Fuel
Economic Analysis of the Potential Value to Petroleum Refiners for Low Carbon
Boosted Spark Ignition Bio-blendstocks
--Manuscript Draft-Manuscript Number:
JFUE-D-22-02495
Article Type:
Research Paper
Keywords:
Refinery modelling, biofuels, boosted spark ignition, economic value, method
development, low carbon
Abstract:
A refinery optimization framework is developed to estimate the benefits of directly
blending high-quality bio-blendstocks into a refinery’s gasoline pool. We hypothesized
that bio-blendstocks with favorable fuel properties could provide an opportunity for
refineries to rebalance operations in potentially profitable ways, and this potential value
of the bio-blendstock is characterized by calculating the breakeven value. In this work,
biofuels are blended directly with refinery sourced blendstocks such that we produce a
finished premium grade gasoline (also termed as Co-Optima Boosted SI gasoline here)
along with other refinery products. The proposed modeling framework relied on
extensive data for projected product demands (including the share of premium
gasoline) over the next few decades, variations in crude oil and refinery product
pricing, and fuel quality specifications. The complete refinery models serve as a basis
for assessing the impact on profitability on representative petroleum refinery design
configurations. Our analysis indicates that breakeven value (BEV) of biofuels varied
widely from $20-$120/bbl depending on the fuel blending level and benchmark crude
prices. Further, the BEV was correlated with the fuel characteristics such octane
numbers, both antiknock index (average of research and motor octane numbers) and
sensitivity (difference between the research and motor octane numbers), with a slightly
higher correlation with the sensitivity. Implications towards refiners are explored
including opportunities to rebalance operations, access to high-value fuel markets, and
synchronization with broader transportation industry trends. Furthermore, results
indicate the value of Co-Optima boosted spark ignition (BSI) efficiency gains can
extend to refiners to incentivize decarbonization and diversified feedstock production.
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Highlights (for review)
Highlights

We demonstrate of a new approach to define the value of a biofuel linked to its fuel characteristics, hereby
characterized by a metric called the breakeven value.

The breakeven value of a biofuel to refiners facing dynamic economic and market conditions, depends on fuel
properties such as octane numbers (antiknock index, AKI i.e., (RON+MON)/2 and sensitivity, S, i.e., (RONMON)) in addition to the benchmark crude oil price.

This approach can be applied to any biofuel in gasoline, diesel, or jet range to find its economic value and
accelerate towards lowering a fuel carbon’s footprint.
Graphical Abstract (for review)
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Manuscript
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1
Economic Analysis of the Potential Value to Petroleum Refiners for Low Carbon Boosted Spark Ignition Bio-
2
blendstocks
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Nicholas A. Carlson*1, Avantika Singh*1, Michael S. Talmadge1, Yuan Jiang2, George G. Zaimes3, Shuyun Li2, Troy R.
4
Hawkins3, Daniel J. Gaspar2, Robert L. McCormick1, Magdalena M. Ramirez-Corredores4, Lauren Sittler1, Aaron Brooker1
5
1
6
2
7
3
8
4
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*Equal contributions. Corresponding authors: Nicholas.Carlson@nrel.gov and Avantika.Singh@nrel.gov
National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, CO 80401
Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, WA 99354
Argonne National Laboratory, 9700 Cass Avenue, Lemont, IL 60439
Idaho National Laboratory, 1955 North Fremont Ave, Idaho Falls, ID 83415
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Abstract
12
13
A refinery optimization framework is developed to estimate the benefits of directly blending high-quality bio-blendstocks into
14
a refinery’s gasoline pool. We hypothesized that bio-blendstocks with favorable fuel properties could provide an opportunity
15
for refineries to rebalance operations in potentially profitable ways, and this potential value of the bio-blendstock is
16
characterized by calculating the breakeven value. In this work, biofuels are blended directly with refinery sourced blendstocks
17
such that we produce a finished premium grade gasoline (also termed as Co-Optima Boosted SI gasoline here) along with other
18
refinery products. The proposed modeling framework relied on extensive data for projected product demands (including the
19
share of premium gasoline) over the next few decades, variations in crude oil and refinery product pricing, and fuel quality
20
specifications. The complete refinery models serve as a basis for assessing the impact on profitability on representative
21
petroleum refinery design configurations. Our analysis indicates that breakeven value (BEV) of biofuels varied widely from
22
$20-$120/bbl depending on the fuel blending level and benchmark crude prices. Further, the BEV was correlated with the fuel
23
characteristics such octane numbers, both antiknock index (average of research and motor octane numbers) and sensitivity
24
(difference between the research and motor octane numbers), with a slightly higher correlation with the sensitivity.
25
Implications towards refiners are explored including opportunities to rebalance operations, access to high-value fuel markets,
26
and synchronization with broader transportation industry trends. Furthermore, results indicate the value of Co-Optima boosted
27
spark ignition (BSI) efficiency gains can extend to refiners to incentivize decarbonization and diversified feedstock production.
28
Keywords
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Refinery modelling, biofuels, boosted spark ignition, economic value, method development, low carbon
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1.
31
The transportation sector is one of the largest contributors to global anthropogenic greenhouse gas (GHG) emissions, and in the
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United States (US) alone, accounted for over 28% of total GHG emissions in 2018 [1], [2]. There is a mounting concern to
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reduce the GHG emissions associated with gasoline and diesel fuels as well as improve the efficiency of combustion engines.
34
The research and development of sustainable gasoline blendstocks which demonstrate a synergistic performance improvement
35
when used in boosted spark ignition (BSI) engines was conducted through the Co-Optimization of Fuels & Engines (Co-
36
Optima) project[3]. Such biofuels, owing to their superior fuel properties such as higher-octane ratings, can be designed for use
37
in low-emission vehicle engines with potential efficiency improvements up to 15% [4], [5]. A recent publication elucidates the
38
benefits of using co-optimized fuels and engines that increase engine efficiency, lower sector wide GHG and other air pollutant
39
emissions, reduce water consumption, and support domestic job market growth [6]. Previous research, from Co-Optima and
40
other projects, has also focused on cost-benefit analysis and scalability of producing bio-blendstocks, but none so far have
41
explored the economic potential for market adoption of biofuels from a full refinery operations perspective [6], [7]. The
42
objective of this work is to complement previous analyses by assessing the potential economic value proposition for petroleum
43
refiners with respect to gasoline-range blendstocks identified in Co-Optima research.
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Commercially available gasoline is a mixture of several blendstocks, produced from a variety of separation and upgrading
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refinery operations that are ultimately blended into a gasoline pool. These blendstocks range from light hydrocarbons such as
46
butane to intermediate and heavy naphtha sourced from crude distillation (straight run), fluidized catalytic crackers,
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hydrocrackers, cokers, visbreakers, alkylation, isomerization, and reforming units. Table A1 summarizes the typical volume
48
concentration of these traditional gasoline blendstocks, the ranges of their octane values, and the sources of their production in
49
the refinery.
50
Progressively stringent fuel standards and heightened regulatory requirements are forcing gasoline producers to modify their
51
operations and creates a unique opportunity for the expanded use of biofuels in refinery operations. Advancements in fuel
Introduction
52
economy standards, known as Corporate Average Fuel Economy (CAFÉ) standards [8], and the proposal from automobile
53
manufacturers to create Research Octane Number (RON) 95 as the new uniform standard for gasoline will require an increased
54
share of high octane blendstocks, such as reformate, in the fuel mix [9]. The rising price of octane over the last five to six years
55
stemming from an increasing demand for premium gasoline and the increasing consumption of light shale oil [10] gives
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evidence that refineries are already facing operational constraints [11]. Additionally, the U.S. Environmental Protection
57
Agency (EPA) introduced Tier 3 regulations that require all gasoline sold in the US to meet a 10-ppm annual sulfur average
58
criterion [12]. Tighter sulfur restrictions could render some refineries unable to sell finished gasoline. Integrating bio-
59
blendstocks with superior fuel properties may help less advantaged refineries remain competitive despite changing market
60
demands and increasingly stringent fuel quality specifications.
61
Co-optima researchers have previously evaluated several bio-blendstocks based on their fuel properties, scalability, and
62
compatibility with existing infrastructure [6]. Candidates for the BSI combustion mode were systematically screened in a tiered
63
manner to down select promising candidates which encompass a range of functional groups [13]. An empirical relationship was
64
developed to estimate the theoretical gains in engine efficiency as a function of bio-blendstock properties such as octane
65
number, sensitivity (defined as the difference between research octane number (RON) and motor octane number (MON)), and
66
heating value, among others [5]. Promising bio-blendstocks which met the fuel performance and efficiency improvement
67
criteria were further evaluated to estimate their production costs using techno-economic principles as well as environmental
68
impact metrics [5], [13], [14]. Of the top Co-Optima BSI bio-blendstocks that were identified, seven of those: ethanol (ETC),
69
iso-propanol (IPR), n-propanol (NPR), iso-butanol (IBU), di-iso-butylene (DII), cyclopentanone (CYC), and a furans mixture
70
(FUR) are investigated in this study, primarily because of the availability of extensive blending data of these bio-blendstocks
71
with hydrocarbon blendstocks for oxygenated blending (BOBs).
72
Experimental biofuels property data from Co-Optima research was leveraged to build economic blending models based on
73
optimization tools, consistent with the methodology often deployed at a refinery [15]. Analysis efforts predicated upon these
74
models have two key outcomes of interest. First, identifying the value propositions of blending performance advantaged
75
biofuels into gasoline, which would be useful both to the refiners and the biofuel producers. Understanding the impact of
76
favorable biofuel properties such as octane, sensitivity, or Reid Vapor Pressure (RVP) on refinery economics can help generate
77
market pull for new bio-blendstocks from refiners. Second, coupling refinery models with life cycle assessment (LCA) can
78
identify the environmental benefits and tradeoffs of Co-Optima fuel blending (this will be the subject of an upcoming
79
publication).
