Incorporating uncertainty in chemical process design for environmental risk assessment

Incorporating Uncertainty in Chemical Process Design for Environmental Risk Assessment Victor R. Vasquez and Wallace B. Whiting Chemical Engineering Department, University of Nevada, Reno, NV 89557; [email protected] (for correspondence) Published online 29 November 2004 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ep.10050

The effects of uncertainty in thermophysical properties on the evaluation of the environmental performance is demonstrated with a chemical process to recover toluene and ethyl acetate by absorption from a gaseous waste stream of a cellophane production plant. In this case study, the environmental performance is defined as the estimation of the volatile organic compounds (VOCs) and total emissions of the plant and of several environmental risk indexes. We found that estimations of VOCs are very sensitive to uncertainty in thermophysical properties such as infinite-dilution activity coefficients, and vapor pressures (through uncertain temperature variations). Additionally, we concluded that calculation of the total emissions can be very sensitive to fuel content factors such as those used to estimate greenhouse gases. This can have such an impact on the emission calculations that a detailed model of the given chemical process might not be required for the estimation of the total emissions. In other words, a simpler process flowsheet model can perform the same task just as well, with the results within the variations caused by uncertainty in the thermophysical properties. We demonstrate a Monte Carlo approach that allows the detection of such uncertainty characteristics in a design, providing a rational basis for prediction of the associated environmental risks. This procedure also enables the deconvolution of various sources of uncertainty, and the estimation of physical property uncertainty through a similarity approach. We concluded that our framework can be used to enhance decision making by uncovering uncertainties and sensitivities in chemical process simulation. © 2004 American Institute of Chemical Engineers Environ Prog, 23: 315–328, 2004 © 2004 American Institute of Chemical Engineers

Environmental Progress (Vol.23, No.4)

Keywords: uncertainty analysis, Monte Carlo methods, risk assessment, environmental risk indexes, infinite dilution activity coefficients, UNIQUAC, UNIFAC, environmental emissions 1. INTRODUCTION

Environmental performance analysis of chemical processes is very important in developing new chemical technologies that can compete in an economy where green engineered processes and products represent a competitive advantage [1]. Similarly, there is an increasing effort by regulatory agencies to promote and enforce regulations and laws for better protection of the environment. The efforts of the scientific and engineering communities toward the design of processes and products that are environmentally friendly are substantial [2–7]. Among the many aspects considered in the design of these processes is the modeling of the environmental performance of existing technologies or processes in the developing phase. Environmental performance analysis consists basically of emission and environmental risk indexes estimations. Reasonable estimation of emissions and other environmental performance indicators for a given technology is very important in the design and simulation of chemical processes, but most important, it plays a fundamental role in decision making when monitoring working processes or in establishing the future of a new technology. Robustness analysis of these calculations is necessary to establish the level of confidence during decision making. Substantial work is being performed at this level [8 –10], including analysis of variables such as potential changes in regulations, local environmental conditions, and the fate and transport of pollutants into the environment among many others [11]. When it comes to the operational analysis of the technology, chemical process simulators are popular December 2004

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tools for this task. Basic uncertainty aspects of the operation are usually considered such as changes in flows or specifications [3, 5, 7], but the effects of uncertainty in thermophysical properties, to the best of our knowledge, have not been analyzed even for simple case studies. We found that the effects of uncertainty in infinite-dilution activity coefficients and vapor pressures can play a significant role in the environmental performance of a chemical process designed to recover the volatile organic compounds (VOCs) (toluene and ethyl acetate) by absorption in n-C14 from a gaseous waste stream generated at a cellophane production plant [6]. This suggests that further work is necessary in this area to enhance the robustness of evaluation procedures used in environmental evaluation of chemical processes. In this work, we discuss in detail the procedures and results that lead to the findings mentioned above using a case study given by Shonnard and Hiew [6]. First, we discuss briefly the main ideas behind emission estimation in chemical processes, pointing out the relative importance of the different sources (see Section 2), then we describe the thermodynamic model used (see Section 3) followed by a description of the Monte Carlo approach used to analyze the effects of uncertainty in the thermodynamic equilibrium properties (see Section 4). Section 5 introduces the methodology for the environmental assessment of the absorption technology case study. Section 6 describes the case study used to illustrate the points and conclusions of this work. In this section, the results are discussed in detail. Finally, a section of concluding remarks is presented with the main conclusions and comments for future work in the area. 2. EMISSION ESTIMATION IN CHEMICAL PROCESSES

