There has recently been a lot of attention to the concept of ‘deep closed-loop geothermal.’ The concept of closed-loop geothermal is to circulate fluid through a wellbore that is 1000s or even 10,000s of ft deep and then back up to the surface. No fluid ever leaves the well. Wells this deep would cost millions of dollars, and so they would need to produce a lot of energy to justify cost.

The design depends on heat conduction to bring energy into the wellbore. In contrast, typical geothermal and EGS designs use *convection* to produce energy – hot water or steam flowing through the rock and into the well.

*Because of its reliance on conduction, the concept of deep closed-loop geothermal is fatally flawed. It has no chance of ever being economically viable, even with revolutionary technology advances.*

The problem is that heat conduction through rock is very slow. The thermal diffusivity of rock is around 1e-6 m^2/s. This is equivalent to the hydraulic diffusivity of a very low permeability shale – around 10 nd. Any design that relies solely on heat conduction to bring energy towards the well will result in extremely low energy production per ft of lateral drilled. Even with revolutionary reductions in the cost of drilling and high energy prices, these designs could not possibly come close to recouping the cost. It doesn’t matter whether you circulate water, or another more exotic fluid through the well.

*The fundamental problem is that heat conduction does not move energy sufficiently rapidly into the well from the surrounding rock. *

This message is important to communicate because deep closed-loop geothermal will divert resources from geothermal energy concepts that have merit, and because it will have a chilling effect on geothermal investment if these projects go forward, and then inevitably fail.

## Enhanced Geothermal Systems

Before I discuss deep closed-loop geothermal, I should state that I am a believer in the potential of Enhanced Geothermal Systems (EGS). The concept of EGS is to use hydraulic fracturing to increase production rates for geothermal energy production. The size of the potential resource is huge, and the technology produces baseload, emission-free electricity. There are technical challenges, but I believe that there are realistic paths forward for economic success. For example, the US DOE FORGE project, DEEP, and Fervo Energy are undertaking projects right now that have real potential to create a genuine breakthrough.

Here are two papers that I wrote on EGS several years ago, explaining why multiple-stage hydraulic fracturing can dramatically improve production, relative to past EGS designs:

- https://pangea.stanford.edu/ERE/pdf/IGAstandard/SGW/2014/Shiozawa.pdf
- https://www.sciencedirect.com/science/article/pii/S0375650516300712

Regardless of my views about EGS, I believe that deep closed-loop geothermal is very unlikely to ever be economically viable, even with revolutionary technology improvements far beyond what is possible today.

This is not a new opinion. In 2009, I participated in a study on deep closed-loop geothermal with Zhe Wang and my advisor Prof. Roland Horne, and we arrived at this same conclusion.

## Quantifying potential production

We can do some quick back-of-the-envelope calculations to assess the energy-producing potential of a closed-loop geothermal system. The equation describing thermal conduction into the wellbore is mathematically identical to the equation for single-phase flow through a hydrocarbon reservoir. In well test analysis for petroleum engineering, we call this equation ‘infinite acting radial flow.’ In well test analysis, the equation for infinite acting radial flow is (in metric units and assuming skin factor is zero):

The equation can be repurposed to solve for heat conduction into a closed-loop system. We replace pressure with temperature, ϕc_{t }(porosity times compressibility) with ρC (density times heat capacity) and k/μ (permeability divided by viscosity) with K (thermal conductivity). Further, let’s rearrange the equation to calculate the heat production rate that would be required to achieve a specified thermal drawdown over a specified period of time. The equation becomes:

I have recently seen proposals for drilling extremely long laterals for use in closed-loop geothermal systems – up to 7 km. I doubt that this would be technically possible in high-temperature applications, but let’s explore this as a ‘best-case scenario.’

If we have a 7 km lateral (h = 7000 m), thermal conductivity is 3 W/(K-m), the wellbore radius is 10 cm, heat capacity is around 2000 J/(kg-K), density of 2650 kg/m^3, and we want to achieve no more than a 15 degree Celsius (27 degrees Fahrenheit) thermal drawdown over the first year of production. How rapidly can we extract heat from this system?

This energy extraction rate is *thermal*. The thermal energy needs to be converted into electricity. In geothermal, a typical efficiency for electricity generation is ballpark 15%. Multiplying by that factor, the electricity generation of this system is 0.072 MWe.

