This chapter introduces novel methodologies for characterizing phase equilibrium and estimating physical properties crucial to polyolefin manufacturing. It presents an in-depth discussion on the polymer nonrandom two-liquid (POLYNRTL) activity coefficient model (ACM), and the polymer Sanchez-Lacombe (POLYSL) and the polymer perturbed-chain statistical fluid theory (POLYPCSF) equations of state (EOS). These innovative approaches offer specific guidelines for selecting the appropriate polymer ACM or EOS tailored to specific polyolefin processes. A significant highlight is the detailed coverage of the POLYNRTL ACM, including a practical workshop for estimating POLYNRTL binary interaction parameters using the UNIFAC method. The chapter also explores the prediction of polymer physical properties through the Van Krevelen group contribution method, providing a hands-on workshop for estimating the physical properties of copolymers. Additionally, it introduces advanced techniques for parameter estimation using data regression tools, applied to both the POLYSL and POLYPCSF EOS models. Furthermore, the chapter addresses the correlation of critical polyolefin product quality indices, such as melt flow rate or melt index and polymer density, providing insights that enhance the understanding and optimization of polyolefin manufacturing processes. This is a preprint version of a chapter from our book - Integrated Process Modeling, Advanced Control and Data Analytics for Optimizing Polyolefin Manufacturing. Please cite the original work if referenced [52,56] 2.1 Property Methods and Thermophysical Parameter Requirements for Process Simulation We present specific guidelines for the selection of an appropriate polymer ACM or EOS for modeling a specific polyolefin process [1,2]. This chapter begins by discussing the property methods and parameter requirements in simulating a polymer process (Section 2.1). We then present the polymer activity coefficient model (ACM), particularly the polymer non-random two-liquid (POLYNRTL) ACM in Section 2.2 and cover a workshop for estimating POLYNRTL binary interaction parameters using UNIFAC in Section 2.3. We discuss the prediction of polymer physical properties using the Van Krevelen group contribution method in Section 2.4. and follow by a workshop to estimate physical properties of a copolymer in Section 2.5. In Section 2.6, we introduce the polymer Sanchez-Lacombe (POLYSL) equation of state (EOS). Section 2.7 presents a workshop to estimate property parameters using data regression tool. Section 2.8 introduces the polymer perturbed-chain statistical fluid they (POLYPCSF) EOS, and Section 2.9 presents a workshop for regression of property parameters for POLYPCSF EOS. In Section 2.10, we conclude this chapter by discussing the correlation of polyolefin product quality indices, such as melt flow rate or melt index and polymer density. Section 2.11 presents the bibliography. Aspen Plus refers to a property method as a collection of models and methods for calculating phase equilibria and various physical properties , such as density, enthalpy, viscosity, thermal conductivity, etc. We will discuss two major categories of property methods, namely, the activity coefficient models (ACM) and equations of state (EOS), in the following sections, and provide guidelines on how to choose an appropriate property method for a specific polyolefin process. Table 2.1 summarizes the key process modeling tasks and the essential thermophysical properties required for completing the tasks. The reader may search the information within Aspen Plus: Help -> Property requirements -> Property requirements for mass and energy balance simulations. Table 2.1 Process modeling tasks and essential thermophysical property requirements We discuss below the two key types of property methods for characterizing the phase equilibrium and estimating physical properties in polyolefin processes: activity coefficient model (ACM), and equation of state (EOS). 2.2 Polymer Activity Coefficient Models (ACM): Polymer Non-Random Two-Liquid (POLYNRTL) Model In Chapter 6, we present the modeling of manufacturing processes for polystyrene (PS) using free radical polymerization, and for poly(styrene-butadiene-styrene) rubber or SBS rubber using ionic polymerization. For both processes, we must account for vapor-liquid equilibrium with a high degree of nonideality in the presence of polar components (such as water) at low to medium pressure (< 10 bar), that is away from the critical region [1,2]. In the discussion below, we follow the explanation in [3 to 5]. 