Vials heat transfer coefficient

A heat transfer coefficient is defined as the ratio of the area-normalized heat flow to the temperature difference between the heat source (the shelf) and the heat sink (the frozen product). For the case of vials resting directly on the freeze dryer shelf, the vial heat transfer coefficient, Kv, is defined by... 

Figure 6 Pressure dependence of vial heat transfer coefficients for selected vials. ( ) W5816 ( ) K5816 (A) 5303. (Data from Ref. 5.)...

Equation (5) is equivalent to stating that sublimation and subsequent transport of 1 g of water vapor into the chamber demands a heat input of 650 cal (2720 J) from the shelves. The vial heat transfer coefficient, Kv, depends upon the chamber pressure, Pc and the vapor pressure of ice, P0, depends in exponential fashion upon the product temperature, Tp. With a knowledge of the mass transfer coefficients, Rp and Rs, and the vial heat transfer coefficient, Kv, specification of the process control parameters, Pc and 7 , allows Eq. (5) to be solved for the product temperature, Tp. The product temperature, and therefore P0, are obviously determined by a number of factors, including the nature of the product and the extent of prior drying (i.e., the cake thickness) through Rp, the nature of the container through Kv, and the process control variables Pc and Ts. With the product temperature calculated, the sublimation rate is determined by Eq. (4). 

The vial heat transfer coefficient is the sum of heat transfer coefficients for three parallel heat transfer mechanisms (1) direct conduction between glass and shelf surface at the few points of actual physical contact, Kc (2) radiation heat exchange, Kr, which has contributions from the shelf above the vial array to the top of the vials, Krt, and from the shelf upon which the vial is resting, Krb and (3) conduction via gas-surface collisions between the gas and the two surfaces, shelf and vial bottom, Kg ... 

A more complex mathematical model (Sadikoglu and Liapis, 1997) has been used by Liapis and Sadikoglu (1998) to estimate the whole temperature profile in the frozen layer of the product and the position of the moving front. Many parameters are needed to perform the analysis, namely the diffusivity and the permeability of the porous layer, the shelf-vial heat transfer coefficient, the temperature and the partial pressure at the top of the vial, thus making its practical in-line application a complex task, even if feasible in theory. 

If the shelf and the tray are as planar as technically possible, the plot marked s = 0 applies. At 0.2 mbar, a heat transfer coefficient of approx. 85 kJ/m2 h °C can be achieved, rising by a factor of two at 1 mbar. In a well designed freeze drying plant with planar trays or vials a heat transfer coefficient of 160 kJ/h m2 °C at 0.9 mbar is possible (Fig. 1.59), while at a pressure of 0.45 mbar, approx. 120 kJ/h m2 °C (Table 1.9) is measured for the heat transfer coefficient A"tot. To sublimate 1 kg of ice per hour and m2 with a coefficient of... 

Tice data depend on the number of vials in the chamber. Tice is the temperature at the sublimation front of the ice at which the heat transfer from the shelf to the ice front is in equilibrium with the energy consumption at this front by the sublimation ofice.The heat transfer coefficient is constant with more or fewer vials the heat transfer surface increases or decreases, producing more or less vapor.The vapor passes the same geometric dimensions of the plant. For mor vapor transport a higher and for less vapor transport a smaller pressure difference is neeeded. Tjce increases with more vials, as shown in Table 1.12.3. pco pc therefor dp for 400 vials is 50% larger than for 50 vials. If, e.g., -35 °C is not to be exceeded, p for 400 vials has to be lowered (see Figure 2.88 and text). 

The computer must determine the rate at which this step develops from the heat of sublimation of the ice in the sample and the uncrystallized water present in the interstitial region. Also, it should take into account the heat transfer coefficient of the sample container — in the case of a vial, not just a single container, but the frequency distribution of an entire lot of containers. From this statistical information, the computer can then determine the highest shelf-surface temperature where, based on knowledge of the batch size, the chances that the heat transfer coefficient of a container would result in a product temperature exceeding the collapse temperature and yielding a defective product are minimal. The frequency distribution of the heat transfer coefficients of the containers would also provide the computer with the information needed to extend the primary... 

