A grand model for chemical product design

Accepted Manuscript Title: A grand model for chemical product design Author: Ka Y. Fung Ka M. Ng Lei Zhang Rafiqul Gani PII: DOI: Reference:

S0098-1354(16)30070-9 http://dx.doi.org/doi:10.1016/j.compchemeng.2016.03.009 CACE 5393

To appear in:

Computers and Chemical Engineering

Received date: Revised date: Accepted date:

28-10-2015 10-3-2016 14-3-2016

Please cite this article as: Fung, K. Y., Ng, K. M., Zhang, L., and Gani, R.,A grand model for chemical product design, Computers and Chemical Engineering (2016), http://dx.doi.org/10.1016/j.compchemeng.2016.03.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights A Grand Product Design Model (GPD-Model) is presented for the design of chemical products. The optimal product with maximum profit is obtained through the GPD-Model.

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The GPD-Model considers product quality, ingredients, structure, process, cost, and pricing.

The GPD-Model also considers factors such as company strategy and government

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policies.

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The GPD-Model is illustrated with two case studies, namely die attach adhesive and hand

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lotion.

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A Grand Model for Chemical Product Design Ka Y. Fung, Ka M. Ng Department of Chemical and Biomolecular Engineering The Hong Kong University of Science and Technology Clear Water Bay, Hong Kong

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Lei Zhang, Rafiqul Gani Department of Chemical and Biomolecular Engineering Technical University of Denmark Lyngby, Denmark

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A manuscript submitted to Computers and Chemical Engineering Original submission: October 2015 Revision submission: March 2016

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Keywords: Product design, product ingredients, product structure, product price, government policies Abstract

Chemical engineering has been expanding its focus from primarily business-to-business products

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(B2B) to business-to-consumer (B2C) products. The production of B2B products generally emphasizes on process design and optimization, whereas the production of B2C products focuses

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on product quality, ingredients and structure. Market and competitive analysis, government policies and regulations have to be explicitly considered in product design. All these

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considerations are accounted for in the Grand Product Design Model, which consists of a process model, a property model, a quality model, a cost model, a pricing model, an economic model as well as factors such as company strategy, government policies and regulations. This article introduces the model and highlights selected aspects of the model with two case studies. One is a die attach adhesive that illustrates how pricing affects profitability, and how product composition changes with market conditions. Another is a hand lotion that illustrates how product quality affects the profit.

Correspondence concerning this article should be addressed to Ka M. Ng.

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Introduction The importance of chemical product design to the development of the chemical engineering profession has long been established (Stephanopoulos, 2003; Cussler and Wei, 2003; Hill, 2004; Gani, 2004a-b; Seider and Widagdo, 2012). Many textbooks have appeared (Bröckel

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et al., 2007, 2013; Ng et al., 2007, Wesselingh et al., 2007; Wei, 2007; Cussler and Moggridge, 2011) that consolidate the scope and approach for chemical product design. Different aspects of consumer-centered chemical product design have been discussed. A systematic framework on

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product design that involves product conceptualization, identification of product attributes,

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selection of ingredients and microstructure, process synthesis, product and process evaluation has been developed and applied for designing products such as creams and pastes (Wibowo and Ng, 2001), powder detergent (Fung et al., 2007), dry toner, cosmetics (Wibowo and Ng, 2002),

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and pharmaceutical tablets and granules (Fung and Ng, 2003; Fung et al., 2006). The framework has been extended to an integrative approach (Cheng et al., 2009) that covers marketing,

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management, finance and economics, product design and prototyping, process design and manufacturing for the development of chemical-based products. Bagajewicz (2007) developed a pricing model which accounts for consumer awareness of and preference for the product in

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comparison to competing products. This leads to a way relating product quality to product price

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and demand. Such a model has been applied to the design of wine (Whitnack et al., 2009), carpet deodorizers (Street et al., 2008), and skin moisturizing lotion (Bagajewicz et al., 2011). Economic analysis in consideration of product price, market share, and make-or-buy analysis has been studied with traditional Chinese medicine dietary supplements as an example (Cheng et al., 2016). Conte et al. (2011, 2012) proposed a systematic methodology which integrates computeraided tools and experimental testing for designing formulated products such as water-based insect repellent and waterproof sunscreen. Mattei et al. (2014) extended the methodology to emulsion-based formulated products. Korichi et al. (2008) presented a multi-level molecular knowledge framework for computer aided aroma design. Martín and Martínez (2013) presented a mathematical optimization-based methodology to simultaneously formulate a laundry detergent product and design its manufacturing process. Similarly, Bernardo and Saraiva (2015) proposed a conceptual model which considers product quality, product use conditions, component property and process functions. Gani and Ng (2015) categorized chemical products into molecules,

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devices, formulated and functional products and provide an overview of the methodology used to design products in different categories. There are four broad questions in product design: (1) What (product) to make? (2) How to make (the desired product)? (3) Do we want to make the identified product (among other

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alternative products) in considering other factors such as sustainability and company strategy? (4) If the above is affirmative, how do we come up with such a product from conceptualization to

questions. A broader perspective is required to answer the last two.

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product launch efficiently and profitably? Most of the studies above address the first two

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This was attempted by Cheng et al. (2009) who proposed a multidisciplinary, hierarchical framework for product design. The design activities span three phases in time – product conceptualization, detail design and prototyping, and product manufacturing and launch. These

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activities can also be classified by five job functions – management; business and marketing; research and design; manufacturing; and finance and economics. Many of the design tasks are

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handled by a chemical engineer, whereas the rest are handled by or with input from personnel from other disciplines. For example, product specifications cannot be fixed by engineers without the input from the business team working on consumers’ preferences, and marketing strategy is

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primarily developed by marketing experts. In fact, skills and knowledge from disciplines such as

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material science, electronic engineering, and finance are also required. The tasks in the multidisciplinary, hierarchical framework have been executed sequentially in the form of workflow and procedures (Cheng et al., 2016). In this study, the framework is captured in the Grand Product Design Model (GPD-Model) which serves two purposes. First, it allows the optimization of product design from a number of selected perspectives. Second, it provides a systematic structure for organizing the methods, tools, databases, and experiments required for executing the design of a specific class of products. Two case studies are performed to highlight a few selected features of the model.

Grand Product Design Model The GPD-Model consisting of six models is given below: Max [e, of]

(1)

subject to s ← Ts(x, pd)

(Process model)

(1a) 4

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(Property model)

(1b)

q ← Tq(p, s, u)

(Quality model)

(1c)

cm ← Tcm(x, pd)

(Cost model)

(1d)

Pprms ← Tprms(q;Y)

(Pricing model)

(1e)

(Economic model)

(1f)

e ← Te(cm, cnm, Pprms) L

U

c ≤ f(p, s, u, x, pd, q, cm, cnm, Pprms) ≤ c

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p ← Tp(x)

(Model parameter constraints)

(1g)

Figure 1 shows how these models fit in the GPD-Model. The first is the process model, s ← Ts(x,

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pd). It relates the product structure (s) to the active and supporting ingredients (x) and process

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design (pd), which includes process flowsheet (pdfs) and equipment operating conditions (pdop). For example, the droplet size of an emulsion cream depends on the chemical constituents of the cream. It is also influenced by the order in which stirring and homogenization steps the cream

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has been subjected to as well as the operating conditions of the corresponding stirred tank and homogenizer. The transformation symbol (←) signifies that the models might involve methods,

