Energy Conversion and Management 236 (2021) 114056

Contents lists available at ScienceDirect

Energy Conversion and Management
journal homepage: www.elsevier.com/locate/enconman

Globally scalable geothermal energy production through managed pressure
operation control of deep closed-loop well systems
AmirHossein Fallah a, *, Qifan Gu a, Dongmei Chen a, Pradeepkumar Ashok a, Eric van Oort a,Michael Holmes bab

The University of Texas at Austin, United States
Eavor Technologies Inc., Canada

A R T I C L E I N F O

A B S T R A C T

Keywords:
Deep closed-loop geothermal system (DCLGS)
Scalable power generation
Thermal-hydraulic modelingManaged pressure operation (MPO)
Open-hole well completion

Closed-loop geothermal systems (CLGS) have been recently proposed as an alternative to the conventional
enhanced geothermal system (EGS) concept to address many of the issues of concern with EGS, such as potential
contamination of the circulating fluid and short-circuiting. Deep CLGS wells drilled in rock formations with insitu temperatures above 200 ◦ C could in theory be drilled anywhere around the world, thereby allowing for
globally scalable geothermal energy production. A novel concept of integrating a managed pressure operation(MPO) system with deep CLGS (DCLGS) is presented here. The concept includes an open-hole completion of thelateral section, while the automatically controlled MPO system maintains wellbore integrity and avoids fluid
contamination. A combined thermal and hydraulic model is also developed to demonstrate the feasibility of thisconcept. Using a robust semi-implicit numerical algorithm, the model can simulate the fast transients in a well,which enables the application of automated MPO control for real-time control of a DCLGS. Simulation results
show that a 7 km deep U-shaped well with a 7 km open-hole lateral with a reservoir temperature of 250 ◦ C cangenerate a thermal power of around 28 MW initially when the pump rate is set to 350 m3/h. The results also
show that casing of the lateral section has little impact on the outlet temperatures and thermal powers. An
optimally insulated return section can increase the output power by 2%. The effect of pump rate is also studied.
Even though the outlet temperature decreases, increasing the pump rate can improve the thermal power by 15%,
when the pump rate is increased from 250 to 450 m3/h.

1. Introduction
Geothermal energy is considered clean and renewable, andgeothermal wells have been drilled and used for heat and electricity
generation for many years [1–3]. However, the economical extraction ofgeothermal energy has been mostly limited to countries and regionswith high subsurface temperature gradients (e.g. areas with active
volcanism and tectonic activity) and permeable aquifers [4,5]. Con­ventional enhanced geothermal systems (EGS) require high rockporosity and permeability, sufficient fluid in place, and adequate fluid
recharge, which are not always available [2,6]. Moreover, the directcontact between fluid and rock through fractures might cause problems
such as fluid contamination, surface gas emissions, and induced seis­
micity [7–9]. To avoid these issues and to enable global scaling ofgeothermal energy generation, closed-loop geothermal systems (CLGS)

were introduced [10]. A CLGS well essentially works as an indirect heatexchanger, where the circulating fluid absorbs energy from the rockformation as it flows through the well, eliminating the reliance on
fractures and the associated issues observed in EGS wells.
Different CLGS designs have been proposed in the published litera­ture [11]. These include pipe-and-annulus designs [12] and the U-sha­
ped loops [13]. Abandoned oil and gas wells are also considered forgeothermal energy production [14–16]. However, these existing con­cepts are mostly based on shallow wells and the estimated electricity
generation in such wells is on the order of a few megawatts only, which
may not be sufficient to generate electricity at a large utility scale (see e.
g. Oldenburg et al. [17]). To generate commercially viable power at any
location, deep CLGS (DCLGS) wells are required to enable access to hightemperature reservoirs. Taking the US as an example, a study by the
Geothermal Laboratory at SMU [18] shows that geothermal reservoirs
with temperatures above 200 ◦ C at the depth of 7.5 km are available in* Corresponding author.
E-mail addresses: afallah@utexas.edu (A. Fallah), qifan.gu@utexas.edu (Q. Gu), dmchen@me.utexas.edu (D. Chen), pradeepkumar@mail.utexas.edu (P. Ashok),vanoort@austin.utexas.edu (E. van Oort), mike.holmes@eavor.com (M. Holmes).
https://doi.org/10.1016/j.enconman.2021.114056
Received 30 September 2020; Accepted 11 March 2021
Available online 27 March 2021
0196-8904/© 2021 Elsevier Ltd. All rights reserved.

