Improved Product Energy Intensity Benchmarking Metrics for

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Improved Product Energy Intensity Benchmarking Metrics for Thermally Concentrated Food Products Michael E. Walker,*,† Craig S. Arnold,‡ David J. Lettieri,§ Margot J. Hutchins,§ and Eric Masanet*,†,‡ †

Northwestern University, Department of Chemical and Biological Engineering, 2145 Sheridan Rd, RM E136, Evanston, Illinois 60208, United States ‡ Northwestern University, Department of Mechanical Engineering, 2145 Sheridan Rd, RM B224, Evanston, Illinois 60208, United States § University of California, Berkeley, Department of Mechanical Engineering, 6143 Etcheverry Hall, Mailstop 1740, Berkeley, California 94720, United States S Supporting Information *

ABSTRACT: Product energy intensity (PEI) metrics allow industry and policymakers to quantify manufacturing energy requirements on a product-output basis. However, complexities can arise for benchmarking of thermally concentrated products, particularly in the food processing industry, due to differences in outlet composition, feed material composition, and processing technology. This study analyzes tomato paste as a typical, high-volume concentrated product using a thermodynamics-based model. Results show that PEI for tomato pastes and purees varies from 1200 to 9700 kJ/kg over the range of 8%−40% outlet solids concentration for a 3-effect evaporator, and 980−7000 kJ/ kg for a 5-effect evaporator. Further, the PEI for producing paste at 31% outlet solids concentration in a 3-effect evaporator varies from 13 000 kJ/kg at 3% feed solids concentration to 5900 kJ/kg at 6%; for a 5-effect evaporator, the variation is from 9200 kJ/kg at 3%, to 4300 kJ/kg at 6%. Methods to compare the PEI of different product concentrations on a standard basis are evaluated. This paper also presents methods to develop PEI benchmark values for multiple plants. These results focus on the case of a tomato paste processing facility, but can be extended to other products and industries that utilize thermal concentration.

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INTRODUCTION Energy and emissions benchmarks are useful tools that can help industry and policy makers manage the energy use and emissions associated with industrial systems. Such information can help establish energy efficiency targets between plants in a region,1 for internal corporate energy programs,2 and for Energy Performance Indicators per the ISO 50001 Energy Management Standard.3 This information also aids development of industrial energy performance awards, such as the Energy Star for Industry plant label and the Superior Energy Performance label,4two U.S. government awards for energy-efficient industrial plants. Furthermore, benchmarking metrics are useful in product lifecycle assessments, which require companies to allocate processing energy use to products within a broader life-cycle system.5−7 Energy and emissions benchmarks are also a prerequisite for emerging cap-and-trade programs for industrial greenhouse gases (GHG) emissions, which are being developed globally as a market-based climate change mitigation strategy.8 Several policy-driven approaches have been adopted to incentivize reductions in GHG emissions in various world regions, including the E.U. emissions trading system, the U.S. Northeast’s Regional Greenhouse Gas Initiative, and California’s cap-and-trade program.9−11 © 2014 American Chemical Society

Product energy intensity (PEI) metrics are particularly wellsuited for benchmarking energy use and emissions at processing facilities in all of the aforementioned initiatives. PEI metrics, as shown in eq 1, can be used to describe facilitylevel energy input (E) on the basis of production output (O) (e.g., kJ/kg product).12 Such product-based metrics are preferred by policy makers developing energy efficiency incentives and emissions cap-and-trade systems,13 and they provide a standard basis for comparison between different processing facilities. PEI =

E O

(1)

Despite the simple form of PEI presented in eq 1, establishing industry-wide PEI metrics can present a number of complications for the manufacturing sector. First, energy use is not always monitored at the process level, and standardized methods to allocate energy use to products are largely absent. Second, yearly variation in feedstock composition can have a Received: Revised: Accepted: Published: 12370

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the energy used in the production of tomato paste, as reported by Karakaya et al.