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tools, databases, and experiments for their application. We will elaborate on these elements of the GPD-Model at a later stage. The second model is the property model p ← Tp(x) which predicts the material properties (p) of the active and supporting ingredients. The product

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structure and material properties collectively determine the product quality (q) in the quality

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model q ← Tq(p, s, u). Note that the product use conditions (u) also affect the product quality. For example, the nozzle used in an inkjet printing machine for printing metallic traces dictates the maximum particle size and thus the quality of the metallic ink. Although product quality is important to meet the consumers’ preferences, profitability is an even more important consideration. The pricing model, Pprms ← Tprms(q; Y), determines the product price (pr) and the market share (ms) of the product for a given market size (Y). The product price and market size are denoted as vectors to signify that the GPD-Model can be applied for the optimization of an entire product line. The market share in turn determines the amount to be manufactured and the required capital investment and operating costs. The product cost is partly captured in the cost model, cm ← Tcm(x, pd), in which the manufacturing component of the product cost (cm) is determined by the amount and cost of the materials used in the product, and the cost in operating the production process. Other non-manufacturing costs (cnm) such as those related to legal issues and marketing have to be included in the total product cost. All of these lead to the economic model, e ← Te(cm, cnm, Pprms), for evaluating the financial 5

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performance of the product being designed. Any financial metrics (e) such as net present value (NPV), internal rate of return (IRR), and return on investment (ROI) can be used in the economic analysis. If other societal-organizational-economic factors (of) such as environmental considerations, sustainability issues, government policies and regulations, company strategy, and

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so on are considered alongside with the profitability analysis, the GPD-Model has to be solved as a multi-objective optimization problem. As shown in Eqn. (1), the objective is often the maximization of profit and some of the factors in of. Note that the model parameters might be

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restricted by various constraints (Eqn (1g)).

Elements for the Grand Product Design Model

Due to the diversity of chemical products, a wide variety of elements – methods, tools,

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databases and experiments – are required to expedite the execution of the GPD-Model. Table 1 gives a list of the representative elements. Note that methods have been further classified into

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rule-based and model-based methods.

For the process model in Table 1, the heuristics used in conceptual process design are examples of rule-based methods. Model-based methods involve the solution of mass, energy

for

various

process

units.

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developed

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and/or momentum balance equations. Many models describing process performance have been Tools

such

as

Aspen

Plus

and

HYSYS

(www.aspentech.com) are available for process simulation. Equipment databases detail the types of equipment and their performance for a specific unit operation. For example, charts are available for selecting a suitable emulsification unit – agitated vessel, colloid mill, toothed disc disperser, pressure homogenizer and ultrasound homogenizer – based on energy consumption and capacity (Wibowo and Ng, 2001). When data such as required energy consumption are presented in charts and tables, it is common to fit those data as a correlating function as it is easier to use correlations in optimization calculations. Experiments can include laboratory and scale-up tests.

For the quality model in Table 1, Quality Function Deployment and heuristics are typical rule-based models. Model-based methods include models for transport processes and experimental correlations. For example, the release of an active ingredient from controlled release pharmaceutical granules can be described by Fick’s law. Software such as COMSOL Multiphysics and gPROMS can be used to model these phenomena and thus product 6

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performance. There is a great deal of experiential information on desirable product qualities. For example, a shear-thinning hand cream is preferred because it does not run on standing and spreads nicely when it is rubbed on the skin. Some qualities such as smell and taste are hard to model and have to be determined by a test panel. With all of this information, it is still hard to

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develop a representative quality model, partly because there are too many interacting factors affecting the product quality, which complicates the development of a reliable model. In many cases, even the physicochemical phenomena cannot be accurately defined. For example, the

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tannins softening reactions in wine aging are poorly understood and the design of the appropriate

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air flowrate in a wine aerator faces a lot of uncertainty.

Consider now the pricing model. There are many rule-based pricing methods which include cost-based pricing, value-based pricing, among others. Pricing models for a single

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competitor and multiple competitors have been developed by Bagajewicz (2007) and Street et al. (2008), respectively. Commercial pricing optimization software such as Vendavo Price Manager

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is available. The price of a competing product is often not hard to find in the public domain although its sales volume and product costs are generally commercial secrets. The rest of Table 1

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is left to the reader to explore.

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Examples Two case studies are discussed below to highlight selected aspects of the model. One is a die attach adhesive, which highlights how the product formulation and profitability are affected by the market factors such as a change in material costs and an occurrence of an economic downturn. Another case study is a hand lotion, which illustrates how the desired product quality set by the consumers impacts the profitability. The case studies are organized as follows. First, the desired product qualities are identified and are related to the material properties and product structure by the quality model. Next, property model and process model are used to fix the ingredients, process flowsheet and equipment operating conditions. After that, the cost model estimates materials and processing cost, followed by the pricing model and economic model evaluate profitability aspects.

Example 1 – Die Attach Adhesive The key component of a light emitting diode (LED) lamp is the LED chip, which undergoes electroluminescence when an electric current passes through it. This LED chip is 7

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attached to a substrate such as alumina by a die attach adhesive (DAA). Despite its relatively high efficiency in converting energy to light, over 50% of the power to an LED is still dissipated as heat. This can result in a high junction temperature between the die and the substrate, which significantly shortens the lifetime of the LED chip. Therefore, fast heat removal from the chip is

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a top priority. A conventional DAA consists of metal microparticles embedded in a polymer matrix. A new product concept is to add metal nanoparticles into the matrix to connect the micron-sized

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particles. With an improved connectivity in the polymer matrix, the thermal conductivity of the

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DAA is expected to increase. An analysis of competing products in the market shows that they have a thermal conductivity of 25-40 W/m K.

The objective of this case study is to obtain a DAA with the desired thermal conductivity

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of 30 W/m K, while maximizing the net present value (NPV). Product attributes such as storage temperature, curing temperature, and curing time are not considered in this example. The models

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used in the GPD-Model are discussed next and the input data are given in Table 2.

Quality model

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Numerous models have been developed to estimate the thermal conductivity of a

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multiphase system (Wang and Pan, 2008). However, the applicability of these models is limited as they fail to capture the complex relationships among thermal conductivity, product structure and material properties. Simulations using COMSOL Multiphysics (www.comsol.com) to determine the thermal conductivity of DAA with different metal loadings and distribution of particles inside the composite are performed to obtain a correlation relating the thermal

conductivity of DAA (

conductivity (

p,

mp,

) in W/m K to the weight fraction (wp, wmp, wnp) and thermal

np)

of polymer, metal microparticles, and nanoparticles.

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(2) The total weight fraction of microparticles and nanoparticles has an upper bound of 0.9 in order to ensure that the DAA contains enough polymer to retain its mechanical integrity.

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(3)

Property model

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Either copper or silver microparticles and nanoparticles can be used in DAA, and the selection can be represented by the binary variables bmp,k and bnp,k for microparticles and

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nanoparticles, respectively.

(4) (5)

Metal particle thermal conductivity can be found in a database, and the thermal conductivity for

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(6)

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metal microparticles λmp and nanoparticles λnp are represented as follows.

(7)

Polymer can be selected from a list of candidates including sulfone-based polymers and ketone-based polymers. Since the polymer thermal conductivity is not readily available, a group contribution method proposed by Zhong et al. (2001) is used to estimate its value at room temperature (298 K).

