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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5395_Библиотеки_им_академика_М_И_Перельмана
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Integrated Synthesis, Crystallization, Filtration, and Drying of Active... 275
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CMAs, CPPs, CVs
crystal size distribution CSD
•
cycle duration Δt
•
drying gas composition c
•
drying gas inlet temperature T
•
pressure drops ΔP
•
slurry volume V
•
slurry concentration c
•
washing ratio W
•
wash solvent composition c
•
cycl e
i,g
drying
slurry
slurry
i,w
Carousel model
filtration model
•
deliquoring model
•
washing model
•
thermal drying model
•
Outputs
impurity and solvent content w
•
Cake physical properties
cake specific resistance α
•
porosity ε
•
i,cake
Fig. 10 Integrated filtration-drying carousel mathematical model: input/output structure
The developed mathematical model of the carousel presents the input/output
structure reported in Fig. 10. Given a set of inputs (critical material attributes
(CMAs), critical process parameters (CPPs) and control variables (CVs)), the model
provides as outputs the solvent and impurities contents in the discharged cake
(CQAs). A cake physical properties module is also implemented within the carousel
model to (approximately) predict the cake porosity and specific resistance from the
slurry CSD, if their experimental measurements are not available. The core of the
carousel simulator is obtained by combining together the stand-alone models of the
four processes occurring in the carousel: (a) slurry filtration, (b) cake deliquoring,
(c) cake washing, and (d) thermal drying. The models are implemented in the
MATLAB/Simulink environment as functions, called by an external wrapper to
mimic the operation sequence of a physical carousel. The deliquoring and drying
models are coded in C and interfaced with MATLAB through C-MEX functions
to reduce the computational burden. The simulator is flexible and robust: it can
simulate carousels with different number of drying stations, and it accounts for
limiting cases in which filtration and/or washing last for more than one cycle
duration due to poor cake filterability or unfavorable operating conditions. The
model was calibrated to the sample process involving paracetamol isolation through
experimental activities reported elsewhere [43].
276 D. J. Laky et al.
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The DS is determined with a probabilistic approach [5], accounting for modeling
uncertainty by assigning a probability distribution to selected model parameters.
First, we build a grid of CPPs (cycle duration t
per cycle V
) and CMAs (crystal concentration in the slurry c
slurry
and amount of loaded slurry
cycle
), uniformly
slurry
sampling the points among reference operation boundaries. For every point of the
grid, we calculate the probability of meeting the target CQAs through Monte Carlo
simulations (400 realizations). For each realization, the uncertain parameters are
sampled from their probability distributions, and the CQAs of the discharged cake
are calculated with the carousel model. The percentage of realizations satisfying
the CQA requirements (residual solvents and impurity content in the discharged
cake below 0.5%) in a grid point corresponds to the probability of meeting the
quality target for the corresponding combination of CPPs and CMAs. The uncertain
parameters are the mass transfer coefficient, the filter mesh resistance, the specific
cake resistance, and the cake porosity. They are all considered normally distributed,
with mean value coming from model calibration and standard deviation set to 5%
of the mean. The only exception is the filter mesh resistance, for which we adopt a
uniform distribution to reproduce the increase of fouling occurring during carousel
operation (filter meshes undergo a cleaning-in-place procedure only after a certain
fouling threshold is reached). We introduce two additional normally distributed
parameters: additive process noise coefficients for c
slurry
and V
, to simulate the
slurry
small fluctuations around their set points occurring from cycle to cycle. Overall, the
selected uncertain parameters aim at accounting on the calculated probability for the
effect of the model error and of the unmodelled disturbances (e.g., small changes in
the CSD of the fed slurry) that can occur during carousel processing.
The calculated probabilities in the CPPs and CMAs grid are reported in Fig.
