Blotechnol. Prog. 1092, 8, 275-284
275
TOPICAL PAPER Modeling Transport Processes in Sterilization-in-Place Paul T.Noble Fluor Daniel GmbH, Kreuzberger Ring 13, D-6200 Wiesbaden 32, Germany
SIP (sterilization-in-place)of equipment using saturated steam is limited by transport processes that restrict the distribution of sterilizing steam. The following are two crucial operations: the removal of air prior to sterilization, and the removal of condensate during the sterilization. Using simple model systems of pipes and tanks, characteristic operating parameters were examined and steady-state models were analyzed. The results were used to evaluate design aspects of SIP, including heat insulation, spacing of steam traps, sloping of lines, steam velocities and consumption, placement of temperature sensors, and scale factors in piping. A more reliable SIP design is achievable by insulating equipment, spacing steam traps to limit condensate buildup, providing an effective air removal operation, and providing reliable, high-quality steam.
Contents
-
1. Introduction 2. Description of the SIP Process
3. Definition of SIP Models for Analysis 4. Characteristic Operating Parameters and Response Times A. Air Purge Step B. Heating Period C. Sterilization Holding Period 5. Steady-State Models and Analysis A. Condensate Layer B. Gas Phase C. Dead Legs 6. Discussion and Conclusions 7. Notation
275 276 276 277 277 278 278 279 279 279 28 1 282 283
1. Introduction The SIP (sterilization-in-place) concept has arisen in the industry as a result of the need to sterilize equipment that is either too large or too inconvenient to place in either an autoclave or oven. Sterilization can be accomplished by thermal, chemical, or other methods, but the FDA (1975) and the EEC (1990) state preference for thermal methods. In the referenced guidelines, two thermal methods are recognized: dry heat and wet steam. Because of its heat-transfer advantages, only wet steam is practically associated with the term SIP, and this report will limit analysis to this basis. SIP should approach the reliability of an autoclave although special problems arise when equipment such as piping and tanks are to be designed for SIP. To design equipment for a reliable SIP, a fundamental knowledge is needed of the processes occurring, down to the dimensions of the microbes themselves. To date, engineers have largely worked on this problem using experience accumulated at their firms, and the public 8756-7938/92/3008-0275$03.00/0
literature is correspondingly sparse. There is a recent introduction to the subject by Agalloco (1990), but published scientific treatments of SIP are lacking. They would be useful as a basis for design and for defining regulatory requirements. To introduce the subject, a short introduction to wet steam sterilization is needed. Saturated steam conditions will result in the destruction of living organisms, by followingfirst-order kinetics, that are species-specificand temperature-dependent. If only saturated steam is present in the gas phase, the sterilizing conditions are completely defined by the temperature because there is then only one degree of freedom. The confidence in wet steam sterilization can be attributed in part to the fact that these conditions have been widely investigated with microorganisms, as can be read in Wallhaeuser (1988). Good manufacturing practice (GMP) requires a sterilization to be validated. Validation attempts to reduce the risk of biologicalcontamination to a minimum, because sterility is impossible to verify without destructive testing or without compromising the integrity of the sterile system. During validation, testing should establish knowledge about the worst case conditions, which would generally correspond to the coldest points in the system. The operating conditions should be reproducible, because not all points can be monitored during operations. The time required for sterilization will be based upon the sterilization temperature and the initial concentration of microbes. For critical applications, where the bioburden is not under complete control and the risk to the consumer is high, the acceptance criteria for a successful validation should be as strict as possible. Settling such standards often results in recognizing design problems late, during validation. This paper will examine the fundamental mass and heattransport processes that are associated with the SIP of piping and vessels using wet steam. A goal is to illuminate the technical limits of this type of SIP.
0 1992 Amerlcan Chemical Society and American Institute of Chemical Englneers
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Dead
8
Leg Process
1
-Q Figure 1. Pipe model system.
Paul Thomas Noble is a Senior Process Engineer a t Fluor Daniel's engineering office in Wiesbaden, Germany. His career in the pharmaceutical industry started a t Cutter Laboratories in 1982 after he received his Ph.D. in Chemical Engineering a t the University of Wisconsin. Engaged as a research engineer a t their blood plasma fractionation facility in Berkeley, CA, he piloted continuous electrophoretic blood plasma separations and published models of the process. Upon moving to plant and design engineering departments, he gained practical experience in pharmaceutical production and eventually became responsible for process design and validation activities. In 1985, he was sent to Bayer AG in Germany on a 2-year assignment as a technical delegate, where he gained additional experience in pharmaceutical manufacture and plant design. Subsequent marriage to a German national resulted in a relocation to Germany and a change of employment. Since 1989,Dr. Noble has been employed with engineering offices specialized for pharmaceutical facilities, most recentlyat Fluor Daniel GmbH. He has been responsible for the design of several pharmaceutical and related facilities, including those using recombinant DNA technology.