To assess environmental risk, emissions estimations are required to calculate the concentration of different molecules and their mixtures in the environment. Usually, emissions are calculated at the source and then fate and transport models are used to study their behavior in the environment. Government agencies, private organizations, and research institutions are responsible for creating and maintaining the different regulations involving the fate of chemicals in the environment. They are also involved with the definition of methodologies to estimate emissions at the source for different unit operations in chemical processes [12–14]. Emissions of chemical processes are commonly classified as primary and secondary depending on the nature of the source. Primary emissions correspond to those that are a direct consequence of the production process such as vents on specific unit operations and fugitive emissions in equipment. Secondary emissions are usually those caused by construction or operation of stationary processes, but the emissions are not a direct product of the process itself [15]. In this work, we are concerned with primary emissions resulting from the operation of the process and with secondary emissions from utility sources. For the former, the most important contributions come from vents and fugitive emissions in major equipment such as columns and tanks. Vent emissions can be estimated 316

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using a chemical process simulator to model the process. For instance, in an absorption process whatever amount that is not absorbed is usually vented or sent to another unit operation. The amounts will strongly depend on the thermodynamic equilibrium of the system. Fugitive emissions are usually estimated using emission factors for equipment such as reactors, columns, dryers, and cooling towers among others. In general, the emissions are calculated using a simple equation of the form E ⫽ EF av ⫻ m ⫻ x VOC

(1)

where E is the emission estimate, EFav is the average emission factor for that particular process or equipment, m is the mass flow rate through the unit, and xVOC is the mass fraction of the volatile organic compound of interest. Average emission factors can be found in different sources [12–14, 16, 17]. Secondary emissions from utility services are an important source of pollution, mainly attributed to combustion processes. The estimation of these emissions are performed using equations of the form E⫽

ED ⫻ EF FV ⫻ EE

(2)

where ED is the energy demand of the process unit, EF is the emission factor of the fuel, FV is the fuel value or energy available in the fuel per unit volume or per unit mass, and EE is an equipment efficiency factor (for example, for boilers it usually ranges between 0.75 and 0.90 [1]). As for the case of fugitive emissions, the emission factors are found in different literature sources (for a starting reference see Allen and Shonnard [1]). It is not the purpose of this section to describe thoroughly emissions estimation methods for chemical processes, but briefly classify them and define the ones of interest in this work. We will show later that uncertainty in the computational approaches used for emissions estimation can significantly affect the predictions and can shadow the effect of other emissions (in terms of amounts estimated). 3. THERMODYNAMIC MODEL

As mentioned earlier, a goal of this project is to show the potential effect that uncertainty in thermophysical properties estimation might have on the evaluation of environmental performance of chemical processes. We use one thermodynamic activity coefficient model for this purpose, the Universal Quasi-Chemical (UNIQUAC) [18], although there are other models that are of interest to study such as the Non-Random Two-Liquid (NRTL) [19]. The details of these models are found elsewhere [18, 19]. We use thermodynamic models to calculate the equilibrium of the VOCs absorbing in a defined solvent. The VOCs in equilibrium in the vapor phase correspond to the amount released to the environment through vents. The equilibrium is calculated using the isofugacity conditions with the ␾ ⫺ ␥ method [20] as follows: Environmental Progress (Vol.23, No.4)

ˆf vi ⫽ ˆf ti

(3)

where fi denotes the fugacity of the component i in the different phases. In the ␾ ⫺ ␥ method, this equation reduces to ˆ i ⫽ ␥ i 共 x i , T兲 x i P sat Py i ␾ i 共T兲

(4)

where yi is the composition of i in the vapor phase, xi is the composition in the liquid phase, P is the total ˆ i is the fugacity coefficient of pressure of the system, ␾ i in the vapor mixture, ␥i( xi, T) is the activity coefficient of i in the liquid mixture, and Pisat(T) is the vapor pressure of the pure component i at the temperature T. (We have ignored the nonideality correction at the pure component vapor pressure and the Poynting correction for pressure, both of which are insignificant for the case at hand.) At ambient pressure and because the VOCs are very dilute compounds in the liquid phase, Eq. 4 can be further reduced to ⬁ y i P ⫽ P sat i 共T兲 x i ␥ i 共T兲

(5)

where ␥i⬁ is the activity coefficient at infinite dilution of i in the liquid phase, which is a function of the compositions of the nondilute components and of the temperature. For the UNIQUAC model, the expressions for ␥i⬁ in a binary mixture are

