PROCEEDINGS, 48th Workshop on Geothermal Reservoir Engineering
Stanford University, Stanford, California, February 6-8, 2023
SGP-TR-224

Enablement of High-Temperature Well Drilling for Multilateral Closed-Loop Geothermal
Systems
Colin A. Brown, Michael Holmes, Vlad Zatonski, Matt Toews
Eavor Technologies Inc., Calgary, Alberta
Colin.Brown@eavor.com, Mike.Holmes@eavor.com, Vlad.Zatonski@eavor.com, Matt.Toews@eavor.com

Keywords: Geothermal, closed-loop geothermal, advanced geothermal systems, Eavor-Loop, Eavor-Deep, high pressure hightemperature, thermodynamics, renewable, green energy, insulated drill pipe
ABSTRACT
Constructing a multilateral closed-loop geothermal system (MCLGS) requires directional tools and magnetic ranging tools in the bottomhole assembly (BHA) to drill and intersect the wellbores and create the closed loop. The levelized cost of energy (LCOE) of such an
MCLGS is largely driven by rock temperature – the hotter the rock, the more energy that is produced from a given well configuration,and the lower the levelized cost. However, these tools have a maximum temperature limit above which they are no longer functional. To
enable drilling of high-temperature rock formations and thereby decrease the LCOE, methods for estimating the temperature of the BHA
critical components are required.
To simulate drilling, two models of increasing complexity were developed. The first model is a one-dimensional pseudo steady state
wellbore + thermal resistance model capable of estimating the temperature and pressure profile of the drilling mud throughout the drill
pipe and annulus. This model allows for the understanding of key performance drivers and technology requirements to achieve hightemperature drilling.
The second model is a transient, two-dimensional heat conduction and wellbore model. This coupled model enables simulation of thefluid temperature and pressure during dynamic drilling processes such as connections, running in hole, pulling out of hole, and circulation.
This paper illustrates the capabilities of the two models and presents case studies and key learnings for high-temperature drilling as wellas field results from Eavor’s deep hot test well drilled in Q4 2022 in New Mexico, USA.
1. INTRODUCTION
1.1 Eavor-Loop™: a Multilateral Closed-Loop Geothermal System
Multilateral closed-loop geothermal systems (MCLGS), a form of Advanced Geothermal System (AGS), are geothermal systems in whicha heat transfer fluid – e.g. water – circulates in a closed-loop configuration. Unlike a traditional geothermal system, there is little-to-no
mass transfer between the MCLGS wellbore and the subsurface. The circulating fluid picks up heat from the subsurface via heat
conduction and transports the heat to the surface which can be used for district heat (common in Europe) or converted into electricity (e.g.
through an Organic Rankine Cycle power plant). MCLGS and other AGS technologies compared to other forms of geothermal systems
are theoretically capable of being developed anywhere without the need for in-situ fluids and reservoir permeability – expanding theapplicability of geothermal energy across the globe.
Eavor’s Eavor-Loop™ technology is a form of MCLGS (and AGS). Over the years, various studies have been completed evaluating thetechno-economic applicability of AGS systems, e.g. Beckers et al (2022). In all such studies, economic viability of an Eavor-Loop™ andother AGS technologies require significant heat transfer surface area, which require complex subsurface completions and high reservoir
temperatures.

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Brown, Holmes, Zatonski, and Toews

Figure 1: Illustration of an Eavor-Loop™
Due to the relatively slow rate of heat transfer via conduction through the subsurface rock, several dozens of kilometers of wellbore need
to be drilled and connected to achieve an economic amount of heat transfer surface area. To achieve the complex subsurface layout of theEavor-Loop™, directional drilling and magnetic ranging tools in the bottom-hole assembly (BHA) are required to drill and intersect themultiple lateral passes. However, the temperature limits of current ranging tools pose a technical challenge. The current generation ofthese tools are rated to temperatures in the range of 150-175 °C, while rock temperatures could reach up to 450 °C. To successfully drilland complete an Eavor-Loop™, the bottom-hole-assembly (BHA) components either need to be re-engineered for higher temperatures orneed to be kept cool during drilling operations.
1.2 Enabling High Pressure, High Temperature (HPHT) Drilling
Creating tools that are tolerant of higher temperatures would require the re-engineering of key components and may require large amounts
of R&D spend. Solutions that keep the tools cool while drilling are simpler, and depending on the solution, are cheaper than completely
re-engineering the tools and/or its components. For example, improving the thermal resistance of the drill pipe will reduce the countercurrent heat exchange between the annular fluid and tubular fluid, thereby reducing the bottom-hole fluid temperatures.
A drill pipe with improved thermal resistance was used to drill Eavor’s hot pilot well, Eavor-Deep™, in New Mexico, USA with promising
results. Drilling operations were safely completed in Q4 of 2022.
1.3 Modelling
Regardless of the approach to enable HPHT drilling, thermodynamic modelling is critical to evaluate the feasibility of drilling andcompletion of HPHT Eavor-Loops™, as well as the evaluation of different “cooling” technologies.
Two thermodynamic models were developed, each of differing complexity, to determine the pressures and temperatures within the
wellbore while drilling. The first model is a one-dimensional pseudo steady-state wellbore model capable of estimating the annular andtubular pressures and temperatures (referred to as the “steady-state” model). This model is limited to estimating steady-state fluid pressuresand temperatures. The second model is a transient two-dimensional heat conduction and wellbore model (referred to as the “transient”
model). Like the steady-state model, the transient model simulates the annular and tubular fluid pressures and temperatures, but thetransient model also reports the pressures and temperatures during transient drilling operations where the drill pipe, circulation rate, andmud characteristics are changing with time.
The difference in the high-level characteristics of the two models are summarized in the table below.
Table 1: Model characteristics summary
Model Characteristic

Steady-State Model

Transient Model

Wellbore equations, momentum

Steady-state

Steady-state

Wellbore equations, energy

Steady-stateTransient

Rock equations

Pseudo-transient

TransientApplication / Language

Microsoft Excel

Python

Run time, order of magnitude

Seconds

Minute to 10’s of minutes (depends onnumber of time-steps)2

Brown, Holmes, Zatonski, and Toews
2. PSEUDO STEADY-STATE MODEL
2.1 Model Formulation
The steady-state model is a pseudo steady-state, 1-D, discretized wellbore drilling model. A schematic of the steady-state model setup is
shown in Figure 2 below.

Drill pipe blocks

j=1

j=2
Drill Pipe

Fluid circulationfrom drilling rig
pumps
Heat transfer fromrock
Heat transfer fromannular fluid to drill
pipe fluid

j=3

Centerline

Open-hole

Annular blocks

BHA & Drillbit

j=n
Fluid leaving the bit
moves the annulus

j-dirFigure 2: Steady-state model schematic. Green arrows indicate mass transfer (flow) while red arrows indicate heat transfer.
The wellbore system is naturally divided into two fluid-bearing sections: (1) the drill-pipe / tubing, and (2) the annular space between the
drill-pipe and the open hole/rock face. The system is further discretized in the well direction (denoted as the j-direction in the schematic).
Since the drill pipe blocks and annular blocks are considered together in the solution of this system, the model effectively only has one
dimension – in the direction of the well.
2.2 Governing Equations and Assumptions
To simplify the resulting model, the following assumptions are made:1.

The change in kinetic energy is neglected in the conservation of energy equation since its contribution is small compared to theinternal energy and enthalpy change of the fluid.

2.

We are interested in the steady-state solution to the conservation of energy equations, i.e. we assume 𝜕𝜕𝑡𝑡 = 0

3.
4.

𝜕𝜕𝜕𝜕

The conservation of mass has been invoked for an incompressible fluid so the mass flux is constant along the length of the
wellbore.
A simplified, pseudo-steady version of the momentum equation is employed whereby the pressure drop is directly related to thefrictional pressure drop using the Colebrook White type correlation.
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Brown, Holmes, Zatonski, and Toews
5.

Neglect the impact of rock cuttings on the fluid properties (e.g. specific heat, density, viscosity), and the energy balance.

The governing conservation equations are derived for the individual control volumes that correspond to the drill pipe blocks and annulus
blocks. Figure 3 illustrates the generalized control volumes for the drill pipe blocks and annulus blocks.

j-1

Drill pipe blocks

Annular blocks

ṁdp,inṁann,out

j

j+1

Qann

Qrock

ṁann,inṁdp,outj-dir

Figure 3: Steady-state model control volume schematics for the drill pipe and annulus blocks
Each of the colored arrows in Figure 3 represent the mass and energy flows within the wellbore system. For each j-section, direction of
the mass and energy flows into and out of each of the blocks will be similar (although magnitudes will differ).
Since we have assumed a steady-state conservation of mass equation, there is no change in mass within each control volume. The massflux into a block is equal to the mass flux out of a block. Therefore,
𝑚𝑚̇ = 𝑚𝑚̇tbg,in = 𝑚𝑚̇tbg,out = 𝑚𝑚̇ann,in = 𝑚𝑚̇ann,out(1)

The use of the simplified pseudo-steady momentum equation gives the following pressure drop equation for a generic drill pipe, andannulus block
Drill pipe:
Annulus:where

𝑝𝑝𝑗𝑗−1 − 𝑝𝑝𝑗𝑗 = �𝑓𝑓D ∙ 𝐿𝐿 ∙𝜌𝜌𝑗𝑗−1

𝑝𝑝𝑗𝑗−1 − 𝑝𝑝𝑗𝑗 = − �𝑓𝑓D ∙ 𝐿𝐿 ∙2𝜌𝜌𝑗𝑗−1
2

𝑣𝑣𝑗𝑗−1 2(2)

