This section describes in detail the methods used to calculate the exergy, GHG emission and land transformation for coal and PV generation of electricity. When possible, several sources with data on state-of-the-art technology were used and minimum, maximum and average values were determined. The term realistic is used to describe the average value or a readily obtained technological value. The equations used to determine the values for exergy, GHG emissions and land transformation for all PV and coal scenarios are stated. SimaPro V8 was utilized and all exergy data is from Cumulative Exergy Demand V1.03 and GHG emissions data is from IPCC GWP 100a. Emissions from the electrical grid are not included in the scope of the LCEA’s for PV or coal.

Pre-operation Exergy, Emissions and Land Use for Coal

The total exergy required for mining coal, β coalmining , for a 1GW power plant over a 50 year lifetime is 6.69 × 104 to 9.21 × 104 GWhrs, without and with CCS, respectively, and is given by:

$${\beta }_{coalmining}={\mu }_{coalmining}\,\ast \,{M}_{coal}\,[{\rm{GWhrs}}]$$ (1)

where,

$${M}_{coal}=\frac{{\beta }_{out}}{{\eta }_{coalplant}\,\ast \,{\varepsilon }_{coal}}\,[{\rm{t}}]$$ (2)

where β is the exergy in GWhrs, μ is the specific exergy in GWh/t coal , M coal is the total amount of coal required for combustion over the lifetime in tons, β out is the desired electrical output of the plant over its lifetime in GWhrs, ŋ is efficiency and ε is the heat content of coal in GWh/ton.

The specific mining exergy for coal is 4.40 × 10−4 GWh in /t coal 39 and the average heat content of coal consumed by electrical power plants in the U.S. is 6.54 × 10−3 GWh/ton56. The amount of coal required for the 1GW power plant without carbon capture technology during its lifetime ranges from 1.41 × 108–1.77 × 108 tons, with a realistic value of 1.52 × 108 tons22,29,36,42,56,57,58,59 and with carbon capture it ranges from 1.85 × 108–2.80 × 108 tons with a realistic value of 2.10 × 108 tons22,29,42,56,57,58,59,60,61. The efficiency of the plant drives the required exergy input and a review of the literature has found it to range from 32.50–40.60% with an average of 37.74% without carbon capture technology and 20.90–31.51% with an average of 27.40% with carbon capture technology22,36,42,56,59,60,62.

The total exergy required for transporting coal for a 1GW power plant over the 50 year lifetime, β coaltransport , is 3.17 × 104 and 4.37 × 104 GWhrs without and with CCS, respectively, and is given by:

$$\begin{array}{c}{\mu }_{coaltransport,truck}\\ {\mu }_{coaltransport,rail}+{\mu }_{coaltransport,marine}+\ast {M}_{coal}\\ {\beta }_{coaltransport}=\end{array}\,[{\rm{GWhrs}}]$$ (3)

where,

$$\mu =\vartheta \ast \phi \,[{\rm{GWh}}/{{\rm{t}}}_{{\rm{coal}}}]$$ (4)

where ϑ is the specific exergy in GWh/ton-km and φ is the specific distance in ton-km/t coal . Coal is transported for electrical generation via three main modes, rail, marine and truck, which account for 88%, 11% and 1%, respectively by ton-km39. Trains transport 1.04 ton-km/kg coal at 1.81 × 10−7 GWh/ton-km, marine transports 130 ton-km/t coal at 1.36 × 10−7 GWh/ton-km and trucks transport 10 ton-km/t coal at 3.46 × 10−7 GWh/ton-km39.

The exergy required for construction, β coalconstruction , is 1.29 × 104 GWhrs for a plant with and without CCS (the procurement of the additional equipment for compressing the CO 2 is assumed to be negligible) and is calculated by:

$${\beta }_{coalconstruction}={\Sigma }({M}_{coalmaterials}\ast {\mu }_{coalmaterials})\,[{\rm{GWh}}]$$ (5)

where M coalmaterials is the tonnage of individual materials63 and μ coalmaterials is the specific exergy of the materials in GWh/t39. Total construction exergy is 9.4% of the total exergy required by upstream activities, detailed in Table 5.