(8)

Here, Cp is the heat capacity at constant pressure, V is the molar volume, v is the Poisson’s ratio, and UR is the molar Rao function. Cp, V, v, and UR are calculated at 298 K by the van Krevelen’s group contribution method (van Krevelen et al., 2009).

Process model The process flowsheet for DAA production involves mixing only. It is important to produce a composite with the nanoparticles dispersed evenly among the microparticles. Since no 9

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fundamental models are available to predict the relationship between the particle distribution inside the DAA and the mixing protocol, experiments are performed to determine the best mixing conditions (Liu et al., 2012, 2014).

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Cost model The manufacturing component of the product cost includes capital and operating costs. With the process flowsheet fixed in the process model, the capital investment for the range of

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production rate under consideration is estimated to be $1.5MM. The operating cost in year j (co,j)

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includes material and processing costs that depend on the product demand of that year (dj). The material costs only account for the metal microparticles and nanoparticles as they are much more expensive than the polymer, whereas the processing costs per unit demand (cm,pc) is fixed in this

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case study.

(9)

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Here, cmp and cnp are the unit costs of metal microparticles and nanoparticles, respectively.

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Pricing model

The pricing model proposed by Bagajewicz (2007) assuming a single competitor is used

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in this paper to relate product price (pj) and sales volume/demand in year j to those of the competition’s ( ,

).

(10) (11)

Here, Y is the total market size and ρ is an adjustable parameter related to elasticity. Note that the model parameters are first assumed during product development and should be replaced by market data after product launch.

αj is a parameter between 0 and 1 that measures how much the consumer knows about the new product and can be raised by increasing the marketing budget. It is related to the advertising budget (Advj) by Eqn (12), which exhibits a αj vs. Advj curve with a shape similar to a Langmuir isotherm and with a maximum value of unity. This is to simulate the market situation 10

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where increasing the advertising budget beyond a certain point only leads to a diminishing increase in consumer awareness. (12)

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β in Eqn. (10) is the consumer preference coefficient that relates the appeal of the competing product in comparison with the new product. The new product is preferred if β is

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smaller than 1. In this example, the consumers’ preference can be related to the relative thermal

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conductivity (key product attribute) between the competing ( ) and the new product (Eqn (13)). It can also be related to other product attributes such as storage temperature, and processing

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parameters such as adhesive viscosity. All these parameters are included in F through Eqn.(13). (13)

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Economic model

(14)

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As only thermal conductivity is considered, β is simplified to

Net present value (NPV) is used as the financial metric for evaluating the economic performance in this case study.

(15)

Here, PCFj is the project cash flow for year j, R is the discount rate, n is the number of years for product development, and m is the number of years for product life. PCFj is represented by the following equation with year j ≤ 0 representing the period for product development and year j > 0 representing the period when the product is on sale. (16) During product development, a fixed development cost (TDCj) and a fixed capital investment (TCIj) for building the plant are needed. In addition, a net working capital (∆NWCj) has to be provided in year 0 for company operations. Revenue starts to come in after the product sales 11

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begin at j=0. The income from operations (IFO) can be calculated by subtracting the product cost (the sum of co,j, Advj, and fixed cost (FCj)) from the net sales (pjdj). PCFj is then calculated by deducting tax from (tax rate = t) and adding depreciation (Dj) to IFO. Modified Accelerated Cost Recovery System (MACRS) is used to determine the depreciation. Note that the net

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working capital has to be added back to PCFj at the end of product life.

Model implementation

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The DAA product design was implemented using GAMS software (GAMS Development

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Corporation, 2011), and the flow diagram of the optimization model is shown in Figure 2. It starts by generating a list of polymer candidates using computer-aided molecular design (CAMD) technique (Satyanarayana et al., 2009). The thermal conductivity of the polymer is then predicted

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by Eqn. (8) if it is not in the database.

The library of polymer candidates and their properties are input information for the

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economic model. The objective function is to maximize NPV. As the quality model, pricing model and the objective function are non-linear, the problem is formulated as an MINLP optimization model and solved using the GAMS BARON solver (Sahinidis & Tawarmalani,

Results

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2005). The numerical details of this example are given in Table 3.

The results of the base-case optimization are given in Table 4. The maximum profit, in terms of NPV, is $80.1 MM. Figure 3 shows the dependence of product demand and NPV on product price. The optimal formulation contains 11.9 wt% polymer, 79.7 wt% copper microparticles, and 8.4 wt% copper nanoparticles, sold at a price of $1351/kg with a demand of 55.5 ton per year throughout the product life. Note that as the advertising costs and thus the consumer awareness (i.e., αj in the pricing model) and the competitor’s price are assumed constant throughout the product life in the base case, the product price and demand are constant as well. Different market scenarios are considered next. First, the impact of metal particle costs on the optimal product formulation is studied. Figure 4a shows the dependence of the optimal formulation on the price of copper microparticles. The price ratio of copper nanoparticles to copper microparticles is fixed at 2. As can be seen, the formulation does not change as the price of copper microparticles is gradually increased to 12

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$975/kg from its base-case value of $500/kg. With a further increase in copper microparticle price, silver nanoparticles are used in place of copper nanoparticles. This is depicted at the bottom of Figure 4a. With a higher thermal conductivity for silver, the total metal (polymer) loading is decreased (increased) to achieve the same target thermal conductivity. In addition, the

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amount of copper microparticles decreases in favor of extra silver nanoparticles. When the price of the copper microparticles is further increased to $1375/kg, silver microparticles with a price of $1500/kg replaces the copper microparticles. Figure 4b shows that an increase in copper particle

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price raises the product price while lowering the product demand and profitability (NPV).

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In another scenario, the company decides to reduce the advertising budget after product launch. The subsequent impact on product price, product demand, and market share is shown in Figure 5. With a decreasing advertising budget, the consumer awareness (α) of the new product

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will also decrease according to Eqn. (12). The product has to be set at a lower price to compete with the competitor’s product. The product demand increases, but the market share decreases

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with time. The NPV is $74.5 MM, 9.7% lower than the base case.

Finally, the effect of an economic downturn as reflected by a decrease in the market size Y on profitability is considered. Figure 6 shows the dependence of the NPV on the market size in

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years 3, 4 and 5. It is assumed that the market remains at the base-case value of $100 MM in

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years 1 and 2 and then changes to a lower size in years 3, 4 and 5. As can be seen, the NPV decreases from $80.1 MM in the base-case to $59.3 MM (a 25.9% decrease) if the market size contracts by 50%.

Example 2 – A Hand Lotion

A cosmetic company decides to produce a hand lotion for maintaining the skin in a moisturized condition. Based on market research, the consumers expect the lotion to feel smooth, and not greasy. It has to be easily applied to the skin. The product also needs to flow well when being poured from the bottle, but should not be runny. The GPD-Model is used to design the optimal product that meets the consumers’ expectations while providing maximum profit to the company. Similar to the first example, the objective function is to maximize NPV. All the models are discussed next and the input data are summarized in Table 5. The design heuristics and equations in the quality and process model are summarized from Wibowo and Ng (2001).