A. Fallah et al.

Glossary
BHP
CLGS
DCLGS
EGS
ERD
HPHT
MD
MPD
MPO
PI
PVT
SBP
TVD
VIT

Energy Conversion and Management 236 (2021) 114056hHḢsourcebottomhole pressure
closed-loop geothermal system
deep closed-loop geothermal systemenhanced geothermal system
extended reach drillinghigh-pressure high-temperature
measured depth
managed pressure drilling
managed pressure operation
proportional integral
pressure–volume-temperaturesurface backpressure
true vertical depth
vacuum insulated tubingkṁsourceṀsourceNupPrq̇wall
ri
ro
R
Re
t
T
v
x
z

NomenclatureA
cross sectional area, L2, m2
cp
specific heat capacity at constant pressure, L2 /t2 T, J/Kg.K
cv
specific heat capacity at constant volume, L2 /t2 T, J/Kg.K
D
diameter, L, meinternal energy, L2/t2, J/Kg
fD
Darcy–Weisbach friction factor
fg
gravitational force, m/L2 t2 , Kg/m2.s2
fw
wall friction, m/L2 t2 , Kg/m2.s2
ggravitational acceleration, L/t2 , m/s2

μρ

convection heat transfer coefficient, m/t3.T, W/m2.K
enthalpy, L2 /t2 , J/Kg
rate of enthalpy inlet from source/sink per unit volume,m/Lt3 , W/m3
thermal conductivity, mL/t3 T, W/m.K
rate of mass inlet from source/sink per unit volume, m/L3 t,
Kg/m3.s
rate of momentum inlet from source/sink per unit volume,m/L2 t2 , Kg/m2.s2
Nusselt number
pressure, m/Lt2 , Pa
Prandtl number
rate of heat transfer from the wall per unit volume, m/Lt3 ,W/m3
inner radius, L, mouter radius, L, m
thermal resistance, Lt3T/m, m3.K/W
Reynolds number
time, t, s
temperature, T, K
velocity, L/t, m/s
length in direction of the well (measured depth), L, mvertical position, L,mviscosity, Pa.s, Kg/m.s
density, m/L3 , Kg/m3

Fig. 1. HPHT tiers and operating range for deep CLGS wells (well information courtesy of Total, 2012 [24]). The box in red shows the operating range for deep CLGS
wells considered here.

most regions within the US, most prominently in the western states andin south-east Texas. Thus, to access these reservoirs, it is necessary todrill wells that are deeper than existing wells.
Drilling deeper CLGS wells with longer lateral sections is technicallydifficult due to the extreme high-pressure, high-temperature (HPHT)
conditions, the challenges associated with accurate directional drillingat depth, well integrity issues, etc. Technologies already developed in
the oil and gas sector have the potential to meet these challenges and canbe extended to deep geothermal drilling. Note that deep vertical wells

have already been drilled up to 12 km true vertical depth (TVD). Two
examples are the deep vertical wells drilled in Russia at the Kola
Peninsula (12+ km) [19] and the KTB site in Germany (9+ km) [20].
Directional drilling techniques have also enabled drilling of very longhorizontal sections [21,22]. Wells with total Measured Depths (MDs) of
up to 15 km have been drilled using directional drilling and extended
reach drilling (ERD) techniques [23]. As of 2012, multiple oil and gas
exploration wells have been drilled in the operating range of the pro­
posed deep CLGS, with in-situ temperature up to 290 ◦ C (Fig. 1). In order2