𝑣𝑣𝑗𝑗−1 2(3)∙ 𝐷𝐷 � − �𝜌𝜌𝑗𝑗−1 ∙ 𝑔𝑔 ∙ �𝑧𝑧𝑗𝑗 − 𝑧𝑧𝑗𝑗−1 ��

𝑝𝑝 is the pressure in the grid block/control volume

H∙ 𝐷𝐷 � − �𝜌𝜌𝑗𝑗−1 ∙ 𝑔𝑔 ∙ �𝑧𝑧𝑗𝑗 − 𝑧𝑧𝑗𝑗−1 ��H

𝑓𝑓D is the Darcy friction factor

𝐿𝐿 is the length of the grid block/control volume in the axial direction𝜌𝜌 is the density of the drilling fluid

𝑣𝑣 is the velocity of the drilling fluid

𝐷𝐷H is the hydraulic diameter𝑔𝑔 is the gravitational constant (i.e. 9.81 m/s2)

𝑧𝑧 is the total vertical depth of the grid block/control volume
𝑗𝑗 is the grid block index in the direction of the well path4

Brown, Holmes, Zatonski, and Toews
For a generic drill pipe block, the steady-state conservation of energy equation can be expressed to include the heat transfer terms impliedby the arrows in Figure 3.

where𝑚𝑚̇ℎdp,𝑗𝑗−1 + 𝑄𝑄̇ann + 𝑚𝑚̇𝑔𝑔�𝑧𝑧𝑗𝑗 − 𝑧𝑧𝑗𝑗−1 � = 𝑚𝑚̇ℎdp,𝑗𝑗(4)

𝑚𝑚̇ is the mass flow rate/circulation rate of the drilling fluidℎdp,𝑗𝑗−1 is the enthalpy of the drilling fluid in the drill pipe segment at j-1ℎdp,𝑗𝑗 is the enthalpy of the drilling fluid in the drill pipe segment at j

𝑄𝑄̇ann is the heat transfer rate from the annulus block to the drill pipe block

Similarly, the steady-state conservation of energy equation for a generic annulus block gives

where𝑚𝑚̇ℎann,𝑗𝑗+1 + 𝑄𝑄̇rock = 𝑚𝑚̇ℎann,𝑗𝑗 + 𝑄𝑄̇ann + 𝑚𝑚̇𝑔𝑔�𝑧𝑧𝑗𝑗 − 𝑧𝑧𝑗𝑗−1 �(5)ℎann,𝑗𝑗+1 is the enthalpy of the drilling fluid in the annulus segment at j+1ℎann,𝑗𝑗 is the enthalpy of the drilling fluid in the annulus segment at j

𝑄𝑄̇rock is the heat transfer rate from the rock formation to the annulus block

The heat transfer rate between the annular fluid and the drill pipe fluid, 𝑄𝑄̇ann , is an expression that combines conductive and convective
resistances:𝑇𝑇ann,𝑗𝑗 −𝑇𝑇dp,𝑗𝑗
𝑄𝑄̇ann,𝑗𝑗 = 𝑅𝑅
ann,𝑗𝑗where

𝑅𝑅ann,𝑗𝑗 = 𝑅𝑅conv,dp,𝑗𝑗 + 𝑅𝑅cond,dp wall,𝑗𝑗 + 𝑅𝑅conv,ann,𝑗𝑗

(6)
(7)

𝑇𝑇dp,𝑗𝑗 is the temperature of the fluid in the drill pipe

𝑇𝑇ann,𝑗𝑗 is the temperature of the fluid in the annulus

𝑅𝑅ann,𝑗𝑗 is the total thermal resistance between the drill pipe and annulus fluids

𝑅𝑅conv,dp,𝑗𝑗 is the convective thermal resistance at the inside face of the drill pipe
𝑅𝑅cond,dp wall,𝑗𝑗 is the conductive thermal resistance through the drill pipe wall

𝑅𝑅conv,ann,𝑗𝑗 is the convective thermal resistance at the outside face of the drill pipe

Generally, convective thermal resistances are defined as follows:

1

where

ℎ𝑐𝑐 is the convective heat transfer coefficient

𝑅𝑅conv = ℎ 𝐴𝐴
𝑐𝑐

(8)

𝐴𝐴 is the heat transfer surface area

The heat transfer surface area is the cylindrical face in contact with the fluid

where

𝐴𝐴 = 2𝜋𝜋𝜋𝜋𝜋𝜋(9)𝑟𝑟 is the radius of the cylindrical face exposed to heat transfer with the fluid
𝐿𝐿 is the length of the cylindrical face (i.e. the length of the grid block)For forced internal convection within pipes, the convective heat transfer coefficient can be expressed in terms of the non-dimensional
Nusselt number:
𝑁𝑁𝑁𝑁∙𝑘𝑘

where

𝑁𝑁𝑁𝑁 is the Nusselt numberℎ𝑐𝑐 = 𝐷𝐷h5( 10 )

Brown, Holmes, Zatonski, and Toews
𝑘𝑘 is the thermal conductivity of the fluid𝐷𝐷ℎ is the hydraulic diameter of the pipe

The Nusselt number can be calculated from several published correlations and will generally depend on the flow regime of the fluid within
the pipe, the Reynolds number, the Prandtl number, and the Darcy friction factor (depending on the correlation). For brevity, the various
Nusselt number correlations are not included here. For the models presented, turbulent pipe flow is handled with the Gnielinksi correlation
for Nusselt number.
Substituting the above into Equation ( 8 ) gives the final expression for the convective thermal resistance between a fluid and the pipewall:
1

𝑅𝑅conv = 𝜋𝜋𝜋𝜋𝑢𝑢𝑘𝑘𝑘𝑘( 11 )

By substituting in values of 𝑘𝑘 and 𝑁𝑁𝑁𝑁 that correspond to the drill pipe fluid, and annular fluid, the convective thermal resistance on theinside and outside of the drill pipe can be determined.
The conductive resistance through the drill pipe wall can be calculated if the bulk drill pipe thermal conductivity is known:

where

𝑅𝑅cond =𝑟𝑟𝑜𝑜 is the outer radius of the drill pipe𝑟𝑟𝑟𝑟iln� o �2𝜋𝜋𝑘𝑘dp 𝐿𝐿( 12 )

𝑟𝑟𝑖𝑖 is the inner radius of the drill pipe

𝑘𝑘dp is the bulk thermal conductivity of the drill pipe

The heat transfer rate between the rock and the annular fluid, 𝑄𝑄̇rock , is not as trivial to define. As described in Toews et al. (2021) ananalytical equation can be derived to estimate the amount of heat transfer from the rock to the wellbore. The equation is analogous to theapproach developed by Ramey (Ramey, 1962), and expanded on by Hasan and Kabir (Hasan et al., 1994), for vertical wellbore under the
key assumption that the heat transfer can be treated as pseudo-steady state radial heat conduction from the rock into the fluid flowing
through the wellbore.
The steady-state radial heat conduction equation is given by:Where

2𝜋𝜋𝑘𝑘r 𝐿𝐿(𝑇𝑇r −𝑇𝑇w )𝑄𝑄̇rock =𝑟𝑟eff

𝑘𝑘r is the thermal conductivity of the rock formation

ln�

𝑟𝑟w

�

( 13 )

𝑇𝑇r is the temperature of the undisturbed surrounding rock𝑇𝑇w is the temperature of the wellbore rockface
𝑟𝑟eff is the effective thermal radius

𝑟𝑟w is the radius of the wellbore/open hole

The steady-state heat conduction is based on an effective thermal radius, 𝑟𝑟eff , for the rock beyond which the temperature of the rock is
unchanged. The effective radius varies with flowing time and is governed by the dimensionless Fourier number, Fo. For this radialconduction problem:
𝛼𝛼 𝑡𝑡

Where

Fo = 𝑟𝑟 r 2𝑘𝑘

𝛼𝛼r is the thermal diffusivity of the rock; 𝛼𝛼r = 𝜌𝜌 𝐶𝐶r
𝜌𝜌r is the density of the rockeff

( 14 )

r 𝑝𝑝,r𝐶𝐶𝑝𝑝,r is the specific heat capacity of the rock

The Fourier number is assumed to be constant for this transient heat transfer problem with the prescribed geometry. The constant Fourier
number was determined from a least-square regression against an Eavor-internal 3D, numerical, transient radial heat transfer
computational fluid dynamics (CFD) model. Equation ( 14 ) can be re-arranged in terms of the effective radius, and then substituted into
Equation ( 13 ):6

Brown, Holmes, Zatonski, and Toews
2𝜋𝜋𝑘𝑘r 𝐿𝐿(𝑇𝑇r −𝑇𝑇w )𝑄𝑄̇rock =𝛼𝛼r 𝑡𝑡ln�

( 15 )

�

Fo
�
𝑟𝑟w

It should be noted that the convective heat transfer coefficient is very high for the fluid in the wellbore compared to the thermal resistanceof the rock. Therefore, the temperature of the wellbore rockface, 𝑇𝑇w , is essentially the same as the bulk fluid temperature, 𝑇𝑇f , at a given
axial location, i.e. 𝑇𝑇w ≈ 𝑇𝑇f .
For the drilling problem presented in this paper, the circulation time, 𝑡𝑡, experienced by the rock will vary with depth – shallower parts of
the well will undergo additional circulation time relative to deeper sections of the well. The circulating time can be expressed as a functionof measured depth and an average rate-of-penetration (ROP).

