Review: An Economic Perspective on Liquid Solar Fuels

How much does it cost to store electricity in a battery on a one-day cycle? The cheapest option may be a car battery (50 $/kWh), even though its warranty is not meant for daily deep discharge over a five-year lifetime. The stored electricity needs to be sold at a higher price to reflect the battery cost and lifetime. For example, if electricity is purchased from the grid for 53 $/MWh, the resale price needs to approximate 103 $/MWh, just to pay for the cost of a new battery and the internal loss of energy due to ohmic drop. This is shown below as the economic analysis is developed (Table I).

With conventional economics we can borrow from the bank to buy a device. The loan principal P varies according to

where P is the outstanding debt, N is the net revenue stream, and r is an inflation-adjusted interest rate (which can also be called the internal rate of return). N includes any operating costs, such as labor. Profit can be built into r, or it can be incorporated into N. It is best to think in terms of inflation-proof dollars.

With N and r taken to be constant, the solution to this differential equation is

P₀ is the original cost of the device. At t = t_L, the life of the device, P must go to zero, and the loan is paid off. Hence,

Battery or energy-storage device

For a battery, or a generalized energy-storage application,

where Q is the capacity (J) and C is the unit cost ($/J). The net revenue stream is

where B is the price ($/J) paid for the stored energy, S is the price at which the stored energy must be sold to a customer, η is the energy efficiency (J out divided by J in), and ω is the number of (deep) cycles of the storage device per unit time. Substitution gives

This result tells us that, if η = 0.25, we must charge at least four times the purchase price B, even before considering how to pay off the loan. The dimensionless number ωt_L times Q is the total amount of energy bought over the life of the device. Dimensionless groups are used to cancel the monetary unit ($), which is different in different countries and varies over time. The inflation-adjusted interest rate (r) appears in the last group, rt_L/(1 − exp ( − rt_L)). Figure 3 shows a parameterized plot of Equation 6.

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Photovoltaic array or energy-producing device

For a PV array, take the price of sunshine to be zero (such as B = 0), so that the economics revolves around the capital cost and the life of the device. The cost can be expressed as

where C is now the cost per average nominal watt, A is the area exposed to sunlight, and I₀ is the nominal insolation (W/m²). The revenue stream is

where S is the sale price for electricity ($/J) and η is the energy efficiency (W of electrical energy per W of insolation) of the device. The result can be written

expressing the required sale price of electricity in terms of the capital cost of the device, its lifetime and efficiency, and the time value of money. The insolation ratio shows how the sale price depends on the location of the installation through the latitude and cloud cover, but the cost of the device depends on the area and construction and is independent of location. The device cost is frequently expressed in terms of the price per peak watt (nominal) C_p. Then one needs to include also the continuity or intermittency factor, f = C_p/C, where f is the effective fraction of time that solar radiation is received or as the ratio of average W to peak W. The RTI International report¹ on PVs suggests a value of 0.18 for f.

Similar economic analysis applies to the other units in Figure 2. An operating cost is included in the revenue stream. For the hydrogen-storage unit, this includes an upstream cost for the intermittent hydrogen stream and the cost of compression of the hydrogen. These are added to the depreciated capital cost for the tank and the compressor to get the cost of the output, steady hydrogen stream. The cumulative costs add as shown in Figure 2.

Comparative storage costs

Optimum current density for the electrolyzer

Newman¹² and Divisek et al.¹³ carry out optimization of the cell potential or current density for fuel cells and electrolyzers. The total capital cost is C; the capital cost per unit area of separator or diaphragm is C/A. The contribution to the cost per unit time and per unit area is (in units of $/m²-y):

The operating cost is power for electricity ViA. As a cost, this is C_eViA, where C_e is the unit cost of electrical energy, i is the current density, V is the cell potential, and A is the separator area. To add this to the capital cost, we need both on a per-unit-area basis. This is C_eVi. Thus,

But we really want this per unit of H₂ product. Therefore, divide by i before minimizing.

