Adding indirect or other energy requirements • EROITools

In this vignette, we show how indirect energy requirements (or other energy requirements) can be added to the energy requirements of a given EROI. Note that the analyst would have to provide the indirect energy requirements (or other energy requirements) to use the functions provided in the EROITools package.

Adding indirect energy requirements

We start by expanding the product-level EROIs to the useful stage using some made-up final-to-useful efficiencies for each product, in a similar vein to what has been done in the other vignettes.

# Constructing final-to-useful efficiencies data frame
# Pushing to tidy useful stage EROIs:
length_to_use <- tidy_AB_erois_dta %>% 
  dplyr::select(Country, Method, Energy.type, Year, Product) %>% 
  dplyr::distinct() %>% 
  nrow()

tidy_FU_efficiencies_dta <- tidy_AB_erois_dta %>% 
  dplyr::select(Country, Method, Energy.type, Year, Product) %>% 
  dplyr::distinct() %>% 
  dplyr::mutate(
    Average_Efficiency_Col = seq(0.15, 1, 0.85/(length_to_use-1))
  )

tidy_useful_erois_dta <- push_to_useful_erois(
    .tidy_io_erois = tidy_AB_erois_dta,
    tidy_FU_efficiencies = tidy_FU_efficiencies_dta,
    eroi_calc_method = "dta"
  ) %>%
  dplyr::glimpse()
#> Rows: 72
#> Columns: 12
#> $ Country                <chr> "A", "A", "A", "A", "A", "A", "A", "A", "A", "A…
#> $ Method                 <chr> "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM"…
#> $ Energy.type            <chr> "E", "E", "E", "E", "E", "E", "E", "E", "E", "E…
#> $ Last.stage             <chr> "Final", "Final", "Final", "Final", "Final", "F…
#> $ Year                   <dbl> 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018,…
#> $ Eroi.method            <chr> "DTA", "DTA", "DTA", "DTA", "DTA", "DTA", "DTA"…
#> $ Type                   <chr> "Gross", "Gross", "Gross", "Gross", "Gross", "G…
#> $ Boundary               <chr> "All", "All", "All", "All", "All", "All", "All"…
#> $ Product                <chr> "Blast furnace gas", "Coke oven coke", "Coking …
#> $ EROI                   <dbl> 5.185227, 7.239824, 91.083095, 33.935281, 26.36…
#> $ Average_Efficiency_Col <dbl> 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50,…
#> $ Useful_Stage_EROI      <dbl> 0.7777841, 1.4479647, 22.7707738, 10.1805843, 9…

Then, we aggregate primary, final, and useful stage EROIs using the functions of the package, and bind all the results in a single data frame of aggregated EROIs.

# Primary stage EROIs:
primary_erois <- aggregate_primary_stage_erois(
  .tidy_erois_df = tidy_AB_erois_dta,
  .tidy_iea_df = tidy_AB_dta,
  eroi_calc_method = "dta"
)

# Final stage EROIs:
final_erois <- aggregate_final_stage_erois(
  .tidy_erois_df = tidy_AB_erois_dta,
  .tidy_iea_df = tidy_AB_dta,
  eroi_calc_method = "dta"
)

# Useful stage EROIs:
useful_erois <- aggregate_useful_stage_erois(
  .tidy_erois_df = tidy_useful_erois_dta,
  .tidy_iea_df = tidy_AB_dta,
  eroi_calc_method = "dta"
)

# All EROIs in single data frame:
all_aggregated_erois <- dplyr::bind_rows(
  primary_erois,
  final_erois,
  useful_erois
)

Next, the analyst needs to provide a data frame containing for each product, year, product group, and energy stage (primary, final), the indirect energy requirements quantified in the same unit that the .tidy_iea_df being used (here the tidy_AB_dta data frame). Here, we make up our own data to demonstrate the package and the structure of the input data frame that the analyst needs to provide.