2.2.1 Vapor-Liquid Equilibrium for an Ideal Vapor Phase and a Nonideal Liquid Phase Figure 2.1 shows a vapor-liquid mixture. We assume that the vapor phase is ideal. The partial pressure of component i in the vapor phase, Pi, is equal to: (2.1) In the equation, xi is the liquid mole fraction of component i, 𝛾௜(𝑥௜,T) is the activity coefficient of component i as a function of liquid composition xi and temperature T, 𝑃௜௦௔௧(𝑇) is the vapor pressure of pure component i, yi is the vapor mole fraction of component i, and P is the pressure. Process modelin g task Essential thermophysical property requirements Mass balance Density or standard liquid volume, phase equilibrium Energy balance heat capacity, heat of formation, heat of reaction, heat of vaporization, liquid vapor pressure Heat transfer Density, heat capacity, thermal conductivity, viscosity Pressure drop Density, viscosity Figure 2.1 A vapor-liquid mixture. For ideal solutions, the partial pressure Pi is equal to xi 𝑃௜௦௔௧(𝑇) according to Raoult’s law [1]. For nonideal solutions, we correct this term by multiplying it with an activity coefficient, 𝛾௜(𝑥௜,T). For an ideal vapor phase, the partial pressure Pi is equal to yi P according to Dalton’s law [1]. 2.2.2 General Vapor-Liquid Equilibrium Relationships Based on Fugacity Coefficient and Liquid-Phase Activity Coefficient Based on Walas [1], we generalize Eq. (2.1) to define the vapor-liquid equilibrium using a gas-phase fugacity coefficient and a liquid-phase activity coefficient: 𝑥௜ϒ௜𝑓௜௢௅= 𝑦௜𝜙௜௏𝑃 = 𝑃௜ (2.2) In the equation, 𝑓௜௢௅ is the liquid-phase reference fugacity, defined as the fugacity of a pure liquid at the temperature T and pressure P of the mixture , and ϕ௜௏ is the partial gas-phase fugacity coefficient of component i computed from an equation of state. 2.2.3 Segment-Based Mole Fraction versus Species-Based Mole Fraction This section follows the discussion in [3]. There are two types of molecular accounting systems that we use to model physical properties and phase equilibrium in polymer-containing systems. Species-based calculations consider polymer chains as single molecules, while segment-based accounting considers every polymer repeat unit (“segment”) as an individual molecule. The segment-based approach can characterize polymer molecules by chemical properties of segments or monomer units that comprise the polymers. This makes it easier to evaluate the effect of polymer composition on thermodynamic properties. The segment-based approach can also consider the chain length, which is important in the modeling of phase equilibrium and physical properties. Figure 2.2 illustrates a segment-based representation of polymer chains in a mixture, which permits the consideration of the interaction between each segment type and solvent molecules. Figure 2.2 A segment-based representation of polymer chains in a mixture. We note that the mole fraction of polymer chains is often of little physical significance. Let us consider a mixture of 1 g high-density polyethylene (HDPE) of a molecular weight 50,000, dissolved in 10 g of n- hexane of molecular weight 86.18. We find the mole fraction of polymer as: xpolymer = (moles polymer)/(moles solvent + moles polymer) = (1/50,000)/[1/86.18 + 1/50,000] = 1.72E-4 Now let us consider the ethylene segment (-C2H4-) of a molecular weight of 28.05. A HDPE polymer of a molecular weight of 50,000 corresponds to a degree of polymerization of 50,000/28.05, or 1534.9 segments. We treat each solvent molecule as a single segment. The segment-based mole fraction of polymer is then: Xpolymer = (moles polymer segments)/(moles solvent + moles polymer segments) =[ (1/50,000) x1534.9]/ [10/28.05 + (1/50,000) x 1534.9] = 7.93E-2 This segment-based mole fraction is more representative of the amount of polymer in the mixture than the species-based mole fraction of polymer. In general, we can convert the species-based mole fraction x to a segment-based mole fraction X according to the relationship [5]: (2.3) where subscript I refers to polymer segments, subscript i refers to a polymer molecule, and ri, I is the number of segment