Article pubs.acs.org/IECR
A Plant-Wide Dynamic Model of a Continuous Pharmaceutical Process Brahim Benyahia, Richard Lakerveld, and Paul I. Barton* Process Systems Engineering Laboratory, Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States S Supporting Information *
ABSTRACT: The pharmaceutical industry has historically benefited from high profit margins for their products, and over the years limited efforts have been made to change the main manufacturing concept from batch into continuous. However, over the past decade, as a result of an increased demand for more efficient and cost-effective processes, interest has grown in the application of continuous manufacturing to address economical and technical issues in the pharmaceutical field. This option is becoming more viable, particularly with the implementation of new process analytical technology (PAT). In this paper, we present a plant-wide mathematical model inspired by a recently developed continuous pharmaceutical pilot plant. This model is first used to simulate a base case that shows typical limitations in achieving simultaneously high productivity and quality. The main critical quality attribute considered is the purity of the final product. To alleviate the base case limitations and improve the pilot plant performance, the effects of several design parameters are investigated and the most critical are identified. In addition, alternative start-up scenarios are considered to improve the transient performance of the pilot plant, particularly time to steady state. The environmental footprint of the pilot plant is evaluated and shown to be low.
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INTRODUCTION The pharmaceutical industry is undergoing rapid changes. Economic, environmental, health, and safety requirements in conjunction with the regulatory environment are driving the sector toward more efficient processes. This requires innovation and cutting edge scientific, engineering knowledge and quality management systems. Despite the specific challenges inherent to the production of drugs, the pharmaceutical industry has enormous opportunities to benefit from a mature process systems engineering field whose tools have already been developed and have undergone decades of improvements and evolution in several sectors such as petrochemical, polymers, and energy. One of the key challenges for the pharmaceutical industry is to reduce their costs, which have soared over the past decade. For instance, the total cost of bringing a new drug to the market is between $0.8 and $2 billion.1,2 This cost has steadily increased at an average rate of over 8% per year over the past 5 years.2,3 Moreover, 10 to 15 years may pass from the inception to the clinical approval of the drug.3,4 As a result, 40 to 50% of the product patent life may have expired at the approval stage,4 which may expose the pharmaceutical producer to increasing competition from generic drug manufacturers who have substantially lower research and development (R&D) and marketing costs. Process engineers have a key role to play in reducing the cost of product development, which can be as high as 30 to 35% of the total costs of bringing a new product to the market.5 In addition, they have to translate the discovery of a new Active Pharmaceutical Ingredient (API) into a safe and cost-effective process in the shortest possible time. To achieve these key objectives, shifting from the traditional batch-wise to continuous manufacturing (CM) becomes one of the most relevant alternatives. In addition, the use of new process analytical technology (PAT), particularly online, enables engineers to gain better understanding and control of the underlying physical and chemical phenomena, making it possible to build efficient and reliable © 2012 American Chemical Society
continuous pharmaceutical plants. The comparison between batch and continuous processing cannot be limited to yields and selectivity, as usually discussed in the literature, but must be extended to all engineering aspects. Continuous processing reduces product variability, delivers lower wastes, and reduces the energy consumption.6 In addition, CM offers the opportunity to integrate more efficient and cost-effective processes such as microreactors and microseparators where the production rate is increased by numbering up instead of scaling up.6,7 This feature can play a key role to reduce time and cost, particularly during preclinical and clinical trials where the supply of the API and the final dosage form are required at different scales. A recent study demonstrated that a substantial overall cost savings up to 44% can be achieved by adopting CM with recycling, particularly when the price of the key intermediates is not very expensive.8 Mathematical models, both dynamic and steady-state, have been widely used for decades in the field of process system engineering. Dynamic models are able to predict the transient response, and therefore, can be used to describe process behavior during start-up and shut-down, to evaluate safety and plant operability, to debottleneck and revamp plant operations, etc. Mathematical models can play a crucial role in the pharmaceutical industry throughout the product life-cycle from development, manufacturing to commercialization by expediting the different stages, and reducing costs.9−11 In addition, these tools can be used to improve the quality of the pharmaceutical product by implementing advanced model-based control12 and/or model based Quality-by-Design (QbD).13 In this work, we present a plant-wide dynamic model of an integrated (upstream and downstream) continuous pharmaceutical Received: Revised: Accepted: Published: 15393
March 8, 2012 July 11, 2012 October 31, 2012 October 31, 2012 dx.doi.org/10.1021/ie3006319 | Ind. Eng. Chem. Res. 2012, 51, 15393−15412
Industrial & Engineering Chemistry Research
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Figure 1. Flow sheet of the continuous pharmaceutical pilot plant.