Now approximate the cell potential with Tafel kinetics and an ohmic potential drop as

where i₀ is the exchange current density, α_a is the transfer coefficient, U is a constant, and L_eff and κ_eff are the thickness and conductivity of the diaphragm. Then

The optimum current density is given by solving for i:

The optimum current density is independent of i₀, but the cost will depend on i₀. Large capital cost (C/C_e) leads to large currents (to pay off the capital cost), and

Small capital cost leads to small currents

Define a dimensionless current density as

(this can be compared to the parameters δ and J presented in reference 14) and a dimensionless capital-cost ratio

Then the above approximate equation (for Tafel kinetics) becomes c = I² + I, which gives the solution (If i_opt gets too small, we need to go away from Tafel kinetics.)

Because Miles et al.¹⁵ provide kinetic data on hydrogen and oxygen evolution on nickel electrodes at 80, 150, 208, and 264°C, we can redo the economics for two electrodes, both in the Tafel regime. The cell potential can be expressed now as

and the total cost (in $ per unit area and per unit time) becomes

Subscripts H and O refer to hydrogen and oxygen. Let us change the definitions of I and c:

and

Then the dimensionless cost of hydrogen is

where D is a complicated constant

The dimensional cost per mass of hydrogen is 2ΞF/iM_H2, where M_H2 is the molar mass of hydrogen.

The determination of the optimum current density works exactly as it did before, with the same expression. Table II gives a set of results using the data of Miles et al.,¹⁵ but supplemented with values of the resistance and cost numbers. For some temperatures, Miles et al. give two sets of Tafel parameters, one for high overpotentials and one for low overpotentials. The optimum current density and hydrogen cost need to be selected corresponding to the correct curve where the value lies.

Table II. Optimum current densities and other operating parameters for an alkaline electrolyzer, based on the kinetic data on Ni of Miles et al.¹⁵ The resistance is taken to be 1 ohm-cm². (Divisek et al.¹³ attained a substantially smaller resistance of 0.05 to 0.09 ohm-cm²). Here C_e = 53 $/MWh, C/A = 2000 $/m², f = 0.5, t_L = 7 y, and r = 0.1 y⁻¹. By taking the life and cost of the electrolyzer to be independent of temperature, one sees the maximum benefit of the improved electrode kinetics on the cost of hydrogen produced. This cost drops from 4.20 $/kg at 80°C to 3.10 $/kg at 264°C. How much of this gain will be lost by corrosion and added capital cost and cost to raise the temperature of the fluids from 80 to 264°C remains to be estimated. Integration with the downstream chemical reactor might modify the answer. About 25% of the projected cost reduction is due to the reduction of U. This neglects the cost of the thermal energy used directly in the process.

Temperature, °C	80	150	208	264
αH	0.5	0.3	0.3	0.53
αO	0.74	0.67	0.71	3.3
I0H, A/cm2	1.1×10−4	9.5×10−3	0.03	0.02
I0O, A/cm2	4.2×10−6	1.8×10−4	3.5×10−3	1.00×10−3
U, V	1.183	1.123	1.074	1.027
iopt, A/cm2	0.366	0.335	0.327	0.366
cost, $/kg H2	4.196	3.962	3.550	3.096
V, V	2.510	2.301	1.996	1.730
elec, $/kg H2	3.537	3.242	2.812	2.437

Electrolyzers based on a polymer membrane separator are also commercial and are said to give comparable cost numbers for the produced hydrogen.¹⁶ These units have also precious metal catalysts and operate at substantially higher current densities. The electrolyzer with the higher current density may not point to the more effective efficiency but rather to the one with the higher capital cost.

Electricity from wind is assumed to be produced at 53 $/MWh.¹⁶ We assume an intermittency factor of f = 0.5, although this factor is already included in the value 53 $/MWh. The total cost is largely capital cost.

Estimates show that U. S. wind resources could provide more than 1.1 TW (average).¹⁷ This is much more than that needed for the military, but it cannot cover all the energy needs of the country. This source assumes that electric power from wind "is available 30% of the time at an average cost of 60 $/MWh." "Worldwide, the cost of generating electricity from wind has fallen by more than 80%, from approximately 380 $/MWh in the early 1980s to a current [2004] range for good wind sites located across the United States of 40 to 70 $/MWh" with average capacity factors of close to 30%.