where

𝑡𝑡 =

𝑀𝑀𝑀𝑀well −𝑀𝑀𝑀𝑀𝑗𝑗( 16 )𝑅𝑅𝑅𝑅𝑅𝑅𝑀𝑀𝐷𝐷well is the measured depth to the bottom of the hole

𝑀𝑀𝐷𝐷𝑗𝑗 is the measured depth location of the jth grid block
𝑅𝑅𝑅𝑅𝑅𝑅 is the average rate of penetration over the wellIn this model, the drilling fluid properties are linear, least-square regressions derived for working fluid properties obtained from NIST
Refprop (National Institute of Standards and technology, 2020) as a function of temperature and pressure. When discretizing the model,
the axial grid spacing is maintained sufficiently small to ensure that temperature and pressure changes between grid blocks is minimal,
maintaining the validity of the assumption of constant thermophysical properties within each grid block. The use of these fluid property
regressions makes it straight forward to implement the steady-state model in a spreadsheet program such as Microsoft Excel.
Substituting the fluid property regressions and the annular heat transfer rate (Equation ( 6 )) into the conservation of energy equation for
the generic drill pipe grid block (Equation ( 4 )), yields𝑚𝑚̇ℎ(𝑇𝑇dp,𝑗𝑗−1 , 𝑝𝑝dp,𝑗𝑗−1 ) +𝑇𝑇dp,𝑗𝑗 −𝑇𝑇ann,
𝑅𝑅ann+ 𝑚𝑚̇𝑔𝑔�𝑧𝑧𝑗𝑗 − 𝑧𝑧𝑗𝑗−1 � = 𝑚𝑚̇ℎ(𝑇𝑇dp,𝑗𝑗 , 𝑝𝑝dp,𝑗𝑗 )( 17 )

Similarly, substituting the fluid property regression, annular heat transfer rate (Equation ( 6 )) and rock heat transfer rate (Equation( 15 ))into the conservation of energy equation for the generic annulus grid block (Equation ( 5 )) gives𝑚𝑚̇ℎ(𝑇𝑇ann,𝑗𝑗+1 , 𝑝𝑝ann,𝑗𝑗+1 ) +2𝜋𝜋𝑘𝑘r 𝐿𝐿(𝑇𝑇r,𝑗𝑗 −𝑇𝑇ann,𝑗𝑗 )
𝛼𝛼 𝑡𝑡
� r
Fo
�
ln�
𝑟𝑟w

= 𝑚𝑚̇ℎ(𝑇𝑇ann,𝑗𝑗 , 𝑝𝑝ann,𝑗𝑗 ) +𝑇𝑇dp,𝑗𝑗 −𝑇𝑇ann,𝑗𝑗
𝑅𝑅ann+ 𝑚𝑚̇𝑔𝑔�𝑧𝑧𝑗𝑗+1 − 𝑧𝑧𝑗𝑗 �( 18 )

The fluid property regressions can also be substituted into the simplified conservation of momentum Equations ( 2 ), and ( 3 ).
After the derivations we are left with four equations for a single j-section – two for each grid block – with the majority of the variables
dependent on the temperature and pressure from the j-1 grid blocks (see summary table below). As explained in the next section, theboundary conditions, user defined inputs, and simplifying assumptions allow for the solution of the pressure and temperatures in the drill
pipe and annulus.

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Brown, Holmes, Zatonski, and Toews
Table 2: Summary of governing equations for steady-state model#

Equation(2)

Drill pipe conservation of
momentum(3)

Annulus conservation of
momentum( 17 )

Drill pipe conservation ofenergy( 18 )

Annulus conservation of energy

Expression
𝑝𝑝dp,𝑗𝑗−1 − 𝑝𝑝dp,𝑗𝑗 = �𝑓𝑓D ∙ 𝐿𝐿 ∙𝜌𝜌dp,𝑗𝑗−1 𝑣𝑣dp,𝑗𝑗−1 2∙
� − �𝜌𝜌dp,𝑗𝑗−1 ∙ 𝑔𝑔 ∙ �𝑧𝑧𝑗𝑗 − 𝑧𝑧𝑗𝑗−1 ��2𝐷𝐷H

𝑝𝑝ann,𝑗𝑗−1 − 𝑝𝑝ann,𝑗𝑗 = − �𝑓𝑓D ∙ 𝐿𝐿 ∙𝑚𝑚̇ℎ(𝑇𝑇dp,𝑗𝑗−1 , 𝑝𝑝dp,𝑗𝑗−1 ) +𝑚𝑚̇ℎ(𝑇𝑇ann,𝑗𝑗 , 𝑝𝑝ann,𝑗𝑗 ) +𝜌𝜌ann,𝑗𝑗−1 𝑣𝑣ann,𝑗𝑗−1 2∙
� − �𝜌𝜌ann,𝑗𝑗−1 ∙ 𝑔𝑔 ∙ �𝑧𝑧𝑗𝑗 − 𝑧𝑧𝑗𝑗−1 ��
2
𝐷𝐷H𝑇𝑇dp,𝑗𝑗−1 − 𝑇𝑇ann,𝑗𝑗−1+ 𝑚𝑚̇𝑔𝑔�𝑧𝑧𝑗𝑗 − 𝑧𝑧𝑗𝑗−1 � = 𝑚𝑚̇ℎ(𝑇𝑇dp,𝑗𝑗 , 𝑝𝑝dp,𝑗𝑗 )𝑅𝑅ann,𝑗𝑗

2𝜋𝜋𝑘𝑘r 𝐿𝐿(𝑇𝑇r,𝑗𝑗 − 𝑇𝑇ann,𝑗𝑗−1 )
𝛼𝛼 𝑡𝑡
� r
Fo
⎛
ln 𝑟𝑟 ⎞ann⎝⎠= 𝑚𝑚̇ℎ(𝑇𝑇ann,𝑗𝑗−1 , 𝑝𝑝ann,𝑗𝑗−1 ) +𝑇𝑇dp,𝑗𝑗−1 − 𝑇𝑇ann,𝑗𝑗−1+ 𝑚𝑚̇𝑔𝑔�𝑧𝑧𝑗𝑗 − 𝑧𝑧𝑗𝑗−1 �𝑅𝑅ann,𝑗𝑗

2.3 Solution Scheme
When we consider the four equations at each j-section, if we assume that the temperature and pressures from the 𝑗𝑗 − 1 blocks/section are
known, then we have a system of 4 equations with four unknowns:
Table 3: Steady-state model system of equations and unknown parameters
EquationsUnknowns

Drill pipe block conservation of momentum

Drill pipe pressure, 𝑝𝑝dp,𝑗𝑗

Annulus block conservation of momentum

Annulus pressure, 𝑝𝑝ann,𝑗𝑗

Drill pipe block conservation of energy

Drill pipe temperature, 𝑇𝑇dp,𝑗𝑗

Annulus block conservation of energy

Annulus temperature, 𝑇𝑇ann,𝑗𝑗

The other variables that appear in the four governing equations can be determined from the user defined inputs:

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Brown, Holmes, Zatonski, and Toews
Table 4: Steady-state model known quantities, and parameters
Variable𝐷𝐷ℎ , hydraulic diameter

Source•Drill pipe and open-hole/annulus diameters are user specified

𝑓𝑓𝐷𝐷 , Darcy friction factor•

Can be determined from published correlations which are generally
functions of roughness and hydraulic diameters.

•

Roughness is a user input

𝑣𝑣dp , drill pipe fluid velocity•

Calculated from the fluid density (from j-1 block temperature, andpressure), pipe/hole cross-sectional areas, and mass flow rate

𝑣𝑣ann , annular fluid velocity•

Mass flow rate is a user input

𝑧𝑧, vertical depth•

The vertical depth of each grid block is a user input (i.e. grid definition)

𝑘𝑘r , rock thermal conductivity•

User input

𝑇𝑇r,𝑗𝑗 , rock temperature•

The thermal gradient and surface temperature are specified by the user•

The vertical depth of each j-coordinate can be used to calculate the virginrock temperature

𝛼𝛼r , rock thermal diffusivity•

User defined𝑡𝑡, rock time exposed to flow•

Depends on the ROP and the grid definition – all user inputs•

Determined from a regression on Eavor-internal CFD simulation results

𝑟𝑟ann , radius of the open hole/annulus•

User defined••

Combination of the convective and conductive resistances
Convective thermal resistances are a function of Nusselt number and fluid
thermal conductivity. Nusselt number can be determined from publishedcorrelations and using the T/P from the j-1 blocks. Thermal conductivity of
the fluid can be based on T/P from the j-1 blocks. Convective resistances
determined for both drill pipe and annulus blocks•

Conductive thermal resistance through the drill pipe wall is user specified.
User can specify an average thermal resistance per unit length, or an averagethermal conductivity and pipe dimensions

Fo, Fourier number

𝑅𝑅ann,𝑗𝑗 , thermal resistance between theannular fluid and drill pipe fluid

Since the solution of the j temperatures and pressures depend on the solution of the j-1 temperatures and pressures, if we can determine
the temperature and pressures at j = 0 (i.e. the boundary conditions for this 1D system), the rest of the system can be solved going from j= 0 (top of the well) to j = n (bottom of the well).
The boundary conditions that are required to solve this system are listed below:
The inlet temperature to the drill pipe. A constant, user specified value

𝑇𝑇dp,𝑗𝑗=0

The standpipe pressure / injection pressure. Unknown, and a function of the total system pressure drop and the backpressure

𝑝𝑝dp,𝑗𝑗=0𝑇𝑇ann,𝑗𝑗=0

The return temperature of the drilling fluids. Unknown. Since we have imposed a steady-state assumption on the energy
equation, and ignoring the fluid kinetic energy, it follows that the enthalpy of the return fluid is the sum of the enthalpy

𝑝𝑝ann,𝑗𝑗=0

Back/return pressure (MPD if applicable). A constant, user specified value

𝑄𝑄̇

of the inlet fluid and the total specific heat transfer from the rock to the wellbore system (i.e. rock). The temperature𝑚𝑚̇
of the return fluid can be back-calculated from the enthalpy regression, and 𝑝𝑝ann,𝑗𝑗=0 (which is known/user inputted).