How much revenue will this generate? Let’s assume that you can sell electricity at 15 cents/kWhr, which is significantly higher than typical wholesale prices. Let’s assume that the power plant is able to operate 100% of the time. Then, revenue in this first year of operation will be:

Keep in mind that drilling deep, hot, U-shaped geothermal wells with 7 km laterals would be extremely expensive. It would cost 10s of millions of dollars. If the system was drilled at the extremely optimistic cost of \$15M, and we ignored all other costs, then the cost of installed capacity would be about \$210,000 per kW. This is two orders of magnitude greater than the cost of economically competitive energy generation. The cost per kW-hr would be – using optimistic assumptions – greater than \$5. Wholesale energy prices are closer to 5 cents per kW-hr.

*You could argue that costs can come down over time. Many alternative energy concepts are expensive with current technology. However, with deep closed-loop geothermal, the problem is that physics fundamentally puts a limit on the ability of the system to extract energy.*

You could drill multiple laterals, and this would increase the amount of energy extraction. For the sake of argument, let’s assume that you have breakthrough drilling technology and can drill ten 7 km laterals, and they are sufficiently far apart that they don’t experience thermal interference. Now, the system generates $950,000 in the first year. A bit better, but the cost of drilling ten 7 km laterals would be astronomical.

How does this compare to the performance of ‘conventional’ EGS? In EGS, the design is to circulate water between two wells, separated by 1000+ ft. The circulation of water extracts heat from the volume of rock between the wells. An aspirational goal for EGS (not yet achieved, but perhaps possible with the right design) is to circulate 100 kg/s between the two wells with mild thermal drawdown over years. At that circulation rate, using the same numbers as above, the annual revenue generation would be (very approximately) $8M.

## ResFrac simulation

To experiment, I ran a few ResFrac simulations of a closed-loop heat exchanger. Even though it’s mainly used as a hydraulic fracturing and reservoir simulator, ResFrac has all the capabilities needed to simulate a closed-loop heat exchanger. It implements a full wellbore flow model and has thermal capabilities. With the ‘compositional’ option, the water properties are calculated precisely as a function of pressure and temperature. To calculate thermal conduction between the surrounding formation and the wellbore, ResFrac uses the semi-analytical method from Zhang et al. (2011).

Based on a recent closed-loop design that I’ve seen presented, I implemented a U loop that went 7 km down, 7 km laterally, and 7 km up, and circulated at 25,000 barrels of water per day (46 kg/s). Please note – such a deep design and long lateral at high temperature and in hard rock is not technically possible with current technology. This is just a hypothetical calculation. The geothermal temperature at the bottom of the well is 450°F.

Temperature versus time is plotted in the left panel. The x-axis for ‘time’ is on a log scale. Production temperature peaks at around 360°F and then fall off quickly. Within a few days, production temperature is lower than 212°F. To generate electricity from geothermal production, the water temperature typically needs to be above 300°F. This system achieves that temperature for less than one day.

I tried to improve the system design. I insulated the vertical section on the production side and decreased the flow rate to 2000 barrels per day (around 3.7 kg/s). The insulation is to minimize heat loss to the surrounding formation as the fluid flows back up to the surface, and the decreased flow rate is intended to avoid cooling down the system too quickly. The result is shown below.

The temperature peaks at 450° F, and thermal drawdown is moderate – 50 degrees of drawdown over a few years. This design actually could be used to generate electricity for a reasonable period of time. However, with a water circulation rate of 3.7 kg/s, the total rate of energy extraction is too low to justify the expense of constructing the heat exchanger. Using the same economic numbers as above, this system would generate around 290k per year in revenue.

### References

Wang, Zhe, Mark W. McClure, and Roland N. Horne. 2010. Modeling study of single-well EGS configurations. Proceedings World Geothermal Congress, Bali, Indonesia.

Zhang, Yingqi, Lehua Pan, Karsten Pruess, Stefan Finsterle. 2011. A time-convolution approach for modeling heat exchange between a wellbore and surrounding formation. Geothermics 40 (4): 261-266, doi: 10.1016/j.geothermics.2011.08.003.