There are three electrolyzer types, alkaline, polymer-electrolyte-membrane (PEM), and solid-oxide. The first two operate at about 80°C and are credited with having comparable overall costs, despite their differences in process chemistry.¹⁶ The last, which operates at 700 to 1000°C, is too immature to be compared with the first two. PEM electrolyzers use precious-metal catalysts (perhaps in oxide form) and have expensive membranes and bipolar separator plates, while alkaline cells use mainly nickel. The PEM electrolyzers operate around 1.5 A/cm², while alkaline cells typically operate in the range of 300 to 500 mA/cm². This may merely point to the higher capital cost of the former, based on the analysis of the optimum current density. For greater efficiency, it is desirable to operate at lower current density, with a consequently larger electrode area. Electrodes tend to be expensive; we use a value of 2000 $/m² for electrodes, compared to 800 $/m² for PVs.

Photoelectrochemical cells are supposed to fulfill the purpose of both the energy source and the electrolyzer in Figure 2 because they produce hydrogen directly from water and sunlight. They currently suffer from severe corrosion problems and do not have a very long life.¹⁸

Carbon dioxide can be absorbed from a gas stream by absorption in a basic solution such as caustic (NaOH or KOH) or ethanolamine. Flue gas from coal- or methane-burning power plants contains 13 or 3% CO₂, respectively. The cost of producing a pure CO₂ stream is 29.5 $(1997)/t(CO₂) for the 13% stream and 43.5 $(1997)/t(CO₂) for the 3% stream.¹⁰ The operating cost is taken to be 18.7 and 25.14 $(1997)/t(CO₂) for the two concentrations, and the depreciated capital cost is 10.83 and 17.85 $(1997)/t(CO₂), respectively.¹⁰ (These numbers do not add exactly to the total of 43.5 $/t(CO₂) given for the 3% stream.) The total rises to at least 85 $/t(CO₂) for recovery from air. (Reference 19 gives a much higher number, 550 $/t(CO₂), for recovery from air.) However, the cost of the produced diesel fuel may rise only from 1883 to 1933 to 2084 $/t(diesel), or by 2.7 and 10.7%, respectively, because the cost of CO₂ is a small part of the overall cost.

The size of the diesel production plant will be comparable to that of a present-day oil refinery. Its size might be governed in part by the location of the source of CO₂ (power plant) and the cost of piping CO₂ from more than one power plant.

As discussed in the Economics section, we were surprised at how much cheaper it is to store energy as hydrogen rather than as electricity; it is still cheaper to store energy as diesel fuel. For this reason, a hydrogen-storage unit was added in Figure 2 after the electrolyzer instead of a battery between the wind-energy source and the electrolyzer. This means that the electrolyzer runs intermittently, although the chemical reactor runs continuously with the steady hydrogen supply from the hydrogen-storage unit. With the intermittency factor of 0.5 used in the calculations, the cost of hydrogen rises about 4.7% between intermittent and steady supply.

The Fischer-Tropsch process was invented in 1924 and was used to make synthetic diesel during the Second World War. Subsequently it has been used extensively in South Africa. The process uses a mixture of CO and H₂. This could be done here by running a reverse water-gas-shift reaction to create CO from CO₂. A possible modification of the original process is to combine the Fischer-Tropsch reaction with the water-gas shift. There are two preferred catalysts for the process, cobalt and iron. Since cobalt is a poor water-gas-shift catalyst, it may be the preferred catalyst when CO is the reactant. Since iron is a better water-gas-shift catalyst, it is the preferred catalyst when CO₂ is the reactant.²⁰ Although the whole process can be run with two reactors if necessary, there is a possible simplification if the CO₂ can be fed into a single reactor. Further research and development can determine the best catalyst, operating temperature and pressure, and ratio of reactants.