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Quality model The quality model relates the consumers’ expectations on product quality to the material properties and product structure by rule- or model-based methods. To provide a non-greasy feel, the hand lotion has to be formulated as an oil-in-water emulsion. The droplet size in the emulsion

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has to be smaller than 5 µm to provide a smooth feel. In order to have a lotion that can rub in quickly and not be runny, the product has to be shear thinning. The required emulsion viscosity

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should be around 0.035±0.005 Pa s at the application shear rate (1000 s-1) and around 20±2 Pa s to avoid appear runny when standing (shear rate = 0.01 s-1) (Wibowo and Ng, 2001). The

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emulsion viscosity µe can be related to the viscosity of the continuous phase µc and the dispersed

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phase µd, and the emulsion droplet size dp (Oldroyd, 1953; Pal 1995) as follows: (17) (18) (19) (20)

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Here, κ is the viscosity ratio, defined as the viscosity of the dispersed phase to that of the

continuous phase,

is the volume fraction of the dispersed phase, NCa is the capillary number,

is the shear rate, and σ is the surface tension.

Property model A hand lotion contains a number of components. The dispersed (oil) phase mainly contains solvent and emollient, whereas the continuous (water) phase contains solvent, humectant and thickener. Numerous chemicals can be selected for these ingredients, primarily based on heuristics. Mineral oil and isopropyl palmitate in equal proportion are selected to be the 14

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emollients. Here, mineral oil also acts as the solvent in the oil phase (Wibowo and Ng, 2001). Thus, the weight fractions of mineral oil (wd,1) and isopropyl palmitate (wd,2) in the dispersed phase equal to 0.5. The viscosity (µd) and the density (ρd) of the dispersed phase are then calculated by the components’ property (µd,i, ρd,i) and the corresponding weight fraction.

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(21)

cr

(22)

Glycerol, with a weight fraction (wc,2) of 0.05, is selected to be the humectant in the

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continuous phase, whereas carbomer acts as the thickener which controls the hand lotion viscosity. The carbomer weight fraction (wc,3) is fixed by the correlation provided by the supplier

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below to obtain the desired µc. Water, with a weight fraction of wc,1, serves as the solvent in the continuous phase. The viscosity of the continuous phase in Pa s is given as (Wibowo and Ng,

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2001):

(23)

(24)

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The density of the continuous phase (ρc) is calculated as follows:

An emulsifier is always needed to stabilize an emulsion. Glycerol monostearate with a weight fraction (we,1) of 0.8 and PEG-40 stearate with a weight fraction (we,2) of 0.2 are selected as the surfactants in the mixture.

Process model

The process flowsheet for the manufacture of hand lotion is depicted in Figure 7. Dispersed phase and continuous phase (with emulsifier) are separately mixed in pre-mixing tanks at room temperature, followed by heating to 75 °C. The two phases are then mixed in a preemulsification mixing unit to produce an emulsion with a relatively large droplet size, followed by homogenization to reduce the droplet size. After that, the emulsion mixture is cooled and filled in bottles. All process units except filling up the bottles are operated in batch mode. As no reaction or separation occurs in these process units, material balance (except filling) is expressed by the following general equation where the material flows (Fi) are conserved: 15

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(25) Several relations need to be set for Fi. First, the emulsifier weight fraction in the hand lotion is fixed at around 3% (Cheng et al., 2009) (Eqn. (26)). Second, the dispersed phase volume fraction is calculated by Eqn. (27). Third, the production rate of the hand lotion F7

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depends on the product sales/demand d (Eqn. (28)), which is calculated by the pricing model.

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cr

(26)

(27)

(28)

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Here, Fc, Fd, and Fe are the amounts of continuous phase, dispersed phase, and emulsifier in the feed, respectively; Nb is the number of batches per day; Wb is the weight of hand lotion per bottle.

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The plant is assumed to operate 300 days a year.

The pre-emulsification mixing unit and the homogenization unit are the key equipment units. An equipment database based on power consumption and capacity is used for equipment

d

selection. Agitated vessels are used for the pre-mixing units (PM1, PM2). Agitated vessel is also

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selected for pre-emulsification (M1) as it requires lower energy density as well, whereas colloid mill is selected for homogenization (CM).

The agitated vessel and the colloid mill have to provide sufficient energy to break up the emulsion droplets and keep them apart. The power density (ε) for having a droplet size of dp,M1 in the agitated vessel has been modelled by Wibowo and Ng (2001), which can be calculated from Eqn. (29).

(29)

Here, Γ is the excess surface concentration, and ms is the surfactant concentration which is assumed to be equal to the critical micelle concentration. The viscosity of dispersed (µd,75) and continuous phase (µc,75) have to be calculated at the operating temperature (75 °C), and are

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related to that at room temperature by the Arrhenius equation. The critical Weber number

is

given as a function of the viscosity ratio (Bentley and Leal, 1986).

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(30) The average power density (εav) is related to the rotational speed NM1 and the impeller diameter

cr

Dimp (Zhou and Kresta, 1998):

(31)

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where Np is the power number. Various charts show the dependence of Np on Reynold’s number NRe for impellers of different geometries (Walas, 1988). The following correlation is used in the

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process model:

(32)

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d

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Using similar charts in Walas (1988), the required blending time can be determined as follows:

(33)

Here, Ntb is the dimensionless blending time and is related to the blending time (tM1) and the vessel geometry as follows:

(34)

where DT is the tank diameter and Dimp/DT is assumed to be 0.8. Similar to the agitated vessel for pre-emulsification mixing, the required shear rate

for

obtaining the desired emulsion droplet size in the colloid mill is given by Eqn. (35), whereas the minimum droplet size that can be achieved is given by Eqn. (36). (35) (36)

17

Page 17 of 49

The shear rate in the colloid mill is related to its rotational speed NCM, rotor radius Rr, and gap width b as follows (Wieringa et al., 1996). (37)

ip t

Cost model

The manufacturing component of the product cost includes capital and operating cost.

cr

The total capital investment in year 0 (TCI0) that accounts for the installation, piping, instrumentation, etc., of the plant equipment, is expressed as a multiple of the total purchased

us

equipment cost (PCT). PCT includes equipment items such as agitated vessels and homogenizer,

an

and is marked up to account for other small equipment and auxiliary items.

(38) (39)

M

Here, PCPM1, PCPM2, PCM1, and PCCM are the purchased equipment cost for premixing tank 1, premixing tank 2, pre-emulsification agitated vessel, and colloid mill, respectively. The equipment costs are obtained from the following cost correlations derived from cost charts

Ac ce pt e

d

(Peters and Timmerhaus, 2003; Harrison et al., 2015). (40) (41)

Here, PCIj is the plant cost index for year j, Vi is the volume of equipment item i which can be related to the amount per batch and material density, and tCM is the operating time for the homogenization unit.

The operating cost includes materials cost cMC and processing cost cPC. (42)

The materials cost is determined by the amount of each component in each batch and their unit cost: (43)

18

Page 18 of 49

Here, cd,i, cc,i and ce,i are the cost of component i in the dispersed phase, continuous phase and emulsifier mixture, respectively. The processing cost only accounts for the electricity cost. Costs for cooling water and waste treatment, etc. are ignored. The power consumption P for the pre-mixing tanks (PM1, PM2)

ip t

and the pre-emulsification mixing unit (M1) is calculated as follows. (44)

cr

The impeller diameter is fixed by assuming Dimp/DT equals 0.8, with the tank diameter DT calculated by the batch volume and assuming tank diameter equals its height.

us

The energy requirements in heaters H1 and H2 (EH1, EH2) for heating up the ingredients to the operating temperature of the pre-emulsification unit (TM1, i.e. 75 °C) are calculated as

(45) (46)

M

an

follows.