冉冊 冋 冉 冊

ln ␥1⬁ ⫽ ln ⫹ l1 ⫺

册

r1 q1r2 ⫹ q1 5 ln ⫺ ln ␶21 ⫹ 1 ⫺ ␶12 r2 q2r1

(6)

r1 l r2 2

and

冉冊 冋 冉 冊

ln ␥2⬁ ⫽ ln ⫹ l2 ⫺

册

r2 q2r1 ⫹ q2 5 ln ⫺ ln ␶12 ⫹ 1 ⫺ ␶21 r1 q1r2

(7)

r2 l r1 1

where li ⫽ [(z/2)(ri ⫺ qi)] ⫺ (ri ⫺ 1), z is the coordination number usually equal to 10, qi is an area parameter for component i, ri is a volume parameter for component i, ␶ij ⫽ exp[ ⫺ (uji ⫺ uii)/RT], ␶ii ⫽ ␶jj ⫽ 1, and uij is the interaction parameter between components i and j. Similar expressions can be obtained for other activity coefficient models such as NRTL and Wilson. Uncertainty in Eqs. 6 and 7 is present in the estimation of the interaction parameters uij. These are usually estimated by regressing experimental equilibrium data when available or by using group-contribution methods such as UNIFAC [21]. Environmental Progress (Vol.23, No.4)

4. MONTE CARLO ANALYSIS OF UNCERTAINTY IN THERMODYNAMIC PROPERTIES

To use the Monte Carlo method in uncertainty analysis applications, one must specify the uncertain variables of interest. In this work, the interaction binary parameters of the UNIQUAC model are the main variables for analysis, but additional ones are considered as well (uncertain operating temperatures in an absorption column). One of the problems is that the uncertainty in infinite-dilution activity coefficients is not well known. Most of experimental data available for dilute systems are for aqueous mixtures and even for those the data are not available for a wide variety of systems. Experimental vapor–liquid equilibrium (VLE) data are commonly used in the determination of binary interaction parameters. Accurate data are essential in process design and simulation, but they can be difficult to obtain. A well-known VLE data collection is the DECHEMA series [22]. Because of its size and reliability, it is very popular among chemical process simulators users. As described in the next section, the components of interest in this work are toluene, ethyl acetate, and n-tetradecane. Experimental VLE data are available for the binary ethyl acetate–toluene. There are no experimental data for the binaries n-C14 –toluene and n-C14 – ethyl acetate. Unfortunately, this type of scenario is often common when modeling chemical processes and that is one of the reasons we chose the case study used in this work. Without values of the interaction binary parameters, it is not possible to estimate the infinitedilution activity coefficients using models such as UNIQUAC or NRTL. Under these circumstances, the most popular approach would be to use a group-contribution method to estimate those parameters. A common choice is the UNIFAC method [21]. The uncertainty associated with estimations from group-contribution methods is not well known either. In this work, we use a similarity approach to estimating uncertainty. That is, the estimation of the uncertainties associated with the UNIFAC estimations are calculated by comparing the UNIFAC’s predictions with reported experimental VLE data for known systems of similar chemical nature to those of interest. For this purpose, we use the binaries of n-hexane, benzene, and ethyl acetate with toluene; the binaries of n-hexane and benzene with ethyl acetate; and the binaries of 1-hexadecane, naphthalene, and benzene with n-tetradecane. Experimental VLE data for all these binaries are found in the DECHEMA data series [23–30]. Table 1 shows the results of the comparison using the UNIQUAC model only. The goal is to obtain an idea of the potential variability that can be observed in the infinitedilution activity coefficients and then use this information to assign appropriate levels of uncertainty in our study. We can see from Table 1 that the percentages of variation between UNIQUAC and UNIFAC predictions are significant. The estimated error percentages vary from ⫺20 to about 95%. These error estimates are the differences between UNIQUAC and UNIFAC results and are used to estimate the error in UNIFAC for systems that have never been studied experimentally. For such systems, only UNIFAC would be available for a process simulation. We estimate the error of such an approach by looking at the UNIQUAC/UNIFAC differDecember 2004

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Table 1. Comparison between UNIQUAC and UNIFAC predictions of infinite-dilution activity coefficients.*

Component 1 n-C6 Benzene EAcetate n-C6 Benzene n-C14 n-C14 n-C14

2 Toluene [26] Toluene [30] Toluene [25] Ethyl acetate [24] Ethyl acetate [23] 1-Hexadecane [29] Benzene [27] Naphthalene [28]

UNIQUAC ␥2ⴥ 1.40 1.35 0.99 0.98 1.20 1.22 2.41 2.62 1.09 1.12 1.08 1.28 1.26 0.85 1.52 1.12

UNIFAC

␥1ⴥ

% ERROR

␥1ⴥ

␥2ⴥ

␥1ⴥ

1.54 0.97 1.10 2.85 1.15 1.01 1.27 2.97

1.57 0.96 1.12 2.67 1.18 1.01 0.84 1.54

9.72 ⫺1.38 ⫺8.27 18.36 5.23 ⫺6.86 1.11 95.53

␥2ⴥ 16.55 ⫺2.19 ⫺7.80 1.84 5.38 ⫺20.95 ⫺0.98 38.03

The UNIQUAC predictions are based on binary interaction parameters obtained using experimental equilibrium data. The percentage error is computed with respect to the UNIQUAC predictions. Numbers in brackets denote the reference used for the experimental VLE data.