Costs are hard to determine from the literature because they are proprietary and because the whole Fischer-Tropsch process involves other processes, like coal gasification and preparation of the synthesis gas, which are not part of the modified process. To arrive at a capital cost, we took designs and costs for a conventional process²¹ and eliminated the parts and cost that are not involved in the modified process. In this way, we obtained 504 $(2006)/kW. This can be compared with 110 $(2006)/kW estimated for a simpler methanol plant. The difference in the resulting cost of diesel may not be so great (perhaps 4%), and one may choose the more expensive diesel ($/MWh) over methanol because of other desirable characteristics such as higher energy density, less corrosion, and an existing infrastructure.

The cost numbers on Figure 2 permit one to allocate the various costs to three main categories, value retained in the final diesel product, costs related to irreversibilities in the system, and the capital cost of units beyond the energy source. Figure 4 shows the breakdown graphically.

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The losses and the depreciated capital cost can be further allocated among the process units, so that one can surmise where to devote attention to achieve cost reductions in the final product. It is clear from Figures 5 and 6 that the electrolyzer deserves the bulk of the attention.

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Since 1972,²² PECs have emerged as a promising means for splitting water into hydrogen and oxygen inexpensively. At the present time, the combination of wind and an electrolyzer is cheaper. This combination, coupled with the downstream processes for making a liquid fuel, could soon compete with fossil fuels, especially if other issues like energy security and economic consequences of fossil-fuel use are taken into account.^5–7 The cost of PV cells has been coming down substantially, and PVs may be needed to supplement wind in the process if one wants more than 1.1 TW of renewable energy within the United States. Even at their immature stage, it is useful to examine the economics of PECs. Table III shows a comparison among wind, PVs, and PECs. The numbers for the last two columns are more speculative, but point to the need to increase the life of the devices. The last row of the table compares the price of hydrogen product by three different methods. The next to the last row should not be used for a direct comparison because it compares the price of electrical energy for PVs and wind with the hydrogen energy of the PECs.

It is impressive how the cost of PVs has been reduced by a concerted effort over more than 30 years by the U. S. Department of Energy and the solar industry.¹ Perhaps a similar cost reduction can be achieved for PECs, although the latter have also been under intensive development over the same 30 years. Table IV provides a comprehensive overview of the state-of-the-art in PEC technology based on an extensive literature survey. Although very impressive water splitting efficiencies have been achieved with PECs, reliable extended lifetime testing of PECs beyond 48 hours is nonexistent in the literature. More often than not, authors report efficiencies without mention of stability. In a few cases, stable photocurrents over 30 hours have been achieved. Further research needs to focus on improving both lifetime and efficiency of PECs.

As shown in Table III, H₂ from PVs coupled to electrolyzers is double the cost of that for wind energy. Column 4 of Table III generously projects a PEC life of 1 year and uses energy efficiency from sunlight to hydrogen of 5%. If the life of PECs could be extended to 25 years and the energy efficiency tripled, the cost of hydrogen would be lower than that from PVs. (This is intended as a worthwhile goal rather than as a prediction of the future.) However, this cost estimate does not take into account key device features like piping and device housing. Because light capture and water splitting occur within the same vessel in PECs, piping that extends over the entire solar array is required to feed water to and remove fuels from the system. In contrast, light capture and water splitting occur separately in PV/water electrolyzers. Similar land areas will be needed for light harvesting for PECs and PVs; however, a significant reduction in piping is expected in the PV/water electrolyzer case due to higher current densities and the ability to stack cells.

In all cases, it becomes desirable to convert the hydrogen into a liquid fuel like diesel, gasoline, or methanol. Figure 2 indicates that the additional cost is small compared to the cost of harnessing energy and generating hydrogen. Nevertheless, PECs cannot presently compete with electrolyzers with either wind or PVs as the energy source due to long-term stability issues.

One way to extend the life of PECs is to separate the electrolyzer part from the PV part, so that corrosion of semiconductors is no longer involved.²³ The overall efficiency may be higher than in the scheme in Figure 2 because of the lower current density in the electrolyzer, but the capital cost may be higher unless the incremental cost of putting the electrolyzer on the back of the PV is suitably small (<24 $/m²). Another way to extend the life of PECs is to change the chemistry (e.g., use less corrosive, near-neutral electrolytes, adopt self-healing strategies,²⁴ and/or utilize semiconductor surface modifications,²⁵ which impede surface corrosion while maintaining interfacial charge-transfer rates).