type I in polymer molecule i. 2.2.4 POLYNRTL: Polymer Nonrandom Two-Liquid Activity Coefficient Model In the POLYNRTL model of Chen [4], the Gibbs free energy of mixing of a polymer solution is the sum of (1) the enthalpy of mixing, based on the nonrandom two-liquid (NRTL) theory [5], and (2) the entropy of mixing, based on the Flory-Huggins (F-H) theory [6 to 8]. The model calculates the activity coefficient as a sum of two contributions: (2.4) where ϒ i is the activity coefficient of species i, superscript s NRTL and F-H represents the NRTL and Flory-Huggins contributions, respectively. We note that POLYNRTL and many other activity coefficient models ignore a third term in Eq. (2.3), representing the free-volume (FV) or compressibility contribution. Oishi and Prausnitz [9] proposed a UNIFAC-FV model to include the FV contribution. Interested readers may search “UNIFAC free volume model” in Aspen Plus online help to learn more detail about the model, but we do not use the model in this text. The NRTL activity coefficient contribution is different for polymers (subscript i =p) and for solvents (subscript i =s). The relevant expressions are as follows. (2.5) (2.6) In the equations, XK is the segment-based mole fraction defined by Eq. (2.3). The parameter GIJ relates the overall segment-based mole fractions to the local segment-based mole fractions. It is related to the binary interaction parameter τij and the nonrandomness factor αij through the following relationship: Gij = exp(-αij τij) (2.7) αij has a value between 0.2 to 0.3, and its value has no significant impact on the behavior of the model [5]. The binary interaction parameter τij is related to the energy of interaction between species i and j, gij , and the energy of interaction between a pair of j species, gjj , according to: τij = (gij - gjj)/RT (2.8) This definition suggests that τii is zero. Aspen Plus databanks provide temperature-dependent relationships for both the binary interaction parameters τij and the nonrandomness factor αij : τij = aij + bij /T + eij lnT + fij T (2.9) αij = cij + dij (T -273.15 ) (2.10) The Flory-Huggins contribution in Eq. (2.4) is as follows: (2.11) For a solvent, φ i = Xi, which is the segment-based mole fraction of the solvent; for a polymer, φ i =Xi , summed over all the segments. mi is the characteristic size of species i. It is related to the degree of polymerization by: (2.12) where si and εi are empirical parameters with default values for both being 1.0 for small molecules. P i is the degree of polymerization of species i. Table 2.2 summarizes the POLYNRTL model parameters. In using the POLYNRTL model within Aspen Plus/Polymers, we only need to enter parameters NRTL/1 to NRTL/8; Aspen Polymers sets the remaining model parameters to their default values. Table 2.2 POLYNRTL model parameters Parameter Name/Element Symbol Default Unit Keyword Comments NRTL/1 aij and aji 0 --- Binary, Asymmetric NRTL/2 bij and bji 0 TEMP Binary, Asymmetric NRTL/3 cij 0.3 --- Binary, Symmetric NRTL/4 dij 0 1/TEMP Binary, Symmetric NRTL/5 eij and eji 0 Binary, Asymmetric NRTL/6 fij and fji 0 1/TEMP Binary, Asymmetric NRTL/7 Tmin 0 TEMP Unary NRTL/8 Tmax 1000 TEMP Unary FHSIZE/1 si 1.0 --- Unary FHSIZE/2 εi 1.0 --- Unary POLDP Pi 1.0 --- Unary 2.2.5 Concept of Henry Components for Vapor-Liquid Equilibrium for a Vapor Phase and a Nonideal Liquid Phase Involving Supercritical Components A serious weakness of activity coefficient models is that they are not accurate in predicting the solubilities of supercritical components in the liquid phase. Those components refer to light gases and low molecular-weight hydrocarbons, such as H2, O2, N2, CO, CO2, H2S, NO2, SO2, CH4, C2H4, C2H6, C3H6, C3H8, etc. Refer to Eq. (2.1) for the vapor-liquid equilibrium relationship between an ideal vapor phase and a nonideal liquid phase: (2.1) For a vapor phase and a nonideal liquid phase involving supercritical components, we modify Eq. (2.1) as: 𝑥௜ϒ௜∗𝐻௜= 𝜑௜௩𝑦௜𝑃 = 𝑃௜ (2.13) In the equation , ϒ௜∗= ϒ௜/ ϒஶ, and ϒஶ is the infinite-dilution activity coefficient. 