GRC Transactions, Vol. 45, 2021

Multilateral Closed-Loop Geothermal Systems as a ZeroEmission Load-Following Resource
Michael Holmes(1), Matthew Toews(1), Jesse Jenkins(2), and Nestor Sepulveda(2)(1) Eavor Technologies Inc.
(2) DeSolve, LLC

Keywords
Geothermal, closed-loop, multilateral, net-zero, load-following, thermodynamics, zero-emission,modelling, renewable, green energy, Eavor-Loop, Eavor-Lite
ABSTRACTThe Eavor-Loop™, a multilateral closed-loop geothermal system (MCLGS), is introduced as a
zero-emission load-following resource (ZELFR) that is globally scalable and can provide baseload
or dispatchable electricity. For any electrical grid to reach net-zero, ZELFR or large-scale energy
storage is required to balance intermittent renewables like solar and wind and provide grid stability.
Given the declining costs of intermittent renewables and their increased utilization in modern
grids, the ability to load follow is both crucial and highly valued.
The objectives of this paper are two-fold. First, we prove the technical feasibility of MCLGS toprovide flexible power using first principles-based models. Second, we demonstrate the valueenhancement of flexible operation with a case study of the United States Western Interconnection
power transmission grid using an electricity resource capacity expansion model.
A transient, fully coupled wellbore + thermal model was developed and validated using over a
year of operating data from the Eavor-Lite™ facility, a full-scale Eavor-Loop™ demonstration
project in Alberta, Canada. Recent modelling work, coupled with field trials, has proven thefeasibility of Eavor-Loop™ to provide flexible energy for load-balancing or peak-matching witha minimal impact on lifetime energy extraction. Transient operation allows the system to rechargeduring low demand periods.
To demonstrate the value of Eavor-Loop™ in a net-zero grid, an electricity resource capacity
expansion model (GenX) was used. GenX is a constrained optimization model that determines themix of electricity generation and storage required to meet electricity demand while minimizing
system cost. Flexible Eavor-Loop™ operation provides stability for the grid, matching electricity
generation with demand, and reduces annual total system cost by up to $20B (21%) in a base caseand up to $403B (81%) in an extreme case. Inclusion of Eavor-Loop™ also reduces land use
required by up to 49%, saving 25 acres in a base case and 48 acres in an extreme case for eachmegawatt of Eavor-Loop™ installed.

Holmes et al.
1. Introduction
Governments and corporations around the world are facing increased pressure to reduce theirgreenhouse gas (GHG) emissions and create plans to transition their energy use away from fossil
fuels. Energy is vital to quality of life, and this theme has been highlighted throughout the COVID19 pandemic as well as events like the Texas power crisis of February 2021. Transitioning awayfrom fossil fuels will not be easy: in 2019, 84% of primary energy use was provided by a
combination of oil, gas, and coal (bp, 2020). Clearly, we have a long way to go.
Several prominent research institutions have analyzed pathways to net-zero, with 2050 being acommon timeline for achieving this goal. The European Commission estimates that the share ofelectricity in final energy consumption will grow from 23% today towards 50% in 2050, with amajority of the growth coming from renewable energy (European Commission, 2020). The
International Energy Agency (IEA) recently released a roadmap to net-zero, concluding that
almost half of the global reductions in CO2 emissions in 2050 will come from technologies
currently at the demonstration or prototype phase, with one of the biggest innovation opportunities
being energy storage (International Energy Agency, 2021). Factoring in increased total energy
demand from a growing global population and improved energy access in developing countries
makes the task even more daunting.
As penetration of intermittent renewables such as solar and wind increases, two challenges emerge:
physical space constraints and concerns regarding grid stability and resiliency. Many countries areconstrained on land area and cannot designate a substantial portion of their land to be covered withsolar panels or wind turbines, especially when this land is required for food production to support
a growing population. To transition to net-zero, these countries will require a zero-emission energy
source with an energy density comparable to that of fossil fuels. Countries with a larger land masscan continue to build solar and wind capacity, but grid stability and resiliency become a concern
as intermittent renewables make up a larger portion of electricity generation. People need energy,
regardless of whether the sun is shining or the wind is blowing. Sepulveda et al. investigated therole of firm low-carbon resources in deep decarbonization and found that availability of firm lowcarbon technologies, such as natural gas combined cycle (NGCC) equipped with carbon captureand storage (CCS), reduces electricity cost by up to 62% in fully decarbonized scenarios(Sepulveda, Jenkins, de Sisternes, & Lester, 2018). Although firm low-carbon technologies candeliver system value, they frequently face public opposition due to their environmental impacts,
namely the fact that they are non-renewable.
Geothermal energy is clean and renewable and has been used for heat and electricity generationfor over a century (Fallah, et al., 2021). However, the requirement of high geothermal gradientsand a permeable aquifer has limited the scalability of geothermal energy, rendering it a nichetechnology suitable only in global hotspots (Rybach, 2010). Closed-loop geothermal systems(CLGS) offer a solution to the scalability issue. CLGS rely only on conductive heat transfer,removing the need for a permeable aquifer. CLGS also have no water use, no fracking, no induced
seismicity, no corrosion/erosion/scaling, no fluid disposal, no requirement for rare earth metals,
and a low environmental footprint (Toews, Riddell, Vany, & Schwarz, 2020). The primarydrawback of CLGS is that they are limited by the rate of conductive heat transfer through rock,which is a slow physical process. The required wellbore area in contact with the hot rock is verylarge to overcome this limitation and make the overall project economical. Drilling multilateralHolmes et al.
closed-loop geothermal systems (MCLGS), whereby a single vertical well is connected to multiple
lateral wells for heat harvesting, is one way to create a sufficiently large contact area.
This paper introduces one such MCLGS, the Eavor-Loop™, as a globally scalable zero-emission
resource capable of providing firm or load-following electricity (a zero-emission load-following
resource, or ZELFR). The objectives of this paper are two-fold. First, we prove the technicalfeasibility of the Eavor-Loop™ to provide flexible power using first-principles based models
validated by 16 months of operational data from an Eavor-Loop™ field demonstration in Alberta,
Canada. Second, we demonstrate the system value of the Eavor-Loop™ in a net-zero grid with acase study of the United States Western Interconnection power transmission grid using anelectricity resource capacity expansion model.
2. Eavor-Loop™ thermodynamic model
2.1 Model formulation
The energy output of an Eavor-Loop™ system can be predicted using various engineering
approaches to model the transient heat transfer from the surrounding rock to the fluid flowing
through the wellbore. This paper introduces a method of numerical simulation of the transient, 2dimensional heat conduction in the rock surrounding the wellbore coupled with a numericalsimulation of the transient 1-dimensional energy and momentum equations for fluid flow inside
the wellbore.
Fourier’s law of heat conduction and the conservation of energy equation can be combined toderive the partial differential equation (PDE) that governs the transient conduction of thermalenergy in rock with a constant thermal conductivity:
𝜌𝑟 𝐶𝑝,𝑟 (