strong impact on PEI in some industries, such as food processing, and technology variation between facilities can lead to large differences in PEI as well. Finally, certain products may be refined to different concentrations with very different PEI values, despite being similar products. Unless these complications can be addressed, the establishment of credible and manageable PEI metrics for concentrated products is not possible, which excludes a number of energy- and emissionsintensive industries. This paper focuses on the example of tomato paste processing as a typical, high-volume concentrated product that is representative of all of the aforementioned complications. While the focus of this paper is on energy use at the manufacturing facility, and the associated primary energy required to generate electricity consumed by the facility, food processing is only one part of a food product’s life-cycle.14 Significant energy use and emissions are also associated with agricultural processes and transportation. However, these lifecycle stages are outside the scope of this study, which focuses on improved energy benchmarking metrics at food processing plants. The methods discussed herein are applicable to the development of PEI metrics for products that undergo thermal concentration in other industries, such as the dairy and juice concentrate industries, as well as the chemicals and gas production industries. PEI metrics have been discussed extensively in the literature. Hyman et al.15 and Freeman et al.12 discussed the benefits of PEI metrics over value-based energy intensity metrics. Liu et al.16 examined how PEI metrics change for production lines that gain, lose, or recycle mass, including those that have separate merging upstream processes. Ke et al.5 examined PEI metrics from a systems engineering perspective, and presented a general framework for industrial energy benchmarking. Seow et al.17 presented a general, product-based approach to the classification of the direct energy required to manufacture a product and the indirect energy required to maintain the production environment. Worrell et al.18 and Arens et al.19 investigated changes in the energy intensity of the iron and steel industry in terms of structural and efficiency changes. Liu et al.20 carried out a study on the energy intensity of alumina manufacturing based on the fraction of final product in each process step and process-level energy use. Barati et al.21 studied the energy intensity of different steelmaking processes, in addition to the CO2 emissions released in each process. While previous studies have presented general approaches and discussed the importance of utilizing product-based metrics, no studies to date address the important influence of product composition on PEI metric development and implementation. Energy use in food production is an important issue that has been discussed in the literature. The U.S. Department of Agriculture analyzed the life-cycle energy use of the U.S. food system and found that food-related energy use grew by 22.4% from 1997 to 2002.22 Pimentel et al.23 discussed reducing fossil fuel use throughout the food life cycle by roughly 50%. Work by Cuellar et al.24 estimated the embedded energy in wasted food at roughly 2030 trillion BTU in 2007. This study provides plant-level metrics that can help reduce the energy and emissions intensities of food processing plants, which can lead to lower-impact food production systems. Previous studies have also investigated the energy intensity of tomato processing.14,25,26 Karakaya et al.14 reported thermal and electrical energy intensities for production of peeled, diced, juiced and paste varieties of tomato products. Table 1 highlights

Table 1. On-Site Energy Use in Tomato Paste Production14 product:

canned tomato paste

note: energy type: process conveying washing sorting crushing pulpinga evaporation pasteurizationa canning carton filling palletizing total

30% solids paste thermal energy MJ/ton input processed

297.8

297.8

electrical energy MJ/ton input processed 0.5 0.7 0.7 2.0 3.3 35.4 0.9 16.9 20.6 20.6 101.6

a

Thermal energy requirements of pulping and pasteurization steps are supplied via heat-integration of hot outlet process streams from the evaporator in this example.

The most energy intensive tomato products include those that require thermally intensive processes such as pasteurization and evaporation.14,25 Furthermore, literature data indicate a wide range of energy intensity values for evaporation in these products, from 200 to 5700 kJ/kg of output produced.14,25,27 This range in PEI is a result of four factors: (1) differences in final solids concentration in products (e.g., tomato paste, puree and juice products); (2) the strong influence of processing technology on evaporation energy use; (3) the influence of raw material composition (e.g., feed solids concentration) on evaporation energy use; and (4) differences in indirect/auxiliary energy use for paste production, which can include equipment cleaning, facility lighting, and facility heating, ventilation, and cooling (HVAC). A few previous studies have investigated energy use in tomato paste evaporator systems. Rumsey et al.27 performed a practical evaluation of multiple-effect systems and reported that their actual efficiency varies greatly throughout the operational day and is on average less than the theoretical efficiency. Others have investigated heat recovery opportunities28 and exergy balances29 in these systems. However, these previous studies did not address the influence of the aforementioned four factors that influence energy use. This paper expands upon the existing literature with an indepth evaluation of the factors that influence the PEI of concentrated products, and presents a method to compare PEI of concentrated products through the application of equivalence factors (EFs). Evaluations were carried out with a thermodynamics-based tomato paste evaporator model, which is presented herein. The results of these analyses are used to highlight the inherent complications of developing PEI metrics for a relatively simple concentrated product such as tomato paste. Together, the methods and EFs proposed here can provide a robust and practical option for constructing standard PEIs for tomato paste products. These methods can be used by facility operators, energy analysts, and policy makers for the purposes of energy and emissions intensity benchmarking, and can be extended to other industries that manufacture concentrated products. 12371

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Figure 1. Simplified block diagram of a tomato paste processing line.