2. Description of the SIP Process A typical SIP process is composed of the followingsteps which mimic the operations of an autoclave: 1.air purge 2. heating period
3. sterilization holding period 4. sterile displacement and collapse of
the steam blanket Although autoclaves generally remove air by pumping it out with a vacuum pump, SIP systems usually attempt to displace the air from the system with the steam. This can save time and avoids the cost of installation of vacuum pumps and piping which can be significant when many systems are present that are to be SIPd. During the air purge step, the drains and vents on the equipment are usually fully open, and the pressure will be close to atmospheric. If the air is not effectively removed by the air purge, two problems can be encountered: (1) A substantial heattransfer resistance can develop as air is swept to the walls by the condensing steam. This type of problem was first recognized in power plant condensers by Othmer (1929). (2) The contribution of air to the system pressure lowers the saturation pressure, and correspondingly the saturation temperature of the steam. Together, these two effects lower the sterilization temperature, and the effect is more pronounced at the wall boundaries, where the air is concentrated. They can be overcome by increasing the steam supply pressure. However, the amount of air trapped in the system cannot be measured, which can raise questions of reproducibility during validation.
During the heating period, the pressure in the system is allowed to approach the supply steam pressure, by closing the exits. Condensate is still removed by either steam traps or orifices placed parallel to the drains and vents. It is important to remove as much condensate as possible, because it has the opportunity to subcool on the walls of the equipment. Steam flow through the system is reduced now to the amount consumed by the traps and/or orifices plus the amount needed for heat-up. When temperature monitors indicate that the desired temperatures are reached, the timed sterilization holding period begins. Process conditions are monitored, and fluctuations either affect the duration of the holding period or abort the run. A small temperature fluctuation is of concern for SIP. The typical kinetic rate constants for sterilization are exponentially dependent upon the temperature, with a temperature drop of 1 "C typically extending the required sterilization time on the order of 25-50 % . Reflecting the technical problems associated with SIP, the FDA (1975) regulations require that a sterilization meet or be equivalent to the following conditions: 121.5 "C maintained for 20 min with saturated steam. Sterilizations, defined as above, have been termed overkill sterilizations because such extreme conditions are theoretically unjustified for most applications. When the holding period is successfully completed, the steam supply is shut off and the steam is usually displaced and collapsed with sterile filtered process air. The system must be prevented from coming under a vacuum during the subsequent cooldown by either maintaining a sterile air blanket on the equipment or opening a vent equipped with a sterilizing vent filter.
3. Definition of SIP Models for Analysis For examining elementary transport phenomena, only simple models are used (shown in Figures 1and 2). The pipe model of Figure 1represents the case where a transfer line between two processes is to be sterilized separately from the attached processes. An additional complication is introduced by the valved-off branch point. This would be encountered when the transfer line is functioning as a distribution line. The tank model in Figure 2 is a common example of an isolated tank that is too large to be autoclaved. It could represent a large fermenter, harvest tank, or formulation tank. SIP is a time-dependent process that should approach a well-defined steady state,corresponding to the sterilizing conditions. The initial conditions for this problem are very poorly defined, however. Initially, one could expect the equipment and air within to be a t a given temperature. The steam quality and properties could be also fixed in the supply line, by suitable equipment installation. The
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Steam
t
7
Table I. Radial Response Times for Convection in a 10-m Pipe
D,m 0.0078 0.0508
E,, m2/s 0.0005 0.0030
tr,
8
0.015 0.1075
t,, max, a
0.032 0.082
derive the approximation W
The half-width of the mixing zone at the pipe exit, corresponding to two standard deviations, is expressed in the dispersion model as
I Figure 2. Tank model system.
initial flow of steam into the equipment to displace the air would still remain difficult to describe, because of the poor understanding of the processes occurring in the mixed steam/air region. Steam would be expected to cool and condense in the gas phase and on the walls of the equipment: the air would be heated, compressed, and displaced. The initial flow profile of steam into the equipment would then be complicated by many processes, including mixing, heat exchange between steam, air, and the equipment, droplet formation, wall condensation, and two-phase flow. Rather than an attempt to model the unsteady-state process, characteristic operating parameters and response times will be used to provide understanding of the relative importance of the various processes in the unsteady case. Then, steady-state models will be used to study possible situations. For much of the analysis, one-dimensional models will be employed.