𝜕𝑇
𝜕𝑡

+ 𝑣𝑟

𝜕𝑇
𝜕𝑟

𝑣 𝜕𝑇

+ 𝜃

𝑟 𝜕𝜃

+ 𝑣𝑧

𝜕𝑇
𝜕𝑧

) = 𝑘𝑟 (

1 𝜕
𝑟 𝜕𝑟

(𝑟

𝜕𝑇
𝜕𝑟

1 𝜕2 𝑇

)+ 2
𝑟

𝜕𝜃 2

+

𝜕2 𝑇
𝜕𝑧 2

) + 𝑔̇

(1)

where 𝜌𝑟 is the rock density
𝐶𝑝,𝑟 is the rock heat capacity
𝑇 is the rock temperature
𝑡 is time𝑣 is velocity
𝑟 is the radial direction
𝜃 is the angular direction𝑧 is the axial direction
𝑘𝑟 is the rock thermal conductivity
𝑔̇ is the rate of heat generation
Assuming transient heat transfer by conduction only, no thermal interaction between adjacent
wellbores, and no angular variation in temperature yields:
𝑣𝑟 = 𝑣𝜃 = 𝑣𝑧 = 0𝜕𝑇=0𝜕𝜃𝑔̇ = 0Equation 1 reduces to:Holmes et al.
1 𝜕𝑇
𝛼𝑟 𝜕𝑡

=

1 𝜕
𝑟 𝜕𝑟

(𝑟

𝜕𝑇
𝜕𝑟

)+

𝜕2 𝑇

(2)

𝜕𝑧 2

𝑘

where 𝛼𝑟 is the thermal diffusivity of the rock: 𝛼𝑟 = 𝜌 𝐶𝑟𝑟 𝑝,𝑟The transient energy equation for the 1D fluid flow in the wellbore along the axial coordinate
system can be expressed as:
𝜕𝜌𝑓 𝑒
𝜕𝑡

+

𝜕𝐺(ℎ+𝑔𝑦)𝜕𝑧= 𝑈(𝑇𝑟𝑤 − 𝑇𝑓 )(3)

where 𝜌𝑓 is the fluid density
𝑒 is the internal energy of the fluid
𝐺 is the mass flux of fluid flowing through the wellboreℎ is the enthalpy of the fluid
𝑔 is the acceleration due to gravity
𝑦 is the position in the vertical direction (parallel to gravity)
𝑈 is the heat transfer coefficient from the rock/wellbore boundary to the fluid
𝑇𝑟𝑤 is the temperature of the rock at the rock/wellbore boundary
𝑇𝑓 is the temperature of the bulk fluid in the wellbore
Note that the change in kinetic energy has been neglected in equation 3 as this contribution is
negligible compared to the internal energy and enthalpy change of the fluid. In addition, theconservation of mass has been invoked for an incompressible fluid so the mass flux, G, is constantalong the length of the wellbore. The heat transfer coefficient U is comprised of any conductive
resistance between the rock and the wellbore (i.e., casing and cement in the vertical sections) andconvective resistance of the flowing fluid.
A quasi-steady state version of the momentum equation is employed whereby the pressure drop of
the fluid is calculated using Colebrook White type correlation. Given the simplicity of the
momentum equation, it is not repeated here.
2.2 Initial and boundary conditions
The temperature field of the rock and fluid at time t=0 must be specified along with boundary
conditions for the temperature, pressure, and flowrate of the fluid at the inlet of the loop. The rockboundary temperature and radius must also be specified. For all simulations, the boundary rockradius is set large enough such that it has not been impacted by the thermal front and the boundary
temperature remains at virgin rock temperature. At the boundary between the rock and the fluid
flowing through the loop, the heat flux must be continuous such that the heat flux calculated using
Fourier’s Law is equivalent to the heat flux entering the wellbore and being transferred to the fluid:
𝑘𝑟