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METHODS System Description. Figure 1 presents a simplified block diagram of a dedicated tomato paste processing line.14 As shown, tomato paste products are manufactured as canned consumer products or as bulk packages for commercial and industrial use. The blocks shown in Figure 1 correspond with the process steps for canned tomato paste production as given in Table 1. This study focused on energy use in evaporation, which is the process step that requires the most energy in tomato paste production, and which will vary the most for different degrees of concentration. Evaporation is a thermal process used in food manufacturing to concentrate a mixture by removing volatile components (commonly a liquid, and most commonly water) from nonvolatile components (commonly solids).30 In an evaporator, heat from an energy carrier, such as steam, provides the necessary energy to volatilize the liquid component. The amount of energy needed to evaporate the volatile liquid, normalized per unit mass of liquid evaporated, is called the latent heat of vaporization, ΔHv(T). In tomato processing, as in many other types of food manufacturing, the volatile liquid is water, a substance with a relatively large heat of vaporization, 2.26 MJ/kg (at 100 °C).31 The large heat of vaporization is the reason that evaporation is one of the most energy intensive processes in the manufacture of concentrated products. There are many types of evaporators used in food manufacturing.30,32−34 Steam economy (SE) is a common metric used to benchmark energy efficiency in evaporator systems. SE is defined as the mass of water removed divided by the mass of steam applied for heating, as shown in eq 2. Modern evaporator systems, such as multiple-effect evaporators, typically achieve SE on the order of 3−5, while vapor recompression evaporator systems can achieve greater SEs. An in-depth discussion of evaporator systems is provided in Supporting Information (SI) Figure S-1. m water,evaporated SE = ms (2)

was calculated using a thermodynamics-based mathematical model, presented below, in eqs 3−8. Equations 3−6 are related to the system mass balance, while eqs 7 and 8 represent the energy balance equations across each evaporator step. A full derivation of the energy balance applied in eqs 7 and 8 is provided in SI Figure S-2. Equations 3−5 represent multiple equations evaluated at different values of “i”, which relate to the feed stream (0) and evaporator effect number (1,2). Additional detail on modeling of evaporator systems can be found in Maroulis and Saravacos.35 Note that the equations presented relate to a 2-effect evaporator, as shown in Figure 2, but can easily be extended for additional effects. mp, i = msolids, i + m water, i |i = 0,1,2

(3)

mp, ixi = msolids, i |i = 0,1,2

(4)

m v, i = m water, i − 1 − m water, i |i = 1,2

(5)

msolids,0 = msolids,1 = msolids,2

(6)

m2ΔHv ,2(T2) + msolid,0Cp,solid(T0 − T1) + m water,0Cp,water(T0 − T1) − mv ,1ΔHv ,1(T1) = 0

(7)

msΔH v,s(Ts) + msolid,1Cp,solid(T1 − T2) + m water,1Cp ,water(T1 − T2) − mv ,2ΔHv ,2(T2) = 0

Energy Use in Tomato Paste Evaporators. Analyses of energy use in evaporator systems focused on three areas: (1) the influence of final product concentration; (2) the impact of technology differences; and (3) the influence of feed material concentration. The analyses presented herein focused on thermal energy use in these systems, as this value will change significantly for different inlet feed and outlet product solids concentrations.35 The sum of electricity consumption in nonevaporation processes (ENE), which includes the electrical energy applied in evaporator systems, was assumed from literature for a tomato paste process with similar operating conditions.14 Thermal energy use in evaporator systems (ETE)

(8)

Figure 2. Simplified process diagram for a counter-current 2-effect evaporator system.