A. Fallah et al.

Energy Conversion and Management 236 (2021) 114056

reserve. Using the MPO system to apply surface backpressure, it ispossible to both control the pressure–volume-temperature (PVT) dy­
namics of the circulating fluid, as well as add additional hydrostaticpressure to maintain mechanical wellbore integrity in the lateral openhole section. Moreover, by maintaining the pressure profile within the
open-hole lateral section, the MPO system avoids reservoir influx into
the wellbore (in case the reservoir rock is permeable) and eliminates
fluid contamination issues. Finally, the energy is extracted from thehigh-temperature fluid in a turbine or heat exchanger, and the cooled
fluid is re-injected into the wellbore.
To evaluate the feasibility of the integrated DCLGS with MPO
concept as an economically viable power source and establish an
analytical foundation for subsequent MPO control design, it is essential
to first develop a thorough understanding of the hydraulic and thermal
behavior of the fluid under the pertaining HPHT conditions of a DCLGS
well. There are a few thermal models for the estimation of temperature
profiles in U-shaped CLGSs in the published literature. Sun et al. [26]provides a literature review of U-shaped systems. Numerical models of
Sun et al. [27] and Sun et al. [28] estimate the steady-state temperature
profile in U-shaped wells using supercritical CO2 as the working fluid.
Schulz [10], Oldenburg et al. [17], and Song et al. [29] have developedmodels for simulating shallow U-shaped geothermal wells using water as
the working fluid. These models can provide estimation of the temper­
ature profiles over the lifetime of low-temperature CLGS wells. How­ever, fast transients and short-term effects, such as those caused bychanging the pump rate, are not considered in these models. Moreover,since capturing pressure wave behavior is required for dynamic wellcontrol, such models can only simulate cases where casing and heat
conducting cement are used to seal off the horizontal section and well­bore stability is already ensured. In order to evaluate the feasibility of
implementing DCLGS with commercial viability and to perform a sub­sequent control design, a transient dynamic thermal and hydraulicmodel is needed.
An integrated thermal and hydraulic model was developed toaddress this need and to evaluate the feasibility of the proposed DCLGS
concept and ensure real-time MPO control. Details of this transientmodel development are presented in this paper, followed by a wide
range of simulation scenarios that illustrate the potential of the DCLGS
design under different conditions. Note that the lifetime performance ofthe geothermal system is beyond the scope of this paper. The long-timethermal depletion around the wellbore and the consequent power
reduction can be estimated using external formation heat transfer
models [30,31]. The main contributions of this paper are 1) introducing
the concept of integrating an MPO control system with a deep CLGS wellthat enables access to high temperature reservoirs globally; 2) consid­
ering an open-hole completion of the lateral section for improved heattransfer and to avoid cementing issues at high temperature; 3) devel­
oping a transient model that can describe the highly coupled dynamic
thermal and hydraulic behavior of the well to pave the way for MPO
control design; and 4) enabling both base load support and transientload tracking to displace the spin reserve.

Fig. 2. Schematic of the MPO-controlled deep geothermal well concept,
including (1) inlet section (cased), (2) lateral section (open-hole), (3) outlet
section (cased or VIT-insulated), (4) MPO choke, and (5) turbine/heat exchanger.

to generalize the existing drilling techniques for deep wells and push theoperation boundary into the red color circled zone of Fig. 1, it isnecessary to develop a thorough understanding of the well hydraulics at
depth and enable the development of transient behavior controller. As
indicated below, the concept of CLGS is first introduced.
1.1. Deep CLGS concept introduction
Fig. 2 shows the concept of a DCLGS well with an integrated
managed pressure operation (MPO) system. The geothermal well in thisparticular example is U-shaped and consists of two vertical wellbores.
These wellbores are drilled to the desired temperature region (200+ ◦ C)
and connected by a long horizontal section (note that other DCLGS
configurations are possible as well, but we are limiting the discussion
here to a U-shaped well). This lateral section is preferably completedwith an open-hole or “barefoot” completion, allowing for direct contact
and efficient heat transfer between the fluid and the high-temperaturerock. Moreover, an open-hole completion of the lateral section avoids
practical problems with running casing and cementing downhole atextremely high temperatures. Due to the varying energy demand expe­
rienced by DCLGS wells and the frequent temperature cycling associatedwith operating, starting, and shutting down of the well, thermal
expansion and contraction of the casing and maintaining integrity of thecement sheet may present major issues. Such problems are eliminatedfor the lateral section when it remains open to the formation as proposedby this study (note that the temperature cycling will still be an issue forthe cased-hole sections of the well). For power generation, lowtemperature working fluid is pumped into the well and is heated as it
flows through the inlet vertical section of the well and the horizontal
lateral section, absorbing energy from the surroundings. The outlet
vertical section of the well could be thermally insulated to avoid heatloss to the formation when the high-temperature fluid returns to surface.
An automatic MPO system, analogous to a managed pressure drilling(MPD) system used for the drilling of challenging oil and gas wells [25],is used to manage the pressure of the fluid flowing out of the exitingwell. The MPO system will not only support the grid base load but also
provide the load following capability that normally comes from the spin