4. Characteristic Operating Parameters and Response Times A. Air Purge Step. Although heat transfer is present during this step, the critical operation is the displacement of air. This is complicated by the simultaneous creation of transport boundary layers on the walls of the system. Here it will be assumed that the equipment and environment start at 25 OC, the system pressure is 1atm, and the entering steam is saturated gas at 100 "C. The initial steam flow rate is limited usually to a velocity of ca. 35 m/s (7200 fpm), in order to minimize pipe erosion and noise generation. For the usual range of pipe sizes, (nominal l/e-2 in.), the Reynolds number lies then in the range of 10 000-90 000, which ensures turbulent flow. For pipes of typical lengths, the convective response times (defined as the length divided by the velocity) are on the order of seconds. Condensationof steam will reduce the velocity and extend the response time, but in most cases turbulent steam flow will be present. Except for extremely short pipes, axial dispersion will be important and will interfere with the displacement by mixing the two components. This mixing zone can be estimated for fully developed turbulent flow by using an effective axial dispersion coefficient. Sherwood et al. (1975) provides a graphical summary (in Figure 4.17) of experimentally measured coefficients, from which we can
Az = (8Ezt,)'/2 (2) where t, is the axial convective response time. Simplification yields Az = (4DL)1'2 (3) Within the mixing zone, air can be swept to the developing transport boundary layers. Because the boundary layers are very thin in turbulent flow, they form very fast and can be assumed to be present in the mixing zone. For a significant amount of air to be trapped, it must be able to move radially to the wall in the mixing zone before leaving the pipe, and the time available becomes
(4) In turbulent flow, radial transport is primarily a result of "eddy diffusion". For the Re range 10000-90OOO, experimental correlationscollected by Sherwood et al. (1975) (in Figure 4.11) indicate a radial dispersion coefficient of 5-30 cm2/s. A response time for radial transport can be expressed with it as
t, = D2/(8E,) (5) When the steam velocity increases, eq 4 decreases more rapidly than eq 5. Table I compares eqs 4 and 5 with maximum steam velocity for a range of pipe sizes. One can interpret that in both cases a significant amount of air can accumulate in a boundary layer. Turbulent flow more effectively removes air from pipes with larger diameters by limiting the time available for transport to the boundary layer. For the tank model system, convection can be poorly defined, and a different analysis is needed. Unless the tank is mixed, displacement of air will be nonuniform and trapped air can be expected. The agitator, that may be present in the tank, cannot be expected to be adequate for mixing the gas phase of steam and air. In practice, the momentum of the inflowing steam is relied upon for agitation. Ideally, the fastest removal of air can be anticipated when the agitation and flow approximate an ideal CSTR. For this to occur, the mixing time must be significantly less than the space time. As a design goal, we can require the following: tH = 0.17
(6)
For a turbulent steam jet, t~ can be estimated from an experimental correlation provided by Henzler (1978): t, = CHdi/ (ui> (7) where the variables with the subscripts i refer to the diameter and velocity of the inflowing jet. The dimensionless mixing number, CH,is (in the turbulent range) a
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Table 11. Heat Transport Parameters of Solid and Liquid Componentse
function only of geometry: cH = l.l(D/di)2.75for L = D
(8) comDonent insulation stainless steel wall condensate
For this geometry, the space time is defined by
Here, it is assumed that steam is not condensing; the actual value would be somewhat larger. By substituting these relations into eq 6, one cannot obtain a ratio, di/D that also ensures turbulent jet flow. The relation in eq 6 is then not feasible, and one can generalize that good mixing, provided by steam inflow, cannot be created inpractice in tanks unless special nozzle developments can improve jet mixing performance. However, the mixing time is less than the space time so that some degree of mixing can be expected. The above equations indicate that the design objective should be to minimize di. Also ( v i ) should be maximized to reduce the processing time and create a turbulent steam jet. A t maximum steam flow, the operation can be characterized by r=-=4 v
( vi)adi2
No. 4
0.0364Vld:
(10)
and w, = pV/r (11) For illustration, settling di = 2.54 cm and V = 1m3,gives T = 56.4 s w, = 0.0213 kg/s = 76.6 kg/h steam at 1 bar gauge
The air purge step should last at least 47 because of the poor mixing conditions. Adams (1988) has also modeled the air purge step of tanks as a wash-out process. By ignoring the quality of mixing as a factor, he falsely predicted that lower steam flow rates over a proportionally longer time period would yield an equivalent air removal. As in the pipe model, it would be useful to estimate the response time for radial transport of air to the vessel wall. However, here the process is of sufficient duration for heat-transfer effects to be important, and an estimation of convection within the vessel would be unreliable without including them. If we assume that this step is of sufficient duration for air to find the tank exit, it can also be assumed that air has sufficient time to migrate to the walls and collect in a boundary layer. An effect of gravity can be of importance in SIP, because air, particularly cold air, is denser than steam. If turbulence created by forced convection is not of greater magnitude than a thermally-induced free convection, trapped air should indeed be predominantly found at the bottom of the enclosure. In the equation of motion, the driving force for forced convection can be described, following Bird et al. (1960) as VP. The corresponding driving force for free convection is Apg, which is related to the Grashof number. For the extreme combination, air at 25 "C and steam at 121 "C
k, k , m w/(m.C) 0.0254 0.05 0.0026 0.001*
6.3 0.686
x 107,
m2/s
tT,s
Rs, (m2-C)/w
7.6 41. 1.7
424. 0.824 2.9
0.51 0.00016 0.0015
a For orientation, see Figure 3. * See Steady-State Models and Analysis section for the derivation of this result.