prepare_nrows_df <- all_aggregated_erois %>%
  dplyr::filter(Energy.stage == "Primary" | stringr::str_detect(Energy.stage, "Final")) %>%
  dplyr::mutate(
    Energy.stage = dplyr::case_when(
      stringr::str_detect(Energy.stage, "Final") ~ "Final",
      TRUE ~ Energy.stage
    )
  ) %>%
  dplyr::ungroup() %>%
  dplyr::select(Country, Year, Product.Group, Energy.stage) %>%
  dplyr::mutate(
    Indirect_Energy = "Included"
  ) %>%
  dplyr::distinct() %>%
  dplyr::glimpse()
#> Rows: 13
#> Columns: 5
#> $ Country         <chr> "A", "A", "A", "A", "A", "A", "A", "A", "B", "B", "B",…
#> $ Year            <dbl> 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018, …
#> $ Product.Group   <chr> "All fossil fuels", "Coal products", "Oil and gas prod…
#> $ Energy.stage    <chr> "Primary", "Primary", "Primary", "Final", "Final", "Fi…
#> $ Indirect_Energy <chr> "Included", "Included", "Included", "Included", "Inclu…

n_rows <- prepare_nrows_df %>%
  nrow()

idE_df <- prepare_nrows_df %>%
  dplyr::mutate(
    Indirect_Energy_ktoe = seq(0, 1000, 1000/(n_rows - 1))
  ) %>%
  dplyr::glimpse()
#> Rows: 13
#> Columns: 6
#> $ Country              <chr> "A", "A", "A", "A", "A", "A", "A", "A", "B", "B",…
#> $ Year                 <dbl> 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2…
#> $ Product.Group        <chr> "All fossil fuels", "Coal products", "Oil and gas…
#> $ Energy.stage         <chr> "Primary", "Primary", "Primary", "Final", "Final"…
#> $ Indirect_Energy      <chr> "Included", "Included", "Included", "Included", "…
#> $ Indirect_Energy_ktoe <dbl> 0.00000, 83.33333, 166.66667, 250.00000, 333.3333…

From there, the indirect energy requirements can easily be added to the energy requirements of each product group using the add_indirect_energy_to_erois function. Note, the add_indirect_energy_to_erois adds indirect energy requirements by calculating, for each product group, the ratio of indirect energy requirements to energy output, as:

\[r = \frac{\textrm{idE}}{e_{\textrm{out}}},\]

the indirect energy requirements are thus those provided by the analyst, the energy output by product group is however calculated internally by the function using the data of the .tidy_iea_df passed as argument. An important note is that the analyst can decide to quantify energy products used as non-energy products as part of the energy output (leading to a lower ratio), or to exclude them (leading to a higher ratio), using the include_non_energy_uses argument — this decision has to be made on the basis of whether energy use should be ascribed to energy products used as non-energy products or not. By default, it is recommended to include non-energy uses as part of the output to ensure consistency with the Physical Supply Use Table calculations, and hence to use TRUE as value.

The inverse of the new EROI including indirect energy requirements is then calculated as:

\[\textrm{EROI}_{\textrm{idE}}^{-1} = \textrm{EROI}_{\textrm{dE}}^{-1} + \frac{\textrm{idE}}{e_{\textrm{out}}},\]

and taking the inverse yields the EROI including indirect energy requirements.

erois_with_idE <- add_indirect_energy_to_erois(
  .tidy_summarised_erois_df = all_aggregated_erois,
  .tidy_indirect_energy = idE_df,
  .tidy_iea_df = tidy_AB_dta
) %>%
  dplyr::glimpse()
#> Rows: 504
#> Columns: 13
#> $ Country         <chr> "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A",…
#> $ Method          <chr> "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM"…
#> $ Energy.type     <chr> "E", "E", "E", "E", "E", "E", "E", "E", "E", "E", "E",…
#> $ Last.stage      <chr> "Final", "Final", "Final", "Final", "Final", "Final", …
#> $ Year            <dbl> 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018, …
#> $ Eroi.method     <chr> "DTA", "DTA", "DTA", "DTA", "DTA", "DTA", "DTA", "DTA"…
#> $ Type            <chr> "Gross", "Gross", "Gross", "Gross", "Gross", "Gross", …
#> $ Boundary        <chr> "All", "All", "All", "All", "All", "All", "Feedstock",…
#> $ Product.Group   <chr> "All fossil fuels", "All fossil fuels", "Coal products…
#> $ Energy.stage    <chr> "Primary", "Primary", "Primary", "Primary", "Primary",…
#> $ Group.eroi      <dbl> 40.526689, 40.526689, 36.172053, 91.083095, 23.074664,…
#> $ Non_Energy_Uses <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
#> $ Indirect_Energy <chr> "Included", "Excluded", "Included", "Excluded", "Inclu…

Adding a sectoral or end-use breakdown at the useful stage

If indirect energy requirements are to be added to EROIs in a way that respects a given breakdown (by final demand sector, end-use, etc.) at the useful stage, then one should use instead the add_indirect_energy_useful_erois_by function.