The process outlined in Figure 2 is technically feasible and produces liquid fuel from renewable sources at a cost presently higher than that of petroleum, without accounting for factors like pollution costs. Investing in such production facilities will generate jobs, spur the economy, promote energy independence, and provide the opportunity for costs to be driven down as innovations are introduced through competition.

It is useful to call attention to specific, but straightforward, tasks that can be pursued in parallel. One innovation involves feeding CO₂ and hydrogen directly into a modified Fischer-Tropsch process without the intermediate step of producing carbon monoxide by the reverse water-gas-shift reaction. This would entail a coherent program of catalyst development, starting with well known Fe catalysts²⁰ of Fischer-Tropsch synthesis, and a definition of the best operating temperature and pressure and ratio of hydrogen to CO₂ in the reactor feed. There are related tasks of best integrating that reactor and its operating conditions with the upstream hydrogen production and the necessary recycle of unreacted reactants and internal energy usage.

Similarly, the production cost of methanol can be reduced if catalysts for methanol synthesis can be developed that reduce the pressure of the reactor toward 15 bar.

As shown in Figures 5 and 6, approximately 70 percent of the overall capital costs and energy inefficiencies are incurred in the electrolyzer. Chlorine production via electrolysis, a major industry, can be used as a guide to improve the operation and economics of the electrolyzer utilized herein. Hydrogen production electrolytically has not been a mainstream process because hydrogen is available more cheaply as a by-product of petroleum and natural-gas processing. A major loss, encountered in many routes for renewable energy, is oxygen evolution. (Chlorine evolution is less demanding.) Data are available in the literature¹⁵ showing how the overpotential for both hydrogen and oxygen evolution decrease in alkaline electrolyzers as the temperature is raised. It will take substantial effort to determine the optimum temperature for the electrolyzer as well as the improvements in materials needed to mitigate corrosion of both the electrodes and the diaphragms. Further attention can be devoted to the best way to get the gases out of the cell and whether operating at a higher pressure is feasible to reduce bubble size and ohmic potential drop and to integrate with the operating pressure of the downstream hydrogen storage and modified Fischer-Tropsch reactor.

World consumption of petroleum and the ecological problems associated with coal demand that large-scale production of renewable synthetic liquid fuels commence. A guaranteed market of a size comparable to the U. S. military needs could launch this new industry.

Renewable synthetic fuels could cap the price to which natural petroleum and other fossil fuels can rise. A plan is also needed to persevere even if the cost of natural fuels dips. If the above guaranteed market is in place, the price of synthetic fuel can be reduced by competition. The value of 5.25 $/gge given in Figure 2 is already close to that of fossil fuels, and it sets a benchmark with which other routes to renewable energy must compete.

The simplified economic analysis presented here guides the choices among alternatives and establishes a methodology for examining the viability of renewable energy. An approximate assessment of the economics can be quantified; with information on life, efficiency, and cost available, one can compare tradeoffs between operating costs and depreciated capital costs and among alternative process modules.

Storage is important in energy and essential in renewable energy. Storage costs are much less for hydrogen than for electricity, and storing a liquid fuel is substantially cheaper.

Any hydrogen made by any means and intended for long-term storage or for transportation use can be converted into liquid fuel by the means outlined here. The comprehensive view of the overall process emphasizes its modular nature, so that improvements can be made in the individual modules, and alternative energy sources can be used if wind proves to be too small a scale or other technologies prove to be cheaper, even in local markets.

The main cost in producing renewable synthetic energy is getting the energy collected from a diffuse source such as the sun. Second in difficulty is getting the energy into molecules, for example in an electrolyzer or a photoelectrochemical process. Getting CO₂ from the atmosphere economically will be a long-term need.

Until PECs can be improved and become cost-effective, presently available methods (Figure 2) could be implemented during the next 10 to 20 years (and perhaps beyond if other alternatives do not pan out).

Dr. Gregory Schoofs made many specific suggestions for improving the manuscript.