the air purge, free convection should be of minor importance, and an intact air body should not remain. Once air and steam become mixed, a gravity-induced polarization will not be a measurable phenomenon in vessels of practical size. First, all major convective flows must cease to allow the concentration gradients to form. Second, these gradients will be insignificant, as predicted using the relation from Bird et al. (1960) (on page 576) employed for a similar problem:
One can conclude then that gravitational effects can normally be avoided. When a tank is effectively purged of air, both the drain and the vent are useful for air removal. B. Heating Period. Heat transfer in the gas phase is poorly defined because of the large number of processes occurring, and discussion will be limited to conduction at the equipment walls. Here it is important to look at the heat-transfer resistances and response times for the system components. For a pipe with D = 2.54 cm, typical values are given in Table 11. Here a thermal response time is estimated from AX2
t -(13) T - 2a where a is the thermal diffusivity, and the thermal resistance is calculated from
Rs = Ax/k (14) The characteristics imply that temperature changes are very rapid in the wall and condensate film, in comparison to in the insulation. The condensate film plays a critical role, where a change in its thickness can dramatically affect the response of the system. This is a result of its relatively low thermal diffusivity. C. Sterilization Holding Period. Here it can be assumed that a pseudo-steady state has been reached, whereby temperatures and concentrations are changing very slowly with time. Since temperature nonuniformities are required to be small, natural convection should be relatively unimportant. Transport of heat and mass will be heavily dependent upon diffusive driving forces; in the defined flow channel of the pipe transport will still be driven by a small pressure differential. Under these conditions, the heat transport can be estimated. One should require that the pipe wall be at the sterilization temperature, assumed here to be 121 "C. For the well-insulated pipe, the heat flux becomes
Apg = 12 N/m3 whereas the average pressure gradient, assuming a 2-atm steam supply and a drain at 1 atm is V P = AP/L i= 105/5= 2 X lo4 N/m3 As long as the steam flow is not seriously throttled during
For most of this paper, curvature effects will be ignored, and the heat flux for the insulated pipe will be defined for
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comparisons as
(QIA),, = 344 w/m2 which is calculated when Ax = D and D is 2.54 cm. For an uninsulated pipe, a correlation is available from Perry and Green (1984) for the convective and radiative heat-transfer coefficient for bare steel pipe in a room at 80 O F . The appropriate result for a diameter of 1 in. is 2.84 Btu/h ft2 F 116.1 w/(m2.C)1. Q/A can then be estimated as (Q/Albme= hbT = 16.1(121- 25) = 1550 w/m2 (16) It is important to realize that these fluxes correspond to the minimum steam flow. From the heat fluxes the required minimum steam flow and the expected condensate flow can be estimated. This minimum flow, w,, is the entering steam flow and the exiting condensate flow:
Figure 3. One-dimensional model.
holding period, the largest nonuniformities in properties are to be expected in this region. A. Condensate Layer. In the condensate layer, heat transfer occurs by conduction only. Conduction can be described by
(QIA) = kc(Ti,t - T,)/Jc
It is clear that near the pipe exit laminar steam flow conditions will prevail. At the entrance of the pipe, turbulent flow will arise if the pipe exceedsa criticallength, corresponding to a value of 2000 for Re at the entrance: Lcrit = 500~$/(Q/A) (18) which is in the range of 10-50 m for these heat fluxes. For the rest of this analysis however, laminarsteam flow during this step will be assumed (which is the worst case). It will also be assumed that the condensate is stratified in horizontal flows. This would be expected from correlations also available from Perry and Green (1984),except for the entrance of very long,bare pipes, where the relative amount of condensate in any case should be small. The depth of the stratified condensate flow can be estimated, recognizing that it is normally a laminar flow. Straub et al. (1958) have shown that open channel flows can be quantitatively predicted when capillary effects are not important. For the case of a round pipe, filled to various depths, an explicit expression for the depth of liquid, Axc, as a function of flow is not simply obtainable. However, a simple relation is available from Straub et al. (1958) for rectangular channels. For the small depths to be encountered in SIP, curvature effects are not so important, and this relation can be used to approximate the real situation: 4aAx:N K where a is the channel width, K is a geometrical constant, and
w, =
N = 2 g (sin j3)/pC (20) with j3the angle between the pipe and the horizontal. For pipes with a diameter 1in., a good approximation is a = 1OAxc,and by substituting in eq 17, we find the following dependence:
(22) If we require that this temperature difference is limited to 0.5 "C, a maximum allowable condensate layer can be derived using the heat fluxes defined earlier: (bc,mar)ins = 1.0x (bc,mar)bare
5. Steady-State Models and Analysis A one-dimensional model is depicted in Figure 3 for the region near a horizontal wall. During the sterilization
= 2.2 x 10-~ m
Relating eq 22 to eq 21, a design aid for spacing steam traps or orifices can be arrived at:
u =(9.28 X 10l6)kCsin j3
(Q/Al5DAP Using a 1-in. pipe sloped to the standard l / in./ft ~ as an example, the length where the condensate builds to create a 0.5 OC drop becomes
(Umar)bare
= 0.057 m
This startling difference reveals the important advantage of insulating piping. A significant subcooling of condensate is practically unavoidable with uninsulated lines. A similar result is obtained by using flow relations for round channels instead of eq 19. Because liquid flow in this model is laminar, it will not thermally mix. A temperature probe in the drain will however, measure the mixed condensate stream. From this average temperature, it will be difficult to measure the extent of subcooling. This average temperature can be computed from
Jo"cu,dx
(24)
In the rectangular flow model, the velocity profile is wellknown, and
(0
Once a limitation is placed upon the depth, this relation can be used to estimate the spacing of condensate traps on horizontal pipe runs.
