf equals 0 and
therefore Nf equals 1. During a run where fouling builds to a sufficient level to affect
the heat transfer, Nf
3.3.2.2 Local measurement of fouling
begins to decrease below 1. The difference between the local and the global measurement of fouling lies in the calculation of the heat flux. A sample calculation is provided in Appendix D.3.
In the local monitoring system, the heat flux was measured directly by thin-foil heat flux sensors (Appendix A.1). The heat flux sensors consisted of thermocouples in
series (thermopile) bonded to two sides of a thin 6 x 18 x 0.2 mm wafer of thermal insulating material, polyimide. When heat flows through the sensor, thermal energy generates a small voltage differential between the junctions on the upper and lower surfaces. Since the temperature differential is proportional to the voltage differential and the thermal conductivity of polyimide is known, the heat transfer rate can calibrated directly against the voltage.
The sensors have a sensitivity of 0.317 µV/Wm-2, a thermal resistance of
0.002 °C/Wm-2, a maximum heat flux of 114 kW/m2 and a response time of 0.4 s. A
photograph of the sensor is shown in Figure 3.12.
Figure 3.12 Photograph of a thin-foil heat flux sensor.
A Type T thermocouple was incorporated on-board the thin wafer that measured the surface temperature of the heat flux sensor. The thermocouple was located near the centre of the thin wafer on the non-contact surface of the probe.
Each heat flux sensor was supplied with a certificate containing an individual calibration factor and a temperature correction graph that related the sensor temperature to a temperature multiplication factor. The calibration factor of the heat flux sensors was not checked independently by the candidate due to the difficulty in building calibration equipment for heat flux. The method to calculate the heat flux from the raw signal of a sensor is described in detail elsewhere (Bennett, 2000) and is reproduced in the Appendix D.2 for the reader’s convenience.
All calculations were performed by the FIX DMACS software in real-time so that calibrated values could be displayed to the operator via the computer interface. All values, including intermediate calculation data, were logged to disk each second. The sensors were attached to the MPHE removable plates using aluminium tape and heat transfer paste compound. At the end of a run, the sensors could be removed from the plates and be reused. This allowed the plate to be washed easily and the height of the fouling above the sensor location to be measured. A photograph of an attached sensor is shown in Figure 3.13.
Figure 3.13 Heat flux sensor attached to a MPHE plate.
The method of attaching the sensor has a strong influence on both the overall heat transfer coefficient and the development of fouling on the plate surface immediately above the sensor location (Bennett, 2000). A basic method was developed during the preliminary commissioning runs of the pilot plant. This method was improved upon several times during the experimentation period to provide more consistent and stable contact between the sensor and the MPHE plate. The final method is as follows:
o Aluminium tape was cut into a rectangle larger than the test plate.
o The desired attachment position of probe was marked on the adhesive
side of the tape with a scribe using one corner of the tape as a reference point. This desired attachment position was generally at the centre of the test plate.
o The probe was placed on the adhesive side of the tape as indicated by
the scribed lines.
o A uniform layer of heat transfer paste was applied to the exposed surface
of the probe.
o The tape with attached probe was placed on the plate so that the
reference corner of the tape was set flush with one corner of the plate. This would result in the probe being located in the centre of the plate.
o The aluminium tape was pressed down ensuring no air bubbles were
caught between tape and plate. It is important to use a paste of high conductivity to minimise added resistances to the system and interference with the fouling development of the product (Bennett, 2000) and air bubbles in the paste should be eliminated.
o The excess tape was trimmed from the plate.
Care was always taken and the same method was always used when applying the sensor to the plate surface to achieve uniformity and consistency between formal experimental runs.
The aluminium tape, the heating medium and the heat flux sensor itself add further
thermal resistances (Ra, Rhm, Rhf) to the stainless wall (Rss). The four of them make
up the resistance Rw in local fouling measurements and they should not change over the duration of the run. Because the heat flux sensor comes with an in-built thermocouple the temperature of the wall surface on the hot side is measured and the accuracy of the calculations were improved by using only the internal overall heat
transfer coefficient, Ui, by cutting out the resistance in the heating medium and
aluminum tape. Therefore, equation (3.6) becomes:
f i i0 p ss c hf f p ss c hf 1 1 1 1 R U U R R R R R R R R R = − = − + + + + + + + (3.8)
where Ui0 = initial internal heat transfer coefficient
With the use of this internal heat transfer coefficient defined by equation (3.8) the resistances of the aluminium tape, Ra, and the heating medium, Rm, are no longer relevant. However, the resistances of the heat flux sensor and the conductive paste still affect this coefficient. The successful use of equation (3.8) hinges on the fact
that the resistances of the paste and the heat flux sensor remain stable during a run. The greatest concern is the possible expansion of an air bubble between the sensor and the stainless steel plate because of prolonged heating of the paste during a run. Therefore, care was always taken to ensure the minimal amount of paste was used during attachment of the sensors. The specified resistances of the paste and the heat flux sensor are relatively insensitive to temperature changes.