2. Thermal and hydraulic modeling
Our integrated thermal and hydraulic model to simulate DCLGS
wells uses transient conservation equations to estimate different pa­
rameters, such as the dynamic temperature profiles and the generated
power during the power generation phase. The model consists of onedimensional conservation equations of the wellbore flow, an external
heat transfer network between the wellbore flow and the rock forma­tion, sub-models that calculate the properties of the water as functions ofpressure and temperature, and a semi-implicit numerical scheme thatsolves the transient conservation equations. Details can be found in
Fallah et al. [32,33], where an advanced thermal and multi-phase flow
simulator was designed for kick simulations during oil and gas welldrilling applications. The transient and steady-state results of the model3

A. Fallah et al.

Energy Conversion and Management 236 (2021) 114056

Fig. 3. Discretization of rock formation for heat transfer calculations for a cased section of the well (with bi-lateral symmetry). The casing and cement sheet areomitted when simulating open-hole well sections.

were validated against experimentally-validated analytical solvers [34]and commercial software [35], where a maximum discrepancy of 2 ◦ C
was observed. Results of the validation are provided in this paper(Appendix A. Model Validation). Note that in the proposed DCLGS
concept, the MPO system controls the PVT behavior of the working fluid
and avoids reservoir influx, reducing the flow to a single-phase liquidflow at all times. The modeling equations are briefly summarized below.

based on the transient flow rate and temperatures at the inlet and outletof the well (e.g., pump inputs). The gravitational force and wall friction
terms in the momentum equation are calculated as [36]:2.1. Conservation equations

fg = ρgcos(θ)(6)

1 fD ρv2
2 D(7)

fw = −∂ρ ∂ρv+= ṁsource
∂t ∂x

(1)

where θ is the hole deviation from the vertical direction, fD is the Dar­cy–Weisbach friction factor (calculated from Ahmed and Miska [37]),
and D is the hole diameter. The external heat transfer in the energy
equation is calculated in the heat transfer network, discussed in thefollowing.
The boundary conditions used to solve Eqs. (1)–(3) include the pumprate and inlet temperature at the wellbore inlet, as well as the wellbore
outlet pressure which is enforced by the automated MPO system. The
inlet pressure, output flow rate, and outlet temperature are calculated by
the numerical scheme.

∂ρv ∂ρv2∂p+= −+ f + f + Ṁ source∂t∂x∂x g w(2)

2.2. Heat transfer network

The conservation equations of the entire system consist of a onedimensional system of mass, momentum, and energy conservation
equations to describe the water flow in the well (Eqs. (1)–(3)). The
equations are derived from the transient Navier-Stokes equations forpipe flow and account for turbulent friction forces, liquid compress­
ibility, and temperature-dependent water properties:(

Heat transfer between the wellbore flow and the rock formation,
which are separated by casing and cement for cased-hole sections andare in direct contact for open-hole sections, as well as inside the rockformation is calculated using the heat transfer network shown in Fig. 3.
The rock formation is discretized radially to account for the formation
temperature dynamics in close vicinity of the well. Due to the negligible
temperature gradients in the axial direction, only the radial heat con­duction inside the rock formation is taken into account [32]. The
number of radial cells used to discretize the rock formation is changed
automatically, such that the temperature change of the cell furthest fromthe well (the leftmost cell in Fig. 3) remains below a predefined
threshold. Once the temperature change in the last cell exceeds thethreshold, a new radial cell is added to the end of the heat transfer
network. The dynamic discretization of the rock formation saves
computational power by only discretizing the rock formation in the re­gions with significant temperature changes.
The heat transfer between the wellbore and the first formation nodeis calculated as:)∂ρ(e + 12v2 + gz) ∂ρv(h + 12v2 + gz) ∂∂T+=k+ q̇wall + Ḣ source
∂x
∂t
∂x
∂x