11. After having set the minimum acceptable probability to 90%, we obtain the
following expression for the DS through multiple linear regression on the calculated
probabilities:
DS =#V
where 1 mL < V
slurry
,Δt
slurry
cyc le,cslurry
of the calibration domain) and with a
a
= 3.06E5 s/kg, and a4= 5.14E1 s. The surface at the boundary of the region
3
described by Eq. (59) effectively delimits the DS (Fig. 11) in all the domain. As
a note, the linearity of the DS boundary for fixed c
low specific resistance of the cakes obtained from the paracetamol crystal mixture
used for model calibration. For the general case, linear and bilinear terms, as seen
with V
slurry
and c
slurry
the DS. Thus, the use of higher-order terms may be desired to accurately fit the DS
boundary.
|Δt
cyc le
≥ a1V
slurry
+ a2c
slurry
+ a3c
slurryVslurry
+ a
$
4
(59)
< 10 mL and 50 kg/m3< c
=−2.78E6 s/m3, a2=−1.05E-1 s m3/kg,
1
< 200 kg/m3(boundaries
slurry
in Eq. (59) is due to the
slurry
in Eq. (59), may be insufficient to produce a reasonable fit of
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Fig. 11 Integrated filtration-drying carousel case study: probabilistic DS, representing the probability of meeting the target CQAs for a given combination of CPPs and CMAs. Green triangles:
probability ≥90%, yellow circles: 80% ≤ probability <90%, orange squares: 60% ≤ probability
<80% and red diamonds: probability <60%. The dark surface represents the DS boundary
calculated with Eq. (59)
The maximum throughput T
paracetamol crystals with acceptable quality that can be isolated with the carousel
per unit of time, is given by the following optimization problem:
subject to
Δt
cyc le
≥ a1V
50 kg/m
where T is the throughput processed in the carousel. Since the optimum of Eqs.
(60)–(61) lies on the DS boundary, the problem can be re-expressed by elimsinating
the explicit dependence of T
max
T
max
T =
+ a2c
slurry
3
<c
1mL<V
max
within the DS, namely, the maximum amount of
= max
V
,Δt
slurry
c
slurryVslurry
Δt
cyc le
slurry
< 200 kg/m3,
slurry
< 10 mL,
slurry
on t
cycle
:
cyc le,cslurry
+ a3c
T, (60)
,
slurryVslurry
+ a4,
(61)
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T
= max
max
V
slurry
,Δt
cyc le,cslurry
T, (62)
subject to
c
T =
a1V
50 kg/m
slurry
3
<c
+a2c
slurry
< 200 kg/m3,
slurry
slurryVslurry
+ a3c
slurryVslurry
+a
,
4
(63)
1mL<V
The gradients of the objective function T with respect to c
are always positive under the constraint domain. Hence, T
the boundary point defined by c
T = T
= 195 mg of crystals per minute. The obtained analytical solution of
max
slurry
< 10 mL.
= 200 kg/m3and V
slurry
slurry
is achieved at
max
= 10 mL, where
slurry
and V
slurry
Eqs. (62)–(63) is confirmed by the plots of the throughput at the DS boundary (Fig.
12). In other case studies of integrated filtration-drying with the carousel, T
max
was
achieved in between the grid bounds, rather than at the bounds themselves [45],
possibly due to higher nonlinearity of the DS boundary. Looking at Fig. 12,a
stationary point of maximum would eventually be reached if the maximum port
capacity were larger than 10 mL. As a final remark, it is recommended to conduct
the process inside the DS and close to the conditions of T
, rather than on the
max
optimal point itself (located on the DS boundary). This choice reflects the greater
importance that product quality compliance has with respect to economic optimality
in pharmaceutical manufacturing.