Here, PH1 (tH1) and PH2 (tH2) are the power consumption (time) required for heating in H1 and H2, respectively, Ti,H1 and Ti,H2 are the initial temperature of the ingredients, Cp,d and Cp,c are the heat

d

capacity of the dispersed phase and the continuous phase, respectively, and are assumed to be the

Ac ce pt e

same as the heat capacity of the solvent used in the respective phases. Thus, the processing cost cPC can be calculated as (47)

Here, ce is the electricity unit cost. The required mixing time in the pre-mixing units (tPM1, tPM2) is fixed at 5 min based on experience. Note that tM1 has been determined in the process model. For colloid mill, there is no available correlation to determine its power consumption and the time required. The power consumption (PCM) is fixed at 50 kW and 5 min is used to reduce the droplet size from 200 µm to 5 µm.

Pricing model The pricing model given by Eqns. (10) and (11) is again used. However, the price and demand of the new and competitor’s product are assumed to remain constant throughout the product life. The consumer preference coefficient β compares the product attributes of our and 19

Page 19 of 49

competing product and is determined in Eqn. (48) by assuming that the consumers consider the three product qualities: emulsion droplet size, emulsion viscosity at low (µe,l) and high (µe,h) shear rate are of equal importance.

ip t

(48) Here, the superscript c represents the quality of the competitor’s product. If the two product qualities are the same, β equals 1 and the consumers have no preference, in terms of quality, over

cr

the two products. The new product is preferred if β is smaller than 1. For the emulsion viscosity

us

at low shear rate (µe,l), the higher the better to prevent the hand lotion be runny, so the product quality for the competitor is placed in the numerator and the new product quality is placed in the denominator so that β is smaller than 1 if the new product is better than the competing product.

M

Economic model

an

The opposite happens to µe,h and dp (i.e. the smaller the better).

Model implementation

d

The economic model given by Eqns. (15) and (16) is again used here.

Ac ce pt e

The hand lotion case study is formulated as an NLP optimization problem which can be directly solved using the GAMS IPOPT solver (Wächter and Biegler, 2006). Because of the model complexity, a relaxed version of the original problem was first solved to obtain the initial values of all variables in the full optimization problem (Figure 8). The relaxed version contains all equations except the equations for determining the equipment operating conditions in the process model, as they are highly non-linear and are mainly used to calculate the processing cost in the cost model. Binary variables are needed for the implementation of the logical constraints Eqn. (29) and Eqn. (32). But, the equations under different situations are tested separately to obtain the feasible solution so that binary variables are not required, which reduces the computation complexity. The numerical details of this example are given in Table 6.

Results

20

Page 20 of 49

The optimization results for the base case are given in Table 7. The product quality in terms of emulsion droplet size and viscosity at different shear rates meets the product specifications. 0.30 wt% of carbomer is added to the continuous phase to provide the required emulsion viscosity. The pre-emulsification unit operating at 133 rpm for 302 s provides a droplet

ip t

size of 175 µm. This is followed by a colloid mill operating at 24.5 rpm to further reduce the droplet size to 5 µm. The optimal product has an NPV of $5.73 MM, and annual sales of 1.312

cr

million bottles at $5.94 per bottle. The price of the competitor’s product is set at $6 per bottle, which leads to annual sales of 1.701 million bottles.

us

Assume that the consumers consider the base-case hand lotion is not smooth enough, the technical team decides to further reduce the droplet size to 3 µm. The emulsion droplet size does

an

not affect the optimal product formulation. As the cream is smoother than the competitor’s cream, the new product has a smaller consumer preference coefficient (1.01) than the original value (1.14) as calculated by Eqn. (48). This results in a small increase in sales (1.314 million bottles)

M

despite the price ($5.97 per bottle) has to be slightly increased to cover a higher utility cost. The final profit (NPV) is increased to $5.83 MM.

Assume that the emulsion seems to be still too runny at low shear rate and the emulsion

d

viscosity is increased to 30 Pa s at low shear rate. This requires an increase in carbomer weight

Ac ce pt e

fraction to 0.35 wt%. However, this also increases the emulsion viscosity at high shear rate to 0.035 Pa s. The change in emulsion viscosity at low and high shear rate both affect the consumer preference coefficient which is reduced from 1.14 in the base case to 1.08 in this scenario, as calculated by Eqn. (48). This leads to a slightly higher NPV ($5.77 MM), and annual sales of 1.312 million bottles at a slightly higher price ($5.96 per bottle) to cover the increase in material cost.

A sensitivity analysis of the material costs and the pricing model parameters shows that ρ, a parameter related to elasticity, in the pricing model has a large impact on NPV, as shown in Figure 9 for product price and NPV for different ρ. With an increase in ρ, the optimal product price is reduced and the NPV becomes negative when ρ > 0.49.

Conclusions

21

Page 21 of 49

Product design is more challenging than process design. In addition to having an optimal process from a technical and cost perspective, selection of appropriate ingredients, product structure, consumer preferences, pricing, and other societal-organizational-economic factors such as sustainability and government regulations need to be considered. The GPD-Model presented

ip t

in this paper considers all these issues using rule-based and model-based methods, tools, databases, and experiments.

Two case studies highlight a few aspects of the GPD-Model. The DAA example shows

cr

how market parameters such as raw material cost and market size affect the company’s profit,

us

whereas the hand lotion example shows how the change in product quality affects the NPV. Many other facets of the GPD-Model such as product macrostructure and microstructure, company strategy, and government policies have yet to be explored. It is expected that the use of

an

multiobjective optimization can help balance out the many sometimes conflicting demands in

M

product design. Research work along these directions is now underway.

Acknowledgement

Ac ce pt e

attach adhesive case study.

d

We thank Faheem Mushtaq for his assistance on formulating the quality model for the die

Notation

Parameters Advj b ce

cc,i, cd,i, ce,i

Advertising cost in year j

Colloid mill gap width Electricity cost per unit

Cost of component i in the continuous phase, dispersed phase, and emulsifier mixture, respectively.

cmp, cnp

Cost of microparticle and nanoparticle, respectively

cm,pc

Processing cost per unit demand

Cp

Heat capacity at constant pressure for the group contribution method

Cp,c, Cp,d

Heat capacity of the continuous phase and the dispersed phase, respectively 22

Page 22 of 49

Emulsion droplet size of the new product and the competitor’s product,

dp,

respectively Depreciation in year j (Example 1)

F

Other factors in consumer preference coefficient

FCj

Fixed cost in year j

m

Number of years for product life

ms

Surfactant concentration

n

Number of years for product development

Nb

Number of batches per day

NPM1, NPM2

Rotational speed in the pre-mixing units PM1 and PM2, respectively

us

cr

ip t

Dj

an

Competitor’s price Power consumption in colloid mill

PCIj

Plant cost index for year j

R

Discount rate

Rr

Colloid mill rotor radius

t

Tax rate

tPM1, tPM2

Mixing time in the pre-mixing units PM1 and PM2, respectively

Ac ce pt e

d

M

PCM

Ti,H1, Ti,H2

Initial temperature of ingredients entering H1 and H2, respectively

TM1

Operating temperature of the pre-emulsification unit

TCIj TDCj UR v V Wb

Total capital investment in year j (Example 1)

Total development cost in year j Molar Rao function for the group contribution method