𝐻௜ is the Henry’s law constant, and 𝜑௜௩ is the vapor-phase fugacity coefficient calculated by an equation of state (EOS). For an ideal vapor phase, we choose the ideal gas law as the EOS; for a nonideal gas (such as a gas phase up to medium pressures), we use the Redlich-Kwong-Soave (RKS) EOS, which is a cubic EOS where the product of the pressure P and the third power (cubic) of the volume of the mixture, 𝑉௠ଷ , is related to the ideal gas law constant R multiplied by the temperature T of the mixture. Interested reader may search “Redlich-Kwong-Soave” on Aspen Plus online help for details of the RKS EOS. The Henry’s law constant 𝐻௜ is typically correlated as a function of temperature. For a supercritical component i and a solvent A, Aspen Plus uses the following correlation: ln( Hi,A) = ai,A + bi,A /T + ci,A lnT + di,AT + ei,A/𝑇ଶ T L< T < T H (2.14) Table 2.3 summarizes the Henry’s law parameters. Table 2.3 Henry’s law parameters Parameter Name/Element Symbol Default Unit Henry/1 ai,A 0 --- Henry/2 bi,A 0 TEMP Henry/3 ci,A 0 TEMP Henry/4 di,A 0 TEMP Henry/5 TL 0 TEMP Henry/6 TH 2000 TEMP Henry/7 ei,A 0 TEMP We demonstrate below how to implement the concept of Henry components and compare the resulting concentrations of light gases in the solvent with and without applying Henry’s law. Consider a simple two-phase flash problem shown in Figure 2.3 and defined in Table 2.4. We save the simulation file as Example 2.1 NRTL Flash with Henry Component.bkp Figure 2.3 A simple flash unit for Example 2.1 Table 2.4 Specifications of Example 2.1 Components Water,H2, N2 Property method NRTL Henry’s components H2, N2 Feed 70°C, 1 bar, Water (1000 kg/hr), H2(50 kg/hr), N2 (50 kg/hr) Flash drum 70°C, 1 bar Figure 2.4 illustrates how to specify Henry components: Properties -> Components ->Henry comps -> New: HC-1 -> Move H2 and N2 from “Available Components” to “Selected Component”. Figure 2.4 Specification of Henry’s components, HC-1. After defining the Henry components, we can see Henry’s law parameters for both H2 and N2 by following the path: Properties -> Methods -> Parameters -> Binary Interaction -> HENRY-1 (see Figure 2.5). Refer to Eq. (2.13) and Table 2.3 for Henry parameters. Figure 2.5 Henry’s law parameter values for H2-N2-water mixture. Next, we enter the feed stream and flash conditions in Table 2.4. Subsequently, an inexperienced Aspen Plus user may follow the habit of clicking on the “Next” button and seeing a message of “required input complete” and proceed to run the simulation (see Figure 2.6). Figure 2.6 Clicking on the “Next” button, seeing the required input complete and clicking “OK” to run the simulation. This results in the mass fractions of H2 and N2 in the LIQUID product being 4.98053E-6 and 5.25986E-5, or 4.98 and 52.5 ppm, respectively. See Figure 2.7. As we show shortly, despite having defined H2 and N2 as Henry components, these mass fractions actually result from the NRTL property method without incorporating the Henry’s law. Figure 2.7 Computed mass fractions of H2 and N2 in the LIQUID product without incorporating Henry’s law into the NRTL property method To incorporate Henry’s law into the calculation of the NRTL property method, we must tell Aspen Plus to do so following the path: Property -> Methods -> Specification -> Henry components -> HC-1 defined in Figure 2.3. We illustrate this step in Figure 2.8. Figure 2.8 Including Henry components HC-1 into the NRTL property method. Running the simulation again, we see in Figure 2.9 the resulting the mass fractions of H2 and N2 in the LIQUID product being 9.47979E-7 and 6.16813E-7, or 0.948 and 0.617 ppm, respectively (compared to the incorrect values of 4.98 and 52.5 ppm in Figure 2.7). The significant difference demonstrates the importance of correctly including Henry components into the NRTL property method. This observation applies to the POLYNRTL property method as well. Figure 2.9 Computed mass fractions of H2 and N2 in the LIQUID product after incorporating Henry’s law into the NRTL property method. To summarize, the POLYNRTL method is applicable to polyolefin processes involving a highly nonideal liquid phase (with polar and hydrogen-bonding species) up to medium pressures of approximately 10 bar. It must be used with Henry’s law when the mixture contains light gases and low molecular-weight hydrocarbons. Two typical processes are polystyrene (PS) using free radical polymerization, and poly(styrene-butadiene-styrene) rubber or SBS rubber using ionic polymerization discussed in Chapter 6. For non-polyolefin systems, we apply the POLYNRTL method to Nylon, PET (polyethylene terephthalate), and PLA (polylactic acid), etc. for step-growth polymerization processes [3]. 