First, we need to define a data frame containing the useful stage EROIs for the different categories. For the sake of the example, we suppose that “Iron and steel” has the highest EROIs, with fuels used in “Others” having only a EROI of half the value, fuels used in “Road transportation” only a third, in “Agriculture” only a fourth, and in “Mining” only a fifth.

list_breakdown_categories <- c("Iron and steel", "Road transportation", "Agriculture", "Mining", "Others")

# Useful stage EROIs:
useful_stage_erois_by <- aggregate_useful_stage_erois(
  .tidy_erois_df = tidy_useful_erois_dta,
  .tidy_iea_df = tidy_AB_dta,
  eroi_calc_method = "dta"
) %>%
  tidyr::expand_grid(
    Categories = list_breakdown_categories
  ) %>%
  dplyr::mutate(
    Group.eroi = dplyr::case_when(
      Categories == "Others" ~ Group.eroi/2,
      Categories == "Road transportation" ~ Group.eroi/3,
      Categories == "Agriculture" ~ Group.eroi/4,
      Categories == "Mining" ~ Group.eroi/5,
      TRUE ~ Group.eroi
    )
  ) %>%
  dplyr::glimpse()
#> Rows: 400
#> Columns: 13
#> $ Country         <chr> "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A",…
#> $ Method          <chr> "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM"…
#> $ Energy.type     <chr> "E", "E", "E", "E", "E", "E", "E", "E", "E", "E", "E",…
#> $ Last.stage      <chr> "Final", "Final", "Final", "Final", "Final", "Final", …
#> $ Year            <dbl> 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018, …
#> $ Eroi.method     <chr> "DTA", "DTA", "DTA", "DTA", "DTA", "DTA", "DTA", "DTA"…
#> $ Type            <chr> "Gross", "Gross", "Gross", "Gross", "Gross", "Gross", …
#> $ Boundary        <chr> "All", "All", "All", "All", "All", "All", "All", "All"…
#> $ Non_Energy_Uses <chr> "Excluded", "Excluded", "Excluded", "Excluded", "Exclu…
#> $ Product.Group   <chr> "All fossil fuels", "All fossil fuels", "All fossil fu…
#> $ Energy.stage    <chr> "Useful (fuel)", "Useful (fuel)", "Useful (fuel)", "Us…
#> $ Group.eroi      <dbl> 2.7410808, 0.9136936, 0.6852702, 0.5482162, 1.3705404,…
#> $ Categories      <chr> "Iron and steel", "Road transportation", "Agriculture"…

We need a data frame containing both EROIs at the final and at the useful stage:

# Final stage EROIs:
final_erois <- aggregate_final_stage_erois(
  .tidy_erois_df = tidy_AB_erois_dta,
  .tidy_iea_df = tidy_AB_dta,
  eroi_calc_method = "dta"
) %>%
  tidyr::expand_grid(
    Categories = list_breakdown_categories
  )

final_useful_erois <- dplyr::bind_rows(
  useful_stage_erois_by,
  final_erois
) %>% 
  glimpse()
#> Rows: 800
#> Columns: 13
#> $ Country         <chr> "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A",…
#> $ Method          <chr> "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM"…
#> $ Energy.type     <chr> "E", "E", "E", "E", "E", "E", "E", "E", "E", "E", "E",…
#> $ Last.stage      <chr> "Final", "Final", "Final", "Final", "Final", "Final", …
#> $ Year            <dbl> 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018, …
#> $ Eroi.method     <chr> "DTA", "DTA", "DTA", "DTA", "DTA", "DTA", "DTA", "DTA"…
#> $ Type            <chr> "Gross", "Gross", "Gross", "Gross", "Gross", "Gross", …
#> $ Boundary        <chr> "All", "All", "All", "All", "All", "All", "All", "All"…
#> $ Non_Energy_Uses <chr> "Excluded", "Excluded", "Excluded", "Excluded", "Exclu…
#> $ Product.Group   <chr> "All fossil fuels", "All fossil fuels", "All fossil fu…
#> $ Energy.stage    <chr> "Useful (fuel)", "Useful (fuel)", "Useful (fuel)", "Us…
#> $ Group.eroi      <dbl> 2.7410808, 0.9136936, 0.6852702, 0.5482162, 1.3705404,…
#> $ Categories      <chr> "Iron and steel", "Road transportation", "Agriculture"…