𝜕𝑇
𝜕𝑟

= 𝑈(𝑇𝑟𝑤 − 𝑇𝑓 )(4)

2.3 Discretization and numerical solution
The PDE describing the transient 2D conduction in the rock can be solved numerically byintegrating equation 2 over a discrete finite control volume, 𝑑𝑉 = 2𝜋𝑟 𝑑𝑟 𝑑𝑧 and specified time
step Δ𝑡:

Holmes et al.
𝑛+1
𝑛
𝑛+1
𝑛+1
𝑛+1
𝑛+1
𝑇𝑖,𝑗
− 𝑇𝑖,𝑗𝑇𝑖+1,𝑗− 𝑇𝑖,𝑗𝑇𝑖,𝑗− 𝑇𝑖−1,𝑗1
2𝜋(𝑟𝑖+1− 𝑟𝑖2 )(𝑧𝑗+1 − 𝑧𝑗 )= 4𝜋(𝑧𝑗+1 − 𝑧𝑗 ) (𝑟𝑖+1
− 𝑟𝑖
)
𝛼𝑟
𝛥𝑡
𝑟𝑖+2 − 𝑟𝑖𝑟𝑖+1 − 𝑟𝑖−1𝑇𝑛

2
+ 2𝜋(𝑟𝑖+1− 𝑟𝑖2 ) ( 𝑖,𝑗+1

𝑛
−𝑇𝑖,𝑗

𝑧𝑗+2 −𝑧𝑗𝑛
𝑇 𝑛 −𝑇𝑖,𝑗−1− 𝑖,𝑗𝑧𝑗+1 −𝑧𝑗−1)(5)where i indexes the radial direction, j indexes the axial direction, and n indexes time.
Note that the radial derivatives on the right-hand side of equation 5 are implicitly calculated at the
new time step (n+1) whereas the axial derivatives are explicitly calculated at the previous time
step (n). This is acceptable as the spacing in the axial direction is much larger than the radial
direction. Consequently, the stability criterion in the explicit numerical treatment in the axial
direction is not violated.
The transient 1D energy equation (equation 3) for the wellbore flow is discretized in the following
manner:
𝜌𝑓 𝜋𝑟𝑤2 ∆𝑧

𝑛+1 ̂𝑛̂0,𝑗(ℎ−ℎ0,𝑗)

𝛥𝑡

𝑛+1
𝑛+1
𝑛
+ 𝐺𝜋𝑟𝑤2 ((ℎ̂𝑗𝑛+1 − ℎ̂𝑗−1) + 𝑔∆𝑦) = 𝑈𝑗 2𝜋𝑟𝑤 ∆𝑧(𝑇1,𝑗− 𝑇0,𝑗)(6)̂) in place of heat capacity and temperature toEquation 6 makes use of the specific enthalpy (ℎproperly model the Joule-Thomson effect, which has a large impact on the temperature change ofthe fluid in the vertical sections of the loop.

Linear, least-squared regression correlations were derived for working fluid thermophysicalproperties (enthalpy, density, viscosity, and thermal conductivity) obtained from NIST Refprop(National Institute of Standards and Technology, 2020). Thermophysical properties are calculated
based on the inlet conditions of each wellbore grid block for each time step. The axial grid spacing
is maintained sufficiently small to ensure that temperature and pressure changes between grid
blocks are minimal, maintaining validity of the assumption of constant thermophysical properties
within each grid block.
The resulting system of algebraic equations for all the control volumes for the rock and wellbore
fluid along with specified boundary conditions are solved using the Tri-Diagonal Matrix
Algorithm to compute the temperature field at the new time step, 𝑇𝑛+1
𝑖,𝑗 based on the previous time𝑛step 𝑇𝑖,𝑗 .
2.4 Field validation of transient model
2.4.1 Eavor-Lite™ overview
The Eavor-Loop™ Demonstration Project (“Eavor-Lite™”) is a full-scale prototype of amultilateral closed-loop geothermal system intended to derisk the key technical components,
including thermodynamic validation, and serve as a research facility for future technology
commercialization. The multilateral closed-loop system, shown in Figure 1 below, consists of alarge U-shaped well drilled to 2.4 km depth, two parallel laterals, each of 1700m length, and apipeline connecting the two sites on surface. A water-based working fluid circulates in the inlet
well (B→C), through the parallel horizontal wellbores (C→D) where the working fluid receives
heat from the rock via conduction, and rises up the outlet well (D→E) at an elevated temperature.
The density difference between the inlet and outlet well creates a thermosiphon which is sufficient
to overcome hydraulic losses, eliminating the need for a circulating pump. A test facility on theHolmes et al.
surface measures all relevant performance data and cools the working fluid for re-circulation in
the pipeline (A→B) and back to the inlet well.

Figure 1: Eavor-Lite™ overview

2.4.2 Prediction of Eavor-Lite™ performance
The transient 2D model introduced in section 2.1 was used to predict the measured performancedata from Eavor-Lite™. The model was history matched using 60 days of time series production
data comprising outlet wellhead temperature, outlet wellhead pressure, and flowing temperature
at various depths measured by a 6-point thermocouple in the outlet well. Time series of measured
circulation rate, inlet wellhead temperature, and inlet wellhead pressure were provided as inputs.
History match parameters were the vertical and lateral rock thermal conductivities. The history
match was performed using a genetic algorithm to minimize an objective function specified as aweighted sum of squared error terms between the model’s prediction and the measured data. Rockthermal conductivities, and accordingly thermal performance of the system, were calculated to bewithin 5% of the values estimated prior to drilling the loop, highlighting the predictability of theEavor-Loop™ system.

