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Chapter 3. Sustainable Hydrocarbon Fuels by Recycling CO2 with Renewable/Nuclear Energy 60 where is the operating cost and is the capital cost of the entire electrolysis system. These costs are in turn given by the above expressions in which is the cost of electricity, is the electricity-to-chemical energy conversion efficiency at which the electrolyzer is operatingvii, is the operating and maintenance cost per unit of output, is the thermoneutral voltage of water electrolysis, is the cell operating voltage, is the current efficiency (the fraction of the current that drives the desired reactions) which is very close to 100% for all types of state-of-the-art electrolysis cells, is the enthalpy of formation of water (or equivalently, the enthalpy of the water electrolysis reaction, or equivalently the higher heating value (HHV) of hydrogen), is 2 (mol of electrons per mol product H2 in the electrochemical reaction), is Faraday’s number (96485 C/mol), is the investment cost of the system including financing, is the average rate at which H2 is produced in kW, respectively, system respectively, thefractionoftimethecellisutilizedoveritslife(sometimescalledthecapacityfactor), isthe current density (e.g. A/cm2), is the active area of the cell, is the equilibrium Nernst potential at the given conditions, and is the internal area-specific resistance of the cell averaged across the operating life. and are the investment cost and lifetime of a cell stack are the investment cost and lifetime of the balance of is the cell operating current averaged across the cell’s operating life, is and This is a simplified method which assumes time-averaged parameters; in reality, many of the parameters vary with time. Clearly, varies with time regardless of the source. might vary with time depending on how the electrolyzer is being operated; if potentiostatic operation (constant ) is used throughout the operating life then the efficiency will not vary with time. varies with time e.g. as unexpected events occur such as equipment failures. may vary with time as the interest rate may vary during amortization. The time variability of the cell operating current may be one of the most important parameters in terms of its potential impact on the capital cost. In reality , and are encompassed together in the equation accounts for the intermittency ( ), which includes start-stop operation and/or smoother time-varying current operation, as well as cell degradation since is also a function of the time-varying internal resistance. may also depend on the functional form of . For example, the end of life may be declared when the operating current drops below half of the initial operating current due to vii Since the electrolysis efficiency is defined as the thermoneutral voltage over the operating voltage and the cell can be operated at a lower voltage than the thermoneutral voltage (where the cell internal resistance does not supply enough heat), theoretically efficiencies greater than 100% are possible if external heat is available to supply the remaining energy required. However, such an external heat supply must be accounted for in the system energy balance, therefore the system will have an upper limit of 100% efficiency. The heat could be supplied by external electrical heating, giving 100% as the upper limit for the net efficiency of electricity to chemicals for the system.PDF Image | Electrolysis of CO2 and H2O
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