This work considered a counter-current, multieffect evaporator system with operational parameters as shown in Table 2. Estimates were developed on the basis of 1 ton of tomatoes processed. When supplied with a given mass flow rate (mp,0), concentration profile (xi’s) and set of effect temperatures (Ti’s), this model (eqs 3−8) calculates the steam required to fuel a 12372

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concentrate with >24% solids. Feed solids concentration was assumed to be 5%, similar to values presented in available literature.14,35 This analysis was performed for both a 3-effect and a 5-effect evaporator system. 3-effect evaporator systems are representative of older technology, while 5-effect systems represent the largest multieffect systems typically employed in industry.27,35 It is increasingly common for paste producers to utilize advanced configurations that employ a combination of multieffect systems and vapor recompression technology. A second analysis was performed to investigate the influence of feed solids concentration on PEI. Here, the PEI of manufacturing 31% solids paste was estimated for feed solids concentrations over the range of 3−6% solids for 3- and 5-effect evaporator system configurations. Work by Beckles41 suggests that this is a typical range of variation for raw tomato solids content, and explains that this variation is due to tomato type (cultivar) and the influence of cultivation. Note that 31% solids was chosen as the basis for this analysis because it is a typical standard concentration to which tomato paste is refined.14

Table 2. Evaporator System Operation Parameters parameter

unit

value

reference

mp,0 ENE T0 Ts Teffect,last ΔTeffect flow direction Cp,water (@ 25 °C) Cp,solid ηboiler lossdelivery lossevap ηeleca

kg MJ/ton input °C °C °C °C

1000 101.6 70 120 90 10 counter-current 4.18 1.25 82 2 3 35

14 assumed 35 35 35 35 31 36 37 38 39 40

kJ/(kg × C) kJ/(kg × C) % % % %

a

Electricity generation efficiency here was assumed based on the U.S. national range of averages for coal, petroleum, nuclear and natural gas power plants range of 31−42%

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multieffect evaporator system based on the mass and energy balances that govern the system. Here, mp,1 and mp,2 refer to process mass leaving the first and second evaporator effects; similarly, mv,1 and mv,2 refer to vapor produced in these effects. In addition, msolids,i and mwater,i refer to the mass of solids/water contained in mp,i. Values ΔHv,x(Tx) were obtained from steam table data.31 The thermal energy supplied to the system (ETE) is described by the term msΔHv,s(Ts) in eq 8. Material feed temperature (T0), steam temperature (Ts), flow direction, and effect temperature data (Teffect,last, ΔTeffect) were assumed or taken from available literature for tomato paste evaporator processing.35 Here, ΔTeffect represents the temperature differential between each effect of the multieffect evaporator. Since the flow configuration assumed is countercurrent, the temperature profile in a 3-effect system would be 70−80−90 °C, and similarly 50−60−70−80−90 °C in a 5effect system. A boiler efficiency (ηboiler) of 82% was assumed for this study, which is representative of a typical industrial natural gas-fired boiler.37 Heat loss during steam distribution (lossdelivery) was assumed at 2% of the total applied steam energy,38 and heat loss from the evaporator system (lossevap) itself was assumed at 3% of the total applied steam energy.39 An efficiency factor of 35% for electricity production (ηelec) was assumed to convert on-site applied electrical energy to the primary energy required to generate this electricity.40 As shown in eq 9, these efficiency/ loss factors were applied to ENE and ETE to calculate PEI in terms of primary energy. Equation 9 also includes a value for ENT and ηNT, which represent thermal processing energy inputs not associated with thermal concentration and the ratio of onsite energy to primary energy for these inputs, respectively. As such, eq 9 is generally applicable, but note that ENT =0 in the example presented herein, as shown in Table 1.

RESULTS Influence of Outlet Paste Concentration and Evaporator Technology on PEI. Modeling results indicate that the PEI for tomato pastes and purees varies by an order of magnitude: 1200−9700 kJ/kg over the range of 8%−40% outlet solids concentration for a 3-effect evaporator, and 980−7000 kJ/kg for a 5-effect evaporator with operation parameters as defined in Table 2. PEI estimates vs outlet solids concentration for both configurations are presented in Figure 3 and SI Table S-1.

Figure 3. PEI vs paste outlet solids concentration.

Figure 3 highlights two important points. First, outlet solids concentration has a strong influence on PEI. This means that comparing the PEI of paste products with different outlet solids concentrations requires a standard correction factor, such as an equivalence factor (EF). Second, evaporator processing technology plays a significant role in the PEI of paste/puree production. This implies that there may be a wide gap in the PEI of concentrated products between facilities and companies, greater than would be expected from typical process efficiency differences between boilers and steam systems. Figure 3 highlights the difference between 3-effect and 5effect evaporator systems, but advanced evaporator systems may also employ vapor recompression technology. Such

PEI = (E TE /(ηboiler − Lossevap − Lossdelivery ) + E NE /ηelec −1

+ E NT /ηNT)(Opaste)