Two of the four boundary conditions are not known prior to solving the system. To solve the system, an iterative “guess-and-check”
solution method is employed. The steps in the iterative solver are summarized in the numbered list below:
1.

Start with guesses for the two unknown boundary conditions (pdp, j=0, Tann, j=0)2.

Starting at j = 1 (first/top grid block),•

Solve the pressures in the drill pipe and annulus from the two conservation of momentum equations
9

Brown, Holmes, Zatonski, and Toews•

Solve the fluid temperatures in the drill pipe and annulus from the two conservation of energy equations (it should
be noted that the quadratic formula is required to calculate the fluid temperature from the enthalpy regressions)

Take the T/P solutions and use them in the solution of the next j-section. Repeat for all grid blocks / j-sections going to thebottom of the well3.

Once the system has been solved, calculate the actual values for two boundary conditions that were originally guessed.
Determine the error between the guess values and the calculated values.

4.

Using a root-finding or optimization algorithm (such as Newton’s method) iteratively update the guess for the boundary
conditions based on the most recent iteration’s error.

5.

Iterate until the error is within some user specified tolerance, or a maximum number of iterations has been reached.

The discretized steady state model has been implemented in Microsoft Excel, and the iterative solution routine is written in VBA using amodified Newton’s method. On average, the model only takes a few seconds to converge on the correct answer.
2.4 Model Case Study Results & Validation
The discretized steady state model is a quick and flexible way of modelling the drill pipe and annular circulating fluid temperatures. The
discretized nature of the model allows for complex well trajectory, rock temperature profiles, and drill pipe designs to be modelled andtheir impacts on circulating temperatures/pressures evaluated.
The results presented in this section serve two purposes: (1) illustrate the typical results of the steady state model, and (2) summarize theimpacts of a thermally resistive drill pipe (a.k.a. IDP, insulated drill pipe) on circulating temperatures.
The table below summarizes the model inputs for two hypothetical drilling cases.

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Brown, Holmes, Zatonski, and Toews
Table 5: Steady-state model case descriptions
Model Input

Units

Case 1:Case 2:

Carbon Steel (CS) String

Hypothetical IDP String

Fluid Properties
Inlet Temperature

°C

30

30

Annulus back pressure

kPag

0

0

Pump rate

m3/min2.50

2.50(Constant tank temperature assumed)

Well Trajectory & Grid Definition
Well depth

m

5,000

5,000

Deviation (from vertical)

°

0

0

# of grid blocks (j-dir)

#

500

500

Grid block size

m

10

10

Geology
Surface Temperature

°C

10

10

Geothermal Gradient

°C/km

50

50

Rock conductivity

W/mK

2.5

2.5

Rock density

kg/m3

2,700

2,700

Rock specific heat capacity

J/kgK

790

790

Well Design / Size
Drill pipe ID

mm

121.4

121.4

Drill pipe OD

mm

139.7

139.7

Open hole diameter

mm

215.9

215.9

Drill pipe roughness

mm

0.05

0.05

Open hole roughness

mm

0.05

0.05

Drill pipe conductive resistancemK/W

5.08 x 10-4

1.0 x 10-2

12.0

12.0

Drilling Rig
Rate-of-penetration (ROP)
•
•
•

m/hr

In this example, no casing strings and cement are modelled (however, the model can accommodate thermal impactsof casing and cement via thermal resistance inputs for each well segment)
In case 2, the bottom 100m of the drill string (10 blocks) is modelled with full carbon steel drill pipe to emulate the
BHA which has very little thermal resistancePressure drop across the BHA components not explicitly modelled

Figure 4 below shows the main outputs of the steady state model – the pressure and temperatures in the drill string and annulus along theentire well path – for case 1.

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Brown, Holmes, Zatonski, and Toews

50

Temperature (°C)
100
150
200

250

300

0

500

500

1000

1000
Measured Depth (m)Measured Depth (m)

0

0

1500
2000
2500
3000
3500
4000

50

60

2000
2500
3000
3500
4000
4500

5000

5000
Drill Pipe

Pressure (MPa)
20
30
40

10

1500

4500
Annulus0

Geothermal

Annulus

Drill Pipe

Figure 4: Steady-state model results for case 1
Although the primary outputs of the model are the circulation temperature and pressure, since the model has been discretized andimplemented in a spreadsheet model, it is possible to interrogate the variation in intermediate parameters and calculated quantities suchas the heat transfer between the annulus and drill pipe along the drill string.
These model results can give the user an idea of the feasibility of drilling various HPHT wells. The maximum downhole circulating
temperatures, and estimated standpipe pressures may be used to refine the design of HPHT wells based on known thermal limitations of
the BHA components, and/or rig pump capacities.
For example, the model can be used to evaluate the impacts on drilling with a drill string that has a significantly higher thermal resistance
relative to standard drill pipe. It is recognized by the authors that the drill pipe thermal resistance included in case 1 does not account for
the various coatings typically found on a standard joint of drill pipe. The figure below illustrates the impact on circulating temperatures
when changing the drill string design.

0

0

50

100

Temperature (°C)
150

200

250

300

500

Measured Depth (m)1000

Annulus - IDP

1500

Drill Pipe - IDP

2000

Annulus - CS

2500

Drill Pipe - CS

3000

Geothermal

3500
4000
4500
5000

Figure 5: Steady-state model results comparison for carbon steel (CS) drill pipe and a hypothetical insulated drill pipe (IDP)
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Brown, Holmes, Zatonski, and Toews
In this theoretical comparison, the maximum downhole circulating temperature for case 1 and 2 are, 178.7 °C and 73.6 °C, respectively.
Typical temperature-sensitive components have limits of ~150 °C. The carbon steel drill pipe would not enable the successful drill andcompletion of this 5 km HPHT well. However, with an IDP drill string, the model suggests a successful well – keeping the circulating
temperatures much below the threshold of common temperature critical components.
To validate the steady-state model, it was compared against Hasan and Kabir’s (1996) analytical model for forward circulation (flowdown the drill pipe). Since the analytical model assumes that the time exposed to flow does not vary with depth, and constant fluid
properties, the steady-state model was adapted to closely replicate the assumptions in the analytical model.
Other than the adaptations to the steady-state model, the results shown in Figure 6 and Figure 7 below use the same inputs as case 1 from
Table 5. The figures compare the steady-state model against the analytical solutions for flowing times of 24 hours, and 7 days (168 hours).

Temperature (°C)
0

0

50

100

150

200

1000

250

300

SSM, Annulus

Depth (m)SSM, Drill Pipe
2000

H&K, Annulus
H&K, Drill Pipe
Geothermal

3000

4000

5000
Figure 6: Steady-state model validation with Hasan & Kabir forward circulation analytical mode (case1, flowing time of 24hours).

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Brown, Holmes, Zatonski, and Toews

Temperature (°C)
0

0

50

100

150

200

1000

250

300

SSM, Annulus

Depth (m)SSM, Drill Pipe
2000

H&K, Annulus
H&K, Drill Pipe
Geothermal

3000

4000

5000
Figure 7: Steady-state model validation with Hasan & Kabir forward circulation analytical model (case 1, flowing time of 168
hours).
The steady-state model slightly overpredicts the fluid temperatures. The error generally gets larger as the flowing time increases. The
average different between the steady-state model and the analytical model is 0.6%, 2.1% in Figure 6, and Figure 7, respectively. In general,
there is good agreement between the steady-state and analytical models.
2.5 Parameter Sensitivities
Because the steady state model is quick to converge to a solution, it can be used to rapidly run a variety of sensitivities to understand theimpact of various parameters on the outputs of the model. Presented below is a simple tornado plot summarizing the impact of the variancein key model inputs. Each bar in the tornado plot represents the change in the maximum circulating temperature in the wellbore with a +/10% change in the respective model input. It should be noted that the likelihood of a +/- 10% change in each model input is not conveyed
with a tornado chart as simple as the one shown in Figure 8.

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Brown, Holmes, Zatonski, and Toews

-10%

+10%

Well depth
Temperature gradientSpecific heat, fluid
Density, fluid
Circulation rate
Conductivity, rockDP Resistance
ROP
Surface rock temp
Viscosity, fluid
Inlet temp
-15.0%-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

Change to Max Circulating Temperature
Figure 8: Sensitivity of maximum downhole circulation temperature with model inputs (case 1)
In order of most impactful to least impactful model inputs:
1.
2.
3.

4.
5.