Table 2. Uncertainty levels used for the

environmental performance evaluation of the VOCs absorption technology.* Notation L1 L2 T1 T2 T3 T4

Description Level 1 for ␥i⬁: ⺥[0.95␥៮ i⬁, 1.25␥៮ ⬁ i ] Level 2 for ␥i⬁: ⺥[0.80␥៮ i⬁, 1.30␥៮ ⬁ i ] Absorber temperature: 300.93 K Absorber temperature: 285.00 K Absorber temperature: 305.00 K Absorber temperature: 310.00 K

⺥[ 䡠 , 䡠 ] means that a uniform distribution with the limits defined is used for sampling in the Monte Carlo runs. T1, . . . , T4 are the operating temperatures used in the absorber. ␥៮ ⬁ i corresponds to the infinite-dilution activity coefficient estimated from UNIQUAC when experimental VLE data are available or estimated from UNIFAC, otherwise.

5. ENVIRONMENTAL ASSESSMENT OF THE ABSORPTION TECHNOLOGY OPERATION

The environmental assessment of the absorption technology follows closely the methodology of Shonnard and Hiew [6]. In this approach, several environmental indexes as a function of the absorption oil flow rate are studied under the uncertain conditions described in Table 2. The environmental indexes are based on a benchmarking concept, which includes the environmental persistence of the chemical (␶), a compartment distribution factor (D), an inherent impact/ toxicity parameter (IIP), and the rates of release from the process (E) [31]. The mathematical form of these indexes is generally defined by the equations li* ⫽

关共D兲共␶兲共IIP兲兴 i 关共D兲共␶兲共IIP兲兴 benchmark

(8)

冘 共I*⫻ E 兲

(9)

and n

I⫽ ence for similar systems because UNIQUAC uses experimental data and UNIFAC is a group-contribution approach. If we exclude the binary tetradecane–naphthalene, then the percentages vary in the range ⫺20 to 20%. This suggests a more reasonable range for the system chosen in this work; however, this analysis also points out that without some experimental evidence, the error in the UNIFAC predictions can be very significant (as in the case of tetradecane and naphthalene). Based on the results of Table 1 and taking into account the possibility of temperature variations in the operation of the absorption column (see Section 6), Table 2 describes the uncertainty levels used in this work. Samples are generated using the uniform distributions described in Table 2 for ␥⬁ i for each of the operating temperatures described in the same table. The values of ␥i⬁ generated randomly are used with Eqs. 6 and 7 to obtain the values of the binary interaction parameters uij - ujj, which are then used in the simulation of the absorption column. 318

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i

i

i⫽1

where n is the number of chemicals emitted from the process. Notice that I has units of emission rate (mass/ unit time), and it represents the equivalent emission of the benchmark compound for each of the impact categories being analyzed or involved in the process. The environmental indexes used in this work are the * ), smog formation (ISF * ), acid rain global warming (IGW * ), human ingestion toxicity (IING * ), human inhalation (IAR * ), and ecotoxicity (IFT * ). Table 3 shows the toxicity (IINH mathematical definitions of these indexes. 6. RECOVERY OF VOCS THROUGH ABSORPTION WITH N-C14 AS ABSORPTION OIL

The case study chosen in this work is the recovery of VOCs (toluene and ethyl acetate) by absorption in n-C14 from a gaseous waste stream generated at a cellophane production plant proposed by Shonnard and Hiew [6]. The gaseous waste stream consists of a flow rate of 12,000 standard cubic feet per minute at a Environmental Progress (Vol.23, No.4)

Table 3. Indexes used to evaluate the environmental

performance of the VOCs absorption technology case study.* * ⫽ NC ⫻ IGW

MwCO2 Mwi

LC50,Toluene ␶i,A Di,A ⫻ ⫻ LC50,i ␶Toluene,A DToluene,A LD50,Toluene ␶i,W Di,W * ⫽ ⫻ ⫻ IING LD50,i ␶Toluene,W DToluene,W MIRi DA,i *⫽ ISF ⫻ MIRFormaldehyde DA,Formaldehyde ARPi DA,i * ⫽ ⫻ IAR ARPSO2 DA,SO2 LC50 f,PCP ␶i Di,W * ⫽ IFT ⫻ ⫻ LC50 f,i ␶PCP DPCP,W * ⫽ IINH