= (E TE,primary + E NE,primary

−1

+ E NT,primary )(Opaste)

(9)

PEI for tomato concentrates was estimated over the range of 8 to 40% solids. This range was chosen due to the FDA (Food and Drug Administration) definition of tomato puree as concentrate with 8−24% solids content and tomato paste as 12373

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industry setting, the application of a correction factor, such as an EF, for feed solids concentration can help to isolate technology-related production energy differences between facilities. The results presented here suggest that, whether or not a correction factor is applied for feed concentration, it is sensible to average energy use data from multiple years to develop PEI metrics. This is especially true for food processing, which can experience a high degree of feedstock variation from year to year.41 Taking data from multiple years will result in a PEI that is most representative of actual energy use. Comparison of PEI for Concentrated Products Using Equivalence Factors (EFs). In contrast to variation in feed concentration, the results presented here demonstrate that variation in outlet product concentration should be accounted for in the PEI of concentrated products, regardless of the intended application. A different amount of energy is required to produce paste with 26% solids than it does to make 33% solids paste, and the constitution of the end products are not the same. This is an important concept that extends to other processing industries like petroleum refining or chemicals manufacture, where products are also refined to different levels of purity. The remainder of this paper demonstrates how products concentrated to various levels can be compared through the application of EFs. Specifically, this section addresses the following: 1. The development of PEIeq (equivalent PEI) from PEIactual and EFs; 2. The development of PEIbench (benchmark PEI) for several facilities from PEIeq; and 3. Evaluation of the ARE (absolute value of the relative error) that results from applying EFs, and the development of a generalized EF form to reduce this error. In the tomato processing industry, the basic mass− concentration continuity relationship shown in eq 10 can be used to calculate the mass of paste at a certain outlet solids concentration, given a starting solids concentration and mass. The simple EF form shown in eq 11 (which is a simple scaling factor of actual to equivalent solids concentration) was used as a starting point for the analyses of EF applicability presented herein.

systems use steam or mechanical compression to increase the pressure of vapor produced by evaporation so that it can be reapplied to provide additional heat to the evaporator system. An advanced system that combines vapor recompression and multieffect technology may achieve a lower overall energy use, as suggested by data from Karakaya et al.,14 which reports energy use at roughly 68% of the value calculated in this study for a 5-effect system. While this study focuses on multiple-effect systems, the methods presented herein to compare energy use in evaporator systems using EFs are applicable to advanced systems as well. Influence of Inlet Tomato Solids Concentration on PEI. Results indicate that the PEI for tomato concentrates varies from 13,000−5900 kJ/kg over the range of 3−6% feed solids concentration for a 3-effect evaporator producing paste at 31% outlet solids concentration, and 9200−4300 kJ/kg for a 5effect evaporator, both as defined in Table 2. PEI estimates vs raw tomato feed solids concentration for both configurations are presented in Figure 4 and Table S-2.

Figure 4. PEI vs Raw Tomato Feed Solids Concentration (31% Outlet Solids).

From year to year, variation in rainfall and growing conditions can affect the solids concentration of the tomatoes arriving at the processing facility.41 As shown in Figure 4, inlet solids content is inversely proportional to PEI. While this trend is intuitive, the magnitude of the variation in PEI over the typical range of feed solids (3−6%) is shown to be significant, and it is clear that the influence of feed solids variation needs to be considered in the development of PEI metrics for concentrated products.

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DISCUSSION The ultimate purpose of establishing PEI metrics for concentrated products is to allow for a standard comparison of the energy required to produce similar products with different compositional characteristics. Since the PEI of tomato paste production is influenced so strongly by both feed and outlet solids concentration, it is important to consider both in the development of PEI metrics. Variability in feed solids concentration presents a particularly interesting problem when using PEI metrics for comparative purposes, because facilities typically have some degree of control over the quality of their feedstock, and may pay less for raw materials that require more energy to process. In the

Oactxact = Oeq,simplexeq

(10)

⎛x ⎞ Oeq,simple = EFsimple × Oact = ⎜⎜ act ⎟⎟ × Oact ⎝ xeq ⎠

(11)