80
With the aforementioned interests in mind, we hereby explore the economic opportunity of blending the most promising Co-
81
Optima BSI blendstocks into the gasoline pool. While all refinery and terminal blending operations are unique based the
82
regional availability and fuel specifications, we hereby demonstrate a framework to evaluate new biofuel options. To the best
83
of our knowledge, such analysis is not comprehensively discussed in scientific literature, and is largely limited to refinery
84
operators, particularly for quantifying the economic value of new bio-blendstocks. So, to establish that framework, this paper is
85
divided into three sections: (1) method development for benchmarking and analysis, (2) key results and discussions, and
86
subsequently, (3) future outlook. In the methods section, we outline the assumptions for establishing a model baseline with an
87
emphasis on the development of refinery pricing structures. Other key underpinnings of the analysis included in the modelling
88
approach are gasoline specifications, fuel demand projections, and blending properties of bio-blendstocks as discussed below.
89
Further, in the results section we dive into the specific quantification of the bio-blendstock value to refineries, particularly as a
90
function of its fuel properties at different blending ratios and different crude oil prices, while the future outlook section
91
highlights some of the challenges and shortcomings of this analysis approach. Overall, the objective of this analysis is to
92
evaluate if there are opportunities to improve the economics of a traditional petroleum refinery by utilizing the unique and
93
potentially valuable properties of the Co-Optima blendstocks.
94
95
2.
96
AspenTech’ s Process Industry Modeling System (PIMS) software [16] was used to develop and optimize three different
97
refinery configuration models using the “Gulf-Coast” (belonging to the Petroleum Administration for Defense District 3,
98
PADD3) example as a starting point. Differentiations between the three refinery configurations included varying complexities,
99
production rate targets, crude oil types, crude and product pricing, and fuel specifications relevant for Co-Optima analysis.
Materials and Methods
100
These are labeled as PADD3-Large, PADD3-Medium, and PADD3-Small intending to represent refineries of decreasing
101
conversion capacity and complexity, all located within the U.S. Gulf-Coast PADD3 region.
102
Information on the crude oils accessible to the refinery and their property characteristics and assays are incorporated in the
103
model based on published information pertaining to the PADD3 region [17]. Primary petroleum processing units and their
104
corresponding capacities shown in Table A2 along with typical yield compositions are also built into the model [18]. Ideas to
105
expand the scope of the model are presented after results in the model customization section.
106
The objective function in PIMS advanced optimization mode aims to maximize the refinery model’s gross margin subject to
107
constraints on crude availability, limitations on process unit capacities and operating conditions, and specifications on finished
108
fuels. The mass and energy balances are consistently maintained in all operations. The refinery models considered here
109
produce two grades of gasoline (a) regular and (b) premium for two blend types - conventional and reformulated - as well as
110
introducing a high-efficiency co-optimized gasoline (similar in specs to reformulated premium) containing one of the several
111
candidate bio-blendstocks. Notably, the co-optimized gasoline blend enacts constraints on two gasoline features to improve
112
efficiency and performance: (i) a novel minimum sensitivity of 10, and (ii) a minimum RON of 98. Table A3 displays the
113
finished fuel specifications applied in the analysis.
114
The following subsections highlight all components incorporated into the refinery models including the following: (2.1)
115
refinery configuration and capacity data, (2.2) product demand projections, (2.3) pricing structure, (2.4) bio-blendstock
116
properties for blending, and (2.5) break-even value calculation. These bases are derived from other Co-Optima projects,
117
published literature, and experimental data provide a comprehensive framework to assess refinery impacts and valuation results
118
for the BSI bio-blendstocks. `
119
2.1 Refinery Configuration and Capacity Data
120
Error! Reference source not found.A2 summarizes the process unit capacities of the refinery models employed in this study.
121
These configurations were developed based on U.S. Energy Information Administration (EIA) data on the US refining
122
infrastructure by each Petroleum Administration for Defense Districts (PADD) [18]. The goal was to develop sets of refinery
123
models that span a wide range of refinery configurations and complexities as indicated by the calculated Nelson Complexity
124
Index values in Table 2 Error! Reference source not found.[19]. Our analysis focuses on the PADD3-Large refinery
125
configuration and PADD3-Small configuration which are intended to serve as bookends.
126
2.2 Product Demand Projections from EIA, OPIS and ADOPT
127
Demand for gasoline range fuels for light duty vehicles is expected to rise in the next 30 years. To isolate the economic impact
128
of biofuels blending, time-based scenarios are designed between years 2020 to 2050 to represent changing market demands.
129
Fig. 1 presents the basis for the refinery operating scenarios with projections for the major refinery product categories such as
130
liquified petroleum gas (LPG), gasoline, jet, distillate, and residual fuels. EIA projections from the Annual Energy Outlook
131
(AEO) provide a complete basis for all product groupings [20]. In addition to the EIA gasoline BOBs projection, a second
132
gasoline projection is also considered in the refinery scenarios from the Automotive Deployment Options Projection Tool
133
(ADOPT) [21]. ADOPT is a consumer choice vehicle model developed by the National Renewable Energy Laboratory (NREL)
134
taking parameters like vehicle price, fuel cost, and range into account, which in turn predicts the fuel demand. The ADOPT
135
results predict a sharper decline in gasoline demand owing to a higher level of projected electrification in light-duty vehicles.
136
Product demand projections in terms of volumes can be found in Table A6.
45%
Propane and
LPG
140%
40%
130%
35%
120%
110%
30%
100%
25%
90%
80%
20%
70%
15%
60%
50%
2020
2025
2030
2035
2040
2045
10%
2050
Gasoline Market Share (%)
Product Demand (% of 2020 Demand)
150%
EIA - Gasoline
BOBs
ADOPT Gasoline BOBs
Jet/Kerosene
Distillate Fuel
Oils
Residual Fuel
Oils
Premium
Gasoline
Market Share
Year
137
138
Fig 1. Projected product demands for refinery product (left Y axis) categories from EIA [20] and ADOPT model [21] alongside
139
projected market share of premium gasoline fuels as a percentage of total gasoline fuels (shown by the dotted line linked to the
140
right Y axis) [11]. Note: the percentage projections here were multiplied by 400,000 barrels/day (BPD) and 45,000 BPD for
141
the PADD3-L and PADD3-S models, respectively, to set the maximum sale quantities for each product category in the refinery
142
models. Capping the sales of each product depending on the year and demand projection source (EIA or ADOPT) simulated
143
the dynamic economic conditions between 2020 – 2050.
144
145
In addition to the projections for overall market demands, scenarios also consider a projection for the market share of premium
146
gasoline relative to total gasoline products (Second Y axis, Fig. 1). Premium gasoline demand is important within the context
147
of the analysis because Co-Optima gasoline is categorized within the premium gasolines grouping. Fig. 1 shows the premium
148
market share interpolation between 2020 and 2050 based on data reported by OPIS [11].
149
2.3 Pricing Structure
150
Crude oil and product pricing models were developed to model the impact of dynamic petroleum markets on bio-blendstock
151
values. To simplify the number of economic inputs feeding the analysis, prices entering the model were correlated to a
152
benchmark crude oil price, namely West-Texas Intermediate (WTI). WTI was chosen because of its longstanding position as
153
the economic benchmark for crude oil pricing in U.S., its prevalence in the PADD3 district being the context for the analysis,
154
and the availability of historical pricing data. Examples for each pricing calculation introduced in this section can be found in
155
the Appendix.
156
2.3.1 Crude Oil Correlation: Quality and Price Determination
157
Historically, different crude oil prices are correlated but not equal due to differences in quality, production costs, or
158
transportation costs. Any crude oil historical pricing data that could be found in timestep with WTI was aggregated from
159
multiple data sources and used to linearly regress the crude’s price as a function of WTI price. After regression, a given crude
160
oil’s price could be modelled using equation 1:
(1) 𝑃𝑐𝑟𝑢𝑑𝑒,$ = 𝑚𝑐 𝑃𝑊𝑇𝐼,$ + 𝑏𝑐
161
162
Where slope (mc) and intercept (bc) were fitted parameters yielded from linear regression. Example of a crude oil pricing
163
calculation is shown in the Example A in the Appendix. Various pricing data sources were utilized including the Energy
164
Information Administration (EIA), Oil Price Information Service (OPIS), Bloomberg Terminal, and Baker & O’Brien’s
165
database to dilute any bias coming from an individual source. Modelling crude oil prices as a linear function of WTI price was
166
the preferred crude oil pricing method because of the high-quality correlations typically observed.
167
When there was an insufficient amount of historical crude oil pricing data, a backup method for obtaining crude oil price as a
168
function of crude qualities was developed. The variables in the pricing model include: the American Petroleum Institute (API)
169
gravity measure, sulfur content (weight %), Total Acid Number (TAN), and WTI benchmark price. API gravity is a commonly
170
reported index of crude oil density and generally reflects the degree of conversion necessary to make high value products such
171
as gasoline and diesel fuel. Sulfur content and TAN were measures intended to reflect the level of impurities in the crude oil
172
and the corresponding level of treatment needed to make finished fuels. The WTI benchmark price was included to give the
173
model a reference point and gave the model identical inputs when compared with the other pricing correlation models being
174
utilized.
