Combustion Dynamics and Fuels—Part 2: Cost of Energy Models with Examples

Last time we looked at the major contributors to the cost of fuel—which is generally tied very closely to the marginal cost of producing a kWh.  If we take a look at the major factors playing into the cost of energy, we can pretty easily determine that the fuel cost per kWh is a pretty simple function:
Pretty simple; but both costs have complex components that can cause them to range widely.  Let’s take a look at the cost of fuel.
I think the above is pretty explanatory—the commodity price of a fuel is what you pay for it at your local gas station.  Getting your fuel to site obviously introduces a level of cost.  Your delivery company will charge you more if they have to go significantly off the beaten path, or if they have to use special equipment to get to you.  Similarly, if your fuel isn’t just plain old gasoline, but requires special fuel tanks (CNG) or handling expertise because it may be hazardous (methanol), there is an additional cost associated with that as well. The factor ε on the end is a coefficient to capture things like taxes, discounts, and other miscellaneous costs that should be taken into account.
Lastly, and most importantly, we divide the cost of fuel by an “Availability” factor.  Availability approaches zero as a fuel gets scarcer; it gets bigger than 1 as it becomes bountiful.  A value of “1” is a “nominal” value when compared to the other parts of the equation.
In some respects, how this factor is realized is routine.  If all the gasoline facilities are off line in your region, there is no amount of money you can spend to buy a drop of gas—such as what happened on the east coast during Hurricane Sandy.  Conversely, if there is too much fuel, it either is wasted, burned off, or you have to pay to have it shipped or stored elsewhere—and the cost of the fuel will plummet.
Looking at this another way, you can consider how the supply and demand for a fuel will influence its price—they call this the elasticity of demand.  When gasoline gets more expensive, by 10% for example, demand decreased by 2.6%.  Demand can also effect supply; for example, a 10% increase in demand may increase prices by 38%.  What does this mean for us as modelers of future fuel prices?  It means that we can use the availability factor to analyze the risk associated with fuel prices (knowing how things can change) and try to take it into account when comparing different fuel sources.
Efficiency modelling is a whole different ball game, and very much changes from generator to generator. Generally, each generator has an operating point where it is most efficient, but generally the loads the power do not always allow them to operate at this point.  The resultant duty cycle can significantly influence the efficiency of the underlying system.
Without going into too much detail into efficiency modelling, I’m going to jump into a couple of different comparisons for various systems using the information we have here.   I’ve selected three technologies routinely used in the oil and gas industry for use in different types of power applications: small Diesel Generators, Fuel Cells, and Thermal Electric Generators (TEGs).  Each are used in different applications and also have different capital costs, (the impact on LCOE of which is not thoroughly analyzed here).  The following chart compares the efficiency of each generator, the relative cost of the fuel on a per kWh basis as delivered, as well as the marginal dollar cost to generate a kWh by each generator Tables for the inputs for this chart is attached at the end.
Figure 1: Select Cost of Energy Comparison for common Oilfield Generators
The diesel generator comes out where you would expect it to, with fuel costs at close to 40 cents per kWh.  The supply chain is relatively simple, with non-road diesel coming in at roughly $4 per gallon, and shipping contracts only adding a marginal cost.  Efficiency can range from the mid-twenties to the low thirties; I picked 30% efficiency since most of these generators run well below their prime rating in the field.
Fuel cells are often chosen for small power applications (<1kW), where reliability is essential, and where the cost of fuel is secondary to the cost of maintenance and the cost of downtime.  While many fuel cells are designed to run very efficiently on propane or natural gas, the fuel reformer found in most of these fuel cells require the fuel to be highly refined, above standards found in more traditional applications.  In this case, we built the model around a European fuel cell that is finding acceptance in the US O&G market. The fuel cell operates on highly refined methanol, which can only be provided by the manufacturer in Europe.  (Having a single source supplier imposes its own supply risks—that availability factor I described earlier, which I did not include here).  The result is a very high cost of energy, however for small applications the cost of fuel is dwarfed by the value of reduced maintenance and downtime.
TEGs are also commonly found in the O&G industry, for use powering very small loads <100W; again they are used where reliability is key, although they are very large and suffer from being very expensive.  As opposed to fuel cells, TEGs have very low efficiency’s (3-5%) but they also have the distinction of being able to run well very poor quality fuel (basically any heat source will do).  In many cases, TEGs operate on pre-pipeline quality natural gas, often found in upstream applications.  In this case the source fuel is plentiful, and cheap—often its face value is below the cost of commoditized natural gas, as it has yet to be transported to market; and in many cases, the operator doesn’t have to pay the lease holder the cost of using the fuel, which equates to an additional 10% discount on the fuel.
As this example illustrates, the cost of operating the very inefficient thermal electric generator is 1/10 the cost of operating a fuel cell, and ½ the cost of operating a diesel generator .  Unfortunately, thermal electric generators do not scale up well in size and value much above the 100W mark.
Table 1: Inputs to Cost of Power Model