(3)

where t is time, x is the length along the direction of the well (measured
depth, MD), ρ is density, v is velocity, ṁsource is the rate of mass gener­
ation per unit volume from sources, p is pressure, fg is gravitational force

per unit volume, fw is wall friction per unit volume, Ṁsource is the rate of
momentum generation per unit volume from sources, e is the internalenergy, g is the gravitational acceleration, z is the vertical depth, h isenthalpy, k is thermal conductivity, T is temperature, q̇wall is the rate ofexternal heat transfer per unit volume through the walls, and Ḣsource isthe rate of enthalpy generation per unit volume from sources. Internalenergy and enthalpy are defined as:∫Te=cv (T)dT + e0
(4)T0

h = e + p/ρ

(5)where cv is the specific heat capacity at constant volume, and T0 and e0
are reference temperature and internal energy.
The two terms on the left-hand side of Eqs. (1)–(3) refer to theconservation and convective terms, respectively. The terms on the righthand side are the source and sink terms for each equation. The rate ofmass, momentum and energy generation from sources are calculatedq̇wall =T1 − TwR(8)

where T1 is the temperature of the first formation cell, Tw is the tem­
perature of the water in the well, and R is the thermal resistance. Total
thermal resistance is calculated by summing the individual resistances
between the water and the first cell (i.e., convection in the water, con
4

A. Fallah et al.

Energy Conversion and Management 236 (2021) 114056

duction through the casing and cement (which is zero in open-hole), andconduction in the rock formation). The heat transfer between the adja­
cent formation cells is calculated similarly, where the resistance is only
the conduction resistance through the rock. Each individual conduction
or convection resistance is calculated as:
Rconduction =Rconvection =Aln(rroi )
2πks
A
hπ D

(9)
(10)

where A is the cross-sectional area of the well, ro and ri are the outer andinner radius of the solid across which heat is being conducted, ks is the
conductivity of the solid, D is the diameter of the wall at which heat isbeing convected, and h is the convection coefficient. The convection
coefficient is defined as:
h=

Nuk
D

(11)

where k is the conductivity of water, D is the diameter of the hole, andNu is the Nusselt number calculated from Eq. (12) [38]:⎧4,laminar flow
⎪
⎪
⎪
( )
⎪
⎪
f
⎨
(Re − 1000)Pr
Nu =
(12)
8
⎪
⎪
⎪
( 2
)√̅̅f̅ , turbulent flow⎪⎪
⎩ 1 + 12.7 Pr3 − 1
8Fig. 4. Solution procedure of the semi-implicit numerical scheme at eachtime-step.

k = − 5.71*10− 6 *T 2 + 1.64*10− 3 *T + 5.69*10− 1

where Re and Pr are the Reynolds number and Prandtl number,respectively.

where temperature is measured in ◦ C, viscosity in Pa.s, specific heat
capacities in J/Kg.K, and thermal conductivity in W/m.K.

2.3. Water properties
In a first approach, we assume that water is used as the circulation
fluid. This is not a restriction of DCLGS wells, and other working fluids
such as supercritical CO2 can also be considered. Due to the extreme
pressure and temperature conditions in the DCLGS well, assuming
constant properties will lead to large errors. Water viscosity, forexample, decreases by a factor of 18 from 0 ◦ C to 300 ◦ C. Therefore,
fitted polynomial models of water properties are used to calculate thedensity, viscosity, specific heat capacity at constant pressure and con­stant volume, and thermal conductivity [39,40]. Density is modeled by afirst-order polynomial function of pressure combined with a secondorder polynomial function of temperature as:ρ=p− 0.0026*T 2 − 0.1594*T + 1001.5515
1490.92.4. Numerical scheme
To solve the conservation equations, the wellbore is discretized in
the axial direction. A semi-implicit numerical scheme is used to enablereal-time simulations. Details of the semi-implicit numerical scheme andthe discretization of Eqs. (1)–(3), as well as the validation of the dis­cretization method are provided by Evje and Fjelde [41]. Using small
time-steps on the order of 10− 3 s (with a mesh size of 25 m), the model
captures the pressure waves in the water column, which is necessary for
operating the automatic controller that maintains the surface back­pressure. The time-step and mesh size are selected such that the solution
is stable, accurate, and independent of the selected time-step and meshsize. Fig. 4 shows a flowchart of the computational scheme used by themodel. The subscripts and superscripts in the figure refer to the cellnumber and time-step, respectively. First, the mass conservation equa­tion and the density model are used to obtain the density and pressure ateach new time-step. Using the updated pressure, the pressure gradientterm in the momentum equation is calculated (implicitly). The implicit
calculation of the pressure gradient guarantees the numerical stability ofthe software [41]. Subsequently, velocity and temperature are updated
using the momentum and energy conservation equations, respectively.