175
A multiple linear regression model performed well in capturing the crude oil pricing variability as a function of the four
176
independent variables described above. Consequentially, crude oil prices determined by equation 2 supplanted pricing data
177
determined by equation 1 when historical data limitations were met:
178
(2) 𝑃𝑐𝑟𝑢𝑑𝑒,$ = 𝑚1 (𝐴𝑃𝐼) + 𝑚2 (𝑆𝑢𝑙𝑓𝑢𝑟𝑤𝑡% ) + 𝑚3 (𝑇𝐴𝑁) + 𝑚4 (𝑃𝑊𝑇𝐼,$ ) + 𝑏
179
An example calculation using the crude quality model can be found in Example B in the Appendix.
180
2.3.2 Product Price Determination
181
Crude oil purchases are proportionally the largest cost associated with refinery operations leading to a high degree of
182
correlation between the prices of crude oils and refinery products. Consequentially, product pricing model development with
183
simple linear correlations was similarly enabled, when compared to the crude oil pricing models, as depicted in equation 3.
(3) 𝑃𝑝𝑟𝑜𝑑𝑢𝑐𝑡,$ = 𝑚𝑝 𝑃𝑊𝑇𝐼,$ + 𝑏𝑝
184
185
Gaseous products such as natural gas or propane are less correlated to crude oil because they aren’t exclusively sourced from
186
crude oil production. However, the lower value of these products ultimately served to dampen the effects of pricing uncertainty
187
on the model’s profitability. Refinery intermediates were also priced to allow the PIMS-model to sell all molecules in case
188
certain finished product specifications could not be satisfied. The same set of diverse sources used for crude oil pricing were
189
again used to lessen the effects of bias from any one data source. An example calculation of gasoline price given a benchmark
190
WTI crude price can be found in Example C in the Appendix.
191
2.3.3 Octane Pricing Correlation
192
The proposed performance-enhancing qualities of co-optimized fuels for BSI engines are two-fold including 1) increased
193
octane which is historically priced by the market through a spread between premium and regular gasolines and 2) increased
194
sensitivity which has not been traditionally priced by the market. In an attempt to reliably and conservatively price co-
195
optimized fuels with otherwise unknown values, an octane pricing model was developed with reference to regular gasoline.
196
The pricing model is conservative due to its lack of accountability for increased sensitivity in the value of the co-optimized
197
fuel. Increased engine efficiencies from higher sensitivity fuels will certainly increase value to end-users so not accounting for
198
sensitivity effectively underprices co-optimized gasolines and the corresponding value bio-blending brings to refiners.
199
A single layer neural network model was adapted to historical data to predict octane value in terms of $/octane-gallon.
200
Therefore, the model’s output (Y) could be utilized in equation 4 to determine a price for co-optimized gasoline.
201
(4)
𝑃𝑐𝑜−𝑜𝑝,$ = 𝑌 (
$
𝑜𝑐𝑡∙𝑔𝑎𝑙
) (𝐴𝐾𝐼𝑐𝑜−𝑜𝑝 − 𝐴𝐾𝐼𝑟𝑒𝑔 )(𝑜𝑐𝑡) + 𝑃𝑟𝑒𝑔,$ (
$
𝑔𝑎𝑙
)
202
where octane value was multiplied by the difference in anti-knock index (AKI – calculated as the average of RON and MON)
203
of the co-optimized gasoline and regular, conventional gasoline.
204
205
The neural network model inputs included a baseline regular gasoline price, total U.S. octane demand, and the differentials of
206
benzene, toluene, and xylene commodity prices to regular gasoline price. The baseline regular gasoline price was included as a
207
predictor to reflect the overall supply-and-demand equilibration constantly induced in the U.S. gasoline market. Total U.S.
208
octane demand was calculated as the sum-product of regular and premium gasoline demands, respectively, and their
209
corresponding octane numbers found. This predictor was included to account for any octane-barrel supply constraints the U.S.
210
refining industry may have faced historically that would have induced higher prices. Price differentials between commodity
211
benzene, toluene, and xylene (BTXs) were also included because aromatics are common high-octane blendstocks refiners use
212
to upgrade their regular gasoline pool. The price difference between regular gasoline and the constituents that must be added to
213
form premium blends quantifies the value of octane to refiners to some degree. Predictors were highly correlated, so they were
214
grouped into two principled components using principled component analysis (PCA) prior to fitting the non-linear neural
215
network. The model was trained on 249 samples yielding a testing set R 2 of 0.97 on 62 samples with ten-fold cross-validation.
216
Fig. A1 shows a parity plot of the model’s predictions and historically realized premium spreads.
217
2.4 Bio-Blendstock Properties for Blending
218
All the identified bio-blendstocks considered in this analysis demonstrate a significant boost in the octane values of final blends
219
relative to the impact predicted by linear volumetric blending alone (Fig. 2, numerical data in Table A4).
120
Neat
10 vol%
20 vol%
30 vol%
10 vol%
20 vol%
30 vol%
Blending RON
120
80
100
60
40
20
60
40
0
ETC
40
80
20
0
IPR
Neat
NPR
10 vol%
IBU
DII
20 vol%
CYC
FUR
30 vol%
35
ETC
140
IPR
Neat
NPR
10 vol%
IBU
DII
20 vol%
CYC
FUR
30 vol%
120
Blending RVP (kPa)
Blending Sensitivity
Neat
140
100
Blending MON
160
30
100
25
20
15
10
5
0
80
60
40
20
0
ETC
IPR
NPR
IBU
DII
CYC
FUR
ETC
IPR
NPR
IBU
DII
CYC
FUR
220
Fig 2. Graphical summary of blending properties applied in this analysis for Co-Optima BSI bio-blendstocks which show
221
nonlinear effect on octane number, RVP, and other properties when combined with petroleum BOBs. Abbreviations are CYC:
222
cyclopentanone, DII: diisobutylene, ETC: ethanol, FUR: furans mixture, IBU: isobutanol, IPR: isopropanol, NPR: n-propanol.
223
The numerical values are described in Appendix Table A4.
224
225
To more accurately reflect the impacts of non-linear blending, effective blending octane numbers were calculated for each
226
blendstock at each blend level. The concept of blending octane number has been the subject of numerous studies [7] and can be
227
summarized as by the relationship shown in Equation 5 where RON i represents the blending research octane number of a given
228
bio-blendstock.
229
𝑅𝑂𝑁𝑏𝑙𝑒𝑛𝑑 = 𝑣𝐵𝑂𝐵 𝑅𝑂𝑁𝐵𝑂𝐵 + 𝑣𝑖 𝑅𝑂𝑁𝑖
(5)
𝑅𝑂𝑁𝑖 =
230
𝑅𝑂𝑁𝑏𝑙𝑒𝑛𝑑 −𝑣𝐵𝑂𝐵 𝑅𝑂𝑁𝐵𝑂𝐵
𝑣𝑖
231
Here, 𝑣𝐵𝑂𝐵 and 𝑣𝑖 represent the volume fractions of BOB and biofuel respectively, 𝑅𝑂𝑁𝑏𝑙𝑒𝑛𝑑 is the measured RON of the final
232
biofuel/gasoline blend, and 𝑅𝑂𝑁𝐵𝑂𝐵 is the measured RON of gasoline BOB. The data for 10%, 20%, and 30% blending levels
233
were found in the NREL’s Fuel Properties Database and are tabularized in Table A4 [22]. Blending research/motor octane
234
numbers and their resulting blending sensitivities were used as inputs to the refinery models to capture the effects of blend
235
level on bio-blendstock values.
236
237
2.5 Bio-Blendstock Breakeven Value (BEV) Characterization
238
The break-even value (BEV) for a bio-blendstock, or any other refinery input, is defined as the calculated maximum
239
purchasing cost that would preserve an equivalent gross margin under the same conditions without the bio-blendstock
240
purchase. The use of this calculation for valuation is consistent with industry practices for decisions like crude purchases as
241
well as other bio-blendstock research [7]. The BEV calculation procedure in this analysis was as follows: 1) fix model inputs
242
including benchmark WTI price, year, demand projection source, bio-blendstock candidate, and blending level 2) optimize
243
PIMS refinery model with no bio-blendstock purchasing and Co-Optima gasoline production allowed to form a baseline 3) re-
244
optimize the PIMS refinery model with bio-blendstock prices set to zero and Co-Optima gasoline production allowed 4) divide
245
the difference between observed profits by the volume of bio-blendstock purchased in the Co-Optima scenario as shown in
246
Equation 6. The units for the BEV are US$ per volumetric unit of bio-blendstock (denoted by BBS below), typically calculated
247
in barrels or gallons.
248
(6)
𝐵𝐸𝑉𝐵𝐵𝑆 =
𝑃𝑟𝑜𝑓𝑖𝑡𝐵𝐵𝑆 − 𝑃𝑟𝑜𝑓𝑖𝑡𝐵𝑎𝑠𝑒
𝐵𝐵𝑆 𝐵𝑙𝑒𝑛𝑑𝑒𝑑 𝑉𝑜𝑙𝑢𝑚𝑒
249
The bio-blendstock BEVs are ultimately a function of product demands, crude and product prices, refinery configurations,
250
refinery process unit capacities and constraints, blendstock properties, and finished fuel specifications. All of these elements
251
are considered by the Aspen PIMS model in optimizing refinery operating scenarios.
252
253
3.
Results
254
3.1 Establishing Baseline Refinery Gross Margin
255
A discussion on prospective refining strategies must consider the major market changes refiners are expected to endure over
256
the next 30 years. As projected in EIA’s Annual Energy Outlook and other industry perspectives, the refinery product slate is
257
expected to undergo substantial transformation with the demand for gasoline in the light duty transportation sector declining
258
while long haul transportation fuel demand is poised to increase [20] [23]. Fig. 3 depicts the PADD3-L model’s projected
259
refinery gross margin extending to 2050 under both demand projections given by EIA and ADOPT projections, respectively.