Table 5 Construction exergy for large scale PV and coal electricity generation, each outputting 376 TWhrs over a 50 year lifetime. Full size table

Total upstream greenhouse gas emissions for a 1GW coal plant, π coalupstream , are 3.92 × 107 and 5.34 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq without and with CCS, respectively and are given by:

$$\begin{array}{rcl}{\pi }_{coalupstream} & = & ((({\alpha }_{coalmining}\ast {{\epsilon }}_{coalmining})+({\alpha }_{coaltransport}\ast {{\epsilon }}_{coaltransport}))\ast {M}_{coal})\\ & & +({\alpha }_{coalconstruction}\ast {\beta }_{yealyoutput})\,[{{\rm{t}}}_{{{\rm{CO}}}_{2}{\rm{eq}}}]\end{array}$$ (6)

where α is the specific emissions in \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /t coal , \({\epsilon }\) is the percent contribution and β yealyoutput is the exergy output per year from the operation phase (not including any downstream processes). The highest individual contributions come from mining and transportation. Specifically, mining emits 0.23 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /t coal (55% of total) and transport emits 0.19 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /t coal (45% of total), which totals 0.41 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /t coal 39. Furthermore, total upstream emissions are 55 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /GWh out , resulting in 0.12 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /t coal 43. The average of these two values provides a total upstream emission factor of 0.27 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /t coal . The yearly output is simply the lifetime output divided by 50, which is 7.5 TWhr/yr when the lifetime output is 376 TWhrs and 17.3 TWh/yr when the lifetime output is 866 TWhrs.

Construction of a large coal power plant emits 0.022 \({{\rm{kg}}}_{{{\rm{CO}}}_{2}}\) eq /kWh-yr63, resulting in less than 1% of the total upstream emissions for the plant under study. More detailed information is provided in Table 6.

Table 6 GHG emission for the construction of a PV farm outputting 376 TWhrs over a 50 year lifetime. Full size table

Mining emissions for the 1GW plant over its lifetime range from 1.14 × 107–4.74 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq with a realistic value of 2.94 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq and 8.74 × 106–3.44 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq with a realistic value of 2.16 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq for a plant with and without capture, respectively39,43.

Transport emissions for the 1GW plant over its lifetime range from 9.30 × 106–3.88 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq with a realistic value of 2.4 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq and 7.15 × 106–2.81 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq with a realistic value of 1.76 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq for a plant with and without capture, respectively39,43.

Land transformation for upstream activities for a 1GW coal plant, A coalupstream , are 17.8 kha and 22.7 kha without and with CCS, respectively and calculated by:

$${A}_{coalupstream}=({\tau }_{coalmining}+{\tau }_{coaltransport})\ast {\beta }_{out}\,[{\rm{kha}}]$$ (7)

where τ coal is the specific land transformation in ha/t coal . In the U.S., there are 195 kha of land leased for coal mining, but only 140 kha of the land actively being used64 with 8.97 × 108 tons of coal mined each year40 giving an average of 1.52 × 10−4 ha/t coal . Surface mining transforms 90–1,820 m2/kt with a realistic value of 300 m2/kt and underground mining transforms 4.5–1,110 m2/kt with a realistic of 30 m2/kton48. Given that on average 70% of the coal mined in the U.S. is from surface mining and 30% from underground mining48, the average of these various values was taken to provide a realistic value of 8.70 × 10−5 ha/t coal .

Specific land transformed by rail infrastructure ranges from 30 m2/GWh in the east to 80 m2/GWh in the west48. Given that 88% of coal shipped to electrical power plants is by rail65 and another 11% by water39 it is assumed the land transformed by rail is representative of the total land transformation. 55% of the coal is mined in the west and 45% in the east66 so a realistic value was assumed to be 5.75 × 10−3 ha/GWh. When multiplied by the ratio of β out over t coal consumed by the plant with and without carbon capture over its lifetime it equates to 1.42 × 10−5 ha/t coal and 1.03 × 10−5 ha/t coal , respectively. Each range from 1.22 × 10−5–1.53 × 10−5 ha/t coal and 7.72 × 10−6–1.17 × 10−5 ha/t coal , respectively.

The land transformed by the upstream activities for the construction of the coal power plant is not included in the scope of this analysis rendering all values for coal conservative over the entire life cycle.