Poisson’s ratio for the group contribution method Molar volume for the group contribution method Weight of hand lotion per bottle

wc,2

Weight fraction of glycerol in the continuous phase

wd,i, we,i

Weight fraction of component i in the dispersed phase and emulsifier mixture, respectively

Y

Total market size

αj

Consumer awareness parameter in year j 23

Page 23 of 49

β

Consumer preference coefficient (Example 1) Shear rate

∆NWCj

Net working capital in year j

cr

ip t

Dispersed phase volume fraction

λ, λc

us

Thermal conductivity of the new product and the competitor’s product, respectively

Thermal conductivity of microparticle and nanoparticle of material k (Ag or Cu), respectively

an

λmp,k, λnp,k

Dispersed phase viscosity

µd,i

Viscosity of component i in the dispersed phase

M

µd

,

Emulsion viscosity at low and high shear rate, respectively, for the

d

competitor’s product

σ ρd, ρe

Ac ce pt e

ρ

Surface tension

ρc,i, ρd,i, ρe,i

Parameter related to elasticity in the pricing model

Density of dispersed phase and emulsifier mixture, respectively Density of component i in the continuous phase, dispersed phase, and emulsifier mixture, respectively

Γ

Excess surface concentration

Variables

bmp,k, bnp,k

Binary variable for selecting material k (Ag or Cu) for microparticle and nanoparticle, respectively

cMC, cPC

Material cost and processing cost, respectively (Example 2)

co,j

Operating cost in year j

dj

Product demand in year j

24

Page 24 of 49

Competitor’s demand in year j Emulsion droplet size after pre-emulsification

Dimp

Impeller diameter

Dj

Depreciation in year j (Example 2)

DT

Tank diameter

EH1, EH2

Energy requirements in heating H1 and H2

Fc, Fd, Fe

Feed amount of the continuous phase, dispersed phase, and the emulsifier

cr

mixture, respectively

ip t

dp,M1

Amount of material adds to a process unit

NCa

Capillary number

NCM

Colloid mill rotational speed

NM1

Rotational speed of the pre-emulsification unit

NP, NRe

Power number and Reynolds number, respectively

Ntb

Dimensionless blending time

NPV

Net present value

M

an

us

Fi

Product price in year j

Ac ce pt e

pj

d

Critical Weber number

PPM1, PPM2, PM1

Power consumption of pre-mixing unit 1 PM1, pre-mixing unit 2 PM2, pre-emulsification unit M1, respectively

PCFj PCT

Project cash flow in year j Purchased equipment cost

PCPM1, PCPM2, PCM1, Purchased equipment cost for premixing tank 1 (PM1), premixing tank 2 PCCM

PM2), pre-emulsification agitated vessel (M1), and colloid mill (CM), respectively

TCIj

Total capital investment in year j (Example 2)

tCM

Milling time for homogenizer

tM1

Blending time

wc,1, wc,3

Weight fraction of water and carbomer in the continuous phase, respectively

25

Page 25 of 49

Weight fraction of microparticle, nanoparticle, and polymer, respectively

Vi

Volume of equipment i

β

Consumer preference coefficient (Example 2)

ε

Power density at the impeller tip of the agitated vessel

εav

Average power density

κ, κ75

Viscosity ratio at room temperature and 75°C, respectively

λ1, λ2

Parameters for the quality model

λmp, λnp, λp

Thermal conductivity of microparticle, nanoparticle, and polymer

cr

us

respectively

ip t

wmp, wnp, wp

Continuous phase viscosity at room temperature and 75°C, respectively

µe, µe,75

Emulsion viscosity at room temperature and 75°C, respectively

ρc

Density of the continuous phase

M

an

µc, µc,75

References

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d

AIChE Journal 2007;53:3155-70.

Ac ce pt e

Bagajewicz M, Hill S, Robben A, Lopez H, Sanders M, Sposato E, Baade C, Manora S, Hey Coradin J. Product design in price ‐ competitive markets: A case study of a skin moisturizing lotion. AIChE Journal 2011;57(1):160-177. Bernardo FP, Saraiva PM. A conceptual model for chemical product design. AIChE Journal 2015;61:802-15.

Bentley BJ, Leal LG. An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows. J Fluid Mech. 1986;167:241-83. Bröckel U, Meier W, Wagner G. (editors). Product Design and Engineering: Basics and Best Practices (2 Volume Set). Weinheim, Germany: Wiley-VCH; 2007. Bröckel U, Meier W, Wagner G. (editors). Product Design and Engineering: Formulation of Gels and Pastes. Weinheim, Germany: Wiley-VCH; 2013. Cheng YS, Lam KW, Ng KM, Ko RKM, Wibowo C. An integrative approach to product development-a skin-care cream. Computers and Chemical Engineering 2009;33:1097-113.

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Cheng YS, Fung KY, Ng KM, Wibowo C. Economic analysis in product design – A case study of a TCM dietary supplement. Chinese Journal of Chemical Engineering 2016;24:202-214. Conte E, Gani R, Ng KM. Design of formulated products: a systematic methodology. AIChE

ip t

Journal 2011;57:2431-49. Conte E, Gani R, Cheng YS, Ng KM. Design of formulated products: experimental component. AIChE Journal 2012;58:173-89.

cr

Cussler EL, Wei J. Chemical product engineering. AIChE Journal 2003;49:1072-5.

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Cussler EL, Moggridge GD. Chemical Product Design. 2nd ed. Cambridge, U.K.: Cambridge University Press; 2011.

Fung KY, Ng KM. Product-centered processing: pharmaceutical tablets and capsules. AIChE

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Journal 2003;49:1193-215.

Fung KY, Nakajima S, Wibowo C, Ng KM. A systematic iterative procedure for determining

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granulator operating parameters. AIChE Journal 2006;52:3189-202. Fung H, Wibowo C, Ng KM. Product-centered process synthesis and development: detergents. Ng KM, Gani R, Dam-Johansen K (eds). Chemical Product Design: Toward a

d

Perspective through Case Studies. 2007: 239-273.

Ac ce pt e

GAMS Development Corporation. General Algebraic Modeling System (GAMS) Release 23.7.3. Washington, DC, USA, 2011

Gani R. Computer-aided methods and tools for chemical product design. Chemical Engineering Research and Design 2004a;28:1494-504. Gani R. Chemical product design: challenges and opportunities. Computers and Chemical Engineering 2004b;28:2441-57.

Gani R, Ng KM. Product design – molecules, devices, functional products, and formulated products. Computers and Chemical Engineering 2015;81:70-9. Harrison RG, Todd PW, Rudge SR, Petrides DP. Bioprocess design and economics. Bioseparations Science and Engineering. New YorK: Oxford University Press; 2015. Hill M. Product and process design for structured products. AIChE Journal 2004;50:1656-61. Korichi M, Gerbaud V, Floquet P, Meniai AH, Nacef S, Joulia X. Computer aided aroma design I – Molecular knowledge framework. Chemical Engineering and Processing: Process Intensification 2008;47(11):1902-1911. 27

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Liu, C., D. Lu, X. Lang, B. Wang, and Z. Li, “High Performance Die Attach Adhesives (DAAs) Nanomaterials for High Brightness LED,” WO Patent Application No. 2012126391 A9, 2012; U.S. Patent Application No. 2014/0001414 A1. Liu, C., D. Lu, X. Lang, A. Choi, and P. W. M. Lee, “Effect of Surface Treatments on the

ip t

Performance of High Thermal Conductive Die Attach Adhesives (DAAs),” 14th International Conference on Electronic Materials and Packaging, 1 (2012).