260
Gross margin values are given as percentages of 2020 gross margin. Whiskers represent the range of values observed over WTI
261
benchmark crude prices varied from $20-100/bbl.
Gross Margin (% of 2020 Value)
120%
110%
100%
90%
80%
EIA
70%
ADOPT
60%
2015
262
2020
2025
2030
2035
2040
2045
2050
2055
Year
263
Fig 3. PADD3-Large refinery gross margins normalized to 2020 values given demand projections from both the EIA’s
264
Annual Energy Outlook (2019) and ADOPT consumer choice model.
265
266
U.S. refineries are typically geared towards gasoline production (45%–50%), with diesel production approximately at 25% of
267
an overall refinery’s product slate [22]. Thus, the higher level of electric vehicle market penetration predicted by the ADOPT
268
model has an increasingly large effect on refinery profitability going out to 2050. The assumptions made in the EIA and
269
ADOPT models may be considered bookends with ADOPT being the least favorable outcome for the refining industry.
270
This work leveraged the expected trends in fuel demand to benchmark the change in refinery profitability with the assumption
271
that the refining sector does not reconfigure. While this was an unlikely scenario, in the absence of any verifiable data, this
272
assumption served as a basis to understand the value of bio- blendstock integration into the gasoline market.
273
3.2 Estimating Bio-Blendstock Break Even Values
274
Fig. 4 depicts each bio-blendstocks’ break-even value when blended at 10, 20, and 30 vol.% with a WTI benchmark crude
275
price of $60/bbl in year 2050 under EIA demand projections. This scenario was treated as a baseline as it represents a middle
276
range WTI price during a fully developed Co-Optima gasoline market in 2050. Bio-blendstocks without a bar corresponding to
277
the 10 vol.% blending level do not have a high enough sensitivity to meet the minimum Co-Optima gasoline sensitivity
278
specification of 10.
279
Break-Even Value of BSI BioBlendstocks ($/bbl)
140
120
100
80
10 vol%
60
20 vol%
30 vol%
40
20
0
ETC
IPR
NPR
IBU
DII
CYC
FUR
280
281
Fig. 4. BSI Bio-Blendstock break-even values ($/bbl) for the following scenario: $60/bbl WTI benchmark crude price, year
282
2050, and EIA demand assumptions.
283
284
3.3 Determining Bio-Blendstock Value and the role of Sensitivity parameter
285
Traditionally, refineries provide value to gasoline consumers by increasing octane to enable consumption in higher
286
performance engines. Co-optimized gasolines leverage increased sensitivity alongside octane to further increase engine
287
performance over modern high compression engines [24]. Common gasoline blendstocks typically have low sensitivities as
288
when compared to the bio-blendstocks sensitives (see Tables A4-A5). Gasoline upgrading units (i.e., reforming, isomerization,
289
alkylation, etc.) focus on increasing octane and provide little to no operational levers to adjust blendstock sensitivities.
290
Blending varying levels of BSI blendstocks being considered in Co-Optima bio-blendstocks featuring relatively high
291
sensitivities and low levels of impurities, to not interfere with other gasoline specifications, could provide a control mechanism
292
for refineries to adjust sensitivity.
293
Figs. 5 and 6 show the break-even values (BEVs), averaged over WTI benchmark prices of 20-100 $/bbl, of the seven bio-
294
blendstocks under consideration at blending levels of 10, 20, and 30 vol.%. Adjoining whiskers represent minimums and
295
maximums, respectively, observed in the 20-100 $/bbl WTI benchmark range. Fig. 5 plots BEVs against blending octanes,
296
accounting for variable octane boosting at different blending levels. A positive correlation is observed between the break-even
297
values and increasing octanes.
200
ETC
IPR
NPR
160
IBU
DII
CYC
140
FUR
Break Even Value ($/bbl)
180
120
100
80
60
40
y = 1.4066x - 85.105
R² = 0.2028
20
0
100
298
105
110
115
120
125
130
135
Blending Octane (RON + MON)/2
299
Fig. 5. Break even values for seven candidate BSI bio-blendstocks, at 10%, 20%, and 30% blending levels plotted
300
against corresponding blending octanes. CYC: cyclopentanone, DII: diisobutylene, ETC: ethanol, FUR: furans
301
mixture, IBU: isobutanol, IPR: isopropanol, NPR: n-propanol.
302
303
Fig. 6 similarly plots break-even values but juxtaposes them against the different bio-blendstock sensitivities taken as the
304
difference between blending RONs and MONs. A stronger correlation between blendstock value and sensitivity is observed
305
when compared to Fig. 5 (determined by the R-squared value). Fig. A2 and A3 plots the same data but shows three individual
306
regression lines for 10, 20, and 30 blending vol.% and shows the bulk of the correlation is attributed to 10 vol.%.
200
Break Even Value ($/bbl)
180
160
ETC
IPR
NPR
IBU
DII
CYC
FUR
140
120
100
80
60
40
y = 2.2572x + 22.01
R² = 0.4697
20
0
7
12
17
22
27
32
37
Blending Sensitivity (RON - MON)
307
308
Fig. 6. Break even values for seven candidate BSI bio-blendstocks, at 10%, 20%, and 30% blending levels plotted
309
against corresponding blending sensitivities determined as the difference between blending RON and MON. CYC:
310
cyclopentanone, DII: diisobutylene, ETC: ethanol, FUR: furans mixture, IBU: isobutanol, IPR: isopropanol, NPR: n-
311
propanol.
312
313
The data indicates that although bringing high octane bio-blendstocks to the refinery is valuable, incremental improvements in
314
sensitivity are more valuable when co-optimized engines create a market demand for high sensitivity fuel. Refineries don’t
315
necessarily need outsourced blendstocks to meet higher octane specifications or to fill excess demand since gasoline demand is
316
projected to remain stable if not decline steadily. The true value proposition bio-blending seems to bring to refineries is the
317
capability of producing specialty fuels with property considerations other than octane. These fuels could become additional
318
value chains for refineries and could supplant lost revenues resulting from decreasing gasoline demands.
319
320
3.4 Determining the Optimal Blending Volumes
321
Fig. 7A also plots break even value averages for PADD3-L, with minimums and maximums observed across the 20-100 ($/bbl)
322
range again represented as whiskers. Each bio-blendstock has a clear optimum blending level, most consistently around the 20
323
vol.% mark except for the furan mixture. The majority of the blendstocks having an optimal value indicates that beyond a
324
certain level, the added sensitivity brought through bio-blending no longer has a marginal benefit to the refinery. As shown in
325
Fig. 2, furans have an octane sensitivity significantly higher than other bio-blendstocks, and therefore a lower blend level is
326
preferred from the economic perspective.
Fig. 7B relates each bio-blendstocks’ optimal blending volume to its pure sensitivity and depicts a clear inverse relationship.
328
Optimal blending volumes were determined by finding the maximums of quadratic functions fit to the data presented in Fig.
329
7A. The furans mixture is excluded because additional runs below the 10% blending level would be required to find an optimal
330
blending volume. With increasing sensitivity, less bio-blendstock is required to meet the co-optimized gasoline pools
331
sensitivity specification.
200
180
160
140
120
100
80
60
40
20
0
30
Optimal Blending Level
(Vol%)
Break Even Value ($/bbl)
327
25
20
15
10
y = -0.7165x + 36.386
R² = 0.7677
5
0
5
10
15
20
25
30
35
15
Bio-blendstock Blending Level (Vol%)
(A)
20
25
30
Blending Sensitivity (RON - MON)
35
(B)
Fig. 7. (A) Bio-blendstock break even values, averaged over 20-100 $/bbl WTI benchmark prices and EIA/ADOPT
projections from 2020-2050, plotted against blending level in co-optimized gasoline. (B) Optimal blending level plotted
against pure bio-blendstock sensitivity. CYC: cyclopentanone, DII: diisobutylene, ETC: ethanol, FUR: furans mixture,
IBU: isobutanol, IPR: isopropanol, NPR: n-propanol.
332
333
334
3.5 Bio-Blendstock Integration Value Over Time
335
Integrating bio-blendstock can give refiners access to novel value-chains with the potential to replace expected lost revenues
336
stemming from declining gasoline demand. Fig. 8 depicts the average break-even value for PADD3-L across all bio-
337
blendstocks and 20-100 ($/bbl) WTI benchmark price levels with observed minimums and maximums as whiskers. Using the
338
specific methods described in this analysis, the value of bio-blending to refiners does not appear to be agnostic to the gasoline
339
market’s projected contraction. The aggregate break-even values appear to correlate with the decreasing refinery gross-margin
340
depicted in Fig. 3 with a more severe decline under ADOPT gasoline demand projections.
140
EIA
ADOPT
Break Even Value ($/bbl)
120
100
80
60
40
20
0
2025
2030
2035
2040
2045
2050
2055
Year
341
342
Fig. 8. Break even values averaged over the seven bio-blendstocks, WTI benchmark prices ranging from $20-100/bbl,
343
and 10%, 20%, and 30% blending levels shown from 2030 to 2050.
344
345
More notably, the average break-even values remain steadily high during the anticipated gasoline market contraction from
346
2030-2050 indicating consistent value to refiners through unfavorable economic conditions. Blending co-optimized fuels
347
combats decreasing gasoline margins by adding new value chains to the gasoline market while diversifying feedstock sourcing
348
with the displacement of traditional fossil feedstocks with bio-derived feedstocks.