intermediate C3 is produced. In addition to the main reaction, many impurities are produced by side reactions (Table 1). The
pilot plant designed for a tablet dosage form. The model is inspired by a pilot plant designed and constructed at MIT for the Novartis-MIT Center for Continuous Manufacturing. However, it does not mimic the real plant exactly. For example, some features such as recycling have not been implemented in the real plant. This plant involves multistep reactions and purification stages as well as solid processing such as drying and extrusion. After analyzing the simulated performance of the pilot plant under specified operating conditions, the mathematical model is used to study the effect of design parameters such as purge ratio, wash factor, and the residence times of some unit operations, on the purity of the final drug product, which is a typical critical quality attribute in the pharmaceutical field, on yield, and on productivity. The critical parameters are identified including their acceptable operating ranges. To improve the transient performance of the process, particularly time to steady state, the dynamic model is used to simulate and assess different start-up strategies. This paper is organized as follows: after a description of the pilot plant, the plant-wide model is presented including the different unit models and descriptions of the main assumptions. Subsequently, the plant-wide model is used to simulate and analyze an illustrative base case. The effect of different design parameters on yield, production, and levels of impurities is presented and discussed in the next section. In the last section, the evaluation of alternative start-up scenarios is presented.
Table 1. Kinetic Scheme and Reaction Rates of the First Reactor C1 + C2
Cat1, k11
←⎯⎯⎯⎯→
C3
R1r1 = k11wcr11
k12
R 2r1 = k12wcr31 k13
I1
R3r1 = k13wcr11
k14
I2
R 4r1 = k14wcr31
k15
I3
R 5r1 = k15wcr31
C1
→
C3
⎯→ ⎯
1 C 2 1
3
1
+ 2 C2 + 2 C3
→
reactor outlet is mixed with two solvents in a second static micromixer and then fed to a liquid−liquid extractor, which consists of a membrane microseparator (LLE-1). The intermediate C3 and the residual reactant C1 are captured by the first solvent while C2 and the catalyst are extracted in the second solvent. The former stream is fed to the first crystallizer to separate C3 where an antisolvent (AS) is added. A second crystallizer operating at a lower temperature is used to improve the crystallization yield. The slurry is fed to a wash and filtration unit to reduce the impurities adhering to the C3 crystals. The outlet wash solution, which contains mainly unreacted C1, residual C3, and byproducts of the first reactor, is purged at a given purge ratio to reduce the accumulation of impurities and then fed to a flash evaporator to remove the solvent. The remaining solution, which contains unreacted C1, C3, and byproducts, is recycled to the first mixer. The wet cake consisting of crystals, residual solvent, and impurities is diluted in a dilution tank (D-1) with an additional solvent stream, then mixed with a catalyst solution in the static mixer M-3 and fed to the second reactor (R-2), to produce an intermediate C4. Additional side reactions that produce more impurities are
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PROCESS DESCRIPTION The flow sheet of the pilot plant is depicted in Figure 1. The process involves two reactors where the main intermediates are produced and can be divided into two major sections: upstream where the API is produced through multistep reactions and downstream for solid processing and excipients addition. First, the reactants C1 and C2 and the catalyst are mixed in a static micromixer before being fed to the first reactor, where an 15394
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Liquid−Liquid Extractor 1. The first liquid−liquid extractor is a microfluidic device that consists of a mixing stage followed by a perfect splitting of the organic and aqueous phases. The corresponding components and total mass balance equations are as follows: Mixing Stage (Mixer 2).
considered here (Table 2). The reactor outlet mixture is then fed with a solution of a reagent C5 to a reactive LLE, where the Table 2. Kinetic Scheme and Reaction Rates of the Second Reactor C3
Cat2, k 21
C4 + I4 + G1
R1r2 = k 21wcr32
k 22
I5 + C2
R 2r2 = k 22wcr42
I6 + I4 + G1
R3r2
⎯⎯⎯⎯⎯⎯⎯→
C4
⎯→ ⎯
C3
Cat2, k 23
⎯⎯⎯⎯⎯⎯⎯⎯→
=
m2 r1 Fout = Fout + FSm2 + FSm2 1 2 m2 m2 r1 r1 Fout (wim2 ,1 εm2 + wi ,2 (1 − εm2)) = Foutwi ,out +
k 23wcr32
m2 wim2 ,1 = K iwi ,2
ρl
nr1 dt
=
−
wir,1j)
+ ρl
r1 Vr1
nr1
ρl
nr2 dt
m2 wie1 ,raf = wi ,1
(8)
m2 wie1 ,ex = wi ,2
(9)
e2 R1e2 = k 31wCat 2
e2 ρraf
d e2 e2 e2 e2 e2 e2 (V raf wi ,raf ) = Fine2win, i − Fraf wi ,raf − Fi dt
ρexe2
d e2 e2 F e2 e2 e2 e2 (V ex wi ,ex ) = FC5wi C5 − Fexe2wie2 ,ex + Si R1 ρex V ex dt + Fie2
(10)
(11)
(12)
Fe2 i