Martín M, Martínez A. A methodology for simultaneous process and product design in the

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formulated consumer products industry: The case study of the detergent business.

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Chemical Engineering Research and Design 2013;91(5):795-809.

Mattei M, Kontogeorgis GM, Gani R. A comprehensive framework for surfactant selection and design for emulsion based chemical product design. Fluid Phase Equilibria

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Ng KM, Gani R, Dam-Johansen K. (editors). Chemical Product Design: Toward a

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Perspective through Case Studies. Computer Aided Chemical Engineering, 23; 2007. Oldroyd JG. The elastic and viscous properties of emulsions and suspensions. Proc. Roy. Soc. A. 1953;218:122-32.

d

Pal R. Oscillatory, creep and steady flow behavior of xanthan-thickened oil-in-water

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emulsions. AIChE J. 1995;41:783-94.

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Sahinidis NV, Tawarmalani M. BARON 7.2.5: Global optimization of mixed-integer nonlinear programs. GAMS User’s manual. 2005. Satyanarayana KC, Abildskov J, Gani R. Computer-aided polymer design using group contribution

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van Krevelen DW, te Nijenhuis, K. Properties of Polymers - Their Correlation with Chemical Structure; Their Numerical Estimation and Prediction From Additive Group Contributions 4th ed. Boston: Elsevier; 2009. Walas SM. Chemical Process Equipment: Selection and Design. Boston: Butterworths; 1988.

ip t

Wang M, Pan N. Predictions of effective physical properties of complex multiphase materials. Materials Science and Engineering R. 2008;63:1-30.

Wieringa JA, van Dieren F, Janssen JJM, Agterof WGM. Droplet breakup mechanisms

cr

during emulsification in colloid mills at high dispersed phase volume fraction. Chem.

us

Eng. Res. Des. 1996;74:554-66.

Wei J. Product Engineering: Molecular Structure and Properties. New York: Oxford University Press; 2007.

an

Wesselingh JA, Kiil S, Vigild ME. Design & Development of Biological, Chemical, Food and Pharmaceutical Products. Chichester, U.K: Wiley; 2007.

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Whitnack C, Heller A, Frow MT, Kerr S, Bagajewicz MJ. Financial risk management in the design of products under uncertainty. Computers and Chemical Engineering 2009;33:1056-66.

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29

Page 29 of 49

Active ingredients Supporting ingredients (solvents, additives)

ip t

Process design, pd Operating conditions, pdop Process flowsheet, pd

Ingredients, x

fs

Temperature Pressure Agitation speed

us

Process model, s Ts(x, pd)

Product structure, s

Physical properties Chemical properties Biological properties

Particle size distribution Phase volume fraction Particle shape Macro form

M

an

Material properties, p

Product use conditions, u

Environment and method of application

Quality model, q Tq (p, s, u)

Cost model, cm Tcm(x, pd)

d

Pricing model, Pprms Tprms(q; Y)

Ac ce pt e

Product price, pr, market share, ms

Product quality, q

Product cost, cm

Nonmanufacturing costs, cnm Legal Marketing

cr

Property model, p Tp(x)

Unit operations Equipment geometry Materials of construction

e

Economic model, Te (cm, cnm, Pprms)

Economic analysis, e

Other factors, of Company strategy Societal needs Sustainability Government regulations

Multiobjective model, Max [e, of] Product for commercialization

Figure 1. The Grand Product Design Model.

30

Page 30 of 49

CAMD Compounds database

Candidate product library generation (N candidates)

Group contribution Property database

us

i=1

cr

Property model

ip t

Start

Quality model Cost model Pricing model Optimization solver

Economic model

i=i+1

an

i≤N

Y

N

End

d

M

Objective value evaluation

Ac ce pt e

Figure 2. Flow diagram for the implementation of the optimization model for example 1.

31

Page 31 of 49

200

ip t

250

us

cr

Product demand (ton/year)

an

150

M

100

NPV (MM$)

Ac ce pt e

d

50 0

-50

0

2000 4000 Product price ($/kg)

6000

Figure 3. Product demand and NPV at different product prices.

32

Page 32 of 49

0.9

ip t

0.3

an

Polymer

0.1

0.7

Weight fraction

cr

Microparticles

us

0.2

M

Weight fraction

0.8

0.6

Ac ce pt e

d

Nanoparticles

0

MP 500 NP 1000 MP NP

750 1500

1000 2000

1250 2500

0.5 1500 3000

Price ($/kg) Copper Ag Copper Silver Selected material (a)

33

Page 33 of 49

90

2100

NPV (MM$)

cr

70

us

60

an

50

1900 1700

M

40 30

Product demand (ton/year)

1500

d

Ac ce pt e

20 10

MP 500 NP 1000

2300

ip t

Product price ($/kg)

80

750 1500

1000 2000

1250 2500

1300 1500 3000

Price ($/kg) (b)

Figure 4. Effect of copper particle price on (a) product formulation (b) NPV, product demand and product price.

34

Page 34 of 49

2

ip t

80 Market share (%)

cr

1.5

us

70

60

M

1

an

Product price (1000$/kg)

Product demand (ton/year)

Ac ce pt e

d

0.5

50

Adv. Cost (MM$)

0

1

2

3 Year

40 4

5

Figure 5. Impact of advertising cost on product demand, product price, and market share.

35

Page 35 of 49

ip t

90

cr us

70

an

NPV (MM$)

80

M

60

60 70 80 90 Market size, Y (MM$)

100

Ac ce pt e

50

d

50

Figure 6. Project NPV for different market sizes in years 3, 4 and 5.

36

Page 36 of 49

Dispersed phase Fd

Pre-mixing PM1

F1

Heating H1

F3

Preemulsification mixing M1

F5

Homogenization CM

ip t

F6

Emulsifier Fe

cr

Heating H2

F4

us

F2

F7 Filling

an

Pre-mixing PM2 Fc Continuous phase

Cooling

Ac ce pt e

d

M

Figure 7. Process flowsheet for the manufacture of hand lotion.

37

Page 37 of 49

Property model

Pricing model

Mass balance equations in process model

Economic model

Quality model

Cost model

Property model

Pricing model

cr

Cost model

Process model

Economic model

us

Quality model

ip t

START

Optimal results

an

Initial values

END

Ac ce pt e

d

M

Figure 8. Solution of the optimization problem for example 2

38

Page 38 of 49

7

ip t

6

cr

5

us

NPV (MM$)

an

4

0

Ac ce pt e

1

Product price $/bottle

0.1 -1

d

2

M

3

0.2

0.3

0.4

0.5

ρ in pricing model

Figure 9. NPV and product price for different ρ values in the pricing model.