349
3.6 Bio-Blendstock Value to Low-Conversion Refinery
350
Although sensitivity has been identified as the key value driver for refineries to integrate Co-Optima bio-blendstocks, the
351
supplemental octane boost can be an additional attraction for certain refineries facing conversion or octane constraints. Lower
352
complexity refineries with less conversion capacity have inherently less flexibility in their blending operations and can often be
353
octane constrained. The value proposition of bio-blending to conversion constrained refineries was studied using the PADD3-
354
Small refinery model. The main changes from the PADD3-Large model included reducing the capacity from 400,000 bbl/day
355
to 43,500 bbl/day and removing the gasoil hydrotreating, catalytic cracking, hydrocracking, and delayed-coking units.
356
357
Without bio-blending, the PADD3-Small model could not produce enough high-octane gasoline blendstocks to sell premium
358
gasoline. As shown in Fig. 9, integrating BSI bio-blendstocks induced a step change in profitability for the small refinery
359
because the bio-blendstocks’ high octane compensated for the refineries lack of octane-barrels. A portion of the refineries’
360
lower-quality gasoline blendstocks could be diluted by the high-quality bio-blendstocks in the co-optimized gasoline pool,
361
featuring a large pricing premium over regular gasoline. At the 10% blending level, there was not enough high-octane bio-
362
blendstock purchasable by the model to compensate for the low-quality gasoline blendstocks, so no co-optimized fuel could be
363
sold. For this reason, Fig. 9 only compares the 20% and 30% blending level scenarios observed for the PADD3-Small and
364
PADD3-Large models.
200
PADD3L
Break Even Value ($/BBL)
180
PADD3S
160
140
120
100
80
60
40
20
0
2025
2030
2035
2040
2045
2050
2055
Year
365
366
Fig. 9. Break even values averaged over the six candidate BSI bio-blendstocks, 20-100 $/bbl WTI benchmark prices,
367
and 20% and 30% blend levels with comparison between the PADD3-Large and PADD3-Small refinery models.
368
369
Fig. 9 shows that bio-blending is more valuable to lower complexity refineries because it not only brings in capabilities to
370
produce specialty, high-value fuels, but also introduces high octane-barrels into their otherwise constrained blending
371
operations.
372
373
4.
374
4.1 Model Customization and Improvement
375
This work demonstrates the approach to define the value of a biofuel linked to its fuel characteristics such as octane number,
376
and sensitivity. Though this analysis demonstrates high sensitivity/RON as fuel properties driving value to refiners producing
377
Co-Optimized BSI gasoline, there are certainly many avenues one could take to extend or reframe the research. As seen in the
Discussion
378
previous section, the value of a bio-blendstocks to a refiner increases as a function of increasing RON and increasing
379
sensitivity. However, when we tried to rank which of these two factors may have a greater impact for the refiner, we find that
380
both octane number and sensitivity are highly correlated and trying to delineate the two did not give a very clear ranking
381
between RON and sensitivity. Higher resolution blending data could better inform the non-linear blending models featured
382
here.
383
Additionally, the modelling approach as discussed here can be customized and adapted for improved accuracy. For example,
384
we were working with limited blending data from 3 summer BOBs (combination of conventional and reformulated BOBs) to
385
obtain blending in numbers. However, previous research has shown that determination of specific BOB characteristics
386
(PIONA, RVP, etc.) would allow for a more specific blending octane number and a higher degree of accuracy rather than a
387
generic calculation for blending octane numbers [25]–[28]. The same applies for RVP [29]–[31]. More specific determination
388
of blending properties (RON, S, RVP) can enable more accurate calculations and can be tailored for specific refinery outputs
389
and characteristics.
390
391
Another notable aspect is the impact on ease of vaporization or the distillation profile (D86 curve), which determines the
392
drivability experience, such as knocking, etc. [29], [32], [33]. In this analysis, we were only solving for regulatory specs such
393
as RVP and octane. However, inclusion of D86 data could be an additional step that can be takes to make the analysis more
394
comprehensive.
395
396
We also would like to highlight that the analysis presented here for gasoline closely mirrors the reformulated summer gasoline
397
specifications, which is more stringent in terms of RVP, as opposed to winter, which has a higher RVP minimum [34]. We
398
hypothesize that high-octane blendstocks which hit the RVP constraint of summer gasoline, for example, could potentially still
399
be valuable for winter gasoline when cheaper naphtha streams and butane are available for blending. This would allow refiners
400
to still create finished gasoline with higher biofuel blending specifically in situations where the constraining criteria is seasonal.
401
402
Similarly, PADD and fuel specifications vary not only in the US but also in other countries (cite). Also, it is known that every
403
refinery is unique in its location, design, crude slate, operating limits, and refined products. Therefore, the analysis presented
404
here is limited in its applicability to the hypothetical refinery models considered. Refineries outside of the PADD3 district
405
which consume different crudes and meet different specifications could also be studied. Hence, this study which was
406
developed for PADD3 refinery configuration can be customized or adapted for more accuracy. The fuel specifications as well
407
as the characteristics of a specific refinery (crude/product slate) vary across different geographies and different continents so a
408
different more specialized refinery case study might be warranted to realize the benefits of biofuels. Here, we are
409
demonstrating a proof of concept as well as a framework on how to approach blending of biofuels and how to value a biofuel
410
for a specific refinery, so this technique should be applicable even with different sets of data leading, potentially leading to
411
different results in the in terms of value of biofuel. Some of these aspects, such as variability in crude pricing, are covered in
412
the results sections before.
413
A potential drawback with this approach stems from the lack of wide scale adoption, i.e., second generation biofuel, from
414
feedstocks such as herbaceous biomass or woody feedstocks, that are not currently available in sufficient volumes and that lack
415
sufficient infrastructure for production, transportation, and distribution [14], [35]. With the limited availability of bio-
416
blendstocks, their prices might be constrained by the supply and demand which can potentially impact refinery economics. In
417
this analysis we assume that sufficient biofuel is available for all refineries to meet their demand, but it would be dictated by
418
supply and demand factors. Some of these aspects are discussed in an upcoming publication.
419
Finally, in this model we correlated the value of products associated with a single WTI price benchmark and octane price gradient
420
and calculated different crude oil prices as well as product prices as a function of WTI. Consequently, there is uncertainty built
421
in the model, as seen by the whisker plots). This approach works to present results as a function of WTI pricing alone for the
422
purposes of this research work. An alternate approach could entail using an average of market data from the previous years as
423
well as future projections to quantify the value of premium fuel.
424
4.2 Outlook and Next Steps
425
The refinery models detailed here could serve as the basis for even more comprehensive models. Potential modifications could
426
range from PIMS sub-model alterations, the addition of new bio-blendstocks/products, to simple backend calculations using the
427
material and cash flows produced by the PIMS models, which may have much wider implications. More specific ideas to build
428
upon the analysis are presented below:
429
1.
Shared value between biofuel producers and refiners: A more complete understanding of each bio-blendstock’s
430
economic feasibility could be obtained be taking the difference between BEV and minimum selling price (MSP),
431
derived from pathway techno-economic analysis (TEA) for producing the bio-blendstock. These differences would
432
represent the potential shared benefits between the bio-blendstock producer and petroleum refiner. Alternatively,
433
calculating the price premiums, over a benchmark gasoline, needed to incentivize the refinery to purchase bio-
434
blendstocks at their TEA derived MSPs, combined with the anticipated efficiency gains expected from Co-Optima
435
engines, would yield an even more comprehensive picture of each bio-blendstock’s economics.
436
437
2.
Integration with SAFs/HD/petrochemical plants: The biggest impact of this work lies in the potential for integration of
438
drop-in biofuels not just for the gasoline pool, but adopting the same approach for the entire product pool at a refinery.
439
This methodology can be applied for sustainable aviation fuels as well as heavy duty fuels, which can alternatively
440
route more fossil derived streams to petrochemicals plants such as BTX or other high value chemicals, ultimately
441
leading to maximum profitability and increased sustainability at a refinery. The potential for biofuel blending in the
442
heavy-duty market is the subject of companion a manuscript.
443
3.
GHG Emissions Reduction: Future work will consider the life cycle greenhouse gas benefits of blending biofuels into
444
the gasoline and diesel-range fuel pools, by coupling ASPEN PIMS refinery simulation with life cycle assessment
445
(LCA). This novel perspective accounts for energy use and emissions in the foreground refinery complex, such as utility
446
requirements and process energy use and emissions across individual refinery processing trains, as well as background
447
changes in the supply chains of purchased goods consumed at the refinery over time (e.g., changes in the carbon intensity
448
of purchased electricity, crude oil supply, etc.). Life cycle impacts can be aggregated refinery-wide, or shown for
449
individual refinery products, and benchmarked against a ‘reference’ refinery case to contextualize the potential
450
emissions benefits. Further, this approach can track environmental impacts over time and across a wide array of
451
sustainability and climate metrics, and thus provides a broad-based understanding of the impact of key parameters such
452
as changes in demand for refinery products, crude oil price, biofuel blending level, etc. on the environmental
453
sustainability of refinery operations.
454
4.
Co-processing as an avenue for more opportunities: A larger refinery-wide optimization with the objective of lowering
455
the carbon footprint as well as maximizing the profitability of the refinery can be accomplished. In this case, we are
456
addressing biofuels blending alone, but coprocessing with pyrolysis oil or algal/terrestrial hydrothermal liquefaction oil
457
can be other potential avenues for bringing bio-derived intermediates into a refinery and upgrading them into finished
458
fuels. This combined system-wide optimization can potentially be done in the near term while the refinery focuses on
459
meeting increasing demands of diesel and jet fields. The California Air Resources Board is actively looking into methods
460
by which they can quantify the biogenic content of the finished fuel from coprocessing, creating markets for new LCFs
461
applications.
462
463
5.
Policy Factors for Adoption: Market dynamics such as policy credits whether they are low carbon fuel standard in
California or federal RIN credits in the US can foster a market for these biofuels and enable faster biofuel adoption.