2.3 Workshop 2.1 Estimating POLYNRTL Binary Parameters Using UNIFAC 2.3.1 Objective: The UNIFAC (UNIQUAC Functional-group Activity Coefficients) method [10,11] is a semi-empirical system for the prediction of non-electrolyte activity in non-ideal mixtures. Over the years, there have been numerous articles and books extending the method to more complex vapor-liquid mixtures. The UNIFAC method attempts to break down the problem of predicting interactions between molecules by describing molecular interactions based upon functional groups, such as functional groups 1005 (>CH-), 1100 (>CH2), 1015 (-CH3), and 2400 (CH2SH), attached to the molecule. A search of Aspen Plus online help for “UNIFAC Functional Groups” will give Tables 3.12 to 3.21 of the functional groups available within Aspen Plus. This workshop demonstrates how to use UNIFAC to estimate POLYNTRL binary parameters. 2.3.2 Estimating POLYNRTL Binary Parameters Using UNIFAC for Polystyrene Manufacturing Figure 2.10 shows some of the components involved in polystyrene manufacturing, where Sty and STY- SEG are styrene (monomer) and STY-SEG are styrene segment (repeat unit), and EB (ethyl benzene) and DDM (n-dodecyl mercaptain) are chain-transfer agents. We save the simulation file as WS2.1 Estimating POLYNRTL Binary Parameters Using UNIFAC.bkp . Figure 2.10 Component specifications for WS 2.1. If a component is present in the Aspen Enterprise Database for pure components and segments, we will see its structure being displayed within the “Molecular Structure” folder, as illustrated in Figure 2.11 for DDM (C12H26S). Additionally, Aspen Plus will automatically complete a representation of the displayed structure as a combination of UNIFAC functional groups, that is, C12H26S = H3C-(CH2) 10-CH2SH = 1*(Group 1015, H3C) +10*(Group 1100, CH2) +1*(Group 2400, CH2SH). In fact, Aspen Plus will do this for all specified components that are present in the Aspen Enterprise Database, which will enable the use of UNIFAC group-contribution method to estimate the binary parameters. We see a “Draw/Import/Edit” button in Figure 2.11. In Section 4.4.3, we will show how to import a molecular structure file, *.mol, from the Internet (such as Chemical Book, www.chemcalbook.com ) for a component not available within Aspen Enterprise Database. In Section 6.1.4, we also demonstrate how to use the drawing tools within Aspen Plus to draw a molecular structure. Figure 2.11 Showing a graphical structure of DDM (n-dodecyl-mercaptan) available in the Aspen Enterprise Database. Next, we follow the path: Properties -> Estimation -> Input -> (1) Estimation Option -> Estimate only the selected parameters; (2) Parameter type -> Binary interaction parameters (see Figure 2.12). Figure 2.12 Specification to estimate binary interaction parameters. In Figure 2.13, we click on the “New” button, and then choose parameter, “NRTL” and method “UNIFAC”. We can specify component i (STYRENE) and component j (STY-SEG) and other i-j component combination one by one. However, this is not necessary; by choosing “ALL” for both components i and j, Aspen Plus will estimate the interaction parameters for all binary component combinations for us. Figure 2.13 Specification of binary interaction parameters to be estimated We then run the property estimation. Figure 2.14 shows the estimated binary interaction parameters, according to Eqs. (2.9) and (2.10) and Table 2.2. We save the simulation file as WS 2.1 Estimating Binary Parameters from UNIFAC.bkp . Figure 2.14 Estimated binary interaction parameters. Additionally, by following the path, Properties -> Methods ->Parameters -> Binary Interaction -> NRTL-1, we also see the estimated parameters being entered as the result (R) of the Physical Constant Estimation System (PCES), that is, R-PCES. See Figure 2.15. Figure 2.15 Entering the estimated binary interaction parameters to the “parameters” form. 2.4 Prediction of Polymer Physical Properties by Van Krevelen Functional Group Method As we discussed vapor-liquid equilibrium according to Eq. (2.12), the POLYNRTL property method uses the POLYNRTL activity coefficient model for the liquid phase and applies the RKS (Redlich-Kwong-Soave) [12] cubic equation of state for the vapor phase. For property calculations, the POLYNRTL property method