The temperature on the product side was measured with a T-type thermocouple located directly above the heat flux sensor. Originally RTDs located in temperature wells were installed for this function however, there were many problems. One of the most important problems was the greater thermal inertia of the thermal well. This meant that the readings from the heat flux sensor thermocouples and the RTD were not synchronised and the lag time between the two sensors varied, depending on the conditions of the experimental runs, introducing errors in the value of the calculated heat transfer coefficient. This problem was avoided when using a thermocouple because the thermocouple was placed directly into the product stream without the use of a thermal well. Figure 3.14 shows a schematic diagram of the local monitoring system including the locations of all sensors.
Figure 3.14 Schematic diagram of the local fouling monitoring equipment implemented in the MPHE rig.
3.3.2.3 Global measurement of fouling
In the tubular heat exchanger the overall heat transfer coefficient was calculated from an energy balance between the heating medium and the product streams using the equation:
m
U A
φ = ∆θ (3.9)
where ∆θm = mean temperature difference between heating and product
streams
Under the assumption that pure counter current conditions exist in the tubular heat exchanger, the mean temperature difference is defined as a logarithmic mean
temperature difference, ∆θLMTD given by:
hm p hm p LMTD hm p hm p ( ) ( ) ln θ − Θ − Θ − θ ∆θ = θ − Θ Θ − θ
(3.10) where θhm Θ= inlet temperature of the heating medium hm
θ
= outlet temperature of the heating medium p
Θ
= inlet temperature of the process fluid
p = outlet temperature of the process fluid
Assuming heat loss to the environment is negligible (the system is insulated), the rate of heat transfer was estimated from the measurement of process fluid flow rate as follows:
hm p cp,p m ( p p)
φ = φ = Θ − θ (3.11)
where φhm
φ
= rate of heat lost by the heating medium p
c
= rate of heat gained by the process fluid p,p
m = mass flow rate of the process fluid
= heat capacity of the process fluid
Figure 3.15 shows a schematic diagram of the global monitoring system including the locations of all sensors.
Figure 3.15 Schematic diagram of the global fouling monitoring equipment implemented in the THE rig.
Note that the THE system uses the overall heat transfer coefficient not the internal heat transfer coefficient used in the MPHE system. Therefore, for a successful estimate of the resistance of the fouling layer it was important to keep the heating side stable. Hence, the flow rate and the temperature of the hot side were controlled
automatically. In addition, the use of the ∆θLMTD
3.3.2.4 Calculations from fouling curves
makes this measurement suitable only for an estimate of global fouling over the entire equipment.
• Fouling rate
The fouling rate was estimated from plots of Nf versus time (often named fouling
curves). As mentioned in section 2.2.3, fouling curves can exhibit three distinct periods (induction, fouling and post-fouling periods). For estimations of fouling rates, only the linear portion of the fouling period was considered. The limits of the linear portion were selected and the slope of the line between these two points was calculated. It was assumed that the fouling curve was completely linear between these two points and the fitted line was represented by the equation:
y m x c= + (3.12)
where m = rate coefficient
The fouling rate was expressed as the rate of change of Nf per second:
f m
dN
dt = 3600 (3.13)
To illustrate this methodology an example fouling curve from a THE run is shown in Figure 3.16. Run time (h) 0 1 2 3 4 Nf 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Point 1: y = 1.0; x = 1.8 Linear portion of fouling period Point 2: y = 0.55; x = 4.0 y = -0.207 x + 1.37
Figure 3.16 Plot of Nf versus run time showing the method used to calculate the fouling rate (R1.4).
In the above case the fouling rate is:
5 1 f dN 0.207 5.76 x 10 s dt 3600 − − = = (3.14)
The slope of the line could have been calculated by performing a linear regression over all of the points in the linear portion of the plots. This was carried out for the above example and the calculated fouling rates differed between the two methods by 1.0 %. A decision was made to use the simpler method in this study.
In some runs part of the fouling curve may exhibit a reduced fouling rate which may be indicative of the post-fouling period mentioned in the literature (section 2.2.3). In these cases the fouling rate would be based on the first linear portion of the curve and this value was used as the fouling rate for the whole run. This phenomenon and other characteristics of fouling curves are discussed further in section 4.2.1.
• Final Nf
The final N
value
f value was determined for fouling curves produced by the local and global systems by averaging the last 2 - 5 minutes of Nf data prior to test surface
isolation. These final Nf