464
California alone has been a big draw for renewable diesel similarly policies as they evolve in other countries or other
465
parts of the world especially in Europe can also then able liquid fuels that have a lower carbon footprint than the current
466
100% fossil derived refinery fuels. Other countries also have policies in effect that encourage more drop-in biofuels for
467
blending.
468
469
5
470
This work demonstrates that Co-Optima initiatives to co-design specialty engines and fuels has incentives for the refining
471
industry as well as gasoline consumers. In the case of Co-Optima BSI bio-blendstocks, refineries can leverage bio-blendstocks
472
with superior properties to produce premium grade gasoline that benefits the environment. This value proposition, taken with
473
the chance for refiners to take part in a more circular and diversified feedstock economy, gives multiple reasons for refiners to
474
consider partaking in a low carbon fuel market. Moreover, this analysis is one example of the framework to evaluate the value
475
propositions of integrating biofuels and the refiners facing dynamic economic and market conditions can produce specialty,
476
high-value fuels to stay competitive.
Conclusion
477
478
Conflicts of interest
479
No conflict of interest to declare
480
Data Availability
481
For any data requests, please reach out to the corresponding authors: Avantika.Singh@nrel.gov and
482
Nicholas.Carlson@nrel.gov
483
Abbreviations
484
BSI
Boosted Spark-Ignition
485
GHG
Greenhouse Gas
486
CAFÉ
Corporate Average Fuel Economy
487
RON
Research Octane Number
488
MON
Motor Octane Number
489
AKI
Anti-Knock Index
490
S
Sensitivity
491
EPA
Environmental Protection Agency
492
ETC
Ethanol
493
IPR
Iso-propanol
494
NPR
N-propanol
495
IBU
Iso-butanol
496
DII
Di-iso-butylene
497
CYC
Cyclopentanone
498
FUR
Furans Mixture
499
BOB
Before Oxygenate Blend
500
RBOB
Reformulated Before Oxygenate Blend
501
RVP
Reid Vapor Pressure
502
LCA
Life Cycle Assessment
503
PIMS
Process Industry Modeling System
504
PADD
Petroleum Administration for Defense Districts
505
LPG
Liquefied Petroleum Gas
506
AEO
Annual Energy Outlook
507
ADOPT
Automotive Deployment Options Projection Tool
508
NREL
National Renewable Energy Laboratory
509
BPD
Barrels-per-day
510
WTI
West-Texas Intermediate
511
OPIS
Oil Price Information Service
512
API
American Petroleum Institute
513
TAN
Total Acid Number
514
BTX
Benzene, Toluene, Xylenes
515
PCA
Principled Component Analysis
516
BEV
Break-Even Value
517
PIONA
N-paraffins, Iso-paraffins, Olefins, Naphthenes, and Aromatics
518
MSP
Minimum Selling Price
519
TEA
Techno-Economic Analysis
520
BBS
Bio-Blendstock
521
DOE
Department of Energy
522
LSR
Light Straight Run Naphtha
523
FCC
Fluid Catalytic Cracking
524
ASTM
American Society for Testing and Materials
525
526
Acknowledgements
527
The authors gratefully acknowledge funding support from the Co-Optimization of Fuels & Engines (Co-Optima) project
528
sponsored by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy, Bioenergy Technologies and
529
Vehicle Technologies Offices. This work was authored in part by the National Renewable Energy Laboratory, operated by
530
Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308.
531
The views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government. The U.S.
532
Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains
533
a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow
534
others to do so, for U.S. Government purposes.
535
Additionally, we would like to acknowledge Amie Sluiter for providing thoughtful comments in her review of this work.
536
537
538
539
540
541
542
543
544
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546
547
548
549
550
551
Appendix A
552
Table A.1. Primary gasoline blendstocks and their typical RON values, volume share, and sources [36] Abbreviations used-
553
LSR: Light straight run; FCC: Fluid Catalytic Cracking; RVP: Reid Vapor Pressure, RON: Research Octane Number, MON:
554
Motor Octane Number.
Description
Typical
Typical
Sources
RON
Volume
Refinery-
Range
Share (%)
Produced
●
Purchased
●
Refinery Process
Comments
Crude Distillation,
High RVP- limited
Catalytic Cracking
during summer
92
2-4
60-70
2-3
LSR Naphtha
60-70
8-10
●
Crude Distillation
Alkylate
93-96
10-12
●
Alkylation
Isomerate
82-86
5-7
●
Isomerization
Potential RVP issues
Large RON/MON
23-25
●
Catalytic
90-100
Reforming
spread
Aromatics
Higher value in
Extraction
petrochemical market
Butane
●
Natural
Gasoline
Reformate
(full range)
Toluene
114
<1
FCC Naphtha
89-95
33-35
●
●
Main gasoline
Catalytic Cracking
component
(full range)
Light
85-88
<5
117
10
●
Hydrocracking
Hydrocrackate
Ethanol
555
556
●
Limited at 10 vol%
557
Table A.2. Refinery configurations applied for Co-Optima refinery impact and bio-blendstock valuation analysis for PADD3
558
representative refineries [18]. Nelson Complexity Index is calculated using the methods shown in [19]. Symbols: * denotes
559
that * not applied in BSI bio-blendstock analysis. Abbreviations: kbbl/day is the volume of thousand barrels crude oil input to
560
the refinery each day. The minimum turndown capacities for each unit operation are set to 50% of the design capacity.
Unit Operation
PADD3
PADD3
PADD3
Large
Medium*
Small
Atmospheric Distillation
400
160
45
Vacuum Distillation
220
87
9.7
Fluid Catalytic Cracking
142
85
Delayed Coking
105
46
Hydrocracking
49
Gas Oil Hydrotreating
72
72
Diesel Hydrotreating
96
101
Jet/Kero Hydrotreating
65
Gasoline Hydrotreating
38
46
Naphtha Hydrotreating
116
54
13.4
Naphtha Reforming
108
52
9.3
Aromatics/Isomerization
30
Alkylation/Polymerization
39
(Capacities in kbbl / Day)
561
562
563
564
565
566
12.8
6
15
567
Table A.3. Finished fuel property specifications applied in Co-Optima BSI impact analysis from American Society for Testing
568
and Materials (ASTM) [24].
Spec
Conventional
Conventional
Reformulated
Reformulated
Co-Optima
Type
Regular
Premium
Regular
Premium
Boosted SI
Max
9
9
7.8
7.8
7.8
Blend Property
RVP (psi)
Research Octane
Min
98
Number, RON
Anti-Knock Index
Min
87
93
87
93
Octane Sensitivity,
Min
10
RON – MON
50 Vol % Evap, °F (°C)
Min
150 (66)
150 (66)
150 (66)
150 (66)
150 (66)
Sulfur, wppm
Max
10
10
10
10
10
569
570
Table A.4. Blending properties applied for Co-Optima BSI bio-blendstocks from Fuels Properties Database [18].
Bio-Blendstock
Blend Vol.%
Blending MON Blending RON
Blending S
Blending RVP (kPa)
10%
106.1
132.8
26.8
116.0
20%
112.7
145.9
33.2
116.7
30%
102.4
128.4
26.0
68.1
Neat BBS
90.0
109.0
19.0
18.6
10%
102.8
117.2
14.4
88.5
20%
109.4
127.7
18.3
85.8
30%
102.5
120.6
18.2
54.8
Neat BBS
96.7
112.5
15.8
14.6
10%
98.3
117.4
19.1
74.0
20%
102.7
127.4
24.7
69.5
30%
94.8
118.7
23.9
48.0
Neat BBS
89.0
104.0
15.0
9.7
10%
95.1
110.3
15.1
53.6
Ethanol
Iso-propanol
N-propanol
Iso-butanol
20%
99.0
118.4
19.5
46.6
30%
93.6
113.0
19.4
38.4
Neat BBS
93.0
107.0
14.0
1.7
10%
99.5
113.4
13.9
33.9
20%
103.1
123.1
19.9
19.8
30%
93.3
117.3
24.1
16.2
Neat BBS
87.0
106.0
19.0
11.0
10%
97.8
108.1
10.3
53.6
20%
101.6
117.4
15.7
43.8
30%
93.4
115.8
22.3
28.3
Neat BBS
89.0
101.0
12.0
1.5
10%
100.7
131.4
30.7
41.6
20%
104.3
141.3
37.0
34.4
30%
93.7
120.5
26.8
36.5
Neat BBS
91.6
109.0
17.4
7.8
Diisobutylene
Cyclopentanone
Furan Mix
571
572
573
Table A.5. Common refinery sourced gasoline blendstock sensitivity values [37].
Gasoline Blendstock
574
575
576
Research Octane
Motor Octane
Sensitivity
Number (RON)
Number (MON)
(RON – MON)
Butane
93.8
89.6
4.2
Hydrotreated light straight run naphtha
50-65
55-60
-5-5
Full-range reformate
94-104
79-92
12-22
Full-range fluidized catalytic cracking gasoline
90-93
79-81
11-12
Alkylate
95
93
2
Isomerate
84
81
3
577
Table A.6. Refinery product demand projections from Energy Information Administration’s (EIA) Annual Energy Outlook
578
(AEO) and the National Renewable Energy Laboratory’s (NREL) Automotive Deployment Options Projection Tool (ADOPT).