In tandem with the formulation development, certain process parameters pertaining to the drier should be known. These will usually have been established during the initial validation of the equipment. It is useful to run a trial with a fully loaded drier, using the same vials that will be used later, but filled with water to 1 cm depth, loosely stoppered. The loss of water in a number of vials at certain time intervals is then monitored. The results will provide useful information about the heat transfer coefficient (see Chapter 8) and also about the uniformity of the sublimation rate across and between shelves (detect possible hot spots and cold spots). The information will also prove useful when scale-up of the pilot process requires certain changes to be made in the process parameters. 

Fig. 3.4 Distribution of the values of the overall heat transfer coefficient for tubing vials of 7 ml according to Hottot et al. (2005) total pressure P—6Pa and shelf temperature T=- 5°C.

Furthermore, it is worth noting that the discussed heat transfer coefficient values are largely dependent on the vial type (molded or tubing), on the vial size, and also on the total gas pressure in the pressure range - between 10 and 70 Pa - usually selected for freeze-drying of sensible drugs (proteins, vaccines, etc.) (Pikal et al., 1984). 

Finally, by coupling a mathematical model of the process to the measurement of the product temperature in the vial (or of the wall temperature of the vial) it is possible to build a soft-sensor that allows estimation in-line of the whole product temperature profile and the mass/heat transfer coefficients this has been called the smart-vial concept (Barresi et al., 2007, 2009a, b, c)... 

Another device that makes use of the measurement of the temperature of the product (or of the vial) is the soft-sensor (or observer) it provides a real-time estimation of some parameters or state variables, for example, the whole product temperature profile and the mass and heat transfer coefficients, using the temperature measure and a mathematical model of the process. Let us consider a dynamic system defined by the following set of differential equations ... 

Milton et al. (1997) proposed the manometric temperature measurement (MTM) the transient pressure response is mathematically modeled under the assumption that four mechanisms contribute to the pressure rise, namely the direct sublimation of ice through the dried product layer at a constant temperature, the increase in the ice temperature due to continuous heating of the frozen matrix during the measurement, the increase in the temperature at the sublimation interface when a stationary temperature profile is obtained in the frozen layer and, finally, the leaks in the chamber. The four contributions are considered purely additive the values of the thickness and of the thermal gradient are needed but they are not known exactly. The values of the vapor pressure over ice, of the product resistance and the heat transfer coefficient at the vial bottom are determined with regression analysis. 

A modification of the previous model was proposed by Obert (2001) who considered also the desorption of the bound water during the primary drying, which can contribute to the increase in the total pressure, and the thermal inertia of the glass wall of the vial. The temperature at the bottom of the vial and the thickness of the frozen layer should be known in order to use this algorithm, but they are only guessed in the proposed procedure. The overall heat transfer coefficient is expressed adopting the heat and mass transfer steady-state hypothesis, while a non-linear regression analysis is carried out in order to estimate the vapor pressure at the interface, the mass transfer resistance in the dried product and the desorption rate. 

Rene, F., WoKf, E., Rodolphe, F., 1993. Vacuum freeze-drying of a liquid in a vial determination of heat and mass-transfer coefficients and optimisation of operating pressure. Chem. Eng. Process. 32 245-251. 

Triantafyllou et al. (2005), in studies on transfer of potential contaminants from paper and board to food, measured partition coefficients between packaging and air for a range of substances. This was, therefore, an attempt to measure the potential for gas-phase transfer. A mixture of acetophenone (b.p. 203 °C), naphthalene (b.p. 218 °C), benzophenone (b.p. 306 °C), dibutyl phthalate (b.p. 340 °C) and methyl stearate (b.p. 443 °C) was placed in a vial together with samples of test liner made from virgin fibres or triplex board made from 100% recycled fibre. There was no contact between the substances and the paper or board. Vials were sealed and heated at 70 °C or 100 °C and then the paper removed and analysed for uptake of substances. Conclusions from the studies were that ... 

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