uses Van Krevelen functional group method to predict physical properties of polymers. The Van Krevelen method is based on the chemical structure of the polymers [13]. Table 2.5 summarizes the key concepts of applying the Van Krevelen method. A search of the online help of Aspen Plus for “Thermophysical Properties of Polymers” will show the large number of polymer properties that we can estimate by the Van Krevelen method. Table 2.5 Applying the Van Krevelen method to estimate properties of a system containing polymers by going from functional groups to segments and then to polymer mixture 1. -CH2- Functional group (Van Krevelen; VK) Estimate segment properties using properties of the functional groups making up the segment(s), e.g., heat capacity 𝐶௣, 𝐶௣=∑𝑛௞௞𝐶௣,௞ k refers to k-th functional group; 𝑛௞ is the number of the k-th functional group. When retrieving the segments from the SEGMENT databank, there is no need to supply functional groups. Otherwise, define the segments based on the VK functional groups. 2. –CH2-CH2- Segment (ethylene) Calculate polymer properties from segment properties, number-average degree of polymerization, and segment composition. 3. …. –Ch2-CH2-CH2-CH2-…. Polymer (polyethylene) Find the mixture properties of the whole component system (polymer, monomer, solvents, etc.). Let us illustrate the concept of the Van Krevelen method by considering the molar volume of a polymeric component, which depends on the temperature and the physical state of the polymer. Figure 2.16 shows a plot of the molar volume versus temperature of a polymer at different physical states. In the figure, V l refers to the molar volume of a polymer liquid, V c indicates the molar volume of a crystalline polymer, and V g represents the molar volume of an amorphous glassy polymer. X c represents the mass fraction of a crystalline polymer. T g and T m are, respectively, the glass transition temperature and the melting transition temperature. These volume and temperature concepts are well explained in most introductory polymer textbooks [e.g., 14]. Figure 2.16 Molar volume versus temperature for different physical states of a polymer. The basic idea of a group contribution method for estimating physical properties of polymers is to calculate the sum of contributions of the constituents (the structural and functional groups) as an approximation. Consider, for example, finding the molar density of a propylene repeat segment illustrated in Figure 2.17. Figure 2.17 A propylene repeat segment C3H6-R. The molecular weight of this structural unit is 42.08 g/mol. From Table 4.5 in Van Krevelen and Nijenhuis [13], we know the Van der Waals volume (V w) contribution of Van Krevelen functional group 100, -CH2-, at 25°C is 16.1 cm3/mol, and that of group 101, -CH(CH3)-, is 33.2 cm3/mol. The additive sum of both volume contributions is 49.3 cm3/mol. Therefore, the molar density of a propylene repeat segment at 25°C is: [42.08 g/mol]/[49.3 cm3/mol], or 0.85 g/cm3. This value is in perfect agreement with the experimental value [13]. We note, however, that not every property prediction by the Van Krevelen method matches perfectly with experimental data. When we cannot neglect the interactions between functional and structural groups, the Van Krevelen method includes correction terms for the interactions. The resulting models are called group interaction models [13]. Interested readers can find additional details about the Van Krevelen method for estimating physical properties by searching Aspen Plus online help for “Van Krevelen group contribution methods”. 2.5 Workshop 2.2 Estimating Physical Properties of a Copolymer Using the Van Krevelen Group Contribution Method 2.5.1 Objective: This workshop demonstrates the procedure of applying the Van Krevelen group contribution method to estimate physical properties of a copolymer. These properties include, for example, CP (heat capacity), K (thermal conductivity), MU(viscosity), RHO (density), TG (glass transition temperature) an TM (melting transition temperature). We use styrene-butadiene rubber (SBR) that we shall discuss in more detail in Chapter 6 as our copolymer, and assume the copolymer with a number-average degree of polymerization (DPN) of 2000. We study the flash operation of a SB copolymer consisting of 50% by mole styrene and 50% by mole butadiene at 250° and 1.01325 bar. We assume the mass flow rates of the styrene, butadiene and SB copolymer are identical, each at 10 kg/hr. We show how to apply the Van Krevelen method according to the following steps: (1) drawing the process flowsheet; (2) specify the unit set and global options; (3) define components, segments and polymer, and characterize their structures; (4) choose property method and enter or estimate property parameters; (5) define streams and blocks; (6) create property sets; (7) define property analysis runs to create property tables; and (8) run the simulation, examining the results and make property plots. 