In the general case in which a new carousel has to be designed for a process,
the simulator can be used for sensitivity analyses on the variations of the CQAs and
of T
with the design variables, such as the station diameter, the maximum port
max
capacity, and the number of stations. In the simulation activity, model uncertainty
can be computed with the aforementioned Monte Carlo approach or neglected, in
first approximation. Considering again the paracetamol isolation process, we repeat
the probabilistic DS calculation varyingthe number of drying ports (Fig. 13). For the
sake of simplicity, the other design variables are considered to be the same as in the
carousel prototype, and c
is fixed to 125 kg/m3. The DS surface considerably
slurry
widens passing from one to two drying stations, and an additional (smaller) gain
is obtained, adding a third drying station. The fourth and the fifth drying stations
do not allow increasing the DS area much more, as filtration becomes the limiting
step (filtration duration against V
is reported as solid line in Fig. 13). Also on
slurry
the maximum throughput side, the fourth and fifth drying stations allow a smaller
improvement: T
is 189 mg/min with one drying station, 349 mg/min with two,
max
517 mg/min with three, 652 mg/min with four, and 790 mg/min with five. However,
the actual selection of the number of drying stations depends on the throughput
requirements of the overall manufacturing line.
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Fig. 12 Integrated filtration-dryingcarousel case study: throughput T at the designspace boundary
(Eq. 59)forvaryingV
slurry
and c
slurry
Carousel Active Control Strategy
Controlling carousel operation is an intrinsically challenging task, given the intensified nature of the unit. An approach to control system design recently proposed
within the QbC initiative [2] includes three hierarchical levels, following the ISA95 Enterprise-Control System Integration Standard. Level 0 consists of simple PID
control and of the built-in control system of the units (sensors, controllers, and
PLCs). Level 1 is made up of advanced PID control loops, while Level 2 relies
on model-based control. The developed carousel model is a useful tool for the
development of all the levels of the control system, as it can be used (a) for modelbased control at Level 2 and (b) as digital twin of the physical unit for quickly and
safely testing different control strategies, either model-free (Levels 0–1) or model
based (Level 2). In the rest of this section, after having described the carousel Level
0 control system, we demonstrate the effectiveness of a Level 1 control strategy
for disturbance rejection through simulations with the carousel model. Thorough
discussion of Level 2 implementation will be covered in the future work.
The built-in control system of the carousel and of the accessory equipment is
sketched in Fig. 14, inside the Level 0 box. All Level 0 controllers (except for
pressure controllers) are contained in the carousel PLC. Each carousel station is
represented as an independent tank (V104–108), instead of being included in the
main carousel body, for the sake of clarity. The transfer of material upon carousel
rotation is given by the streams among tanks V104–108 (controller FC102 opens
the stream valves at each cycle switch). V109 is, instead, the wash solvent tank.
The carousel cleaning solvent vessel is not reported for conciseness. V101 is the
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Fig. 13 Integrated filtration-drying carousel case study: comparison of the DS of carousel
configurations with different number of drying stations: (a) one station, (b) two stations, (c)three
stations, (d) four stations, and (e) five stations. The solid line represents the filtration duration. The
marker’s legend is as in Fig. 11,andc
upstream crystallizer, from which the slurry is moved into an intermediate storage
tank (V102) with a peristaltic pump (P101). At the beginning of every cycle, the
set V
(controlled by FC101) is drawn into the charge cell V103 through the
slurry
action of vacuum pump P102. P102 is connected to V103 only during this charging
slurry
is 125 kg/m
3
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Fig. 14 Integrated filtration-drying carousel case study: P&ID with Level 0 (built-in control) and
Level 1 (advanced PID) control systems
phase, through a three-way valve. During the rest of the cycle, P102 is connected
to the filtrate receiver V110 and, hence, to the bottom of V104–107, providing
the driving force for liquid and gas displacement. The fan P103 can be used for
increasing the pressure drops in each station, or the top portion of V104–107 can be
directly connected to the atmosphere (i.e., eliminating F103 from the P&ID). PC101
and PC102 are, respectively, the built-in pressure controllers of P103 and P102.