Holmes et al.
Figure 2 below shows the measured and predicted outlet temperature. The vertical line separates
the data used for the history match (left) from the extrapolation and prediction (right). Circulation
rate is shown for reference. Note that periods where there is no measured wellhead temperaturecorrespond to periods where the loop was shut down (circulation rate of 0) for thermal recharge
testing. To date, the model has been used to successfully predict over 16 months of operating datawith a mean absolute error of only 0.19°C (0.37%).

Figure 2: Measured and simulated outlet wellhead temperature for the Eavor-Lite™ demonstration project

Several trials have been run to prove the ability of the Eavor-Loop™ to operate in a flexible
fashion. The focus of this paper will be on the first trial, run from September 22 to October 6,
2020. During this trial, circulation was stopped completely for 14 days to validate the thermal
recharge predicted by the model, a critical requirement for proving flexible operation. The
predicted and measured temperatures in the outlet wellbore thermocouple string are shown in
Figure 3. Closer to the surface, where the virgin rock temperature is cooler, a larger reduction instagnant wellbore temperature is observed both in the field data and the model. The rate of heatdissipation is governed by the thermal drawdown during circulation prior to the shut in as well as
the thermal diffusivity of the surrounding rock. The ability of the model to accurately predict theobserved temperature drawdown in the vertical well gives confidence that all the relevant physics
are captured and the calculated thermal conductivities are correct.

Holmes et al.
ff

Temp 2 at 1666 m (ºC)
Temperature (°C)

Temperature (°C)

Temp 1 at 1999m (ºC)
70
60
50
40
30
20
10
0

Measured

70
60
50
40
30
20
10
0

Simulated

MeasuredTemp 4 at 999 m (ºC)
Temperature (°C)

Temperature (°C)

Temp 3 at 1332 m (ºC)
70
60
50
40
30
20
10
0

Measured

70
60
50
40
30
20
10
0

Simulated

Measured

MeasuredfSimulated

Simulated

Temp 6 at 333 m (ºC)
Temperature (°C)

Temperature (°C)

Temp 5 at 666 m (ºC)
70
60
50
40
30
20
10
0

Simulated

70
60
50
40
30
20
10
0

Measured

SimulatedfFigure 3: Measured and predicted temperature falloff in the outlet well thermocouple during the thermal
recharge test

Figure 4 and Figure 5 show the predicted temperature profile along the lateral wellbore on
September 21, 2020 (immediately prior to the recharge trial) and October 4, 2020 (at the end of
the recharge trial prior to commencing circulation), respectively. Figure 6 and Figure 7 show how
the radial rock temperature at the heel and toe, respectively, change during and after the trial. The
thermal recharge of the rock is evident, most notably at the heel of the well where the near-wellbore
temperature increased from 36°C during circulation to 64°C after 14 days of recharge. This is
intuitive given the fluid temperature is lowest, and therefore the heat flux is the highest, at the heel.

Holmes et al.

Figure 4: Simulated temperature profile along the lateral wellbore immediately prior to thermal recharge trial

Figure 5: Simulated temperature profile along the lateral wellbore at the end of the recharge trial prior tocommencing circulation

Holmes et al.

Figure 6: Radial rock temperature profiles at the heel of the well showing thermal recharge of the near-wellbore
regionFigure 7: Radial rock temperature profiles at the toe of the well showing thermal recharge of the near-wellbore
regionHolmes et al.
2.5 Extrapolation to future projects
The same physics outlined in this paper, built into Eavor’s transient model, and validated with
Eavor-Lite™ can be used to estimate the performance of future Eavor-Loop™ projects. To betruly scalable with a low levelized cost of electricity (LCOE), novel drilling technology is required
to enable deeper Eavor-Loops™ in hotter and harder crystalline basement rock – “Eavor-Loop™
2.0” as illustrated in Figure 8. Such a configuration will massively reduce the LCOE of the EavorLoop™ system, enabling widespread adoption at gigawatt scale.

Figure 8: Eavor-Loop™ evolution

This paper considers a case study for a futuristic project drilled in a high geothermal gradientenvironment, where the Eavor-Loop™ is drilled into rock with an average temperature exceeding
200°C. While drilling such a project is not possible with today’s technology, Eavor has been
progressing numerous research and development initiatives to make such a project a reality. The
details of these initiatives are both proprietary and outside the scope of this paper, but Eavor has
line of sight to LCOE below US$50/MWh with technology anticipated to be proven in 2022.
The proposed deep Eavor-Loop™ was modelled utilizing Eavor’s transient model. Net heat topower efficiency was calculated based on the outlet wellhead temperature, an assumed utilization
efficiency of 50% (relative to Carnot efficiency), and an assumed cold sink temperature of 15°C:

Holmes et al.
𝜂 = 0.5 (1 −15+273.15
𝑇𝐻 +273.15)(7)

where 𝜂 is net heat to power efficiency
𝑇𝐻 is the produced fluid temperature at the outlet wellhead
The simulated electrical power for operation with a constant flowrate is shown in Figure 9.
Alternatively, the loop can be operated with a variable flowrate to give a constant power output
suitable for baseload operation, shown in Figure 10. Both simulations were run for a period of 20
years.