Well design inputsi.
Well depth (i.e. TD)
Geological inputsi.
Geothermal (temperature) gradientii.
Rock conductivity
Drilling mud/fluid inputs
i.
Specific heatii.
Densityiii.
Viscosity (to a lesser extent)
Drilling Rig inputsi.
Circulation Rate
Drill string inputs
i.
Drill pipe thermal resistance

Although modifying the mud design could improve wellbore cooling during circulation, factors other than circulating temperature are
typically prioritized when designing a mud blend. Higher circulation rates can reduce circulating temperatures; however, rates are limitedby the maximum flow rates through the BHA, as well as pressure and rate limitations of surface equipment. That leaves the drill pipe
resistance as being one of the few levers available to the well design team to influence the circulating temperatures.
Relative to the impact of well depth and geothermal gradient, the circulating fluid temperature is less sensitive to the thermal resistanceof the drill pipe. In order to accommodate a deeper well, or a higher geothermal gradient, the drill pipe thermal resistance needs to increaseat least an order of magnitude more than the change in depth or gradient.
2.6 Drill Pipe Technology Limits
Assuming that the drill pipe can be engineered to achieve a range of thermal resistances, the steady-state model can be used to determine
the maximum drillable depths for a given geothermal gradient for a fixed maximum circulating temperature (i.e. the temperature
limitations of the BHA components).
For illustrative purposes, the same 5-1/2” drill pipe designs in cases 1 and 2 above are considered:15

Brown, Holmes, Zatonski, and Toews
Table 6: Drill pipe designs
Base Pipe

Thermal Resistance(ID x OD)

(mK/W)

Bare Carbon Steel

121.4 x 139.7

5.08 x 10-4

Hypothetical IDP

121.4 x 139.7

1.00 x 10-2

Description

IDP constructions with varying insulative layers was explored by Finger et al. (2000).
When coupled with the steady-state model, the maximum drillable depths for each of the drill string designs can be determined(temperature considerations only). Other model inputs are consistent with those in Table 5, and the maximum allowable bottomhole
circulating temperature of 150 °C is assumed.

15,000Well Depth (m)13,00011,000
9,000
7,000
5,000
3,000

20

30

40

50

60

70

80

Geothermal Gradient (°C)
Bare SteelHypothetical IDP

5km, 50 °C/km

Figure 9: Max drillable well depths for the illustrative drill pipe designs
The regions under each of the lines represent the gradient-depth combinations that can be feasibly drilled with a given drill pipe design.
Visualized in another way, the corresponding drillable bottom-hole rock temperatures (BHRT) for each string design can be plotted.

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Brown, Holmes, Zatonski, and Toews

550
500

Virgin BHRT (°C)

450
400
350
300
250
200
150
100

20

30

40

50

60

70

80

Geothermal Gradient (°C)
Bare SteelHypothetical IDP

5km, 50 °C/km

Figure 10: Max drillable bottom-hole rock temperatures for the illustrative drill pipe designs
As mentioned above, the economics of a MCLGS improves with increasing BHRT. By incorporating an insulated drill pipe into a drilling
program, higher rock temperatures can be drilled and exploited, improving the overall project economics and prospective investor returns.
The figures above also confirms that drill pipe resistances need to change by orders of magnitude in order to materially influence bottomhole circulating temperatures.
3. TRANSIENT MODEL
The steady-state model provides a wellbore temperature and pressure solution that only represents a “snapshot” in time. However, during
the normal drilling of a geothermal well, there are transient operations that cannot be properly modelled by a pseudo steady state model.
For example, some transient events that should be modelled to understand their impacts on wellbore temperatures are:
•
•
•
•
•
•
•

Connections,
Formation kicks,
Loss of circulation,
Running/tripping in hole,
Pulling/tripping out of hole,
Changes in circulation rate with time, andChanges in inlet temperature with time

The transient model presented in this section takes a comparatively more rigorous approach to modelling. The transient model employs anumerical solution of the transient 2-D heat conduction in the rock surrounding the wellbore coupled with a numerical solution of thetransient energy equation for the fluid flow inside the wellbore (drill pipe and annulus).
3.1 Model Formulation
The transient model is a 2-D, discretized rock and wellbore drilling model. A schematic of the transient model is shown in Figure 9.

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Brown, Holmes, Zatonski, and Toews
Drill pipe blocks

i=1

Annular blocks

i=2

Rock blocks

i=6

i=5

i=4

i = m-1

i=mRadial direction, i-dir

i=3

j=1

j=3

Centerline

Direction of well trajectory

j=2

j=n

j-dir

Figure 11: Transient model schematic
Similar to Figure 2 for the steady-state model, the green and red arrows in Figure 9 represent the mass and energy flows within the coupledrock-wellbore system, respectively.
3.2 Governing Equations and Assumptions
3.2.1 Rock Equations
Fourier’s Law of Heat conduction and the conservation of energy equation can be combined to derive the partial differential equation(PDE) that governs the transient conduction of thermal energy in rock with a constant thermal conductivity:
𝜕𝜕𝜕𝜕

where

𝜕𝜕𝜕𝜕

𝑣𝑣 𝜕𝜕𝜕𝜕

𝜕𝜕𝜕𝜕

1 𝜕𝜕

𝜕𝜕𝜕𝜕

1 𝜕𝜕 2 𝑇𝑇

𝜕𝜕 2 𝑇𝑇𝜌𝜌r 𝐶𝐶𝑝𝑝,r � 𝜕𝜕𝜕𝜕 + 𝑣𝑣𝑟𝑟 𝜕𝜕𝜕𝜕 + 𝑟𝑟𝜃𝜃 𝜕𝜕𝜕𝜕 + 𝑣𝑣𝑧𝑧 𝜕𝜕𝜕𝜕 � = 𝑘𝑘𝑟𝑟 �𝑟𝑟 𝜕𝜕𝜕𝜕 �𝑟𝑟 𝜕𝜕𝜕𝜕 � + 𝑟𝑟 2 𝜕𝜕𝜃𝜃2 + 𝜕𝜕𝑧𝑧 2 � + 𝑔𝑔̇𝜌𝜌r is the rock density

𝐶𝐶𝑝𝑝,r is the rock specific heat capacity

𝑇𝑇 is the rock temperature

𝑡𝑡 is time

𝑣𝑣 is velocity

𝑟𝑟 is the radial direction18( 19 )

Brown, Holmes, Zatonski, and Toews
𝜃𝜃 is the angular direction
𝑧𝑧 is the axial direction

𝑘𝑘r is the rock thermal conductivity
𝑔𝑔̇ is the rate of heat generation

Assuming transient heat transfer by conduction only, and no angular variation in temperature yields:
𝑣𝑣𝑟𝑟 = 𝑣𝑣𝜃𝜃 = 𝑣𝑣𝑧𝑧 = 0
𝜕𝜕𝜕𝜕
=0
𝜕𝜕𝜕𝜕
𝑔𝑔̇ = 0Equation ( 19 ) reduces to:
1 𝜕𝜕𝜕𝜕

where

𝛼𝛼r 𝜕𝜕𝜕𝜕

1 𝜕𝜕

𝜕𝜕𝜕𝜕

𝜕𝜕 2 𝑇𝑇= 𝑟𝑟 𝜕𝜕𝜕𝜕 �𝑟𝑟 𝜕𝜕𝜕𝜕 � + 𝜕𝜕𝑧𝑧 2( 20 )𝑘𝑘

𝛼𝛼r is the thermal diffusivity of the rock: 𝛼𝛼r = 𝜌𝜌 𝐶𝐶rr 𝑝𝑝,r

3.2.2 Wellbore Equations
The transient energy equation for the 1D fluid flow in the wellbore along the axial coordinate system can be expressed for both the fluidin the drill pipe, and the annular space:
Annular fluid:
Drill pipe fluid:where𝜕𝜕𝜌𝜌f,ann 𝑒𝑒ann𝜕𝜕𝜕𝜕+𝜕𝜕𝜕𝜕(ℎann +𝑔𝑔𝑔𝑔)
𝜕𝜕𝜕𝜕𝜕𝜕𝜌𝜌f,dp 𝑒𝑒dp
𝜕𝜕𝜕𝜕

= 𝑈𝑈rockface �𝑇𝑇wr − 𝑇𝑇f,ann � + 𝑈𝑈dp �𝑇𝑇f,dp − 𝑇𝑇f,ann �+𝜌𝜌f,ann is the fluid density in the annulus

𝜕𝜕𝜕𝜕(ℎdp +𝑔𝑔𝑔𝑔)
𝜕𝜕𝜕𝜕= 𝑈𝑈dp �𝑇𝑇f,ann − 𝑇𝑇f,dp �( 21 )( 22 )

𝜌𝜌f,dp is the fluid density in the drill pipe

𝑒𝑒ann is the internal energy of the fluid in the annulus

𝑒𝑒dp is the internal energy of the fluid in the drill pipe

𝐺𝐺 is the mass flux of the fluid flowing through the wellboreℎann is the enthalpy of the fluid in the annulusℎdp is the enthalpy of the fluid in the drill pipe

𝑔𝑔 is the constant due to the acceleration due to gravity

𝑦𝑦 is the position in the vertical direction (parallel to gravity)

𝑧𝑧 is the axial direction

𝑈𝑈rockface is the heat transfer coefficient from the rock/wellbore boundary to the fluid
𝑈𝑈dp is the heat transfer coefficient between the annular fluid and the drill pipe fluid

𝑇𝑇wr is the temperature of the rock at the rock/wellbore boundary𝑇𝑇f,ann is the temperature of the bulk fluid in the annulus

𝑇𝑇f,dp is the temperature of the bulk fluid in the drill pipe

The change in kinetic energy has been neglected in Equations ( 21 ) and ( 22 ) as this contribution is negligible compared to the internalenergy and enthalpy change of the fluid. In addition, the conservation of mass has been invoked for an incompressible fluid so the massflux, 𝐺𝐺, is constant in the drill pipe and annulus (although in different directions).
19

Brown, Holmes, Zatonski, and Toews
The heat transfer coefficients, 𝑈𝑈rockface and 𝑈𝑈dp , are comprised of any conductive resistance between the rock and the wellbore (e.g.
casing and cement, and/or drill pipe wall) and convective resistances of the flowing fluids. Similar to the governing equation derivations
for the steady-state model, the heat transfer coefficients can be expressed using resistance theory and the standard thermal resistanceequations for cylindrical conductive heat transfer, and cylindrical convective heat transfer of a fluid. These equations and their combination
to create the total heat transfer coefficients will not be repeated here.
A pseudo-steady state version of the momentum equation is employed whereby the pressure drop of the fluid is calculated using theColebrook White type correlation. Because of its similarity to the equations detailed for the steady-state model, the simplified conservationof momentum equations are not repeated here.
Ultimately, the following assumptions and simplifications are made to derive the fluid equations above:
1.
2.
3.