io9 m
Tint- (Tint-
TW)/6 (25) where the cold spot is associated with T,. One can see that the temperature deviations are damped severely in the result ( T). B. Gas Phase. A model for the one-dimensional condensation of vapor in the presence of a noncondensible gas is well-known and used in psychrometric calculations. The starting point for this development can be
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found in Bird et al. (1960) (example 18.5-1). The equations are modified here for the altered boundary conditions. Basic equations to be solved are heat transport, mass transport, air properties (ideal gas law assumption), and steam properties (obtained from curve fits to the steam tables). Further, the sum of mole fractions is limited to 1, and the pressure is constrained to be constant over the boundary layer. The heat-transport equation becomes dT -(Q/A) = -k- dx + N,M,(C,(T - Tint)+ H ) (26) where the constant N, is the molar flux of steam to the wall of the model, and signs have been added to account for direction. The molar flux is constant in this model, and it is the solution for diffusion through a stagnant film: (27)
Here, a constant concentration has been assumed and set to the log mean average. The variation in concentration is normally insignificant. There are two degrees of freedom in this model. The wall temperature can be fixed at a suitable sterilization temperature [ 121 "Cl. The other variable will be the amount of air in the boundary layer. A simple analytical expression cannot be presented. The solution method is to assume a value of N , which is constrained to be between 0 and N,,,,
= -(Q/A)/(HMJ
0.4
0,2
~
,
0 0
0.05
0,l
0,2
0,15
0,25
0,3
0.35
fa
Figure 4. Magnitude of gas-phase heat-transfer resistance.
Conditions studied in the pipe model: D = 0.0254 m; Tint = 121 "C; QIA = 1550 w/m2 (for bare pipe). The air fraction, fa, is calculated from eq 36. AT is the temperature span in the gas shows the contribution of air to the total phase, and PT,~/P,,,,~ pressure.
The total system pressure is then P,,, = + 8313.7~,,~,~(T~,~ + 273.16) (35) which is a rough measure of the amount of air trapped in the system. The exact fraction of the original air that is trapped can be expressed as (36)
(28)
which would exist when no resistance to mass transfer in the gas phase existed.
No. 4
From eq 27, this can be derived to be
With the constant B defined as (29) the integration of eq 26 can be expressed as T, = (Tint+ B ) exp(N,M,C,G/k) - B
(30)
Given now the temperatures at the boundaries, the steam partial pressures can be evaluated from the following quadratic fit to the steam table over the range 120-141 "C: P, = (8.91534 X 10') - (1.76864 X 104)T+ 99.28p (Pa) (31) Also, the molar concentrations of steam can be determined by a similar curve fit: c, =
0.8892 ((kgsmol)/ m3) 134.829 - 1.60466T + 0.004999P (32)
The concentration of air can be expressed from the ideal gas law, arriving at the following relation:
Converting mole fractions to concentrations with
x,= c,/(c, + ca)
(34)
These relations can be solved simultaneously with eq 27 to find the concentrations at the two limits.
Upon examining the equations, the solution space can be defined by two parameters; 6N, and (Q/A)IN,. As these parameters increase, the gas-phase resistance increases. Since N, is not itself a quantity of interest, the space will be shown in terms of f a , (QIA), and D. Under the stated assumptions, the boundary layer thickness is related simply to D by 6 = 012 (38) Parameters used in the analysis are listed with the list of symbols and reflect steam properties at 121 "C. The diffusivity is estimated from a prediction developed by Slattery and Bird for low pressure mixtures of steam and nonpolar gases, available in Bird et al. (1960). In Figure 4, a typical case is plotted to show the magnitude of the gas-phase resistance. For simple piping and tank systems, one would expect from the earlier analysis that the fraction, f a , should be small (less than O.l), and gas-phase resistance would be relatively unimportant in this example. In Figure 5, the limiting value of f a is plotted as a function of pipe diameter for a maximum temperature drop in the gas phase of 0.5 O C . One sees that gas-phase resistance i n smaller pipes can be generally neglected since air removal requirements are not large. A gas-phase resistance only becomes important for larger pipes and, by analogy, tanks. Earlier, it was shown that air can be effectively removed from large pipes using high-velocity steam. In contrast, the air purge of the tank model cannot be expected to be so successful from the previous discussion. From Figure 5 , one could expect, then, that gas-phase heat-transfer
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0.8
insulated Pipe
\ 0.4
0.3 0.2
1 I 2
1
0
L3
4
5
e
I
I
I
I
7
I
I
I
I 8
I
1 7
e
1 0
D,cm. Figure 5. Limits of trapped air as a function of pipe diameter for a temperature drop of 0.5 OC. For the gas-phase temperature span of 0.5 O C , the interface temperature was fixed at 121 O C . The trapped air is expressed as fa, which is calculated from eq 36.