Figure 9: Simulated electrical power for the deep Eavor-Loop™ 2.0 under constant flowrate operation

Holmes et al.

Figure 10: Simulated electrical power for the deep Eavor-Loop™ 2.0 under baseload operation

As validated by the thermal recharge tests at Eavor-Lite™, the transient model can predict thethermal response of the rock matrix to changes in circulation rate. This capability can be used todemonstrate the ability of the Eavor-Loop™ to operate in a flexible fashion, storing energy byramping down (or shutting in) during periods of low demand and then increasing the flowrate andproducing that energy during periods of high demand. The rock, coupled with the large subsurface
volume of the loop itself, acts as a battery, controlled by manipulating the flowrate. To produce
the excess power on demand, no design changes to the loop are required but the surface heat topower capacity must be increased. The key parameters for modelling flexible operation are thedispatch ratio d, defined as the maximum power output of the system divided by the rated(baseload) capacity; and the recharge ratio r, defined as the power output during the recharge phase
divided by the rated (baseload) capacity. For lossless diurnal flexibility, the cumulative generation(MWh) at the end of the day remains constant for all values of d and r. Enforcing this daily energybalance gives the following equation for how many hours per day the loop can operate at its peak
power output:
𝑡𝑑 =24(1−𝑟)𝑑−𝑟(8)

And accordingly:
𝑡𝑟 = 24 − 𝑡𝑑

(9)

In this section, two cases are presented:
1. Dispatch ratio = 1.5, recharge ratio = 0.3 (low ratio flexibility)
2. Dispatch ratio = 2.0, recharge ratio = 0.0 (high ratio flexibility)
Both cases were modelled for 20 years of diurnal cycles. A snapshot of the transient behaviour ofcases 1 and 2 are shown in Figure 11 and Figure 12, respectively. Cumulative power generation at

Holmes et al.
the end of 20 years for all four cases are compared in Table 1. These results prove the ability of
the Eavor-Loop™ to store energy and operate in a flexible manner over a multi-decade period.

Figure 11: Load-matching power output and circulation rate profile for 3 representative days of case 1(dispatch ratio = 1.5, recharge ratio = 0.3)

Figure 12: Load-matching power output and circulation rate profile for 3 representative days of case 2(dispatch ratio = 2.0, recharge ratio = 0.0)

Holmes et al.
Table 1: Cumulative power generation after 20 years of simulation for various Eavor-Loop™
operating modes

Constant flowrate
Baseload
Flexible (low ratio)
Flexible (high ratio)

Cumulative power
generation in 20 years
(GWh)
1,669
1,640
1,665
1,552

Average power
generation (MW)Change relative toconstant flowrate case

9.53
9.36
9.51
8.86

-1.8%
-0.2%
-7.0%

3. Electrical grid modelling
3.1 Model overview
To demonstrate the value of Eavor-Loop™ in achieving a net-zero electricity grid, an electricity
resource capacity expansion model (GenX) was used. GenX is a constrained optimization modelthat determines the mix of electricity generation and storage required to meet electricity demand
while minimizing total system cost (Jenkins & Sepulveda, 2017). A case study of the United States
Western Interconnection grid was analyzed in a net-zero 2050 scenario.
The Western Interconnect grid was divided into six zones (Figure 13). Each zone is treated as anode and capacity constraints are defined on inter-zone electricity transmission. Within each zone,
electricity demand and resource availability are modelled at hourly intervals, with 3,360
representative hours (20 weeks) used to model a single year. The GenX model determines the
optimal mix of resources and their operation to match supply and demand at each hour while
minimizing total system cost.

Figure 13: Western Interconnect grid zonal divisions for GenX model

The optimal resource mix is heavily dependent on total electricity demand as well as cost andavailability of competing resource types. Two competing technology cost scenarios, summarizedHolmes et al.
in Table 2, and two demand scenarios, summarized in Table 3, were defined. All costs are in USD
and are on a per kilowatt basis, unless otherwise specified.
Table 2: Competing technology cost assumptions
Wind
Solar
Battery (capacity)
Battery (energy) ($/kWh)
Nuclear
New natural gas combined cycle (NGCC) +carbon capture and storage (CCS)
Retrofit NGCC with CCS
Retrofit combined cycle (CC) for zero-carbon
fuels
Retrofit combustion turbine (CT) for zerocarbon fuels
New CC for zero-carbon fuels
New CT for zero-carbon fuels
Zero-carbon fuel ($/MMBTU)
Equivalent cost assuming hydrogen ($/kg)
Natural gas (Pacific) ($/MMBTU)
Natural gas (Mountain) ($/MMBTU)

Low cost
$761
$516
$73
$84
$4,650$1,599High cost$1,121
$669
$121
$139
n/a
$3,198Reference
(1)
(1)
(1)
(1)
(1)
(1)

$1,279
$419

n/a
$419

(1)
(1)

$333

$333

(1)

$856
$667
$9
$1.20
$3.61
$3.73

$856
$667
$18
$2.43
$7.27
$7.77

(1)
(1)
(2)
(2)
(3)
(3)

(1) (National Renewable Energy Laboratory, 2020)(2) (Larson et al., 2020)
Table 3: Electricity demand assumptions
Annual demand (TWh)Flexible EV capacity (MW)
Flexible heat pump capacity(MW)
Flexible water heat capacity(MW)