The change in kinetic energy is neglected
A simplified, pseudo-steady version of the momentum equation is employed
No impact of the rock cuttings on the fluid properties (e.g. specific heat, density, viscosity)

3.2.3 Initial and Boundary Conditions
The temperature field of the rock 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 drill pipe. The rock boundary temperature and radius must also be specified. For all simulations, theboundary rock radius is set large enough such that it has not been impacted by the thermal front and the boundary temperature remains atvirgin rock temperature.
To couple the sets of wellbore equations and rock equations, the heat flow at the rock-wellbore interface must be continuous such that theFourier law of heat conduction in the rock at the boundary equals the transfer to the fluid in the annulus.
𝜕𝜕𝜕𝜕( 23 )

𝑘𝑘r 𝜕𝜕𝜕𝜕 = 𝑈𝑈rockface �𝑇𝑇wr − 𝑇𝑇f,ann �

3.2.4 Discretization and Numerical Solution
The PDE describing the transient 2-D conduction in the rock can be solved numerically by integrating Equation ( 20 ) over a discrete
finite control volume, 𝑑𝑑𝑑𝑑 = 2𝜋𝜋𝜋𝜋 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 and specified time step, Δ𝑡𝑡:𝑛𝑛
𝑇𝑇 𝑛𝑛+1 −𝑇𝑇𝑖𝑖,𝑗𝑗

12𝜋𝜋�𝑟𝑟𝑖𝑖+1− 𝑟𝑟𝑖𝑖2 ��𝑧𝑧𝑗𝑗+1 − 𝑧𝑧𝑗𝑗 � 𝑖𝑖,𝑗𝑗 Δ𝑡𝑡𝛼𝛼r

𝑇𝑇 𝑛𝑛+1 −𝑇𝑇 𝑛𝑛+1

𝑛𝑛+1
𝑇𝑇 𝑛𝑛+1 −𝑇𝑇𝑖𝑖−1,𝑗𝑗

𝑖𝑖,𝑗𝑗= 4𝜋𝜋�𝑧𝑧𝑗𝑗+1 − 𝑧𝑧𝑗𝑗 � �𝑟𝑟𝑖𝑖+1 𝑖𝑖+1,𝑗𝑗− 𝑟𝑟𝑖𝑖 𝑟𝑟𝑖𝑖,𝑗𝑗
𝑟𝑟 −𝑟𝑟𝑖𝑖+2

𝑖𝑖

𝑖𝑖+1 −𝑟𝑟𝑖𝑖−1𝑛𝑛𝑛𝑛
𝑇𝑇𝑖𝑖,𝑗𝑗+1−𝑇𝑇𝑖𝑖,𝑗𝑗2
� + 2𝜋𝜋�𝑟𝑟𝑖𝑖+1− 𝑟𝑟𝑖𝑖2 � � 𝑧𝑧

𝑗𝑗+2 −𝑧𝑧𝑗𝑗

Where 𝑖𝑖 indexes the radial direction, 𝑗𝑗 indexes the axial direction (along the wellbore), and 𝑛𝑛 indexes time.

𝑛𝑛
𝑛𝑛
𝑇𝑇𝑖𝑖,𝑗𝑗−𝑇𝑇𝑖𝑖,𝑗𝑗−1− 𝑧𝑧

𝑗𝑗+1 −𝑧𝑧𝑗𝑗−1�( 24 )

Note that the radial derivatives on the right-hand side of Equation ( 24 ) are implicitly calculated at the new time step (n+1) whereas theaxial derivatives are explicitly calculated at the previous time step (n). This is acceptable as the typical grid 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 for the annulus and drill pipe are discretized in the following manner. For the drill pipe:22𝜌𝜌f,ann 𝜋𝜋�𝑟𝑟ann− 𝑟𝑟dp,o�Δ𝑧𝑧

𝑛𝑛+1
𝑇𝑇2,𝑗𝑗�𝑛𝑛
𝑛𝑛+1
�ℎ2,𝑗𝑗�−ℎ2,𝑗𝑗

Δ𝑡𝑡

2
𝑛𝑛+1
𝑛𝑛+1
𝑛𝑛+1
𝑛𝑛+1
𝑛𝑛+1
2
+ 𝐺𝐺𝐺𝐺�𝑟𝑟ann− 𝑟𝑟dp,o� ��ℎ2,𝑗𝑗− ℎ2,𝑗𝑗+1
� + 𝑔𝑔𝑔𝑔� = 𝑈𝑈rockface,𝑗𝑗 Δ𝑧𝑧�𝑇𝑇3,𝑗𝑗− 𝑇𝑇2,𝑗𝑗
� + 𝑈𝑈dp,𝑗𝑗 Δ𝑧𝑧�𝑇𝑇1,𝑗𝑗−( 25 )

𝑛𝑛+1
𝑛𝑛+1
where the term 𝑈𝑈rockface,𝑗𝑗 Δ𝑧𝑧�𝑇𝑇3,𝑗𝑗− 𝑇𝑇2,𝑗𝑗
� is the heat transfer from the rock to the wellbore. For the annulus:2𝜌𝜌f,dp 𝜋𝜋𝑟𝑟dp,i
Δ𝑧𝑧

𝑛𝑛
𝑛𝑛+1
�ℎ1,𝑗𝑗�−ℎ1,𝑗𝑗

Δ𝑡𝑡

2
𝑛𝑛+1
𝑛𝑛+1
𝑛𝑛+1
𝑛𝑛+1
+ 𝐺𝐺𝐺𝐺𝑟𝑟dp,i− ℎ1,𝑗𝑗−1
� + 𝑔𝑔𝑔𝑔� = 𝑈𝑈dp,𝑗𝑗 Δ𝑧𝑧�𝑇𝑇2,𝑗𝑗− 𝑇𝑇1,𝑗𝑗���ℎ1,𝑗𝑗( 26 )

𝑛𝑛+1
𝑛𝑛+1
where the term 𝑈𝑈dp,𝑗𝑗 Δ𝑧𝑧�𝑇𝑇2,𝑗𝑗− 𝑇𝑇1,𝑗𝑗
� is the heat transfer from the annulus to the drill pipe fluid.

The discretized wellbore equations above make use of specific enthalpy, ℎ, instead of specific heat capacity and temperature to properly
model the Joule-Thomson effect, which has a large impact on temperature change due to pressure drops experienced through the drill bit
and the other BHA components.
Thermophysical properties are calculated using NIST Refprop, or the open-source CoolProp library (Bell et al. 2014) (usage will depend
on what libraries are installed on the user’s local machine).
The governing equations and their discretization are similar to those described by Holmes et al. (2021) for Eavor’s transient MCLGS
model and have been proven to match field operating data at the Eavor-Lite™ demonstration project. However, unlike the MCLGS model,
the system of algebraic equations describing the drill-pipe-annulus-rock system cannot be directly solved using the Tri-Diagonal Matrix
20

Brown, Holmes, Zatonski, and Toews
Algorithm (TDMA). Instead, the system of linear equations are divided into three discrete solution routines/steps and iteratively solved
until convergence to a user-specified tolerance is met. The three solution routines are described in the section below.
3.3 Solution Scheme
𝑛𝑛+1
The solution of the large sparse matrix to compute the entire temperature field at the new time-step, 𝑇𝑇𝑖𝑖,𝑗𝑗, is achieved through iteration
to reach convergence.

3.4 Handling Transient Operations
Throughout any major drilling program, many parameters are constantly changing. While drilling, circulation rates are varied, inlet mud
temperatures can change due to ambient and return temperatures, and the depth of the drill pipe changes as the well is drilled deeper, andwhile tripping. The changes in these parameters with time cannot be explicitly handled by the steady-state model. The transient model,
however, allows for the manipulation of these key variables with time.
3.4.1 Drilling
During drilling, the following model inputs can be varied with time to account for the changing operations over the life of a program:••••

Drill pipe depth (e.g. to model drilling, and tripping in and out of the hole)
Hole depth
Inlet mud temperatures (e.g. to model mud cooling, or the change with ambient temperatures throughout the day)Mud rheology (e.g. to model changes in mud design over a program)

Additionally, the properties of the full length drill string are defined as a function of measured depth at the start of the simulation. During
the simulation, as the drill pipe is moved up and down in the hole, the transient model will account for the change in drill pipe position in
the hole following a last-in-first-out methodology. If the thermophysical properties of the drill string vary along its length, the physicalimplications of their relative location in the well will be explicitly accounted for throughout the duration of the simulation.
3.4.2 Kicks & Lost Circulation
The addition/removal of drilling fluids into/out of the wellbore can also be changed with time to model kicks and periods of lost circulation(LOC). More specifically, the size and rate of a kick, or LOC event can be varied to allow the user to sensitize on the impacts to wellbore
temperatures.
3.5 Model Case Study Results and Comparison
The model case study presented below follow the same inputs as described in the steady-state section (for cases 1 and 2), with the following
additional transient model related inputs:
Table 7: Additional transient model inputs
Model Input