Year
579
580
581
582
EIA (Billion Gallons / Year)
Gasoline Jet /
LPG
BOBs
Kero
Distillates
Residuals
ADOPT (Billion Gallons / Year)
Gasoline Jet /
LPG BOBs
Kero
Distillates
Residuals
2020
48.65
133.28
30.30
67.65
4.72
48.65
129.12
30.30
67.65
4.72
2021
49.46
132.20
30.16
66.97
4.62
49.46
128.12
30.16
66.97
4.62
2022
50.53
130.39
29.95
67.15
3.95
50.53
126.97
29.95
67.15
3.95
2023
51.54
127.96
29.98
66.48
4.81
51.54
125.70
29.98
66.48
4.81
2024
52.28
125.41
30.13
66.30
4.88
52.28
124.62
30.13
66.30
4.88
2025
52.80
122.79
30.39
66.03
4.92
52.80
123.52
30.39
66.03
4.92
2026
53.22
120.78
30.63
65.97
4.72
53.22
122.24
30.63
65.97
4.72
2027
53.62
119.05
30.89
65.63
4.65
53.62
121.01
30.89
65.63
4.65
2028
54.10
117.52
31.19
65.48
4.34
54.10
119.75
31.19
65.48
4.34
2029
54.58
116.14
31.47
65.13
4.32
54.58
118.30
31.47
65.13
4.32
2030
55.16
114.97
31.76
64.63
4.65
55.16
116.68
31.76
64.63
4.65
2031
55.65
113.98
32.05
64.36
4.62
55.65
114.94
32.05
64.36
4.62
2032
56.11
112.94
32.35
64.07
4.61
56.11
112.99
32.35
64.07
4.61
2033
56.55
111.99
32.64
63.82
4.57
56.55
110.97
32.64
63.82
4.57
2034
57.02
111.08
32.92
63.69
4.56
57.02
108.82
32.92
63.69
4.56
2035
57.52
110.20
33.19
63.57
4.51
57.52
106.61
33.19
63.57
4.51
2036
57.90
109.51
33.46
63.56
4.20
57.90
104.40
33.46
63.56
4.20
2037
58.29
108.92
33.74
63.39
4.17
58.29
102.20
33.74
63.39
4.17
2038
58.67
108.44
34.00
63.29
4.07
58.67
100.09
34.00
63.29
4.07
2039
59.10
108.07
34.28
63.18
4.02
59.10
98.02
34.28
63.18
4.02
2040
59.56
107.87
34.58
63.25
3.94
59.56
96.00
34.58
63.25
3.94
2041
59.98
107.76
34.88
63.26
3.99
59.98
93.99
34.88
63.26
3.99
2042
60.52
107.76
35.19
63.39
3.81
60.52
92.07
35.19
63.39
3.81
2043
60.96
107.85
35.52
63.53
3.77
60.96
90.19
35.52
63.53
3.77
2044
61.47
108.02
35.86
63.76
3.63
61.47
88.40
35.86
63.76
3.63
2045
61.98
108.22
36.22
63.90
3.71
61.98
86.63
36.22
63.90
3.71
2046
62.58
108.53
36.60
64.17
3.55
62.58
84.91
36.60
64.17
3.55
2047
63.08
108.93
36.99
64.38
3.52
63.08
83.23
36.99
64.38
3.52
2048
63.57
109.34
37.38
64.54
3.50
63.57
81.69
37.38
64.54
3.50
2049
64.18
109.79
37.79
64.73
3.46
64.18
80.35
37.79
64.73
3.46
2050
64.58
110.31
38.20
64.83
3.42
64.58
79.05
38.20
64.83
3.42
583
0.10
Predicted Premium Spread ($/gal)
0.09
0.08
0.07
0.06
0.05
0.04
0.03
R2 = 0.97
0.02
0.01
0.00
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
Historical Premium Spread ($/gal)
584
585
Fig A.1. Parity plot of predicted versus actual premium gasoline spreads dating between 1994 and 2019.
140
Break Even Value ($/BBL)
120
100
y = -0.3114x + 120.07
R² = 0.1675
80
y = -0.6757x + 146.92
R² = 0.7153
60
40
10%
y = 4.0683x - 388.6
R² = 0.5886
20%
20
30%
0
100
586
105
110
115
120
125
130
135
Blending Octane (RON + MON)/2
587
Fig A.2. Break even values for seven candidate BSI bio-blendstocks, at 10%, 20%, and 30% blending levels plotted
588
against corresponding blending octanes. CYC: cyclopentanone, DII: diisobutylene, ETC: ethanol, FUR: furans
589
mixture, IBU: isobutanol, IPR: isopropanol, NPR: n-propanol.
590
140
Break Even Value ($/bbl)
120
100
y = 0.1068x + 81.157
R² = 0.0234
10%
80
60
20%
40
30%
y = 0.3549x + 65.989
R² = 0.1118
y = 4.2709x - 23.188
R² = 0.8889
20
0
5
591
10
15
20
25
30
35
40
Blending Sensitivity (RON - MON)
592
Fig A.3. Break even values for seven candidate BSI bio-blendstocks, at 10%, 20%, and 30% blending levels plotted
593
against corresponding blending sensitivities. CYC: cyclopentanone, DII: diisobutylene, ETC: ethanol, FUR: furans
594
mixture, IBU: isobutanol, IPR: isopropanol, NPR: n-propanol.
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
Appendix B
612
Example A: Crude Oil Price Calculation from Benchmark
613
The following data was collected from both the Bloomberg and Baker & Obrien databases. The prices in timestep of both
614
Cabinda and West Texas Intermediate (WTI) crude oils were plotted against one another revealing a high degree of correlation
615
enabling an expression of Cabinda price as a simple linear function of WTI price.
140
y = 1.22x - 6.55
R² = 0.95
Cabinda ($ / BBL)
120
100
80
60
Bloomberg Terminal
40
Baker & Obrien
Database
20
0
30
40
50
60
70
80
WTI ($ / BBL)
90
100
110
616
617
Fig B.1. Cabinda crude historical prices plotted with reference to West Texas Intermediate (WTI) crude prices.
618
Linear regression dictated a slope (m) of 1.22 with intercept (b) -6.55. Therefore, given a WTI price of 60 $/bbl, the price of
619
Cabinda could be calculated as:
𝑃𝐶𝑎𝑏𝑖𝑛𝑑𝑎 = 1.22 ∙ 60
620
$
$
− 6.55 = 67
𝑏𝑏𝑙
𝑏𝑏𝑙
621
Example B: Crude Oil Price Calculation from Properties
622
Some crude oils, such as Escalante, had little to no pricing data available in the multiple resources used for this analysis. In
623
order to price these crude oils, a multiple linear regression model of crude oil price was fit as a function of API gravity, sulfur
624
weight percent, and total acid number (TAN). Using the fitted parameters of this model, a price for Escalante given a
625
benchmark West Texas Intermediate price of 60 $/bbl could be calculated using the property data below:
626
API Gravity = 23.2°
627
Sulfur = 0.16 wt%
628
TAN = 0.50
𝑃𝐸𝑠𝑐𝑎𝑙𝑎𝑛𝑡𝑒 = 0.22(23.2𝐴𝑃𝐼 ) − 1.71(0.16𝑆𝑢𝑙𝑓𝑢𝑟 ) − 1.11(0.61 𝑇𝐴𝑁 ) − 13.86 = 72.8
629
$
𝑏𝑏𝑙
630
Example C: Refinery Product Price Calculation from Benchmark
631
Refinery product pricing data was also collected in timestep with West Texas Intermediate (WTI) crude oil prices. The
632
following RBOB data was collected from Oil Price Information Service (OPIS), Bloomberg, Energy Information
633
Administration (EIA), and Baker & Obrien datasets.
3.5
RBOB ($ / Gal)
3.0
y = 0.03x + 0.24
R² = 0.91
2.5
2.0
1.5
1.0
OPIS
Bloomberg
EIA
PRISM
0.5
0.0
20
40
60
WTI ($ / BBL)
80
100
634
635
Fig B.2. Reformulated Before Oxygenate Blending (RBOB) gasoline blend historical prices plotted with reference to
636
West Texas Intermediate (WTI) crude prices.