Pre-operation Exergy, Emissions and Land Use for PV

The exergy required for upstream activities, β PVupstream , is 2.00 × 104 GWhrs for PVs1 and 4.60 × 104 GWhrs for PVs2 and is calculated by:

$${\beta }_{PVupstream}=({\dot{{\rm{t}}}}_{EPB}\ast {\beta }_{yearlyoutput})+{\beta }_{PVconstruction}\,[{\rm{GWhrs}}]$$ (8)

where \({\dot{{\rm{t}}}}_{EPB}\) is the energy payback time in years, which ranges from 1.7–5.5 years, with an average of 2.7 years49,50. This was multiplied by the yearly output to determine the upstream exergy input of 5.3 × 10−2 GWh in /GWh out . Individually, the energy contribution from the modules and BOS are 63% and 37% of the total, respectively67. The construction exergy was calculated by multiplying the tonnage of material by the upstream exergy for each material39,63, more detailed data is provided in Table 5.

The upstream GHG emissions, π PVupstream , are 8.92 × 106 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq and 1.70 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq for PVs1 and PVs2, respectively and is calculated with:

$${\pi }_{PVupstream}=(\frac{{\alpha }_{PVupstream}\ast {\beta }_{out}}{2})+{\pi }_{PVconstruction}\,[{{\rm{t}}}_{{{\rm{CO}}}_{2}{\rm{eq}}}]$$ (9)

where α PV is the specific GHG emissions in \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /GWh out in its life cycle, which range from 8.74–187 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /GWh out , with a realistic value of 46.98 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /GWh out 38,49,50,68,69. The individual contributions of modules and BOS to total emissions are 38.9% and 61.1%, respectively67. The emissions from construction are detailed in Table 6. LCAs typically assumed a lifetime of 20–30 years. The values given in this paper assume that a negligible amount of greenhouse gases are emitted and after 25 years of operation, and a negligible amount of GHG’s are emitted.

Land transformation from upstream activities, A PVupstream , are 0.58 kha and 1.12 kha for PVs1 and PVs2, respectively and is calculated with:

$${A}_{PVupstream}=\frac{({\tau }_{PVmodules}+{\tau }_{PVBOS})\ast {\beta }_{out}}{2}\,[{\rm{kha}}]$$ (10)

where τ PV is the specific land transformation in ha/GWh out . Land transformation for upstream activity is 1.84 × 10−3 ha/GWh out and 7.5 × 10−4 ha/GWh out for modules and BOS, respectively48. The upstream land transformation for materials and processes specific to construction of the PV farm were not included so total values can be considered conservative.

Operation Exergy, Emissions and Land Use for Coal

The exergy into the coal plant during operation is comprised entirely from the latent energy in the coal. The exergy inputs required, β coaloperation , are 9.95 × 105 and 1.37 × 106 GWhrs without and with CCS, respectively and are calculated by:

$${\beta }_{coaloperation}=\frac{{\beta }_{out}}{{{\rm{n}}}_{plant}}\,[{\rm{GWhrs}}]$$ (11)

The efficiency of a state-of-the-art plant without CCS ranges from 32.5–40.6% with a realistic value of 37.74%, requiring an input range from 9.25 × 105–1.16 × 106 GWh with a realistic value of 9.95 × 105 GWh22,29,36,42,57,60,62. With various forms of CCS, the efficiency ranges from 20.90–31.51% with a realistic value of 27.4% requiring an exergy input range from 1.21 × 106–1.83 × 106 GWh with a realistic value of 1.637 × 106 GWh22,29,42,57,59,60,61. Thus, carbon capture technology necessitates 37.74% more coal, which creates additional GHG emissions. The realistic capture in this study is taken as 82.2%.

The carbon capture efficiency ranges from 81–91% capture of total emissions22,29,41,42,57,59,60,61. The most common and technologically mature method of carbon capture at the plant is post-combustion capture using MEA. Several other carbon capture processes were included in the purview of the study and are shown in Table 7. The efficiency drop due to CCS comes from the high energy intensity of the carbon capture process. Large-scale MEA processes can consume 92–119 MW el and an additional 0.72–1.74 MW th /MW eloutput . This results in and average of 0.11 GW el and 0.99 GW th for a ~1GW power plant41. These values are conservative because the carbon capture percentage in the study was 60–65%. The average energy efficiency of a state of the art coal plant in the U.S. is used after having identified the energy efficiency for the top 10% of the fleet36.