Moderate demand
1,410
81,974
27,239High demand
1,685
134,726
31,480

Reference
(3)
(2)
(2)

5,526

5,988

(2)

(3) (U.S. Energy Information Administration, 2020)
In addition, the following assumptions were made on the ability to retrofit existing infrastructure:••

Capacity for retrofitting NGCC with CCS limited to 50% of existing NGCC capacity
Capacity for retrofitting CC for zero-carbon fuels limited to 50% of existing CC capacity
when CCS upgrades available, 100% when CCS not available

Holmes et al.
3.2 Model incorporation of Eavor-Loop™
Each of the 6 zones were discretized into candidate project areas (CPAs) on the order of 10 km2
per CPA. Within each CPA, geothermal gradient was mapped using Curie point data (Li, Lu, &Wang, 2017). Exclusion zones were applied for non-developable areas, such as water bodies,mountain ranges, national parks, military land, and proximity to critical infrastructure. Twotransmission costs were calculated for each CPA, with the lower of the two used by the model.
The first cost assumes construction of a new spur line directly from the CPA to a load center. The
second cost assumes construction of a new spur line to an existing high-voltage line andtransmission on the high-voltage line to a load center.
Curves were generated for Eavor-Loop™ power output as a function of geothermal gradient using
the thermodynamic model and assuming operation in baseload mode. Capital and operating costs
were calculated based on Eavor’s proprietary technology roadmap and internal cost assumptions.
For each CPA, a generation potential was calculated using the Eavor-Loop™ footprint, area of the
CPA, and power generated from a single Eavor-Loop™ based on the CPA’s geothermal gradient.
Each CPA was also assigned an LCOE inclusive of transmission using the cost assumptions
already discussed. The CPAs within each region were aggregated and ranked to produce theregional Eavor-Loop™ supply curves shown in Figure 14.

Figure 14: Eavor-Loop™ regional supply curves used as inputs to the GenX model

To model flexible operation, costs were further divided into a capacity (surface) component and acharge (subsurface) component. The total Eavor-Loop™ investment cost is the sum of the capacity
and charge components. GenX was modified to optimize investments in surface and subsurface
capacity independently to deliver the lowest total system cost. For example, if the model chooses

Holmes et al.
to build 1 GW of subsurface capacity with a dispatch ratio of 1.5, it would build 1.5 GW of surface
capacity. At any point in time, the system can deliver up to 1.5 GW of power but is constrained toan average power output over the representative week of 1 GW (or a total generation of 168 GWh
per week). The energy “charge” from the subsurface is assumed to be constant, and the discharge
rate is governed by the surface capacity and the optimal system dispatch to supply demand at
minimum cost.
All cases are compared based on the total system cost, mainly comprised of annuitized capital
investment and any fixed or variable operating and maintenance costs. All scenarios were run withand without Eavor-Loop™ as an option to quantify the technology value as the total system costsavings when Eavor-Loop™ is available. For Eavor-Loop™ scenarios, key outputs are thecapacity built, total energy produced, and hourly dispatch patterns.
3.3 Model results
This paper will focus on the two extreme cases for Eavor-Loop™ adoption: high demand and highcost alternative generation technologies (most optimistic case for Eavor-Loop™); and moderatedemand and low-cost alternative generation technologies (most pessimistic case for EavorLoop™).
3.3.1 Optimistic case: high demand and high-cost alternative generation
In the high demand and high-cost alternative generation scenario, the total annual system costswith and without Eavor-Loop™ are $75.4B and $95.6B, respectively. Inclusion of Eavor-Loop™
in the capacity optimization results in annual system cost savings of over $20B (a 21% reduction).
Without Eavor-Loop™, generation is provided primarily by solar and wind (Figure 15). Over 50%
of total system cost is allocated to providing firmness and reliability, split primarily amongst gas+ CCS, zero carbon fuel, batteries, and other renewables (hydrothermal) (Figure 16). When themodel has the option to build Eavor-Loop™, it supplies 40% of the total electricity generation.
The $32B annual cost of the Eavor-Loops™ is more than offset by $35B in reduced spending on
the aforementioned firmness and reliability-providing technologies. The remainder of the costsavings are realized through reduced investments in wind and solar.
Building 90 GW of Eavor-Loop™ capacity eliminates the need for 200 GW of other capacity,
reducing total capacity required to meet demand by 110 GW (Figure 17). This reduction includes
35 GW of reduced solar and 91 GW of reduced wind capacity. Any type of capacity requires landuse, and both solar and wind have large footprints, with median energy generation densities of
6.63 and 1.84 W/m2 for solar and wind power, respectively (van Zalk & Behrens, 2018). Internal
calculations give the energy generation density of Eavor-Loop™ at 363 W/m2. In this case,inclusion of Eavor-Loop™ reduces total land requirement for solar and wind by approximately
9,000 km2 (2.2 million acres or 43%), equivalent to land savings of 25 acres/MW of Eavor-Loop™
capacity.

Holmes et al.

Figure 15: Energy share profiles without Eavor-Loop™ (left) and with Eavor-Loop™ (right) for the highdemand and high-cost alternative generation scenario

Figure 16: Components of total system cost with and without Eavor-Loop™ for the high demand and high-cost
alternative generation scenario

Holmes et al.