637
Linear regression dictated a slope (m) of 0.03 with intercept (b) 0.24. Therefore, given a WTI price of 60 $/bbl, the price of
638
RBOB could be calculated as:
𝑃𝑅𝐵𝑂𝐵 = 0.03 ∙ 60
639
$
$
+ 0.24 = 1.82
𝑏𝑏𝑙
𝑔𝑎𝑙
640
Example D: Octane Price Calculation
641
A neural network with the format below was developed to predict the incremental price of octane ($/octane-gallon) based on 5
642
independent variables being conventional regular gasoline price ($/gal), benzene to regular gasoline price differential
643
($/octane-gallon), toluene to regular gasoline price differential ($/octane-gallon), xylenes to regular gasoline price differential
644
($/octane-gallon), and total U.S. octane demand (octane-gal/day). These five input variables were ultimately determined by the
645
West Texas Intermediate (WTI) benchmark price, refinery product demand model (ADOPT or EIA), and the year in the
646
following way:
647
Assuming:
648
WTI Price = 60 $/bbl
649
Demand Projection = EIA Assumptions
650
Year = 2030
651
1) Conventional Regular Gasoline Price:
652
Given a benchmark WTI price of 60 $/bbl and using the method described in Example C with linear regression
653
yielding slope (m) of 0.03 and intercept (b) of 0.27 the price of conventional regular gasoline octane with AKI of 87
654
can be calculated as:
655
𝑃𝑐𝑜𝑛𝑣−𝑟𝑒𝑔 𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒 = 0.03 ∙ 60
656
2) Benzene to Conventional Regular Gasoline Price Differential:
$
$
+ 0.27 = 1.81
𝑏𝑏𝑙
𝑔𝑎𝑙
657
The price of benzene is calculated given a benchmark WTI price of 60 $/bbl and linear regression coefficients of slope
658
(m) of 0.04 and intercept (b) of 0.50 as:
𝑃𝑏𝑒𝑛𝑧𝑒𝑛𝑒 = 0.04 ∙ 60
659
660
Implying,
𝑃𝑏𝑒𝑛𝑧𝑒𝑛𝑒−𝑑𝑖𝑓𝑓 =
661
662
$
$
+ 0.50 = 2.68
𝑏𝑏𝑙
𝑔𝑎𝑙
𝑃𝑐𝑜𝑛𝑣−𝑟𝑒𝑔 𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒
𝑃𝑏𝑒𝑛𝑧𝑒𝑛𝑒
2.68 1.81
$
−
=
−
= 0.0026
𝐴𝐾𝐼𝑏𝑒𝑛𝑧𝑒𝑛𝑒 𝐴𝐾𝐼𝑐𝑜𝑛𝑣−𝑟𝑒𝑔 𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒 115
87
𝑜𝑐𝑡 ∙ 𝑔𝑎𝑙
3) Toluene to Conventional Regular Gasoline Price Differential:
663
The price of toluene is calculated given a benchmark WTI price of 60 $/bbl and linear regression coefficients of slope
664
(m) of 0.03 and intercept (b) of 0.32 as:
𝑃𝑏𝑒𝑛𝑧𝑒𝑛𝑒 = 0.03 ∙ 60
665
666
667
668
$
$
+ 0.32 = 2.32
𝑏𝑏𝑙
𝑔𝑎𝑙
Implying,
𝑃𝑡𝑜𝑙𝑢𝑒𝑛𝑒−𝑑𝑖𝑓𝑓 =
𝑃𝑐𝑜𝑛𝑣−𝑟𝑒𝑔 𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒
𝑃𝑡𝑜𝑙𝑢𝑒𝑛𝑒
2.32 1.81
$
−
=
−
= 0.0016
𝐴𝐾𝐼𝑡𝑜𝑙𝑢𝑒𝑛𝑒 𝐴𝐾𝐼𝑐𝑜𝑛𝑣−𝑟𝑒𝑔 𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒 104
87
𝑜𝑐𝑡 ∙ 𝑔𝑎𝑙
4) Xylenes to Conventional Regular Gasoline Price Differential:
669
The price of xylenes is calculated given a benchmark WTI price of 60 $/bbl and linear regression coefficients of slope
670
(m) of 0.04 and intercept (b) of 0.35 as:
𝑃𝑏𝑒𝑛𝑧𝑒𝑛𝑒 = 0.04 ∙ 60
671
672
Implying,
𝑃𝑡𝑜𝑙𝑢𝑒𝑛𝑒−𝑑𝑖𝑓𝑓 =
673
674
$
$
+ 0.35 = 2.48
𝑏𝑏𝑙
𝑔𝑎𝑙
𝑃𝑐𝑜𝑛𝑣−𝑟𝑒𝑔 𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒
𝑃𝑡𝑜𝑙𝑢𝑒𝑛𝑒
2.48 1.81
$
−
=
−
= 0.0003
𝐴𝐾𝐼𝑡𝑜𝑙𝑢𝑒𝑛𝑒 𝐴𝐾𝐼𝑐𝑜𝑛𝑣−𝑟𝑒𝑔 𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒 118
87
𝑜𝑐𝑡 ∙ 𝑔𝑎𝑙
5) Total U.S. Octane Demand
675
Under EIA Assumptions, in year 2030 the U.S. gasoline demand is projected to be 31,500,000 gal/day with a premium
676
market share of 23%. Therefore, the octane demand can be calculated as:
677
𝐷𝑜𝑐𝑡 𝑑𝑒𝑚𝑎𝑛𝑑 = 31,500,000 ∙ (1 − 0.23) ∙ 87𝐴𝐾𝐼 + 31,500,000 ∙ 0.23 ∙ 92𝐴𝐾𝐼 = 2,780,000,000
𝑜𝑐𝑡 ∙ 𝑔𝑎𝑙
𝑑𝑎𝑦
678
679
Prior to entering the neural network, the input variables were centered by subtracting the mean, scaled by dividing the standard
680
deviation, and grouped into two principled components using principled component analysis (PCA) as show below
681
682
1) Center and scaling:
𝑃𝑐𝑜𝑛𝑣−𝑟𝑒𝑔 𝑔𝑎𝑠𝑜𝑙𝑖𝑛𝑒,
𝑠𝑐𝑎𝑙𝑒𝑑
=
1.81 − 1.52
= 0.36 = 𝑋1
0.81
683
684
𝐷𝑜𝑐𝑡 𝑑𝑒𝑚𝑎𝑛𝑑,
𝑠𝑐𝑎𝑙𝑒𝑑
=
2,780,000,000 − 4,157,396,000
= −0.98 = 𝑋2
1,405,534,000
685
686
𝑃𝑏𝑒𝑛𝑧𝑒𝑛𝑒−𝑑𝑖𝑓𝑓,
𝑠𝑐𝑎𝑙𝑒𝑑
=
0.0026 − 0.0019
= 1.54 = 𝑋3
0.0005
𝑃𝑡𝑜𝑙𝑢𝑒𝑛𝑒−𝑑𝑖𝑓𝑓,
𝑠𝑐𝑎𝑙𝑒𝑑
=
0.0016 − 0.0011
= 1.10 = 𝑋4
0.0005
𝑃𝑥𝑦𝑙𝑒𝑛𝑒𝑠−𝑑𝑖𝑓𝑓,
𝑠𝑐𝑎𝑙𝑒𝑑
=
0.0003 − (−0.0003)
= 1.36 = 𝑋5
0.0004
687
688
689
690
691
692
2) Principled Component Reduction
693
After principled component analysis, a series of weights are determined that can applied to the original input variables
694
to form a series of principled components that are orthogonal, meaning they have no correlation. Two principled
695
components were calculated for the neural network:
696
697
698
𝑃𝐶1 = 0.55 ∙ 𝑋1 + 0.48 ∙ 𝑋2 + 0.54 ∙ 𝑋3 + 0.35 ∙ 𝑋4 − 0.22 ∙ 𝑋5
= 0.55 ∙ 0.36 + 0.48 ∙ 1.54 + 0.54 ∙ 1.10 + 0.35 ∙ 1.36 − 0.22 ∙ (−0.98) = 2.23
699
700
701
𝑃𝐶2 = 0.20 ∙ 𝑋1 − 0.38 ∙ 𝑋2 + 0.25 ∙ 𝑋3 − 0.56 ∙ 𝑋4 − 0.65 ∙ 𝑋5
= 0.20 ∙ 0.36 − 0.38 ∙ 1.54 + 0.25 ∙ 1.10 − 0.56 ∙ 1.36 − 0.65 ∙ (−0.98) = −0.36
702
703
After pre-processing, the principled components were fed to a neural network with five units in one hidden layer using a
704
sigmoidal transfer function. The hidden layer outputs are computed as follows:
705
706
707
ℎ1 = −0.50 ∙ 𝑃𝐶1 − 1.19 ∙ 𝑃𝐶2 − 0.47 = −0.50 ∙ 2.23 − 1.19 ∙ (−0.36) − 0.47 = −1.15
→ 𝑠𝑖𝑔(ℎ1 ) =
1
1+𝑒 −ℎ1
=
1
1+𝑒 1.15
= 0.24
708
709
710
ℎ2 = −0.32 ∙ 𝑃𝐶1 + 0.15 ∙ 𝑃𝐶2 − 1.59 = −0.32 ∙ 2.23 + 0.15 ∙ (−0.36) − 1.59 = −2.36
→ 𝑠𝑖𝑔(ℎ2 ) =
1
1
=
= 0.09
−ℎ2
1+𝑒
1 + 𝑒 2.36
711
712
713
ℎ3 = −0.62 ∙ 𝑃𝐶1 − 1.51 ∙ 𝑃𝐶2 − 0.13 = −0.62 ∙ 2.23 − 1.51 ∙ (−0.36) − 0.13 = −0.96
→ 𝑠𝑖𝑔(ℎ3 ) =
1
1
=
= 0.28
−ℎ3
1+𝑒
1 + 𝑒 0.96
714
715
716
ℎ4 = −0.44 ∙ 𝑃𝐶1 − 0.25 ∙ 𝑃𝐶2 − 1.85 = −0.44 ∙ 2.23 − 0.25 ∙ (−0.36) − 1.85 = −2.74
→ 𝑠𝑖𝑔(ℎ4 ) =
1
1
=
= 0.06
−ℎ4
1+𝑒
1 + 𝑒 2.74
717
718
719
720
ℎ5 = −0.50 ∙ 𝑃𝐶1 − 0.88 ∙ 𝑃𝐶2 − 2.00 = −0.50 ∙ 2.23 − 0.88 ∙ (−0.36) − 2.00 = −2.78
→ 𝑠𝑖𝑔(ℎ5 ) =
1
1
=
= 0.06
1 + 𝑒 −ℎ5 1 + 𝑒 2.78
721
Ultimately, the neural network output being the incremental octane price under the given economic conditions was computed
722
as:
723
𝑌 = −0.84 ∙ 𝑠𝑖𝑔(ℎ1 ) + 0.22 ∙ 𝑠𝑖𝑔(ℎ2 ) + 0.54 ∙ 𝑠𝑖𝑔(ℎ3 ) − 0.45 ∙ 𝑠𝑖𝑔(ℎ4 ) + 0.54 ∙ 𝑠𝑖𝑔(ℎ5 ) + 0.07
724
= −0.84 ∙ (−1.15) + 0.22 ∙ (−2.36) + 0.54 ∙ (−0.96) − 0.45 ∙ (−2.74) + 0.54 ∙ (0.06) + 0.07
725
= 0.04
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
$
𝑜𝑐𝑡 ∙ 𝑔𝑎𝑙
744
References
745
746
747
748
749
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