Table 7 Range of pulverized coal plant efficiencies equipped with various forms of carbon capture. Full size table

The GHG emissions to the atmosphere during operation, π coaloperation , are 3.38 × 108 and 6.07 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq without and with CCS, respectively and are calculated by:

$${\pi }_{coaloperation}={\alpha }_{coaloperation}\ast {\beta }_{out}\,[{{\rm{t}}}_{{{\rm{CO}}}_{2}{\rm{eq}}}]$$ (12)

where the specific GHG emissions from coal plants without carbon capture range from 807–1100 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /GWh, with a realistic value of 900 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /GWh38,44,45,58. Emissions from plants with capture range from 124–203 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /GWh, with a realistic value of 160 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /GWh22,44,45,58.

Land transformation caused by the plant itself, A coaloperation , is 202 ha and calculated by:

$${A}_{coaloperation}={\tau }_{coaloperation}\ast {\beta }_{out}\,[{\rm{kha}}]$$ (13)

where the specific land transformation ranges from 6.0 × 10−4–3.3 × 10−3 ha/GWh out , with an average of 9.0 × 10−4 ha/GWh out 48.

Operation Exergy, Emissions and Land Use for PV

In the operation phase, the solar irradiation accounts for the entirety of the exergy input, β PVoperation , totaling 3.50 × 106 and 8.05 × 106 GWhrs for PVs1 and PVs2, respectively and is calculated by:

$${\beta }_{PVoperation}={\Sigma }(\frac{{\beta }_{yearlyoutput}}{{{\rm{\eta }}}_{PVyearly}})\,[{\rm{GWhrs}}]$$ (14)

where,

$${{\rm{\eta }}}_{PVyearly}={{\rm{\eta }}}_{0}\ast {(1-d)}^{n}\,[ \% ]$$ (15)

where ŋ 0 is the initial exergy efficiency of the PV system, d is the degradation rate in %/yr and n is the years of operation. The exergetic efficiency of PV was found to range from 7.8–16.1%, with a realistic value being 12.1%51,52,70,71,72. The degradation rate ranged from 0.35–0.8%/yr with a realistic average of 0.49%/yr37,73. System Advisor Model (SAM) from the National Renewable Energy Laboratory (NREL) was employed to ensure the accuracy of values from the calculations above74.

The GHG emissions released to the atmosphere during operation, π PVoperation , are 8.69 × 104 and 2.01 × 105 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq for PVs1 and PVs2, respectively, and calculated by:

$${\pi }_{PVoperation}=\frac{{\alpha }_{PVoperation}\ast {\beta }_{out}}{2}\,[{{\rm{t}}}_{{{\rm{CO}}}_{2}{\rm{eq}}}]$$ (16)

A range of 0–46.3 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /GWh out 38 are emitted during installation of a PV farm. The worst case assumes locating a PV farm in a heavily forested area with CO 2 emissions from loss of forest sequestration, soil respiration and oxidation of cut biomass. An assumption of 0.46 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\)/GWh (1%) from deforestation was employed for this study as forests are not typically clear cut for PV farms.

Land transformation due to the PV farm, A PVoperation , is 3.94 and 9.51 kha and 9.22 and 26.46 kha for PVs1 and PVs2, respectively and are calculated as the average of two approaches:

$${A}_{PVoperation}={\tau }_{PVoperation}\ast {C}_{NP}\,[{\rm{kha}}]$$ (17)

$${A}_{PVoperation}={\tau }_{PVoperation}\ast {\beta }_{out}\,[{\rm{kha}}]$$ (18)

where \({\tau }_{PV}\) is the specific land transformation in ha/GW and C NP is the nameplate capacity. The PV farms themselves ranges from 2.02–3.23 kha/GW38, while a review of three of the largest PV farms in the United States (Solar Star, Mount Signal and California Valley) reveals that they are 2.25, 3.89 and 5.20 kha/GW, respectively, giving an average of 3.32 kha/GW75,76,77. Land transformation for the modules and BOS combined range from 1.64 × 10−2 ha/GWh out to 4.62 × 10−2 ha/GWh out , with a realistic value of 3.59 × 10−2 ha/GWh out 48. These were multiplied by nameplate capacity or lifetime exergy output and then averaged together to determine the final values. It should be noted here that the PV farms are best suited from an environmental standpoint or barren land or existing man-made structures (e.g. rooftops, sound barriers, parking lot awnings, etc.) and should be used before fertile land is used because of the negative impacts on food price and availability.