In this way, EFs can be utilized to develop PEIeq, which represents the amount of energy any individual plant would require to manufacture a standard concentration of paste, for example, 31% solids. As shown in eq 12, PEIeq is simply the ratio of production energy input to the equivalent product output, and is obtained by combining eq 1 and 11. Such standardized PEIeq values will reflect the production efficiency of any specific process line, and can be used to compare the PEI of tomato processing lines that manufacture different concentrations of tomato paste on an equivalent basis. Furthermore, such standardized values can be used to establish PEIbench based on an average PEIeq for a given set of n plants, as shown in eq 13. 12374

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Environmental Science & Technology PEIeq =

PEIactual E E = = Oeq Oact × EF EF

PEIbench =

Article

As shown in Figure 5, the application of EFsimple results in a PEIef‑simple vs outlet concentration relationship that agrees well with PEIactual only around the equivalence point of 31% solids. Clearly, differences between PEIactual and PEIef‑simple increase as outlet concentration moves away from the equivalence point (31%). Results (SI Table S-3) indicate that the AREsimple (absolute value of the relative error using EFsimple − eq 16) is ≤2.9% over the range of 24−40% outlet solids concentration, and grows to 39% for an outlet concentration of 8%. This implies that EFsimple may not be a valid metric for plants with outlet concentrations that deviate significantly from the equivalence point. Note, however, this error is quite minor when compared to errors introduced by not applying EFs at all (PEIno‑ef), in which case all concentrations are considered to have the same PEI.

(12)

n ∑i = 1 PEIeq. i

n

(13)

Benchmark values developed in this way are useful tools to help industries that manufacture concentrated products compare their energy use and process emissions on an equivalent basis. This allows industry to identify underperforming facilities and focus on improvement in these facilities. From a policy standpoint, PEIbench values developed on this equivalent basis can be used to reward the most energy efficient facilities, and can be used to incentivize underperforming facilities. Investigating the Accuracy of EF Application. To demonstrate the utility of EFs for the representation of PEI for different levels of product concentrates, a set of PEIef curves were constructed using a single PEIeq value for paste at 31% solids and the specified EF form. These curves were plotted against PEIactual data from the modeling results for the 5-effect evaporator system given in SI Table S-1, from which the PEIeq value at 31% solids (5300 kJ/kg) was also obtained. The agreement between these curves is presented graphically in Figure 5 and numerically in SI Table S-3. These results

ARE(%) = 100 × |PEIactual − PEIef |/PEIactual

It was postulated that the discrepancy between PEIactual and PEIef‑simple results from the fact EFsimple compares PEI on the basis of concentration, while the energy use of thermal concentration is more closely tied to the amount of water evaporated. To account for this, an adjusted EF form (EFevap) was developed, through which equivalent production is calculated in proportion to the ratio of water evaporated in the actual product over water evaporated for producing paste at the equivalence point, e.g., 31% solids. As shown in eq 17, EFevap has a form similar to that of EFsimple, with the addition of “−x0” in the numerator and denominator. (x0: feed solids concentration) ⎛x − x ⎞ 0⎟ Oeq,evap = EFevap × Oact = ⎜⎜ act ⎟ × Oact ⎝ xeq − x0 ⎠

highlight the applicability of the various EF forms discussed in this section. Throughout this section, the subscripts “simple”, “evap”, and “general” are used to delineate between different forms of EFs. In the evaluation of ARE, these subscripts are used to differentiate between back-calculated PEIef values determined using these varied EF forms. PEIef curves were generated as shown in eqs 14 and 15. Here, Eallocated represents the amount of processing energy that is attributed to a specific outlet concentration, based on a standard PEI value and equivalent output value.

PEIef =

(17)

As highlighted by the PEIef‑evap line in Figure 5 and SI Table S-3, use of EFevap also provides a good estimate of the energy used in paste production. The differences between PEIef‑evap and PEIactual get larger as output concentration moves away from the equivalence point, similar to EFsimple. For example, the AREevap (absolute value of the relative error based on EFevap) is shown to be ≤2.8% over the range of 24−40% outlet solids concentration, and grows to 38% at 8% outlet solids. The magnitude of this error is similar to that of AREsimple, although the application of the different forms, EFsimple and EFevap, lead to over/underestimates in opposite fashion, shown clearly in Figure 5. Interestingly, it is observed that when ETE ≫ ENE, AREevap is minimized, and when ETE ≪ ENE, AREsimple is minimized. These results are summarized in SI Figure S-3. Given this observation, a generalized EF form, EFgeneral, was formulated in an attempt to develop a generally applicable EF for processes that utilize thermal concentration, regardless of the relative magnitude of individual processing energy components. This relationship is presented in eq 18. Here, the values ETE, ENE, and ENT are taken at the equivalence point. This relationship assumes that ENE and ENT are relatively constant for different product concentration levels. As shown in Figure 5 and SI Table S-3, the application of EFgeneral results in much closer agreement for all product concentrations. AREgeneral is observed to be ≤0.6% over the range of 24−40% outlet solids concentration and grows to only 8% at 8% outlet solids. Furthermore, as shown in SI Figure S-3, PEIgeneral matches well with PEIactual, regardless of the relative magnitude of the individual processing energy elements.