Units

Value

# of axial grid blocks (j-dir)#500

Axial grid block sizem

10

Grid outer radiusm15# of radial grid blocks (i-dir)#

40

Radial grid block sizemvariesNote: the radial direction is discretized such that the radial blocks are growing exponentially away from thewell
The run starts with the model drilling at a constant ROP of 12 m/hr, and then once it hits TD at 5,000 m circulates on bottom for theremainder of the simulated time. The tripping of the drill pipe in and out of the hole has been excluded from this simulation intentionally.
The steady-state model cannot account for tripping, so to make a direct comparison between the two models, it has been neglected fromthis transient model run.
Unlike the steady-state model, the transient model is capable of modelling changes in stand-pipe pressure (inlet pressure), inlet
temperature, tubing depth and open hole depth with time. This allows for the estimation of temperature and pressure effects due to thenormal transience encountered when drilling HPHT geothermal wells.
The figure below shows the time-series input data for the run:21

Brown, Holmes, Zatonski, and Toews

05

Inlet T (degC)
25

30

1000

Depth (m)

2000
3000
4000
5000

30
25
20
15
10
5
0

6000
Tubing Depth (m)Inlet Volumetric Flow (m3/min)

35
Temp (°C) & Flow Rate (m3/min)

0Time (days)
10
15
20

0

5

10

15

20

25

30

Time (days)

Hole Depth (m)Figure 12: Transient model time-series inputs
The transient drilling model (TDM) reports the pressure and temperature results for each time step. The results can be plotted to show thechange in temperature and pressure at specific points in the well (e.g. at temperature-critical component locations) throughout thesimulated time, or snapshots of the entire wellbore temperature/pressure profiles at specific points in time.
The figure below shows the variation in temperature and standpipe pressure (SPP) with time, as well as the steady-state model (SSM)
solutions for case 1:

Max Ann T, TDM

Outlet T, TDM

750m from DP bottom, Ann T, TDM

Max Ann T, SSM

Outlet T, SSM

Rock Temperature @ Bottom of hole300

Temperature (°C)

250
200
150
100
50
0

0

5

10

15

20

Time (days)

Figure 13: Temperature outputs from transient model (case 1)

22

25

30

Brown, Holmes, Zatonski, and Toews

Standpipe Pressure, TDM

Standpipe Pressure, SSM

8Pressure (MPa)

7
6
5
4
3
2
1
0

0

5

10

15

20

25

30

Time (days)

Figure 14: Standpipe pressure output from transient model (case 1)
A comparison of the wellbore temperature and pressure profiles between the two models is shown in the figures below.

0

0

50

100

Temperature (°C)
150
200

250

300

TDM, Ann

1000
Depth (m)TDM, DP
SSM, Ann

2000

SSM, DP
3000

Geothermal

4000
5000
Figure 15: Wellbore temperature solution comparison between transient and steady-state models (case 1)

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Brown, Holmes, Zatonski, and Toews

0

0

10

20

Pressure (MPa)
30

40

50

60

Depth (m)1000

TM, Ann
TM, DP

2000

SSM, Ann
SSM, DP

3000
4000
5000

Figure 16: Wellbore pressure solution comparison between transient and steady-state models (case 1)
Case 2 (hypothetical IDP) model results are below:

Max Ann T, TDM

Outlet T, TDM

750m from DP bottom, Ann T, TDM

Max Ann T, SSM

Outlet T, SSM

Rock Temperature @ Bottom of hole300

Temperature (°C)

250
200
150
100
50
0

0

5

10

15

20

Time (days)

Figure 17: Temperature outputs from transient model (case 2)

24

25

30

Brown, Holmes, Zatonski, and Toews

Standpipe Pressure, TDM

Standpipe Pressure, SSM

7

Pressure (MPa)

6
5
4
3
2
1
0

0

5

10

15

20

25

30

Time (days)

Figure 18: Standpipe pressure output from transient model (case 2)

0

0

10

20

Temperature (°C)
30
40
50

Depth (m)

1000

60

70

80

TM, Ann
TM, DP

2000

SSM, Ann
SSM, DP

3000
4000
5000

Figure 19: Wellbore temperature comparison between transient and steady state models (case 2). Geothermal gradient omitted
to improve horizontal axis resolution.

25

Brown, Holmes, Zatonski, and Toews

0

0

10

Pressure (MPa)
30

20

40

50

60

Depth (m)1000

TM, Ann
TM, DP

2000

SSM, Ann
SSM, DP

3000
4000
5000

Figure 20: Wellbore pressure solution comparison between transient and steady-state models (case 2)
Since the form of the momentum/pressure equations are similar between the transient and steady-state models, their pressure solutions
are nearly identical. The steady-state model predicts on average 1.1% higher wellbore pressures than the transient model.
However, the differences in the temperature solutions between the two models is greater. The tables below summarize the percent
difference in the temperature and pressure solutions.
Table 8: Percent difference between the steady-state and transient model temperatures (calculated as SSM relative to TDM)
Case 1: Carbon Steel (CS) String
Average

10th

Percentile

50thPercentile

Case 2: Hypothetical IDP String
90th

Percentile

Average

10th
Percentile

50thPercentile

90thPercentile

EntireWellbore

6.0%

4.0%

6.6%

6.9%

2.9%

1.8%

3.2%

3.4%

Drill Pipe

5.9%

3.7%

6.6%

6.8%

2.5%

1.1%

2.9%

3.2%

Annulus

6.1%

4.4%

6.6%

6.9%

3.3%

3.1%

3.3%

3.4%

Table 9: Percent difference between the steady-state model and transient model pressures (calculated as SSM relative to TDM)
Case 1: Carbon Steel (CS) String
Average

10th

Percentile

50thPercentile

Case 2: Hypothetical IDP String
90th

Percentile

Average

10th
Percentile

50thPercentile

90thPercentile

EntireWellbore

1.1%

-0.1%

0.4%

2.4%

1.1%

0.2%

0.5%

2.1%

Drill Pipe

1.0%

-0.1%

0.7%

2.6%

0.9%

0.2%

0.6%

2.1%

Annulus

1.2%

-0.1%

0.2%

2.0%

1.4%

0.2%

0.4%

2.0%

3.6 Modelling Transient Operations
3.6.1 Connections (No Circulation)
When making a connection while drilling, the following actions are taken:
26

Brown, Holmes, Zatonski, and Toews
1.
2.
3.
4.

Circulation is ceased (“pumps-off”)
Joints are made-up and connected to the top of the string
Circulation initiatedDrilling continues (drill string gradually lowers)

While circulating, the fluid keeps the bottom-hole fluid temperatures relatively low. Once circulation stops, the stagnant fluid in the
wellbore begins to heat up gradually from the surrounding rock. It is feasible that during pumps-off, the wellbore fluid heats up beyond
the temperature limits of the BHA components.
The transient model can help evaluate the maximum connection times at various depths in the well at which the temperature limits of key
components are not exceeded.
Using the case 2 transient model from the previous section, we can model a connection being made at a depth of 5 km:

17.2

17.8

18

4600

2.5

4700

2.0

4800

Connection
Time

1.5

4900

1.0

5000

0.5

5100

0.0

Drill Pipe Depth (m)Temp Limit

300

3.0

250
Temperature (°C)

17

BHA T (degC)

Circulation Rate (m3/min)

Depth (m)4500Time (days)
17.4
17.6

200
150
100
50
0

17

17.2

17.4

17.6

17.8

18

Time (days)

Circulation Rate (m3/min)Figure 21: Connection transient model results
During pumps-off, while the connection is being made, the stagnant fluid at the bottom of the well begins to heat up dramatically due tothe high rock temperatures at these depths (virgin rock temperature = 260 °C).
The time it takes the bottom-hole fluid to reach the 150 °C temperature limit is about 233 minutes. With this hypothetical IDP, the rig has
more than enough time to make connections before the temperature-sensitive components heat up beyond their limits. However, at deeper
depths (i.e. hotter rock), and with less thermally resistive IDP, the time it takes to reach the 150 °C limit will decrease – potentially puttingpressure on the rig to make connections fast enough to avoid excessive wellbore heating during pumps-off.
3.6.2 Formation Kicks
In addition to modelling standard drilling operations, the model is also capable of modelling fluid kicks from the formation. While drilling,
the circulating fluid will keep the wellbore and the BHA components cool. However, in the case of hot fluid ingress from the surroundingrock formation, there may be a risk that the circulating fluid is not enough to dilute the hot kick fluids to••maintain the wellbore below the temperature limit, or
prevent flashing of return fluids at surface

The transient model can be used to explore the impact of kicks on the fluid temperatures in the well, as well as return temperatures atsurface. Again, using the case 2 transient model, we can model taking a kick at 5 km deep:

27

Brown, Holmes, Zatonski, and Toews
Table 10: Case 2 transient model + kick model inputs
Model Input

Units

Value

Kick Fluid

-

Water

Kick Volume

bbl

10

Kick Ratem3/min1.0

Kick Duration

min

1.6

Kick fluid temperature°C

260 (rock temperature)

The figure below shows the annular fluid temperature profile during and after the kick:

0

40

60

Temperature (°C)
80
100

120

140

1000
Start of kick

Depth (m)2000

End of kick
5 min after start of kick3000

20 min after start of kick

4000
5000
6000
Figure 22: Modelled results of formation kick on annular temperature profile
During the kick, bottomhole temperatures climb quickly due to entry of hot kick fluids into the wellbore but is quickly diluted by the cold
drilling fluid leaving the bottom of the drill string. As the slug of hot fluids moves upwards in the annulus, the temperature cools as it
continues to be diluted with cold circulating drill fluids and heat exchange with the drill pipe fluids. By the time the slug reaches the topof the annulus, the excess heat has largely left the annular fluid, and the outlet temperatures are relatively unaffected.