Downstream Exergy, Emissions and Land Use for Coal

The exergy input from solar irradiation for bio-sequestration of GHG emission from coal without CCS, β coalbio , is 2.57 × 108 GWhrs and calculated by:

$${\beta }_{coalbio}=G\ast N\ast {A}_{coalbio}\,[{\rm{GWhrs}}]$$ (19)

where G is the average U.S. solar incidence of 15,000 GWh/ha * yr78, N is the number of years over its lifetime and A coalbio is the land transformation required by the switchgrass for upstream and operation activities without CCS in hectares, explained in equation 32 below.

The exergy input for bio-sequestration of GHG emissions from coal with CCS into a saline aquifer, β coalCCS , is 8.14 × 107 GWhrs and calculated with:

$${\beta }_{coalCCS}={\beta }_{coalCCSbio}+{\beta }_{C{O}_{2}cond}\,[{\rm{GWhrs}}]$$ (20)

$${\beta }_{coalCCSbio}=G\ast N\ast {A}_{coalCCSbio}\,[{\rm{GWhrs}}]$$ (21)

$${\beta }_{C{O}_{2}cond}={\mu }_{C{O}_{2}cond}\ast \gamma \,[{\rm{GWhrs}}]$$ (22)

where A coalCCSbio is the land transformation required by the switchgrass for upstream, operation and downstream activities with CCS into a saline aquifer in hectares explained in equation 33 below, \({\mu }_{C{O}_{2}cond}\) is the specific exergy required to condition the CO 2 (compress and transport) after its been separated and measured in GWh/\({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) and γ is the total CO 2 captured in \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\). CO 2 is typically transported via pipeline in a supercritical state, between 8.6–15.3 MPa43. The specific energy required to compress CO 2 is between 112–119 kWh/\({{\rm{t}}}_{{{\rm{CO}}}_{2}}\), realistically being 116 kWh/\({{\rm{t}}}_{{{\rm{CO}}}_{2}}\)41,78. The pipelines have been found to lose between 4–50 kPa per 100 km79, thus requiring 6.5 kWh/\({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) to boost the pressure for longer transport43 but the assumption in this study is that no pressure boosters are required. The average distance for CO 2 to travel for sequestration purposes is 190.5 km32 and the Weyburn case demonstrates that CO 2 can be transported 330 km without additional boosting energy78. The total CO 2eq captured is the difference between GHG emissions from a coal without CCS and a coal plant with CCS, which are 3.38 × 108 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq and 6.02 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq , respectively.

The exergy input for bio-sequestration of GHG emission from coal with CCS for EOR,β coalEOR , is 2.13 × 108 GWhrs and calculated with:

$${\beta }_{coalEOR}={\beta }_{coalbio}+{\beta }_{coalCCSbio}+{\beta }_{oilextraction}+{\beta }_{oiltransport}+{\beta }_{oilrefine}\,[{\rm{GWhrs}}]$$ (23)

where,

$${\beta }_{oilextraction}={\mu }_{oilextract}\ast {M}_{oil}\,[{\rm{GWhrs}}]$$ (24)

$${\beta }_{oiltransport}={\mu }_{oiltransport}\ast {M}_{oil}\ast {D}_{oil}\,[{\rm{GWhrs}}]$$ (25)

(26)

where,

$${M}_{oil}=\gamma \ast {\theta }_{oil}\,[{\rm{t}}]$$ (27)

and where μ oilextract is the specific exergy required to pump the oil from the reservoir in GWh/t oil , M oil is the amount of additional oil extracted with the EOR process in t oil , \({\mu }_{oiltransport}\) is the specific exergy to transport the oil to the refinery in GWh/ton-km oil , D oil is the average distance oil travels to the refinery in km, ŋ refinery is the efficiency of the refinery, \({{\epsilon }}_{oil}\) is the energy content of crude oil and θ oil is the specific oil production from the EOR process in t oil /\({{\rm{t}}}_{{{\rm{CO}}}_{2}}\).