2.5.2 Draw the Process Flowsheet, and Specify the Unit Set and Global Options Our simple flash unit is the same as in Figure 2.3. We choose the unit set METCBAR in Setup in both Properties and Simulation, as demonstrated previously in Figure 1.7. For global options, we follow the path: Simulation -> Setup -> Global settings -> Flow basis: choose “Mass” (see Figure 1.6). 2.5.3 Define Components, Segments and Polymer, and Characterize Their Structures Figure 2.18 shows our component specifications. We note two points: (1) We purposely do not specify the component name and alias (chemical formula) of the styrene segment, STY-SEG, as we want to demonstrate how to use Van Krevelen functional groups to specify this segment; and (2) We specify the styrene-butadiene copolymer with a number-average degree of polymerization, DPN, defined in Eqs. (1.5) and (1.11), of 2000, as a “generic polymer component” with an alias “polymer”. Figure 2.18 Component specifications To characterize the polymer component, we follow the path: Properties -> Components -> Polymer -> Segments -> Segment definition: Choose “Repeat” unit for both STY-SEG and BUT-SEG. Figure 2.19 shows our selection of the built-in polymer attributes for “Properties Selection” for our SB copolymer. See Figure 1.19. We have previously explained all the selected attributes in Sections 1.3.2 and 1.3.3. Figure 2.19 Choosing the built-in “Properties selection” attribute group. Next, we check the path: Properties ->Components -> Molecular structure -> Structural and functional groups, and note that segment BUT-SEG, and pure components BUTADIEN and STYRENE are available within Aspen Plus segment and component databanks, and we see their structures being displayed. We do not need the structure of the generic polymer component, SB copolymer, but we need to specify the structure of the segment STY-SEG, as shown in Figure 2.20. Figure 2.20 Structure of STY-SEGA A search of Aspen Plus online help on “Van Krevelen Functional Group Parameters” shows that we can represent STY-SEG as a sum of three Van Krevelen (VK) functional groups: (1) VK group 100, -CH2-; (2) VK group 131, >CH-; and (3) VK group 146, benzyl group. We specify these groups according to Figure 2.21. Figure 2.21 Specifications of Van Krevelen functional groups for STY-SEG 2.5.4 Choosing Property Method and Entering or Estimating Property Parameters We choose the POLYNRTL property method for the current problem, as in our detailed styrene- butadiene rubber (SBR) workshop in Chapter 6. Following exactly Workshop 2.1, Section 2.6, we estimate all missing binary interaction parameters. Figure 2.22 shows the estimated binary parameters. Figure 2.22 Estimated binary interaction parameters 2.5.5 Specifications of Feed Stream and Flash Block Figure 2.23 shows the specification of feed stream. Under component attributes, we need to specify the SFRAC, SFLOW and DPN for SB copolymer. Figure 2.23 Specification of feed stream with component attributes SFRAC, SFLOW and DPN for the generic polymer component, SB copolymer. For the flash unit, we enter a temperature of 250°C and a pressure of 1.01325 bar. 2.5.6 Creating Property Sets A property set is a collection of thermodynamic, transport, and other properties that we can use in stream reports, physical property tables and analysis, heating and cooling curves of unit operation models (e.g., exchanger, condenser, and reboiler), distillation column stage property reports, reactor temperature profiles, etc. We create a property set to display the property values that we find from a physical property analysis. We define a property set in either the Properties or Simulation environment, and the resulting property set will appear in both environments. We