m
I
1
I
/
I
z=o
I
Figure 6. Dead leg model.
resistance in these simple models should be important in tanks but can be avoided in pipes. This analysis has assumed constant values for the transport properties of the gas mixture. This is allowed as long as nonuniformities remain relatively small. C. Dead Legs. The one-dimensional models cannot be used to analyze dead legs in the model systems. Dead legs are quite common in red systems, since they are also created by instruments ports and various seal systems on equipment. They will therefore receive special attention. A two-dimensional dead leg model is shown in Figure 6. Unlike the pipe or the tank, neither air displacement by convection nor a wash-out process as in the tank can be expected to displace the air. As a worst case, it can be assumed that the air within must diffuse out. Its orientation is also an important design aspect. Condensate must be able to drain out of the entrance, but the operation of the apbaratus may also require that the air be displaced with the process liquid. This often dictates an orientation close to horizontal. Such an orientation means that the problem of subcooling of stratified condensate can be treated as in the earlier analysis. For the vertical orientation, the flow of
condensate along the wall can be expected to create a convective steam flow through viscous drag. After diffusive flows are examined, the importance of this effect will be discussed. The importance of a gas film resistance can be expected to be much greater in dead legs because of channeling effects; i.e., the effective fluxes at the entrance are significantly larger than in the one-dimensional analysis. An analytical solution to the detail of the onedimensional model is not simple. A numerical solution was attempted by the author, but the solution of the coupled relations, eqs 39 and 40, by standard relaxation methods does not converge for boundary conditions specifying a heat flux dependent upon the temperature. If some simplifying assumptions are made, an analytical solution with usefulness can be arrived at. One startswith the continuity relations in vector notation:
V*Ne= 0
(39)
V-e = 0
(40)
and expresses them in terms of the r and z coordinates: (41)
The flux relations for a stagnant film are again utilized, which appear as (43)
e = -kVT
+ Nfle(Cp(T- Tint)+ H)
(44)
Recognizing from the earlier analyses that conductive, gasphase heat transport is practically insignificant in SIP,we
Biotechnol. Prog., 1992,Vol. 8, No. 4
282
can focus attention upon eq 39, and assume that N, must accomplish all of the heat transfer. A simplifying set of boundary conditions is N,, = constant = -N,,
at z = 0
(45)
N,, = constant = N,,
at r = R
(46)
1
.O-1".
L-40
'
J ?
//
where the constant is the constant flux required for a uniform temperature at the boundaries: (47) N,, = hCTi,, - 25)1(M,H) Because N,, is not a function of r at the boundaries, nor is N,, a function of z , a separation of variables can be performed in eq 41: -6
-5,301
-5
-4,301
-4
t o g (PtOt / P S . 5
The integrated relations become
N,, = -C,Z - N,,
(49)
The underlined term is dropped to provide for the symmetry requirement N,,= 0 atr = O The constant C1 can then be determined to be
(51)
C, = 2N,dR (52) At the channel entrance, the effect of channeling is reflected in this model: (53)
In practice, the length of a dead leg is often four pipe diameters. In eq 53, the flux at the entrance would then be 17 times larger than at the wall. An estimation of the magnitude of the temperature nonuniformities in this model can be only qualitative since conduction has been ignored. The model will tend to overstate the nonuniformities. The temperatures in the model can be estimated from the concentration distributions predicted from eqs 49 and 50, by recognizing that the concentration of steam at constant pressure specifies the temperature. The largest variations will be found in the z-direction. Substituting eq 43 into eq 49 and integrating yields the distribution
Fixing the mole fraction at one boundary in effect defines the amount of air in the system. The temperatures can be found from the relations in eqs 31, 32, and 33. Figure 7 shows predictions from the model for dead legs of varying shape. The distribution in eq 54 contains a geometrical scaling criterion, 62/R+ 6. One cannot defend a scale-up based upon a constant ratio of length to diameter from this. As longer dead legs are required, an increase in pipe diameter will not usually be able to avoid an impact upon the temperature distribution, as is evident in Figure 7. Also noteworthy in the figure is the sensitivity of the model to air in the system. Assuming the conditions at the entrance to the dead leg reflect the rest of the SIP
-3,699
-
-3,301
-3
1)
Figure 7. Temperature drop in an insulated dead leg. The axial gas-phase temperature drop is estimated as noted in the text. The entrance is fixed at 121 "C. The abscissa reflects the contribution of trapped air to the total pressure.