Then, we can prepare the values of indirect energy requirements for each product group:

prepare_idE_df <- final_erois %>%
  dplyr::filter(stringr::str_detect(Energy.stage, "Final")) %>%
  dplyr::mutate(
    Energy.stage = dplyr::case_when(
      stringr::str_detect(Energy.stage, "Final") ~ "Final",
      TRUE ~ Energy.stage
    )
  ) %>%
  dplyr::ungroup() %>%
  dplyr::select(Country, Year, Product.Group, Energy.stage) %>%
  dplyr::mutate(
    Indirect_Energy = "Included"
  ) %>%
  dplyr::distinct()

n_rows <- prepare_idE_df %>%
  nrow()

idE_by_category_df <- prepare_idE_df %>%
  dplyr::mutate(
    Indirect_Energy_ktoe = seq(0, 1000, 1000/(n_rows - 1))
  ) %>% 
  glimpse()
#> Rows: 10
#> Columns: 6
#> $ Country              <chr> "A", "A", "A", "A", "A", "B", "B", "B", "B", "B"
#> $ Year                 <dbl> 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2…
#> $ Product.Group        <chr> "All fossil fuels", "Coal products", "Natural gas…
#> $ Energy.stage         <chr> "Final", "Final", "Final", "Final", "Final", "Fin…
#> $ Indirect_Energy      <chr> "Included", "Included", "Included", "Included", "…
#> $ Indirect_Energy_ktoe <dbl> 0.0000, 111.1111, 222.2222, 333.3333, 444.4444, 5…

and finally, useful stage EROIs including indirect energy requirements respecting the breakdown by category can be determined using the add_indirect_energy_useful_erois_by function as:

res_idE <- add_indirect_energy_useful_erois_by(
  .tidy_aggregated_erois_by_df = final_useful_erois,
  .tidy_indirect_energy = idE_by_category_df,
  .tidy_iea_df = tidy_AB_dta,
  aggregation_category = "Categories"
) %>% 
  glimpse()
#> Rows: 1,200
#> Columns: 16
#> $ Country           <chr> "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A…
#> $ Method            <chr> "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PCM", "PC…
#> $ Energy.type       <chr> "E", "E", "E", "E", "E", "E", "E", "E", "E", "E", "E…
#> $ Last.stage.x      <chr> "Final", "Final", "Final", "Final", "Final", "Final"…
#> $ Year              <dbl> 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018, 2018…
#> $ Eroi.method       <chr> "DTA", "DTA", "DTA", "DTA", "DTA", "DTA", "DTA", "DT…
#> $ Type              <chr> "Gross", "Gross", "Gross", "Gross", "Gross", "Gross"…
#> $ Boundary          <chr> "All", "All", "All", "All", "All", "All", "All", "Al…
#> $ Non_Energy_Uses.x <chr> "Excluded", "Excluded", "Excluded", "Excluded", "Exc…
#> $ Product.Group     <chr> "All fossil fuels", "All fossil fuels", "All fossil …
#> $ Energy.stage      <chr> "Useful (fuel)", "Useful (fuel)", "Useful (fuel)", "…
#> $ Group.eroi        <dbl> 2.7410808, 1.2271781, 2.7410808, 0.9136936, 0.409059…
#> $ Categories        <chr> "Iron and steel", "Iron and steel", "Iron and steel"…
#> $ Indirect_Energy   <chr> "Included", "Included", "Excluded", "Included", "Inc…
#> $ Last.stage.y      <chr> "Final", "Final", NA, "Final", "Final", NA, "Final",…
#> $ Non_Energy_Uses.y <chr> "Excluded", "Excluded", NA, "Excluded", "Excluded", …