TC101 manipulates the heater (H101) jacket temperature to control the temperature
of the drying air entering V107. TA101 and the connected low selector take care of
preventing the jacket temperature togo beyond 150
◦
C forsafety reasons. Additional
sensors are available for monitoring and control applications. PI101 measures the
pressure at the bottom of the carousel stations, FI101 measures the air flow rate
entering the carousel, FI102 (a scale installed below V110) measures the flow rate
of filtrate entering V110, and TI101–103 are, respectively, the thermocouples for
jacket temperature, gas temperature at the dryer inlet, and gas temperature at the
dryer outlet.
Operating the carousel requires fixing the set points of the Level 0 controllers,
namely, of the CPPs t
cycle
and V
and of multiple CVs: the pressure drop in
slurry
the ports, the inlet temperature of the drying air, and the amount of wash solvent
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to be used per cycle. Appropriate set points for the CVs can be chosen based on
heuristic considerations. For instance, the largest pressure drop and inlet drying air
temperature that can be achieved in a given carousel setup should be selected to
maximize their contribution to meeting the CQA target values. Suitable t
V
set points can instead be selected through the DS calculation and throughput
slurry
maximization procedures outlined earlier in this section, based on the value of c
cycle
and
slurry
in the slurry fed from upstream. Proceeding this way, the process operates as open
loop with respect to quality. In the occurrence of severe disturbances, the product
might have to be rejected due to compromised quality. To tackle this issue, we
conceived a Level 1 control system (Fig. 14), with advanced PID loops controlling
the CQAs (i.e., the solvents and impurities content in the cake discharged from
V108). Since the CQAs are not measured online, AC101 controls them by inference.
Actually,the residual solvents and impurities content in the cake are correlated to the
outlet drying gas temperature profile. At the beginning of drying, a temperature drop
is registered because of the latent heat of vaporization. With the progress of drying,
temperature starts increasing back, since the residual solvents and impurities, and
the energy consumed by their volatilization, are always lower. Exploiting this
correlation, AC101 controls the CQAs by tracking a reference temperature profile
obtained in normal operating conditions. Suppose that cake drying is progressing
more slowly than usual, for example, due to F104 fouling or to abnormally large
initial solvent content. TI103 will measure an error with respect to the reference
temperature profile, and AC101, a split range controller, will react, increasing the set
points of one or more of the following: the pressure drop in the processing stations
(PC101), the drying gas inlet temperature (TC101), and/or t
(FC102). At first,
cycle
only the pressure drop set point willbe increased. If this is not enough tocompensate
for the disturbance, AC101 will then increase the drying gas inlet temperature set
point. The set point of t
will be increased only as last resource, as a higher
cycle
cycle duration causes a reduction of the process throughput. On the other hand, if
drying is progressing faster than in the reference conditions, AC101 will react in
the opposite direction, eventually reducing t
and increasing the throughput.
cycle
Control of the CQAs is also achieved at Level 1 through the action of flow rate
controller FC103. FC103, another split-range controller, controls the filtrate flow
rate by increasing/decreasing the set points of the pressure drop and/or of t
cycle
with the same heuristics adopted for AC101 to maximize the throughput. FC103
compensates for disturbances increasing the filtration duration, such as fouling of
F101–104, or cake resistance increase. Since both AC101 and FC103 act on the
pressure drop and t
set points, two high selectors are included in the Level 1
cycle
control system (Fig. 14).