system, the differenceP T ~P,~ at - the entrance is the partial pressure of air remaining after the air purge. Given the entrance temperature is 121 "C, a partial pressure of air equal to 1 mbar corresponds to -3.3 on the abscissa. When the axial temperature variation is limited to 0.5 "C, the model predicts the linear relations shown in Figure 8. Again, the advantage of insulating piping is evident. The values derivable for the partial pressure of air would demand a very effective air removal operation, equivalent in performance to the vacuum pumping systems of autoclaves. Returning to condensate flow, it will be compared with the gas flow, to estimate a possible interaction. Expressions for the velocity at the surface of a falling film can be found in such sources as Bird et al. (1960). We consider here the worst case, the vertical orientation, and present only a summary for brevity. The velocity at the surface is not a function of D and is only dependent upon channel length to the 2 1 3 power. It is found to be smaller than but of similar magnitude to the diffusional gas velocity, expressed as N,,Ic. The effect of condensate flow upon the gas resistance can be ranked then as a perturbation of the model that tends to improve heat transfer by creating gas convection. The perturbation becomes less important as the channel lengthens. 6. Discussion and Conclusions A reliable SIP process must be based upon sufficient knowledge of the operation, which should be verified during validation and supported by on-line measurement and control. Reproducibility is a good indication that the process is under control. This analysis has identified at a fundamental level where special attention must be paid to the design to ensure that the knowledge base is sufficient. Special attention is needed when the sterilization temperature in the system is not likely to be uniform and may be difficult to predict or measure. A significant temperature nonuniformity in the gas phase was found to be likely in tanks and large-diameter pipes, unless the removal of air is very effective. With the normal air purge step, the amount of air left in the system cannot be easily measured or predicted. Removal of air by applying a vacuum does document with the pressure how much air is left. It also allows an integrity test by means of a vacuum hold test. However, the temperature nonuniformity in the gas phase does not reflect the coldest temperatures, which are
283
Bbtechnol. Rog., 1992, Vol. 8, No. 4 25
insulated, L
q d
154
s
10
40
//
0 4 -3
-
1
-4
-5
-6 Log ( P t O t I P S - 6
- 1)
Figure 8. Length of dead leg for a temperature drop of 0.5 "C. Entrance temperature is 121 "C;the temperature at z = 0 is 120.5 "C. The abscissa reflects the amount of air left in the system. found to be at the system boundaries, the walls. In principle, these temperatures can be measured, and they usually are during validation by clamping thermocouples to the outside of the walls. Since this type of installation is not as robust and thermocouples are not as accurate as RTDs, the primary temperature monitors are usually RTDs inserted a t the drains. These will measure a mixed stream temperature, and they may not have sufficient sensitivity to detect changes in temperature a t the walls. Significant temperature nonuniformities are almost unavoidable in uninsulated equipment. Here, the higher heat losses contribute not only to a larger amount of condensate but also to a larger temperature gradient in the condensate layer. Although condensate depths would be reduced in vertical pipe runs, steam traps will only be effective a t the bottom of the run, where the accumulated condensate amount can become large. Although it is clearly desirable to have uniform steam distribution and minimal temperature nonuniformities, real systems often cannot achieve this because of either incomplete air removal or poor condensate draining. Some examples follow. When steam capacity is limiting, it may not be possible to provide sufficient flow for an effective air purge. This will be common when the vessels are large. Poorly suited steam traps may not effectively remove condensate. This can easily arise because steam traps are normally designed to conserve steam. Complicated piping networks are difficult to insulate, slope properly, and purge. The driving force for this complexity is the desire to sterilize linked units simultaneously. This approach simplifiesoperations and avoids the uncertainty of sterility at the junctions between units (which would become dead legs when SIPd separately). Filters are another recognized problem area [addressed by Myers and Chrai (1982)],but have not been examined here because of their geometrical complexity. The difficulty in sterilizing filters may lie not only in the problem areas identified here but also on interactions between the microbes and the filter surfaces and pores. A particularly difficult problem in SIP systems to address is the SIP of the dead legs since they are especially vulnerable to a gas-phase heat-transfer resistance. The design of piping should be optimized to minimize their lengths and find the best placements and orientations. Special attention needs to be made in the selection of instrumentation and equipment so that these lengths are minimized or avoided entirely. Also in many cases, a dead leg can be effectively eliminated by employing a double block valve arrangement with a steam trap.
As SIP systems continue to evolve, increased understanding of the transport processes occurring can lead to better designs and help in comparing alternative methods. In some cases, steam sterilization may not have a clear advantage over chemical sterilizing methods, since they avoid the problems of heat transfer. From this article, one could falsely conclude that it is difficult to perform a SIP. But they are routinely performed in industry. Temperature nonuniformities can be compensated for by higher steam pressures and longer cycle times. The use of an overkill process coupled with a normally low bioburden usually brings the necessary margin of safety. However, in high-risk applications, such as sterile filling and packaging of intravenous products, the margin of safety should be better understood, and this can be fostered when the system has minimal temperature nonuniformities.