(13)

where pressure is measured in Pa, temperature in ◦ C, and density in kg/
m3.
Neglecting the effect of pressure, the viscosity, specific heat capac­
ities, and thermal conductivity are assumed to be functions of temper­
ature and are modeled as:{μ=

3.27*10− 11 *T 4 − 9.14*10− 9 *T 3 + 9.93*10− 7 *T 2 − 5.56*10− 5 *T + 1.79*10− 3 , T < 100 ◦ C− 2.025*10− 11 *T 3 + 1.72*10− 8 *T 2 − 5.18*10− 6 *T + 6.44*10− 4 ,T ≥ 100 ◦ C

cp = 1.16*10− 4 *T 3 − 2.35*10− 2 *T 2 + 1.61*T + 4.17*103(15)

cv = 3.40*10− 5 *T 3 − 1.01*10− 2 *T 2 − 3.95*T + 4.24*103

(16)

(17)

(14)

The energy equation is assumed to be de-coupled from the mass andmomentum equations since the temperature dynamics are much slower
than the mass dynamics. Finally, the properties of the water and source/
sink terms in Eqs. (1)–(3) are updated for the next time-step.
5

A. Fallah et al.

Energy Conversion and Management 236 (2021) 114056

2.5. Automated choke control

Table 1
Relevant geometrical, formation, fluid and geothermal parameters used in thesimulations.

Due to the high temperatures in the well, water will boil as it is being
circulated back to surface. Large differences between the densities ofliquid water and water vapor lead to a large drop in hydrostatic pres­sure. This change in pressure makes control over the bottomhole pres­sure (BHP) and maintaining well integrity (in the case of an open-holecompletion) challenging. Reservoir fluids could also enter the well(through any exposed permeable formations and fractures) and pollute
the water that is circulated out of the well. Moreover, evaporation could
lead to excessive pressures on surface due to the expansion, resulting insafety hazards and risks and compromising wellbore integrity control.
To address these issues and control the water’s PVT behavior, return
flow is controlled using an automatic choke such that the entire opera­tion is under MPO control at any time. The proposed MPD system isanalogous to the MPD system used in the oil and gas industry(Appendix B. Managed Pressure Operation). A polynomial fit of thepressure as a function of temperature is presented in Eq. (18). The
boiling pressure monotonically increases with the temperature [39]. At
any given temperature, water starts boiling if the pressure is below theboiling pressure threshold.

Geometry
Vertical depth
Horizontal length
Build radius
Hole size (open-hole)
Hole size (casing)

31.788 cm

Casing/cement
1 cm/2.5 cm
thickness
Geothermal Temperature
Downhole
250/340 ◦ Ctemperature
Temperature gradient0.03 ◦ C/mWorking fluid

Water

Density
Viscosity
Specific heat
capacities
Thermalconductivity
Formation Properties

Eq. (13)
Eq. (14)
Eq. (15) and(16)
Eq. (17)