Figure 17: Breakdown of new capacity built with and without Eavor-Loop™ for the high demand and highcost alternative generation scenario

3.3.2 Pessimistic case: moderate demand and low-cost alternative generation
In the moderate demand and low-cost alternative generation scenario, the total annual system costswith and without Eavor-Loop™ are $50.0B and $52.2B, respectively. Even in this worst-casescenario for Eavor-Loop™ value, its inclusion results in annual savings of over $2B and it provides
19% of the total electricity generation (Figure 18). All trends observed in the previous scenario
remain, albeit with a reduced magnitude given the lower overall system cost and the smaller, but
still significant, penetration of Eavor-Loop™ into the grid. Generation without Eavor-Loop™ isstill provided primarily by solar and wind. Over 50% of total system cost is once again allocatedto providing firmness and reliability, and the annual cost of Eavor-Loop™ ($10B) is nearly entirely
offset by reduced spending for such technologies ($8B) (Figure 19). The remainder of the costsavings come from reduced spending on solar and wind. Again, inclusion of Eavor-Loop™
reduces total capacity required to meet demand. In this case, capacity is reduced by 43 GW(including 22 GW reduced solar and 26 GW reduced wind), land usage due to solar and wind isreduced by 2,800 km2 (700 thousand acres or 20%), and land savings are 22 acres/MW of EavorLoop™ capacity.

Holmes et al.

Figure 18: Energy share profiles without Eavor-Loop™ (left) and with Eavor-Loop™ (right) for the moderatedemand and low-cost alternative generation scenario

Figure 19: Components of total system cost with and without Eavor-Loop™ for the moderate demand and lowcost alternative generation scenario

Holmes et al.

Figure 20: Breakdown of new capacity built with and without Eavor-Loop™ for the moderate demand andlow-cost alternative generation scenario

Holmes et al.
3.3.3 Additional sensitivities
In the absence of Eavor-Loop™, GenX relies heavily on other zero-emission firm capacity,
primarily gas + CCS and zero carbon fuels. Neither of these technologies are currently at acommercially viable stage and are by no means guaranteed to be available in the future, let alone
at the prices assumed in the model. To understand the impact of this assumption, additional
sensitivities were run in which no zero-emission firm capacity options were available (except for
Eavor-Loop™ as applicable). In these scenarios, all future demand must be met by a
combination of wind and solar, with batteries available to time-shift the output as necessary tomeet demand.
In the high demand and high-cost alternative generation scenario, total annual system cost withand without Eavor-Loop™ was $96.8 and $499.7B, respectively. Without zero-emission firm
resources, the total system cost for the no Eavor-Loop™ scenario increased 5-fold (from $95.6B
to $499.7B) while the scenario with Eavor-Loop™ increased by only 28% (from $75.4B to$96.8B). The substantial cost savings come from reduced spending on wind and batteries as well
as a significant penalty associated with demand curtailment (Figure 21). The demandcurtailment, or value of lost load, refers to the social cost of not serving demand. It means themodel could not provide supply to match demand at a cost below $9,000/MWh, triggering
unserved demand. In real life, this indicates a grid reliability issue and would translate to forced
curtailment or rolling blackouts.
In the moderate demand and low-cost alternative generation scenario, total annual system costwith and without Eavor-Loop™ was $57.0B and $106.4B, respectively. In this case, the absenceof zero-emission firm resources doubled the no Eavor-Loop™ scenario costs (from $52.2B to$106.4B), while the scenario with Eavor-Loop™ saw only a modest cost increase of 14% (from$50.0B to $57.0B). In this scenario, there was no substantial demand curtailment and costsavings are realized primarily through reduced spending on wind and batteries (Figure 22).
In addition to the cost savings, both scenarios give substantial land savings, summarized below.
Table 4: Key land use reduction metrics for the sensitivity cases
High demand, high-cost
alternative generation

Moderate demand, low-cost
alternative generation

13,60011,5003.4 million

2.8 million

Reduction in land usage (%)

49%

45%

Land savings (acres/MW
Eavor-Loop™ capacity)

48

36

Reduction in land usage(km2)
Reduction in land usage(acres)Holmes et al.

Figure 21: Components of total system cost with and without Eavor-Loop™ for the scenario with high demand,high-cost alternative generation, and no firm capacity (other than Eavor-Loop™). Note thediscontinuous y-axis.

Figure 22: Components of total system cost with and without Eavor-Loop™ for the scenario with moderatedemand, low-cost alternative generation, and no firm capacity (other than Eavor-Loop™)

Holmes et al.
3.3.4. Flexible operation
As discussed in section 3.2, GenX was modified to optimize investments in surface and subsurface
capacity independently to deliver the lowest total system cost. Model results give optimized EavorLoop™ dispatch ratios ranging from 1.00 (baseload operation) to 1.81, depending in part on thecontribution of solar and wind to the zone’s overall electricity generation (Figure 23). These
dispatch ratios are well within the range modelled and proven to be feasible in section 2.5, thus
confirming the ability of the Eavor-Loop™ to operate as a zero-emissions load-following resourcein an economically optimized fashion.

Figure 23: Optimized Eavor-Loop™ dispatch ratio as a function of grid dependency on intermittent renewablegeneration

Analysis of the dispatch patterns revealed diurnal cycling of the Eavor-Loops™ inversely
correlated with solar output. Two representative dispatch patterns are shown below. Figure 24
shows one representative week from the Southern California zone, powered 56% by solar and 15%
by wind. A dispatch ratio of 1.54 and recharge ratio of 0 are observed. Figure 25 shows one
representative week from the Northern California zone, powered only 14% by solar with no wind.
Here, a dispatch ratio of 1.23 is observed, with recharge ratio ranging from 0 to 0.69.