Notation a
b B C
CH
CP
cz
c1,
D di 2, e
E
fa g
h
H k K L M N N8
P h o t
&/A r
R Rs t tH
T u
V
P W X
X 2
a
B 6 6 P 7
M
width of rectangular channel height of rectangular channel constant defined by eq 29 molar concentration mixing time constant specific heat capacity at constant pressure, J/kg integration constants diameter diameter of nozzle on tank binary diffusivity, m2/s energy flux, w/m2 turbulent dispersion coefficient, m2/s fraction of original air left in system gravitational constant, m/s2 heat transfer coefficient, w/(m2.K) specific latent heat, J/kg thermal conductivity,w/ (m.K) constant in eq 19 length molecular weight parameter in eq 19 molar flux of water pressure, Pa total system pressure heat flux, w/m2 spatial radial coordinate ideal gas constant; value of r at wall in pipe thermal heat transfer resistance time, s mixing time in a stirred tank for 95% homogeneity temperature, "C velocity volume partial molal volume mass flow rate, kg/s spatial coordinate in one-dimensional model mole fraction axial spatial coordinate thermal conductivity angle of slope thickness of layer; length of dead leg vector of unit length in eq 43 density space time, calculated for a stirred tank viscosity
Biotechnol. Pmg., 1992, Vol. 8, No. 4
204 V
kinematic viscosity
Subscripts a air C condensate S steam T thermal conv convective int interface W wall ins insulated bare not insulated Note: SI units are used, except where noted. Parameters Used in Gas Transport Analysis k 0.0264 w / ( m C ) MS 18 kg/(kg.mol) CP 2127 J / ( k g C ) H 2 196 000 J/kg Bas 0.000 025 m2/s
Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; Wiley & Sons: New York, 1960. EEC. Supplementary Guidelines-Manufacture of Sterile Medicinal Products, pt #50; In International Drug G M P s ; Anisfeld, M. H., Ed.; Interpharm Press: Grove, IL, 1990. FDA. Current Good Manufacturing Practice for Blood and Blood Components. Code of Federal Regulations Title2l;November 18, 1975, Chapter 1, part 606.60. Henzler, H. J. Untersuchungen zum Homogenisieren von Fluessigkeiten oder Gasen. VDI Forschungsheft N r . 587; VDI Verlag: Duesseldorf, 1978. Myers, T.; Chrai, S. Steam-in-Place Sterilization of Cartridge Filters In-Line with a ReceivingTank. J.Parenter. Sci. Technol. 1982,36 (3), 108-112. Othmer, D. F. Ind. Eng. Chem. 1929,21, 576. Perry, R. H.; Green, D. W. Chemical Engineers' Handbook, 6th ed.; McGraw-Hill: New York, 1984. Sherwood, T. K.; Pigford, R. L.; Wilke, C. R. Mass Transfer; McGraw-Hill: New York, 1975. Straub, L. G.; Silberman, E.; Nelson, H. C. Open-Channel Flow at SmallReynolds Numbers. Trans. Am. SOC.Civil Eng. 1968, 123, 685-717. Wallhauser, K.H. Praxis der Sterilisation Desinfektion-Konservierung, 4th ed.; G. Thieme Verlag: Stuttgart, 1988.
Additional Reading Acknowledgment I am indebted to Fluor Daniel for allowing the time t o prepare this article. I also wish t o t h a n k m y industrial colleagues, especially those at Miles, Inc. (formerly Cutter Laboratories), for their valuable insight. Professor Lightfoot at t h e University of Wisconsin deserves mention for teaching m e analytical approaches t o transport phenomena.
Literature Cited Adams, A. Sizing Clean-Steam Generators. Biopharm. 1988,l (ll),36-44. Agalloco, J. Steam Sterilization-in-Place Technology. J . Parenter. Sci. Technol. 1990,44 ( 5 ) , 253-256.
Berman, D.; Myers, T.; Chrai, S. Factors Involved in the Cycle Development of a Steam-in-Place System. J . Parenter. Sci. Technol. 1986,40 (4), 119-121. British Parenteral Society. Tutorial Booklet N r . 2 Validation of Steam Sterilisers; BPS: Swindon, Wiltshire, U.K., 1990. FDA. Guidelines on Sterile Drug Products Produced by Aseptic Processing; Div. of Manufacturing and Product Quality, FDA Rockville, MD, 1987. Myers, T.; Chrai, S. Design Considerations for Development of Steam-in-Place Sterilization Processes. J. Parenter. Sci. Technol. 1981,35 ( l ) , 8-12. Seiberling, D. Clean-in-PlaceiSterilize-in-Place (CIPISIP) in 01son, W. P., Groves, M. J., Eds., Aseptic Pharmaceutical Manufacturing; Interpharm Press: Prairie View, IL, 1987. Accepted May 7, 1992.