39

Page 39 of 49

40

Page 40 of 49

d

Ac ce pt e us

an

M

cr

ip t

cr us

Process model • Heuristics for flowsheet development

• Six tenths rule for scaling capital cost

ce

Cost model

• Cost-based pricing • Value-based pricing • Financial metrics

Ac

Pricing model

Economic model

• UNIQUAC • UNIFAC

ed

Quality model

• Kopp’s rule for the specific heat of a solid compound • Quality Function Deployment

pt

Property model

Model-based methods • Mass and energy balance • Fluid mechanics

M

Rule-based methods

an

Table 1. Elements used in the Grand Product Design Model

Tools • • • • • •

• Mechanistic models •

• Cost correlations

• Microeconomic models • Financial models

• • • • •

• •

Aspen Plus HYSYS GAMS MATLAB ICAS Commercial process simulators COMSOL Multiphysics gPROMS ICAS-MoT Aspen Capital Cost Estimator ICAS-ECON Pricing optimization software Excel Software for capital planning and budgeting, and multi-objective optimization

Databases • Equipment database

• Chemical database

Experiments • Laboratory experiments • Scale-up experiments • Measurement of properties

• Information on • Panel tests for harddesirable properties to-quantify qualities such as smell and taste • Chemical and • NA utility cost database • Price database on • NA competitor products • Modified Accelerated Cost Recovery System

• NA

41 Page 41 of 49

cr us an M ed pt ce Ac

42 Page 42 of 49

Table 2. Input data for base case in example 1 30 W/m K

ip t

$500 /kg $1000 /kg $1500 /kg $2000 /kg $0.016 MM/kg $100 MM 0.6 0.7 1 5 0.2 0.4 $0.5 MM for j≥1 $1 MM for j = -1 $0 for j ≠ -1 $1.5 MM for j = 0 $0 for j ≠ 0 $1 MM j = 0,5 $0 j ≠ 0, 5 $0.5 MM for j≥1

M

an

us

cr

Product quality Thermal conductivity of the composite, λ Product pricing and economics Price of copper microparticles, cmp,Cu Price of copper nanoparticles, cnp,Cu Price of silver microparticles, cmp,Ag Price of silver nanoparticles, cnp,Ag Processing cost per unit demand, cm,pc Total market size, Y Consumer awareness parameter in pricing model for year 1 (j = 1), α1 Pricing model parameter, ρ Number of years for product development, n Number of years for product life, m Discount rate, R Tax rate, t Advertising cost, Advj Fixed development cost, TDCj Fixed capital investment, TCIj

d

Net working capital, ∆NWCj

Price,

Ac ce pt e

Fixed cost, FCj Competitor’s product Thermal conductivity of the composite,

25 W/m K $3000 / kg

43

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Table 3. Numerical details of example 1 39 51 7 37

Ac ce pt e

d

M

an

us

cr

ip t

Number of constraints Number of real variables Number of discrete variables Number of iterations

44

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Table 4. Base case results for example 1

O ¤ O

Material

Cu

O

an

79.7

Cu

8.4 $80.1 MM $1351 / kg for j≥1 55.5 ton/year for j≥1 8.36 ton/year for j≥1

Ac ce pt e

d

Product demand, dj Competitor’s demand,

11.9

M

Weight fraction (wt %) Product pricing and economics Net present value, NPV Product price, pj

us

¤

cr

Microparticles

30 W/m K Nanoparticles

ip t

Product quality Thermal conductivity of the composite, λ Polymer Product formulation

45

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Table 5. Input table for base case in example 2 Product quality and product parameters Emulsion viscosity at low shear rate (0.01 s-1), µe,l Emulsion viscosity at high shear rate (1000 s-1), µe,h Emulsion droplet size, dp

ip t

0.035±0.005 Pa s 20±2 Pa s 5 µm 0.15

cr

Dispersed phase volume fraction,

Ac ce pt e

d

M

an

us

Interfacial tension, σ Component property and price Weight fraction Viscosity (Pa s) Density (kg/m3) Symbol Value Symbol Value Symbol Value Dispersed phase Mineral oil wd,1 0.5 0.012 800 µd,1 ρd,1 wd,2 0.5 0.0075 854 Isopropyl µd,2 ρd,2 palmitate Continuous phase Water 1000 ρc,1 wc,2 0.05 1261 Glycerol ρc,2 Carbomer 1200 ρc,3 Emulsifier we,1 0.8 970 Glyceryl ρe,1 monosteartae PEG-40 stearate we,2 0.2 900 ρe,2 Process design and equipment operating conditions Number of batches produced per day, Nb Weight per bottle, Wb Excess surface concentration, Γ Surfactant concentration, ms Activation energy for calculating µc at higher temperature Activation energy for calculating µd at higher temperature Ratio between impeller diameter and tank diameter, Dimp/DT Blending time of pre-mixing tank 1 and 2, tPM1, tPM2 Rotational speed of pre-mixing tank 1 and 2, NPM1, NPM2 Initial temperature in heating unit 1 and 2, Ti,H1, Ti,H2 Heat capacity of continuous phase, Cp,c Heat capacity of dispersed phase, Cp,d Operating temperature of pre-emulsification unit M1, TM1

0.02 N/m

Cost ($/kg) Symbol Value cd,1 cd,2

5 5

cc,1 cc,2 cc,3

0.0005 1.05 15

ce,1

1.25

ce,2

2

10 batch/day 0.5 kg/bottle 1×10-6 kg/m2 30 kg/m3 15800 J/mol 17200 J/mol 0.8 5 min 50 rpm 25 °C 4190 J/kg K 1670 J/kg K 75 °C 46

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Power consumption of colloid mill, PCM Product pricing and economics Total market size, Y Consumer awareness parameter in pricing model, αj Pricing model parameter, ρ Number of years for product development, n Number of years for product life, m Discount rate, R Tax rate, t Advertising cost, Advj Fixed development cost, TDCj

d

ip t

Emulsion viscosity at low shear rate (0.01 s-1) of competitor’s product,

Ac ce pt e

Emulsion viscosity at high shear rate (1000 s-1) of competitor’s product, Price,

$18 MM 0.1 for j≥1 0.1 1 5 0.2 0.4 $3 MM for j≥1 $2 MM for j = -1 $0 for j ≠ -1 $2 MM j = 0,5 $0 j ≠ 0, 5 $2 MM for j≥1 0.12 $/kWh 389.5 395.6 576.1

cr

an

M

Fixed cost, FCj Electricity cost per unit, ce Plant cost index in 1998, PCI1998 Plant cost index in 2002, PCI2002 Plant cost index in 2014, PCI2014 Competitor’s product Emulsion droplet size of competitor’s product,

us

Net working capital, ∆NWCj

50 kW

5 µm 20 Pa s 0.022 Pa s $6/bottle for j≥1

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Table 6. Numerical details of example 2

ip t

88 92 0 710

Ac ce pt e

d

M

an

us

cr

Number of constraints Number of real variables Number of discrete variables Number of iterations

48

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Table 7. Base case optimization results for example 2 Product quality Emulsion droplet size, dp

ip t 0.0343 Pa s

cr

0.30 wt%

Ac ce pt e

d

M

an

us

Emulsion viscosity at low shear rate, µe,l Emulsion viscosity at high shear rate, µe,h Product formulation Mass fraction of carbomer (thickener) in the continuous phase, wc,3 Equipment dimensions and operating conditions (major units) Pre-emulsification unit (agitated vessel) Droplet size after pre-emulsification, dp,M1 Tank diameter, DT Rotational speed, NM1 Blending time, tM1 Homogenization unit (colloid mill) Rotational speed, NCM Product pricing and economics Net present value, NPV Consumer preference coefficient in the pricing model, β Product price, p Product demand, d Competitor’s demand, dc

5 µm 22 Pa s

175 µm 0.65 m 133 rpm 302 s

24.5 rpm $5.73 MM 1.14 $5.94 / bottle 1.312 million bottles / year 1.701 million bottles / year

49

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