Why do We Use RTD?s to Monitor the Freeze Drying Process?

Why do We Use RTD?s to Monitor the Freeze Drying Process?
June 2003
Thomas A. Jennings, Ph.D.
Insight
The question posed by the title of this INSIGHT is one that I have often asked myself and posed to others. I have yet to receive what I consider a satisfactory explanation. The reader should be aware from the very start that I have no opposition to resistance thermal devices, commonly referred to as RDT?s or perhaps PT100. If there is any one single thing I oppose in the field of lyophilization or freeze drying it is that ever prevailing tenant that states ?If you do something wrong long enough it soon becomes right.? For proof of that I only have to refer the reader to INSIGHT Vol. 1 No. 7 that describes the confusion that continues to confuse by defining the shelf fluid temperature as the shelf temperature. When in fact, under the heat load of primary drying or freezing, nothing could be further from the truth. But even to this day we stubbornly cling to the fluid temperature as being the shelf temperature.
But this INSIGHT is about the inappropriate use of the RTD to measure the product temperature. If you feel that this INSIGHT does not concern you because you don?t even measure product temperature then you are courting other problems and I suggest that you might wish to read INSIGHT Vol. 1 No. 2. Thus for those of you who do indeed measure product temperatures to monitor the lyophilization process, this INSIGHT will first aquaint you with how an RTD functions and then, using two examples, discuss the value of the temperature measurements during various stages of the lyophilization process.
Description of the RTD: An illustration of the basic parts of the RTD is shown by Figure 1. The RTD is a relatively simple thermal transducer that consists of (a), a sealed outer casing that is fabricated from either glass or metal; (b) thin wire which is configured to serve as an electrical resistor and (c), two electrical leads that pass through a vacuum seal and serve to provide a known voltage to the resistor element and in addition provide mechanical support for the resistor wire. The resistor element extends nearly the entire length of the device housing.

The RTD uses a basic property of most metals that is the resistivity () of the wire will change with temperature (T). The change in resistivity with temperature is referred to as the resistance temperature coefficient (alpha) and is defined as
alpha = d(rho)/dT = dR/dT ohms/oC (1)
where R is the resistance (ohms) of a metal wire having a defined configuration and (rho) is the resistivity of the metal. Since the RTD will be used over a temperature span of -100 oC to 100 oC, it must be shown that is not significantly temperature dependent and if it is what will be its function. For the purposes of our discussion we shall assume that is independent of temperature for the above range of temperatures.
With a knowledge of the value of the and the above assumption, the RTD can now determine the temperature of a system from the following general expression for R of the wire
R = Ro + alpha( 0 oC + Tx) (2)
where Ro is equal to resistance at 0 oC and Tx is the temperature of the wire. Thus from expression (2) one can now determine Tx simply as
Tx = (R - Ro )/alpha (3)
Therefore, when R = Ro then Tx = 0 oC or when R > Ro then Tx > 0 oC but when R < Ro then Tx < 0 oC.
Finally, one last condition for the use of the RTD, and this is most IMPORTANT, is in order to achieve the accuracy limits defined by the RTD, the temperature across the resistor must be uniform. If it is not uniform then the measurements will be in error. The error will be directly related to the difference in temperature between the ends of the resistor.
Let us now consider the use of the RTD during a lyophilization or freeze drying of a formulation in a vial when using two different fill volumes as illustrated by Figure 2 where the horizontal line in Examples 1 and 2 represents the fill height.
Freezing:
Example 1 As seen by this example, perhaps the only times when the RTD provides an accurate measure of the temperature is just after filling and the vial, the formulation and RTD are all at the same ambient temperature and at the end of the freezing process if the entire system comes to some quasi steady state. However, during the actual freezing process, the results will be erroneous. It is true there will be some indication of the degree of supercooling but, given the apparent temperature gradient across the resistor, the value obtained will not be representative of the true supercooling properties of the formulation.
Example 2 In this example the formulation covers the entire sensor. As in the case of Example 1, the temperature values will certainly be accurate at ambient temperature and after the system has reached some form of quasi steady state at the end of the freezing process. However, during the actual freezing process there will be some question as to the accuracy of the measurement if there exists a significant difference in temperatures at T(1) and T(2). Unless, supercooling occurs throughout the entire fill volume, the sensor will not accurately indicate the correct degree of supercooling. This error will be enhanced if the vial is loaded onto a cold shelf because of the possibility that only a small volume of the formulation will undergo supercooling and hence there again there would be a significant difference in T(1) and T(2).
I feel it is fair to say, that regardless of the relationship between the fill height to the length of the sensor casting, one can, with any real degree of confidence, only consider that the temperatures are accurate at ambient and the final freezing temperature. The RTD in example 2 may give an accurate reading of the degree of supercooling if and only if the entire volume of the formulation undergoes supercooling.
Primary Drying:
Example 1 The primary drying will require an increase in shelf temperature. The actual shelf temperature, as it pertains to the product temperature and chamber pressure, that will be required has been discussed elsewhere and is beyond the scope of this INSIGHT [1]. However, it is imperative that you accurately know the product temperature because it will serve as a check on both the pressure in the chamber and the shelf temperature (see INSIGHT Vol. 5 No. 2.). Thus during sublimation of the ice, the product temperature will be lower than that of the shelf temperature. The vial will receive energy from the shelf upon which it rests and also from radiant energy from the shelf above it. Thus one would expect a difference in T(1) and T(2) beginning with the commencement of the primary drying. Only at the very end of the primary drying process, when the product temperature approaches that of the shelf temperature, will T(2) approach T(1). Thus in this example one cannot place much confidence in the output of the RTD being representative of the actual product temperature during the actual primary drying and the temperature readings will tend to be false high.
Example 2 As long as the sensor remains in the frozen matrix, T(1) will be close to T(2). However, as the drying front proceeds down the product and a portion of the sensor casing extends above the drying front, there can now be a significant difference between T(1) and T(2) with the result that there will be a gradual increase in the product temperature throughout the drying process. This increase in product temperature may not have anything to do with the actual temperature of the product but with temperature differential across the resistor that results from the receding drying front. As in the case of Example 1, the accuracy of the measurement of Example 2 will increase as the product temperature approaches that of the shelf temperature. Thus even in spite of the fact that the sensor was completely immersed in the fill volume, the only time that the use can have any real confidence in the temperature readings is at the start and completion of the primary drying. At all other times during the primary drying there will be error in the measurements, i.e., false high temperatures, whose magnitude will be dependent on the sublimation rate.
Secondary Drying:
Example 1. At this stage of the drying process one must now deal with a new problem and that is the difference in the mass between the sensor and the resulting cake. If the mass of the sensor far exceeds that of the cake, the temperature measurements will be that of the RTD and may not represent that of the cake. While there may be some confidence in knowing the product temperature at the completion of the freezing and primary drying, if there is a significant difference in mass between the RTD and cake when the mass of the cake is far less than that of the RTD, there could be some serious doubts as to the actual temperature in those vials not containing a temperature sensor.
Example 2.
Given the mass of the RTD far exceeds that of the cake, the above may well hold true even for Example 2.