Density
Heat capacity

2700 kg/m3
1000 J/kg.K

Thermalconductivity

2.5 W/m.K

drilled from the two independent wells that intersect at their endpoints), referred to as the “7/7” geometry. The wellbore diameter inthe open-hole lateral section is assumed to be 31.115 cm (12.25 in, inline with industry standard production hole diameters in oil and gas
wells) and the build radius of the curve sections of the well is assumed to
be 200 m. The initial temperature of the water in the well is assumed tobe equal to the temperature profile of the surrounding rock, linearly
increasing from 40 ◦ C at surface to 250 ◦ C at 7 km TVD (a temperaturethat is observed at this vertical depth in locations such as the Los Angeles
metropolitan area [18]). The second well has a TVD of 10 km with a 5
km lateral section, referred to as the “10/5” geometry. The geothermal
temperature gradient with depth is assumed to be constant and the samefor the two geometries, leading to a bottomhole temperature of 340 ◦ C
for the “10/5” geometry. For both geometries, the density, heat capac­
ity, and thermal conductivity of the rock formation are set to be 2700
kg/m3, 1000 J/kg.K, and 2.5 W/m.K, respectively. These values repre­
sent average crust properties [43]. While these values depend on therock formation, they do not vary significantly among different rocktypes [44]. Hence, for different sets of formation properties, the resulted
output temperature and generated thermal power behavior are similar
with small variations. Table 1 provides the parameters used in thesimulations. In these case studies, water is pumped continuously for 20
h. During the simulation, the automatic controller is used to apply
enough backpressure to avoid water evaporation and associated pres­sure reduction in the wells. The inlet and outlet vertical sections use
33.973 cm (13.375 in) outer diameter casing. Casing and cement
thicknesses for the cased sections are set to be 1 cm and 2.5 cm,
respectively.
Figs. 5 and 6 show the water, rock formation (first node), and initial
temperatures versus MD at different times into the simulation for the “7/7” and “10/5” geometries, respectively. Water temperature is initiallyassumed to be in thermal equilibrium with the rock formation (e.g., afteran extended shut-in period of no circulation). When pumping starts,
high-temperature water in the horizontal section is pumped out of thewell and replaced by cold water from the inlet section of the well. Aftercontinuing pumping for a few hours, a semi-steady-state is reached inwhich all the water is displaced by the cold water from the inlet sectionof the well. During the process, the surrounding rock temperature con­tinues to decrease due to the heat transfer to the water (i.e., thermal
depletion of the well). As the water is circulated up in the return section,
the temperature of the surrounding rock drops, causing a heat loss fromthe water to the cold rock formation near surface. The maximum
gradient in the temperature profile is observed at the beginning of thehorizontal section, where the temperature difference between the waterand un-cased formation is at a maximum. It is observed that theincreased pump rate between 13 and 16 h into the simulation reduces
the temperature profile along the well. This is because with thepboil = 1.57*10− 3 *T 4 − 2.44*10− 1 *T 3 +3.30*101 *T 2 − 1.77*103 *T +3.46*104(18)
In Eq. (18), temperature is measured in ◦ C and pressure in Pa. Deepin the wellbore itself, the hydrostatic pressure of the water column ap­
plies sufficient pressure to avoid boiling downhole, even for extreme
temperature gradients and high absolute downhole temperatures. The
well location where boiling is most likely to occur is on surface at theoutlet (see Fig. 3) due to the reduced hydrostatic pressure. Therefore, aproportional integral (PI) controller that enables MPO was designed tomaintain a surface backpressure (SBP) above the boiling pressure byadjusting the choke opening automatically. Note that the MPO system
plays a crucial role in the proposed DCLGS concept. The MPO system
controls the fluid PVT behavior, maintains pressure control across theopen lateral, ensures well integrity, and avoids reservoir influxes andfluid contamination. Simulating the automated choke control behavior
relies on capturing the pressure wave dynamics and the fast transientsassociated with rapid choke adjustments. In this paper, we simulate
choke opening manipulation such that:psurface = pboil (T) + SM

Fluid Properties
7000/10000m
7000/5000 m
200 m
31.115 cm(19)

where psurface is the SBP that is maintained by the choke, pboil is theboiling pressure on surface (which is a function of the outlet tempera­ture), and SM is an additional safety margin that may also account forexcess pressure needed for maintaining wellbore stability in exposed
open-hole sections in the well (note that this term can be further
delineated if real-time estimation of pore pressure and the pressure re­quirements for wellbore stability is possible, see e.g. Zoback [42]).
Temperature data collected at a one-minute-or-higher frequency areused in the model to calculate the boiling pressure and maintain therequired SBP. For the simulations presented here, the safety margin is set
to 1 MPa.
3. Simulation scenarios
To demonstrate the utility of the model in simulating the operation
and well control of DCLGS wells, two cases with different geometries are
discussed here. In both cases, water is pumped at 300 m3/h into a Ushaped well for 13 h, followed by a 3-hour pumping at 400 m3/h, and 4 hof pumping at 350 m3/h. The simulated scenario shows how the dy­
namic temperature and generated power change with the changes of thepump rate. The first well consists of two 7 km deep vertical sections(which would be drilled independently) that are connected through a 7
km horizontal section (which could be drilled as two 3.5 km sections
6

A. Fallah et al.

Energy Conversion and Management 236 (2021) 114056

Fig. 5. Temperature profile at different times for the “7/7” geometry (with open-hole lateral).