follow the path: Properties -> Property sets -> New; name- PS- 1 -> Properties and Qualifiers (see Figures 2.24 and 2.25). Note the pull-down menu of physical properties and the corresponding units for the user to choose. We include CP (heat capacity), K (thermal conductivity), MU(viscosity), RHO (density), TG (glass transition temperature) an TM (melting transition temperature) in the property set. Figure 2.24 Including physical properties in the property set PS-1 Figure 2.25 Qualifiers for selected properties in the property set. To ensure that the stream report from our flash unit includes values of the specified properties in the property set PS-1, we follow the path: Simulation -> Setup -> Report Options -> Streams -> Click on “Property Sets” button -> Property Sets: Move PS-1 from Available property sets to Selected property sets -> Close. See Figure 2.26. Figure 2.26 Including specified property set PS-1 in the stream report 2.5.7 Defining Property Analysis Run to Create Property Tables We can use property analysis tool to generate tables and plots of physical properties of pure components and mixtures as a function of temperature, pressure, and composition. We should emphasize that both property analysis and regression tools in Aspen Plus do not support polymer attributes. Therefore, for property analysis and regression runs, we should define a polymer as an oligomer. By doing so, we eliminate the need to enter any attribute information. We should specify its number of repeat units or segments, and segment composition (following the path: Components -> Polymers -> Characterization -> Oligomers ->Oligomer Structure -> Fill in the number of repeat units), and degree of polymerization. Alternatively, as in the current example, we specify the SB copolymer as a generic polymer component with an alias “polymer”, and specify its attributes, particularly segment composition by SFRAC and its degree of polymerization (see Figure 2.18 and 2.23). We create an analysis of stream properties by following the path: Process flowsheet -> Right-click the name of FEED steam -> Choose “Analysis” on the pull-down menu -> Choose analysis type, “Stream Properties”. See Figures 2.27 and 2.28. We then click on the “Run Analysis” button on Figure 2.28 to do stream property analysis. When the analysis is completed, we click on the “Results” button displayed in Figure 2.28 and follow the same approach as in Figures 1.22and 1.23 to make a “custom” plot of properties (CP, K, MU and RHO) versus temperature. Figures 2.29 and 2.30 illustrate the resulting plots of thermal conductivity and mass density versus temperature. The tabulated analysis results also show the glass transition temperature and the melt transition temperature of the SB copolymer are 45.3472°C and 225.23°C, respectively. This concludes the current workshop. We save the simulation file as WS 2.2 Estimating Physical Properties of a Copolymer Using VK Group Contribution Method.bkp. Figure 2.27 Initiating an analysis of stream properties for FEED stream Figure 2.28 Specification of stream property analysis (SPROP-1) Figure 2.29. Thermal conductivity (K) of styrene, butadiene, and SB copolymer versus temperature. Figure 2.30 Mass density (RHO) of styrene, butadiene, and SB copolymer versus temperature. 2.6 Polymer Sanchez-Lacombe Equation of State (POLYSL) To simulate polyolefin processes at high pressures, activity coefficient models, such as POLYNRTL, suffer from some weaknesses, as most of them are applicable only to incompressible liquid solutions. Additionally, activity coefficient models fail to predict correctly the phase behavior of polymer solutions at the lower critical solution temperature (LCST) below which the components of a mixture are miscible for all compositions. Activity coefficient models also fail to predict an upper bound to a temperature interval of partial miscibility, called the upper critical solution temperature (UCST). By contrast, an equation of state (EOS) can accurately represent the relationship among temperature, pressure, volume (or density) and composition of a vapor-liquid, or vapor-liquid-liquid mixture over the entire fluid region. EOS models can evaluate the physical properties of any fluid phase, liquid and/or vapor at medium to high pressures, as long as the fluid mixture does not contain any polar components .