Figure 15 shows the response of Level 1 control system to a fouling disturbance
(complete process conditions are not reported for conciseness). Shortly after the
process onset, the filter mesh resistance starts increasing with a linear ramp, until
the cleaning-in-place procedure is triggered, restoring the initial fouling conditions
(150 min after the beginning of the process). As detailed above, filter mesh
resistance was considered an uncertain parameter with uniform distribution for the
purposes of DS calculation, accounting for the increase of mesh fouling during
,
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Fig. 15 Integrated filtration-drying carousel case study: control system response to (a) a fouling
disturbance, including (b)t
variable). Both Level 0 (built-in control, open loop) and Level 1 (advanced PID control, closedloop) responses are reported
operation. As a result, the values of t
(manipulated variable) and (c) the CQA (controlled-by-inference
cycle
in the DS for given V
cycle
slurry
and c
slurry
conditions are conservative by considering many fouling conditions, among those
the highest fouling conditions before cleaning is triggered. When the filter meshes
are clean, smaller t
a t
of 2 min meets the desired quality target with the clean meshes. However,
cycle
values could be used, increasing the throughput. In Fig. 15,
cycle
with a Level 0 control system (open loop), the cakes produced in Cycles 7–71
have to be rejected, as they do not meet the desired quality (Fig. 15c). The quality
target is eventually reached again, from Cycle 72 onward, only after the meshes are
cleaned. Instead, Level 1 controllers react very fast to the abnormal CQAs, at first
by increasing the pressure drop and the inlet drying air temperature. A few minutes
after the disturbance onset, the set points of the pressure drop and of the drying air
inlet temperature saturate, and Level 1 controllers start increasing t
Due to the increased t
, with Level 1 control, only 65 cycles are completed in
cycle
cycle
(Fig. 15b).
the same amount of time in which Level 0 control completes 115 cycles (Fig. 15b).
However, with Level 1 control, the CQAs always adhere to the quality threshold.
Upon filter mesh cleaning, Level 1 controllers automatically start decreasing t
cycle
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(Fig. 15b), effectively increasing the throughput again. This example shows that
the proposed Level 1 control system is capable of rejecting disturbances known to
occur during carousel operation, such as fouling, trying to (suboptimally) maximize
the throughput at the same time. Improved throughput maximization in the presence
of disturbances can also be obtained, manipulating V
goal through PID control loops is a cumbersome procedure. A Level 2 control
system is required for proper real-time optimization.
. However, achieving this
slurry
4 Conclusions
In pharmaceutical manufacturing, QbD and QbC provide key benchmarks for
digital analysis of pharmaceutical manufacturing systems. Although QbD may be
implemented on single unit operations in pharmaceutical manufacturing systems,
as manufacturing practices proceed to end-to-end continuous or hybrid batchcontinuous operation, integrated analysis is required to implement meaningful
process control schemes and maintain the design space dynamically.
To highlight the advantages of integrated design and optimal operation of pharmaceutical manufacturing systems, we presented two case studies on multiple-unit
subprocesses for the synthesis-crystallization and filtration-drying of paracetamol,
using an integrated process simulation and optimization framework utilizing digital
twins. In the first case study, we showed process optimization of the synthesiscrystallization of paracetamol utilizing gradient-free optimization followed with
a narrowed uniform grid search for optimal operating points. We utilized the
new, open-source simulation tool, PharmaPy, to understand whether end-to-end
continuous or hybrid batch-continuous operation was optimal. We found that in
this case, the end-to-end continuous process provided a nearly equivalent mass
output rate, but for the optimal operating conditions, it provided larger crystal
sizes, favoring a PFR-MSMPR setup to a hybrid, PFR-batch crystallization setup.
As process integration and modernization continue, more detailed frameworks
and metrics for direct comparison of such operating mode choices will become
an important analysis tool for the automated comparison potential manufacturing
routes.
In thesecond case study, we analyzed thebehavior of the filtration-drying process
of a paracetamol slurry in an integrated carousel unit. The probabilistic design space
was quantified and successfully identified feasible operating regions for critical
process parameters of the carousel. For this particular case, a function describing
the relevant probabilistic front can be fit and justified, resulting in a closed-form
equation that is vital for quantitative validation that CQAs are satisfied within the
operating region. Then, an online control system was implemented and shown to
successfully control the carousel operation.
This model-based framework for process optimization and control showcases
process digital twins and the capability of generating optimal operating conditions,
quantifying feasible design spaces, and controlling integrated processing systems.
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