where is the interfacial mass transfer rate of the component i expressed by e2 Fie2 = kLe2(wraf − K iwexe2)
Sir,1lR lr,1j)
(13)
The total mass balance equations in the raffinate and the extract are derived by
l=1
e2 ρraf
ρexe2
e2 dV raf e2 = Fine2 − Fraf − dt
dV exe2 = FC5 − Fexe2 + dt
nc
∑ Fie2 i=1
(14)
nc
∑ Fie2 i=1
(15)
To capture the start-up behavior from empty, we assume no outlet flow until we reach the maximum volume. At this point, we assume a perfect control of the volume. Those assumptions will be used throughout this work for similar unit operations. As a result, the outlet flow rates are derived by the following: e2 If (Ve2 raf + Vex ) < Ve2 then
3
= Finr2(wir,2j − 1 − wir,2j) + ρl r2
(7)
The component mass balance equations in each phase are derived as follows:
(1)
dwir,2j
m2 0 = Fout (1 − εm2) − Fexe1
k 31
where Vr1 is the reactor volume, wri,j1 is the mass fraction of the component i in the jth CSTR, and Sri,l1 is the stoichiometric coefficient of the component i in the lth reaction. The first reactor, which has a small volume, is assumed to be prefilled with reactants at the initial composition (before recycling). In a similar way, the second reactor is assumed prefilled and initialized at the actual composition of the third mixer. Reactor 2. The second reactor is assumed to be a perfect plug flow approximated by nr2 CSTRs. In addition to the intermediate C4 produced by the main reaction, more impurities are produced during this stage as described in Table 2. The component mass balance equations are derived as follows: r2 Vr2
(6)
Cat 2 + C5 → C6 + S2 ,
5
(∑
m2 e1 0 = Fout εm2 − Fraf
Liquid−Liquid Extractor 2. The two phases, raffinate and extract, are considered perfectly mixed. Cat2 and C5 are considered to react according to eq 10. Due to their poor solubility in S1 (see Table 2 in the Supporting Information), the reaction is considered to take place exclusively in the extract phase.
PLANT-WIDE MODEL The mathematical models of the different unit operations are developed in this section with a brief description of the main assumptions. Reactor 1. The first reactions described in Table 1 take place in a tubular reactor, which is assumed to be an ideal plug flow, approximated by nr1 continuous stirred tank reactors (CSTRs) in series. The kinetic scheme includes the main equilibrium reaction and side reactions. The component mass balance equations are derived for each CSTR as follows: Finr1(wir,1j − 1
(5)
Split Stage.
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dwir,1j
FS2
+ FSm2 wi 2
(4)
catalyst is neutralized. The resulting mixture is simultaneously separated where the raffinate containing the intermediate C4 and impurities is fed to an adsorption column to remove traces of solvent S2. Due to the limited adsorption capacity of a single column, a practical approach consists of alternating between regeneration and adsorption by using two columns. Nevertheless, one column can be designed to have sufficient capacity for a full run. However, this approach is less flexible. The adsorption outlet stream is fed to a reactive crystallizer (C-3) where a solution of C7 is added. A rapid reaction takes place in the solution and produces the API (eq 45), which crystallizes during this stage. A second crystallizer operating at a lower temperature is used to improve the yield. The slurry is washed with a stream of the solvent S1 and filtered to produce a wet cake of the API crystals. In the downstream part, the wet cake is diluted in a dilution tank (T-2) and mixed with an excipient X1. The resulting slurry is fed to a drum dryer followed by a screw dryer to remove the solvent S1 and achieve the required solvent content. The dry material obtained is combined with an excipient (X2) in a melt extruder where a high homogeneity is achieved. The molten material is molded to produce tablets, which are dip-coated at the final stage.
r1 Vr1
(3) F FSm2 wi S1 1
Vr2 (∑ Sir,2lR lr,2j) nr2 l = 1 (2) 15395
e2 Fraf =0
(16)
Fexe2 = 0
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Industrial & Engineering Chemistry Research
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otherwise e2 Fraf
Fine2
=
nc
−
∑
wCc13,sat = αc1e βc1(Tc1− 273.15) Fie2
Fexe2 = FC5 +
In addition, only the impurity (I2) is considered to cocrystallize with the main component (C3). The corresponding mass fraction in the solid phase is evaluated by
(18)
i=1
nc
∑ Fie2
wIc12,s = K Ic12 wIc12, l
(19)
i=1
e2 rC5Fine2wCat MCw5 2,in F
w wC5C5MCat 2
(20)
Crystallizer 1. The first and second continuous crystallizers are used to purify C3. All crystallizers used in this work are assumed to be well mixed. By assuming the crystallizer inlet as a perfect mixer, we obtain the following total and component balance equations: e1 Finc1 = FAS + Fraf
(21)
FAS e1 e1 Finc1wic1 + Fraf wi ,raf ,in = FASwi
(22)
e1 e2 FAS = rAS,mFraf wi ,raf
(23)
εc1 = 1 − k vc1μ3c1
(26)
L3n(L , t ) dL
=
If Vc1