For enhanced oil recovery, it takes 4.40 × 10−5–1.38 × 10−4 GWh/t oil , with a realistic value of 7.40 × 10−5 GWh/t oil to extract crude oil61,80. The exergy required for recycling and re-injecting the CO 2 continuously ranges between 3.21–9.00 kWh/\({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) injected , with a realistic value of 6.10 kWh/\({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) injected 43,80. The exergy required for recycling the CO 2 is captured under the extraction exergy.

An additional exergetic input of 8.15 × 108 GWh/t oil is needed to transport it to a refinery and the average distance crude oil travels to a refinery is 1200 km43.

A typical refinery operates at 90.1% efficiency80 and approximately 93% of this turns into combustible products43. The crude oil was assumed to have a heat content of 1.17 × 10−2 GWh/ton78 and all the refined product to have a heat content of 1.14 × 10−2 GWh/ton39. The exergy required to transport the refined product is considered negligible43.

The specific tonnage of oil produced from EOR ranges from 0.18 to 0.89 t oil /\({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) injected with an average of 0.43 t oil /\({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) injected 34,46,80,81,82.

Equations 28–32 calculate the GHG emissions of coal without CCS, π coalbio , coal with CCS into a saline aquifer, π coalCCS , and coal with CCS for EOR, π coalEOR , which are 3.77 × 108, 1.18 × 108 and 3.11 × 108 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq , respectively.

$${\pi }_{coalbio}={\pi }_{coalupstream}+{\pi }_{coaloperation}\,[{{\rm{t}}}_{{{\rm{CO}}}_{2}{\rm{eq}}}]$$ (28)

$${\pi }_{coalCCS}={\pi }_{coalupstream}+({\pi }_{coaloperation}\ast (1-\gamma ))+{\pi }_{leak}\,[{{\rm{t}}}_{{{\rm{CO}}}_{2}{\rm{eq}}}]$$ (29)

$${\pi }_{coalEOR}={\pi }_{coalCCS}+{\pi }_{EOR}\,[{{\rm{t}}}_{{{\rm{CO}}}_{2}{\rm{eq}}}]$$ (30)

where,

$$\begin{array}{c}{\rho }_{reservoir}\ast N\ast \gamma \\ {\alpha }_{C{O}_{2}transport}\ast {D}_{C{O}_{2}}\\ {\pi }_{leak}=\end{array}\,[{{\rm{t}}}_{{{\rm{CO}}}_{2}{\rm{eq}}}]$$ (31)

$${\pi }_{EOR}=[({\rho }_{extraction})+[({\theta }_{transport}+{\theta }_{refine}+{\theta }_{combust})\ast {\varepsilon }_{oil}]]\ast \gamma \,[{{\rm{t}}}_{{{\rm{CO}}}_{2}{\rm{eq}}}]$$ (32)

where ρ reservoir is the leakage rate from the oil and gas reservoir in %/yr, α CO2transport is the specific emissions from the pipeline transport of CO 2 in \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\)/km, \({D}_{C{O}_{2}}\) is the distance CO 2 travels in the pipe from the plant to the reservoir in km, ρ extraction is the CO 2 released to the atmosphere during the recycling and re-injection and θ is the specific emissions in \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\)/bbl, where bbl is short for a barrel of oil and 7.33 bbl equate to one metric ton of crude oil.

The downstream processes of EOR emit significant amounts of greenhouse gas. Separating and recycling the CO 2 for re-injection is important to curtail emissions during EOR. Alternating floods of water and CO 2 gas are injected into oil deposits to increase oil production. For EOR optimized for carbon sequestration, it can take months for the CO 2 to start being extracted with the crude oil and will continue to be extracted for years after flooding has stopped46. During crude oil extraction, 13.7% of the total injected CO 2eq is lost to the atmosphere when assuming that CO 2 is injected for 10 years and then recycled for another 10 years. 11% of these losses come from recycling, 38% from venting CO 2 and 42% from venting CH 4 46. Transport of crude oil to the refinery emits 4 × 10−3 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /bbl, refining the crude emits 3 × 10−2 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /bbl and combusting the refined product emits 0.43 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /bbl46. The energy content of crude oil is 41.9 GJ/ton80. Transportation of the refined product is considered negligible43.