Global warming Inhalation Ingestion Smog formation Acid rain Ecotoxicity

In the global warming index, NC is the number of carbons in the compound and Mw is the molecular weight. For the smog formation index, MIR is the tabulated maximum incremental reactivity of the compound [32]. ARP is the tabulated acid rain potential of the chemical [33]. D is defined as the mole fraction partitioned to the air (subscript A) and water (subscript W) compartments. LC50 and LD50 are, respectively, the lethal concentration and lethal dose values of 50% mortality of rats in an acute exposure environment [34] and ␶ is the reaction half-life in air (subscript A) and water (subscript W) [35]. Finally, in the ecotoxicity index, the subscript PCP represents the benchmark compound (pentachlorophenol).

temperature of 349.85 K and a pressure of 1 atm. The composition is 0.5% (vol) of toluene and ethyl acetate (the toluene and ethyl acetate mixture is 50/50% by weight) in dry nitrogen. Figure 1 shows the process flowsheet with heat integration. The gaseous waste stream is cooled down before entering the absorber column to a temperature of 300.93 K (level T1 in Table 2). Nitrogen containing some VOCs is released to the atmosphere, whereas the tetradecane leaves the bottom of the column with most of the solvents absorbed. Then the VOCs are separated from the absorber bottom stream using a distillation column, with toluene and ethyl acetate exiting the top of the column, which can be further purified and stored. The bottom of the distillation column is mainly tetradecane at 523.15 K. Heat integration between the feed to the distillation column (cold stream) and the recycled oil (hot stream) is incorporated in this process and illustrated in Figure 1. The recycled oil is then cooled down for refeeding to the absorber. Shonnard and Hiew [6] present simulation results for the VOC percentage recoveries and the environmental indexes mentioned earlier as a function of the absorption oil flow rate using the detailed process flowsheet described in Figure 1. They used the chemical process simulator HYSYS in their analysis. The simulation of this process flow diagram (PFD, Figure 1) requires care because of the mass and heat recycle streams. In other words, it is not easy to converge this flowsheet. By examining the PFD one notices that the major sources of emissions are the absorber and the reboiler of the distillation column, the latter contributing secondary emissions as combustion products such as CO2, CO, SOx, NOx, and other organic compounds. The flow of absorber oil is large compared with the flow of the VOCs; therefore, the energy requirement of the boiler

Figure 1. Process flow diagram for the recovery of VOCs using absorption with n-C14 as the absorbing oil [6].

The Figure was generated with HYSYS process simulator (Aspen Technology, Inc., Cambridge, MA). [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com].

Environmental Progress (Vol.23, No.4)

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Figure 2. Modified process flow diagram of the distillation section of the recovery process of VOCs. This

flowsheet is used for the quick estimation of the heating requirements of the process described in Figure 1. The figure was generated with ChemCAD process simulator (Chemstations, Inc., Houston, TX). [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com].

in the distillation column is roughly proportional to the stripping sector vapor flow [36]. In other words, Q R ⫽ ␭V៮

(10)

where ␭ is the latent heat of vaporization of the absorber oil and V៮ is the stripping sector vapor flow rate. This suggests that the flow of combustion gases at high flow rates of the absorber oil might contribute significantly to the total emissions estimation and it might easily shadow the contribution of other sources such as fugitive emissions in valves and other smaller equipment components. Additionally, this possibility also suggests that the detailed modeling and simulation of the PFD given by Figure 1 might not be necessary for the evaluation of the environmental performance of the process. We evaluate the validity of the aforementioned hypothesis by simplifying the PFD of Figure 1 as follows: first, we simulate the absorber only with our own FORTRAN code using the sum-rates method with the Burmingham–Otto algorithm [37]. This allows us more flexibility in terms of running multiple simulations for different sample values of the infinite-dilution activity coefficients (see Section 4). Second, we perform a single simulation of the distillation column and the heat integration process using the simplified PFD shown in Figure 2. This allows us to determine the heat requirements per unit of absorber oil in the reboiler of the distillation column and the heat exchanger used to preheat the feed of the distillation column to 523.15 K (in this case study, the bottoms of the distillation column are roughly at this temperature). The one-time simulation of the distillation column is performed using a reflux ratio of (approximately optimum [38]) 1.2 times 320