Figure 5. PEIactual and PEIef for Different Equivalence Factor Forms (Ceq = 31%).

Eallocated = PEIeq,31% × Oeq

(16)

(14)

PEIeq,31% × Oeq Eallocated = = PEIeq,31% × EF Oact Oact (15) 12375

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constitute or imply its endorsement, recommendation, or favoring by the California State Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the California State Government or any agency thereof.

Oeq,general = EFgeneral × Oact ⎛ ⎞⎞ ⎛ E TE ⎜ xact − x0⎜ ⎟⎟ ⎜ ⎝ ETE + E NE + E NT eq ⎠ ⎟ =⎜ × Oact ⎞⎟ ⎛ E TE ⎟ ⎜x − x ⎜ ⎟⎟ 0 E +E +E ⎜ eq ⎝ TE NE NT eq ⎠ ⎠ ⎝

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LIST OF SYMBOLS AND ACRONYMS ARE Absolute value of the relative error: PEIactual vs PEIef (for specified EF form) ΔHv,x(T) Latent heat of vaporization for stream x, function of boiling point temperature ENE Nonevaporation related electricity input (includes auxiliary electricity used in evaporator unit) ENT Nonevaporation related thermal energy input ETE Evaporation related thermal energy input EF Equivalence factor GHG Greenhouse gases mwater,evaporated Total mass of water evaporated ms Mass of boiler steam used to drive evaporator system Oact Product output in terms of mass (actual) Oeq Product output in terms of equivalent mass Oeq,x Product output in terms of equivalent mass for specified EF: x (x = simple, evap., or general) PEI Product energy intensity PEIactual PEI modeling results expressed in terms of actual outlet concentration and mass PEIef PEI estimated on the basis of specified PEIeq and outlet concentration for specified EF PEIeq PEI expressed in terms of equivalent mass (or concentration) SE Steam economy xact Actual solids concentration of tomato paste product xeq Standard tomato paste equivalent concentration

(18)

Therefore, it is clear from the results of the analyses presented herein that the PEI of concentrated products can be compared on an equivalent basis with the help of EFs. As such, EFs can be used to develop benchmark PEI values for a number of facilities, despite differences in the degree of concentration carried out at various facilities. PEI information is a valuable tool to communicate the energy and emissions performance of products to consumers and to develop internal performance benchmarks for facilities. PEI metrics are also particularly wellsuited to serve as a comparative basis between facilities in an industrial GHG emissions cap-and-trade system, and can be used by policymakers to establish incentive programs to curb energy use and emissions. While this work focuses on the example of tomato paste processing, the methods presented herein should be broadly applicable to other industries that manufacture similar products to different compositions, including other food industries, as well as chemicals and gas manufacturing.

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ASSOCIATED CONTENT

S Supporting Information *

Evaporator systems: background and discussion (Figure S-1); derivation of energy balances (eqs 7 and 8) (Figure S-2); PEI vs paste outlet solids concentration (Table S-1); PEI vs. raw tomato feed solids concentration (31% outlet solids) (Table S2); PEIef and ARE vs paste outlet solids concentration for various EF forms (Table S-3); and AREgeneral, AREadj, and AREsimple vs paste outlet concentration for various levels of ENE (Figure S-3). This material is available free of charge via the Internet at http://pubs.acs.org/

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REFERENCES

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AUTHOR INFORMATION

Corresponding Authors

*Phone: (847)-467-2806; e-mail: [email protected]. *Phone: (847)-467-2806; fax: (847)-491-3728; e-mail: eric. [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the support of the California Environmental Protection Agency and the California Air Resources Board (CARB). This work was performed in support of CARB primary contract 10-115 with Ecofys, U.S., under subcontract 033520 to University of California, Berkeley, and subcontract 00008013 to Northwestern University. Neither the California State Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily 12376

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