The target for leakage from geological storage, like that used in saline aquifers and EOR, should be between 1 × 10−2–1 × 10−1%/yr or 1 × 10−3–1 × 10−2%/yr31,83, so a realistic value of 2.75 × 10−2%/yr is used. There are over 4,500 km of CO 2 pipelines83 which emit 4.64 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq each year10, resulting in emissions of 1.03 × 104 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq /km and the average distance the CO 2 is pumped is 190.5 km32.

The land transformation required for bio-sequestration for coal without CCS, A coalbio , coal with CCS into a saline aquifer, A coalCCS , and coal with CCS for EOR, A coalEOR , is 343, 109 and 284 kha, respectively and calculated using:

$${A}_{coalbio}=\frac{{\pi }_{coalbio}\ast \sigma }{\omega \ast N}\,[{\rm{kha}}]$$ (33)

$${A}_{coalCCS}=\frac{({\pi }_{coalbio}+{\pi }_{leak})\ast \sigma }{\omega \ast N}\,[{\rm{kha}}]$$ (34)

$${A}_{coalEOR}=\frac{({\pi }_{coalbio}+{\pi }_{leak}+{\pi }_{EOR})\ast \sigma }{\omega \ast N}\,[{\rm{kha}}]$$ (35)

where σ is the molar ratio of carbon to CO 2 , which is \((\frac{12}{44})\) and ω is the rate of carbon uptake by switchgrass, which is 6 t C /ha-yr84. The scenario without CCS does not have any GHG emissions from leakage or EOR and the scenario with CCS into a saline aquifer does not have any GHG emissions from EOR. The pipelines used to transport CO 2 are considered to be buried and hence have a negligible amount of land transformation.

Downstream Exergy, Emissions and Land Use for PV

Solar incidence on the land required for sequestration accounts for the total exergy into this phase of the analysis. The exergy inputs, β PVbio , are 1.29 × 107 and 2.59 × 107 GWh for PVs1 and PVs2, respectively are calculated with:

$${\beta }_{PVbio}=G\ast N\ast {A}_{PVbio}\,[{\rm{GWhrs}}]$$ (36)

where,

$${A}_{PVbio}=\frac{({\alpha }_{PVupstream}+{\alpha }_{PVoperation})\ast {\beta }_{yearlyoutput}\ast \sigma }{\omega }\,[{\rm{kha}}]$$ (37)

Switchgrass offers the best carbon sequestration potential of 6 t C /ha-yr84 and is assumed to sequester the CO 2eq released by the implementation of the PV farm. The sequestration potentials of various biomass can be seen in Table 8. It has been shown to sequester steadily for over 50 years with little maintenance85.

Table 8 Carbon uptake rates of various types of biomass. Full size table

The total emissions from PV to be sequestered by biomass, π PVbio , are 9.01 × 106 and 1.72 × 107 \({{\rm{t}}}_{{{\rm{CO}}}_{2}}\) eq for PVs1 and PVs2 respectively, over the 50 year lifetime and are calculated by:

$${\pi }_{PVbio}={\pi }_{upstream}+{\pi }_{operation}\,[{{\rm{t}}}_{{{\rm{CO}}}_{2}{\rm{eq}}}])$$ (38)

It should be noted that the values for PV can be improved further in the future as widespread PV recycling becomes widespread86,87. To date the vast majority of PV is still operational, however, in the future recycling of PV will become significantly more important. Advanced recycling can reduce the embodied energy of PV on the manufacturing end by enabling industrial symbiosis88,89,90. This transfer to waste products back into the wealth created by PV electricity generation can directly benefit the circular economy91.

Lastly, it should be pointed out that all more efficient dual uses of land were not considered (e.g. mounting PV on the rooftops of CCS facilities or using the surface area in-between rows of PV for agricultural farming (agrivoltaics92,93,94,95).