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the minimum reflux ratio. The simulation was performed using the chemical process simulator ChemCAD with a feed molar flow rate of 300 kmol/h. We performed other simulations at different values of the feed molar flow rate to verify the assumption of proportionality in the heat requirements with respect to the feed molar flow rate. The results confirm this and the proportionality constants obtained are the following: Q R ⫽ 0.0100656N˙ feed

(11)

and Q HE ⫽ 0.052843N˙ feed

(12)

where QR is the heat duty of the reboiler in J/h, QHE is the heat duty of the preheater in J/h, and N˙feed is the feed molar flow rate in kmol/h. To validate the accuracy of this simulation approach, Figure 3 shows the percentage recovery of VOCs as a function of the absorption oil flow rate. These results are in very good agreement with the results of Shonnard and Hiew [6], suggesting that the simplified version of the process model is of good quality for the purposes of this work, in particular, the modeling of the absorption column. It is important to notice from this figure that the ethyl acetate is the compound constraining the absorber oil flow rate. In other words, a reasonable toluene recovery fraction is achieved with a substantially lower absorber oil flow rate than the one required to obtain the same recovery fraction of ethyl acetate. We therefore condense a flowsheet when the initial “full” simulation shows the dominance of individual units or groups of units in determining the environmenEnvironmental Progress (Vol.23, No.4)

Figure 3. VOCs recovered using absorption with varying n-C14 flow rates. Results reported at the operating conditions of Shonnard and Hiew [6]. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com].

tal risk indexes. This is a form of Pareto analysis. The dominant sensitivity is most likely associated with the dominant contributor to these indexes. In some cases, some units can buffer the sensitivity of others; therefore, we include all units with significant sensitivity to the indexes. To compute the CO2 emissions product of the heat requirements, we use the CO2 emission factor of fuel oil [1], which is approximately 78.0 kg/GJ (notice that there is significant uncertainty associated with this type of factor). The composition of the combustion gases is assumed to be the same as that reported by Shonnard and Hiew [6] in their absorption technology option. They report the following ratios for the combustion products: CO/CO2 ⫽ 0.42/1602, SOx/CO2 ⫽ 12.63/ 1602, and NOx/CO2 ⫽ 1.66/1602. With this information and that given by Eqs. 11 and 12, the estimation of the emissions product of heating requirements is straightforward. Figures 4 and 5 show the variation of the environmental indexes with varying absorption oil flow rates. Figure 4 is in very good agreement with the Shonnard and Hiew [6] results, but for Figure 5 there are disagreements on the magnification factors of the curves, although their general trends are very similar. At this point, we are not certain about the source of the disagreement, but it seems to be that there are some discrepancies between Figure 5b and Table 3 in the Shonnard and Hiew [6] results. The next step is to study how uncertainty in the infinite-dilution activity coefficients and in the absorber operating temperature affect the behavior of figures such as 3, 4, and 5. Figure 6 shows the recovery fractions of VOCs as a function of the absorber oil flow rate under the different uncertainty scenarios described in Environmental Progress (Vol.23, No.4)

Table 2. Notice that without uncertainty considerations, at 300 kmol/h of the absorber oil, a good VOC recovery fraction for the ethyl acetate is obtained. However, under the effects of uncertainty, the variation of the ethyl acetate recovery fraction at this flow rate is very significant. Under the normal operating temperature (T1 in Table 2), the L1 uncertainty scenario causes a variation of approximately 13% in the ethyl acetate recovery fraction. For the second uncertainty scenario (L2), the variations observed are around 20 –25% for T1, T3, and T4. It is also very interesting to observe the effect of the operating temperature in the absorber. Clearly, temperature control would have a major role in the environmental impact of this technology. From this preliminary analysis, it seems that T2 is a very favorable operating temperature for the absorber running at 300 kmol/h of absorber oil under either of the uncertainty scenarios for the infinite-dilution activity coefficients. Another important issue to discuss from Figure 6 is the significance of the variations observed. The analysis framework presented in this paper uncovers and displays the uncertainties; engineering judgment is still required to evaluate how significant these variations are in terms of decision making. If they are considered significant, then the next step is to perform a more thorough modeling of the process including a more rigorous quantification and evaluation of the uncertainty. If more detailed modeling is not possible or the results with better modeling approaches are still quite uncertain for decision-making purposes, then extensive experimental measurements may be necessary. In other words, this type of uncertainty analysis can be very helpful in determining whether process modeling and simulation constitute a viable and reasonable opDecember 2004

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Figure 4. Variation of the environmental indexes IGW, IAR, and ISF as a function of the n-C14 flow rate. Results

reported at the operating conditions of Shonnard and Hiew [6]. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com].