Holmes et al.

Figure 24: Dispatch pattern of Eavor-Loop™ and solar in one representative week in the Southern California
zone

Figure 25: Dispatch pattern of Eavor-Loop™ and solar in one representative week in the Northern California
zoneHolmes et al.
4. Conclusion
The Eavor-Loop™ was introduced as a multilateral closed-loop geothermal system that is globally
scalable and capable of providing grid stability and resiliency. A transient, fully coupled wellbore+ thermal model was developed and validated using over 16 months of operational data from an
Eavor-Loop™ field demonstration project in Alberta, Canada. Recent modelling work, coupledwith field trials, has proven the feasibility of the Eavor-Loop™ to provide flexible energy
generation for load-balancing or peak-matching with a minimal impact on lifetime energy
extraction. Transient operation allows the system to recharge during low demand periods anddischarge this stored energy during high demand periods.
The value of the Eavor-Loop™ in a net-zero grid was modelled with a case study of the UnitedStates Western Interconnection power transmission grid using an electricity resource capacity
expansion model (GenX). The modelling indicates that the Eavor-Loop™ can reduce the annual
total system cost by up to $20B (21%) in a base case and up to $403B (81%) in an extreme case.
These cost savings are achieved through:
1. Reduced spending on other technologies providing firmness and reliability such as gas +CCS, zero carbon fuel (i.e., hydrogen), and batteries
2. Reduced spending on intermittent renewables, namely solar and wind
Inclusion of the Eavor-Loop™ enables 100% renewable energy power systems while reducing
required installed capacity of land-heavy resources such as solar and wind by up to 49%, saving
22 acres in the base case and up to 48 acres in the extreme case for each megawatt of EavorLoop™ installed. The Eavor-Loops™ are operated in a diurnal pattern inversely correlated to solar
power generation. The system is allowed to recharge while the sun is shining and then dispatches
the stored energy when the sun goes down. Optimized dispatch patterns from the GenX model
were validated with the transient thermodynamic model, proving both the technical feasibility andvalue potential of the Eavor-Loop™ technology.

Holmes et al.
REFERENCES
bp. (2020). Statistical review of world energy.
European Commission. (2020). Powering a climate-neutral economy: An EU Strategy for
Energy System Integration. Brussels.
Fallah, A., Gu, Q., Chen, D., Ashok, P., van Oort, E., & Holmes, M. (2021). Globally scalable
geothermal energy production through managed pressure operation control of deep
closed-loop well systems. Energy Conversion and Management.
Horne, R. (1980). Design considerations of a down-hole coaxial geothermal heat exchanger.
Geothermal Resources Council Transactions.
International Energy Agency. (2021). Net zero by 2050: A roadmap for the global energy sector.
Jenkins, J. D., & Sepulveda, N. A. (2017). Enhanced decision support for a changing electricity
landscape. Cambridge, MA: MIT Energy Initiative.
Kutun, K., Tureyen, O., & Satman, A. (2015). Analysis of wellhead production temperature
derivatives. Fortieth workshop on geothermal reservoir engineering. Stanford, CA:
Stanford University.
Larson et al. (2020). Net-Zero America: Potential Pathways, Infrastructure, and Impacts.
Princeton University.
Li, C.-F., Lu, Y., & Wang, J. (2017). A global reference model of Curie-point depths based on
EMAG2. Scientific Reports.
Morita, K., Tago, M., & Ehara, S. (2005). Case study on small-scale power generation withdownhole coaxial heat exchanger. World Geothermal Congress. Atalya, Turkey.
Nalla, G., Shook, G., Mines, G., & Bloomfield, K. (2005). Parametric sensitivity study ofoperating and design variables in wellbore heat exchangers. Geothermics.
National Institute of Standards and Technology. (2020). REFPROP.
National Renewable Energy Laboratory. (2018). Electrification futures study: scenarios ofelectric technology adoption and power consumption for the United States. Golden, CO.
National Renewable Energy Laboratory. (2020). Annual Technology Baseline.
Oldenberg, C., Pan, L., Muir, M., Eastman, A., & Higgins, B. (2016). Numerical simulation ofcritical factors controlling heat extraction from geothermal systems using a closed-loop
heat exchange method. 41st workshop on geothermal reservoir engineering. Stanford,
CA: Stanford University.
Ramey Jr, H. (1962). Wellbore heat transmission. Journal of Petroleum Technology, 427-435.
Rybach, L. (2010). The future of geothermal energy and its challenges. World Geothermal
Congress.

Holmes et al.
Sepulveda, N. A., Jenkins, J. D., de Sisternes, F. J., & Lester, R. K. (2018). The role of firm lowcarbon electricity resources in deep decarbonization of power generation. Joule.
Toews, M., Riddell, D., Vany, J., & Schwarz, B. (2020). Case study of a multilateral closed-loop
geothermal system. World Geothermal Congress. Reykjavik.
U.S. Energy Information Administration. (2020). Annual Energy Outlook.
van Zalk, J., & Behrens, P. (2018). The spatial extent of renewable and non-renewable power
generation: A review and meta-analysis of power densities and their application in the
U.S. Energy Policy.