28

Brown, Holmes, Zatonski, and Toews

160
140

Temperature (°C)

120
100Kick - Max Ann T

80

Kick - Outlet T

60

No Kick - Max Ann T

40

No Kick - Outlet T

20
0

0

20

40

60

80

100

120

Time After Start of Kick (min)Figure 23: Max downhole circulating, and return temperatures during a kickDue to the finite-difference approach to modelling, the authors recognize the impact of numerical dispersion on the simulation of the“slug” flow of hot kick fluids up the annulus (similar to the numerical dispersion often seen in reservoir modelling of immiscible flood
fronts). Reducing the axial grid block size would reduce the impact of numerical dispersion on the simulation results.
Regardless, the kick functionality of the transient model can be used to sensitize the impacts of kick size and influx rate on fluid
temperatures. The follow-on effects on temperature sensitive components in the BHA and drill string, as well as the return temperatures,
can be evaluated.
3.6.3 Running-in-hole (RIH)
As mentioned, and illustrated above, fluid circulation minimizes the fluid temperatures within the wellbore. However, during periods of
no-flow, the wellbore fluids quickly start to equilibrate with virgin rock temperatures.
When swapping drill bits, the drill string is tripped out of and back into the hole. During these operations while the rig is not circulating,
the wellbore fluid temperature will begin to increase. As the BHA is lowered back into the hole, there is a risk that it may encounter fluid
temperatures greater than the limits of the sensitive components. The transient model can be used to model the heating of the stagnant
wellbore fluids, and subsequently the temperatures observed by the BHA while tripping back in.
Using the case 2 transient model, we can model a bit change at 5 km deep:
Table 11: Case 2 transient model + bit change parameters
Model Input

Units

Value

Tripping out of hole speed

ft/hr

1,500

Tripping in hole speed

ft/hr

1,000

Time to change bit

min

240

29

Brown, Holmes, Zatonski, and Toews

19

1000

2.5

2000

2.0

3000

1.5

4000

1.0

5000

0.5

6000

0.0

Temp Limit

250

3.0

200
Temperature (°C)

15

BHA T (degC)

Circulation Rate (m3/min)

Depth (m)0Time (days)
16
17
18

150
100
50
0

Tubing Depth (m)

15

16

17

18

19

Time (days)

Inlet Volumetric Flow (m3/min)Figure 24: Running-in-hole transient model results

Although the insulated drill pipe keeps the circulating temperatures much below the 150 °C temperature limit, once circulation ceases,
the temperatures quickly equilibrate with the virgin rock temperature. While running in hole, the temperatures observed at the BHA far
exceed the tolerable temperatures.
To prevent the BHA from experiencing temperatures >150 °C, periods of circulation can be introduced to the tripping in hole procedure(a.k.a “washing-in”) to gradually cool the wellbore fluids while descending. The refinement of tripping in procedures can be guided bysimulation results produced by the transient model.
3.7 Field Validation of Transient Model
3.7.1 Eavor-Deep™ Overview
The Eavor-Deep™ project utilized Eavor’s proprietary drilling technology – including an insulated drill pipe – to drill a single well, withsidetrack, > 5km deep in granite with rock temperatures of ~250°C. The well was constructed in New Mexico, USA where local
geothermal gradients can exceed 50 °C/km. The insulated drill pipe technology developed by Eavor is a 5.5” base pipe with several
insulating layers that can handle very high torque and tensile loads, and enable drilling techniques at depths 7 km or greater.
The purpose of the Eavor-Deep™ Project was to demonstrate all the technical elements required to construct commercial Eavor-Loops™
in deep, high temperature hard rock. The single well and sidetrack design was selected to replicate the first half of a commercial EavorLoop™ (i.e. the inlet or outlet well).
In addition to temperature measurements from Measurement While Drilling (MWD) tools, temperature sensors were located in various
parts of the drill string to record annular fluid temperatures for the purposes of validating Eavor’s transient thermodynamic drilling model.
3.7.2 Prediction of Eavor-Deep™ Drilling Temperatures
The transient model was used to predict the temperatures experienced while drilling Eavor-Deep™. The model was history matched using
3 bit runs worth of data spanning ~4 days, comprised of••••

Return temperatures,
MWD temperatures,
Sensor temperatures, andStandpipe pressure

Inputs into the model consisted of
•
•
•
•
•

Tubing depth,
Hole depth,
Circulation rate,
Inlet fluid temperature, andMud rheological parameters
30

Brown, Holmes, Zatonski, and Toews
History match parameters included:•••

Drill pipe thermal resistance,
Rock thermal conductivity, andTemperature gradient

The bounds on the history matching parameters were based on the range of expected pre-drill estimates for each. The history match was
performed using a genetic algorithm to minimize an objective function specified as a weighted sum of squared errors between the model’s
prediction and the measured data.
Figure 23 below shows the measured and predicted sensor temperatures every 5 minutes. Over the displayed period, the sensor was locatedbetween 215-220 m above the bottom of the drill string. The period used for history matching the model and the model’s forecast are
denoted with the vertical line and accompanying annotations. The training and matching period was selected because of its relative highdata quality, deep depths (between 4,100 and 5,100 m), and spanning portions of the well where estimated rock temperatures were in therange of 200 °C.
225
200

Temperature (°C)

175
150
125
100
75
50
25

Measured

Predicted

Est. Rock Temp @ Bottom of Hole2022-11-14

2022-11-13

2022-11-12

2022-11-11

2022-11-10

2022-11-09

2022-11-08

2022-11-07

2022-11-06

2022-11-05

2022-11-04

2022-11-03

2022-11-02

0

Training Period

Figure 25: Eavor-Deep™ measured and predicted BHA sensor temperatures
Visually, the model does a good job of matching the transient temperature measurements over both the training and hold-out data.
Circulating temperature error statistics are summarized in the histogram and Table 12 below.

31

Brown, Holmes, Zatonski, and Toews
Training

Hold-out

0.350
0.300
Density

0.250
0.200
0.150
0.100
0.050
> 30%

[27.5%, 30%)

[25%, 27.5%)[22.5%, 25%)

[20%, 22.5%)[17.5%, 20%)

[15%, 17.5%)[12.5%, 15%)

[10%, 12.5%)[7.5%, 10%)[5%, 7.5%)[2.5%, 5%)[0%, 2.5%)[-2.5%, 0%)[-5%, -2.5%)[-7.5%, -5%)[-10%, -7.5%)[-12.5%, -10%)[-15%, -12.5%)[-17.5%, -15%)[-20%, -17.5%)[-22.5%, -20%)[-25%, -22.5%)[-27.5%, -25%)[-30%, -27.5%)< -30%

0.000% Error Bin

Figure 26: Histogram of circulating temperature model errors (at sensor)
Table 12: Transient model circulating temperature summary statistics for Eavor-Deep™
10th Percentile
Error

50th Percentile
Error

90th Percentile
Error

Between +/- 10%
Error

Between +/- 15%
Error

Training

-4.7%

1.2%

4.5%

97.4% of points

100% of points

Hold-out-14.8%

-0.9%

4.9%

83.2% of points

89.3% of points

PeriodAs expected, the match on the data between the training period is better than the hold-out period. However, the median (50th percentile)model error is in the 0% range for both periods.
The transient model provides accurate predictions of real circulating wellbore temperatures while drilling.
3.7.3 Theoretical IDP Cooling
As shown in Figure 25, the IDP used in the Eavor-Deep™ trial was able to maintain circulating temperatures below 150 °C at the bottomof the hole. The same history matched model was run with standard drill pipe thermal resistance numbers and re-simulated to show thetheoretical cooling provided by the IDP technology .

32

Brown, Holmes, Zatonski, and Toews
250

Temperature (°C)

200
150
100
50

TM, Standard DP

TM, IDP2022-11-14

2022-11-13

2022-11-12

2022-11-11

2022-11-10

2022-11-09

2022-11-08

2022-11-07

2022-11-06

2022-11-05

2022-11-04

2022-11-03

2022-11-02

0

Est. Rock Temp @ Bottom of Hole

Figure 27: Simulated circulating temperatures for IDP and standard drill pipe
Over the simulated period, the IDP reduced downhole circulating temperatures by up to 90°C (with a median of 61°C). The model suggeststhat standard drill pipe would have been unable to maintain circulating temperatures below the 150°C tool limit and therefore drilling thiswell was possible only because of Eavor’s IDP technology
In addition to proving out other drilling technologies, Eavor-Deep™ has proven that IDP unlocks hotter exploitable rock temperatures for
MCLGS.
CONCLUSIONS
Eavor’s proprietary MCLGS Eavor-Loop™ technology allows for the exploitation of geothermal energy around the globe. The levelized
cost of energy (LCOE) is largely driven by rock temperatures – the hotter the rock, the better the economics of a MCLGS project. To date,directional drilling and magnetic ranging tools, which are critical to the development of MCLGS projects, have an upper temperature limit
above which they are no longer functional.
To enable the drilling of HPHT wells for MCLGS, the developer needs to ensure cool wellbore fluid temperatures to prevent BHA
component malfunction.
The steady-state and transient models presented above can predict operational temperatures in the wellbore, allowing for effectiveengineering design of HPHT well and drilling programs, as well as operational support during execution. The steady-state model can beused as an effective tool to quickly evaluate a range of scenarios, while the transient model can be used for detailed design.
As proven at Eavor-Deep™, drill pipe with increased thermal resistance (IDP) is a feasible method for maintaining cool downhole
circulating temperatures, enabling the drilling of high-temperature hard rock formations for development of MCLGS projects.
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