Figure 5. Variation of the environmental indexes IFT, IING, and IINH as a function of the n-C14 flow rate. Results

reported at the operating conditions of Shonnard and Hiew [6]. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

tion before important decision making in the environmental evaluation of process technologies. If one concludes that measurements are necessary for the evaluation of the environmental performance of this process, then Figure 6 provides additional useful 322

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information for the design of the experiments. Notice that to have a reasonable recovery of ethyl acetate, the absorber oil flow rate required is such that almost 100% of the toluene is always recovered. This means that one has to measure the ethyl acetate emissions only, which Environmental Progress (Vol.23, No.4)

Figure 6. Recovery fraction of VOCs under the effects of uncertainty according to the scenarios of Table 2. The

different scenarios in the figure are: (A) L1T1, (B) L1T2, (C) L1T3, (D) L1T4, (E) L2T1, (F) L2T2, (G) L2T3, and (H) L2T4. For example, the scenario L1T1 means that the Monte Carlo simulations are performed using the uncertainty level L1 with the absorber operating temperature at T1 as defined in Table 2.

translates into cost savings and a more efficient measurement schedule. Figure 7 shows the behavior of the environmental indexes IGW, IAR, and ISF under the same uncertainty scenarios of Figure 6. At first, it looks like the effect of uncertainty in the operating temperature and infinitedilution activity coefficients is not very significant, but one has to realize that the IGW and IAR indexes are Environmental Progress (Vol.23, No.4)

substantially affected by the estimation of the combustion products of the heating requirements (see Table 4). ISF is affected by the presence of CO, but the amounts present are relatively small. We can see that any uncertainty present in the fuel emission factors will substantially affect the behavior of Figure 7. In this case, it is not necessary to perform Monte Carlo simulations to obtain this conclusion because the indexes IGW and IAR December 2004

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Figure 7. Variation of the environmental indexes IGW, IAR, and ISF under the effects of uncertainty according to

the scenarios of Table 2. The different scenarios in the figure are: (A) L1T1, (B) L1T2, (C) L1T3, (D) L1T4, (E) L2T1, (F) L2T2, (G) L2T3, and (H) L2T4. For example, the scenario L1T1 means that the Monte Carlo simulations are performed using the uncertainty level L1 with the absorber operating temperature at T1 as defined in Table 2.

are proportional to the combustion products generation. As pointed out previously, the operational temperature T2 seems to be favorable for the operation of the absorber. In this case, we notice that the overall behavior of the IGW and ISF changes significantly at this temperature. To isolate the potential effect of the fuel emission factor, we study the behavior of indexes IGW and ISF in the operation of the absorber only. In other words, we assume that the whole process flowsheet is composed by the absorber. Figure 8 shows the results obtained using the same uncertainty scenarios. In this figure, the effects of uncertainty in ␥i⬁ and T can be noticed more clearly. The effects are very similar for both indexes, with a noticeable change in the behavior for the case of 324

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operating temperature T2. At 300 kmol/h, the effects are significant with the exception of the case at T2. The other set of environmental indexes studied are the IFT, IING, and IINH. These do not depend strongly on the amounts of the combustion products generated from heating requirements. Only IINH is a function of the amount of CO, which is small in this case study. Figure 9 shows the results for this set of indexes. We can see that the effects of the different uncertainty scenarios are quite significant. The patterns are similar for most of the cases, with the exception of temperature T2 (see Figures 9B and 9F). For T2 and at an absorber flow rate of 300 kmol/h, the indexes are negligible; however, under the other scenarios the variations of the indexes are significant. These types of Environmental Progress (Vol.23, No.4)

Table 4. Dimensionless relative risk indexes [31] for the compounds involved in this work.*

Index Compound Toluene Ethyl acetate SOx NOx CO2 CO n-C14

I*GW 3.34 2 0 40 1 2 3.1

I*SF 4.3 0.9 0 0 0 0.9 0

I*AR 0 0 1 0.7 0 0 0

I*ING 1 110 0 0 0 0 0

I*INH 1 3.3 0 0 0 50 0

I*FT 0.02 0.76 0 0 0 0 0

Definitions of the indexes are given in Table 3.

Figure 8. Variation of the environmental indexes IGW, IAR, and ISF under the effects of uncertainty according to

the scenarios of Table 2. In this case, the contribution of fuel emission factors required for heating requirements is not taken into account. The different scenarios in the figure are: (A) L1T1, (B) L1T2, (C) L1T3, (D) L1T4, (E) L2T1, (F) L2T2, (G) L2T3, and (H) L2T4. For example, the scenario L1T1 means that the Monte Carlo simulations are performed using the uncertainty level L1 with the absorber operating temperature at T1 as defined in Table 2.

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Figure 9. Variation of the environmental indexes IFT, IING, and IINH under the effects of uncertainty according to

the scenarios of Table 2. The different scenarios in the figure are: (A) L1T1, (B) L1T2, (C) L1T3, (D) L1T4, (E) L2T1, (F) L2T2, (G) L2T3, and (H) L2T4. For example, the scenario L1T1 means that the Monte Carlo simulations are performed using the uncertainty level L1 with the absorber operating temperature at T1 as defined in Table 2.

indexes are very important in decision making and in determining the environmental impact of a chemical or other technological process. It is clear that uncertainty can have a major impact in environmental assessment and therefore attention should be given to issues dealing with uncertainty. It is noteworthy to point out that there are many other potential sources of uncertainty. 326

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This study shows only the potential effect that uncertainty in thermophysical properties estimation and in operating temperature variation might have on the environmental performance of a chemical process technology. Other potential sources of uncertainty include the effect of the error in the model chosen for thermophysical properties estimation and variations in other Environmental Progress (Vol.23, No.4)

operational conditions such as pressure. Variations in operational conditions can also be random, which have not been considered here. 7. CONCLUDING REMARKS

We have presented a framework to uncover uncertainty in process simulations used for environmental risk assessment. Although the technique is general, we have demonstrated it by studying the effect that uncertainty in thermophysical properties estimation has on the calculation of emissions in a chemical process design, specifically, the recovery of VOCs (toluene and ethyl acetate) by absorption in n-C14 from a gaseous waste stream generated at a cellophane production plant. Also, we studied how this uncertainty affects the environmental performance indexes for global warming (IGW), smog formation (ISF), acid rain (IAR), human ingestion toxicity (IING), human inhalation toxicity (IINH), and ecotoxicity (IFT). We find that the effect of temperature (it has a direct effect on vapor pressures and thermodynamic equilibrium) is the most significant in the environmental performance of the operation followed by the uncertainty in the infinite-dilution activity coefficients. Additionally, we conclude that major players in the uncertainty of emissions calculations are the factors used for secondary greenhouse gas emissions from fuel combustion. The reason for this is that the total emissions of the process are heavily influenced by the greenhouse gases and any uncertainty in these factors will proportionally affect the CO2 estimation. This effect has also other important consequences. For instance, if one needs to estimate the total emissions of the plant regardless of the chemical nature of the compounds, a detailed model of the process flowsheet might not be required, as shown in the results of the case study of this work. The results also show that the impact of uncertainties in thermophysical properties can be important enough to affect significantly the calculations of VOCs (keep in mind that variations in the operation temperature and pressure strongly affect the thermodynamic behavior of the system), suggesting that for reliable estimation of VOC emissions one has to have a thorough evaluation of the uncertainties present in the calculations. Otherwise, extensive experimental measurements might be necessary. Although the results of this work are only for a relatively simple case study, they clearly show the potential effects that uncertainties in thermophysical properties may have on the estimation of emissions. Additionally, the effect of uncertainties can be more significant when dealing with substances of high toxicity where small amounts can have a significant environmental impact or represent an important health risk. It is of value to notice that for many modeling applications, in particular those associated with diluted components in nonaqueous phases, experimental thermodynamic data are scarce. This causes the process modeler to use empirical or semiempirical thermodynamic models to study the behavior of such diluted mixtures. Unfortunately, the calculation procedures in chemical process simulators are automatic, including the selection of thermodynamic models, making the Environmental Progress (Vol.23, No.4)

user unaware of the lack of experimental information for the system under study. This type of situation can produce misleading results if one is not aware of the effects of uncertainties in the calculations. There are other sources of uncertainties in process simulation, such as model error, systematic and random error in data other than thermophysical, process measurement errors, convergence characteristics, disturbances, and the like. Although we focused here on thermophysical property uncertainty, the framework presented can be used to assess these other uncertainties. This is being undertaken currently. Finally, we believe that the results presented also show the danger of using chemical process simulators or process flowsheet models in general, without taking into account the effects of uncertainty. It is clear that the issues of uncertainties in thermophysical properties in the evaluation of environmental assessment of chemical processes require further investigation, and this work reaffirms such needs. ACKNOWLEDGMENTS

We acknowledge Lucrecia Rodriguez-Barahona for some prior work on this case study performed in our research group. LITERATURE CITED

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