Fig. 6. Temperature profile at different times for the “10/5” geometry (with open-hole lateral).

increased pump rate and fluid velocities within the wellbore, water hasless time to be heated up as it moves along the well.
In the lateral section, water temperature increases along the welldirection due to the heat transfer with the formation at 250 ◦ C or 340 ◦ C
for the “7/7” and “10/5” geometries, respectively. The temperature
gradient along this section slowly decreases as the water and formation
temperatures increase towards the geothermal temperature, reducing
the temperature difference (cf. Figs. 5 and 6). Theoretically, in an infi­
nitely long lateral section, water temperature will reach the maximum

possible downhole temperature, which is equal to the undisturbed insitu formation temperature. However, as the lateral length increases,
the total cost and complexity of drilling increases, while the gain in
power generation declines. Therefore, there exists an optimum lateral
length beyond which the gain in power generation does not compensate
for the extra cost of drilling. This optimum length depends on otherparameters as well, most importantly the TVD (or equivalently, themaximum geothermal temperature reached), the pump rate, and thehole size. The developed model can be used to determine the optimum
7

A. Fallah et al.

Energy Conversion and Management 236 (2021) 114056

Fig. 7. Pressure profile at different times for geometries (with open-hole lateral).

Fig. 9. SBP and choke opening versus time for both geometries (with openhole lateral).

demand of the pumps. The thermosiphon effect is reduced as the tem­
perature in the outlet section of the well decreases towards the steadystate temperature. With the changes in pump rate (at 13 h and 16 h
into the simulation), the frictional pressure drops along the wellchanges. It is observed that the increased pump rate of 400 m3/h at 950
min into the simulation results in a higher BHP compared to the BHP at
1200 min (350 m3/h) and 750 min (300 m3/h). The BHP changes need
to be accounted for when determining the required SBP for well control
over the open-hole lateral section.
Fig. 8 shows DCLGS outlet temperature, the net thermal power
generation, and the outlet flow rate for both geometries while thepumping rate begins at 300 m3/h, increases to 450 m3/h between 780
and 960 min, and reduces to 350 m3/h after 960 min. It is noted that thepower values do not include any losses at surface due to power con­version in e.g., steam turbines: the numbers reflect the net thermal
power that is generated by the producing well only. While the pumpflow rate is kept at 300 m3/h for the first 780 min into the simulation,
oscillations are observed in the outlet flow rate during the early stages ofpower generation. These variations are mainly caused by the compres­sion and expansion of the water due to pressure changes in the well(Fig. 7), as well as the thermal expansion behavior of the water within
the wellbore. During the first 50 min, the hydrostatic pressure decreases
due to the elevated temperatures in the return section of the well. This
causes water expansion in the well and increases the outlet flow rate. At

Fig. 8. Outlet temperature, thermal power and outlet flow versus time for bothgeometries (with open-hole lateral).

well geometry and pump rate for well design and efficient power gen­eration for a given set of subsurface pressure and temperature
conditions.
Fig. 7 shows the pressure profile at different times for both geome­tries. The pressure profile is affected by the hydrostatic pressure, fric­tional pressure drop, and SBP. While the pressure is mostly determinedby the hydrostatic pressure, a small pressure drop is observed in thehorizontal section due to friction for both geometries. At around 100
min, hot water that was initially in the well reaches surface and SBP isincreased due to the higher outlet temperature, requiring a higher
pressure to avoid boiling. At this time, because of the high temperature
difference between the inlet and outlet sections of the well, the density
and hydrostatic pressure in the outlet section of the well reduces,resulting in a lower BHP. The higher hydrostatic pressure gradient in theinlet section of the well results in a zero pumping pressure, a situation
known as the thermosiphon effect [45], which reduces the power8

A. Fallah et al.

Energy Conversion and Management 236 (2021) 114056

Fig. 10. Temperature profile at different times for the “7/7” geometry (with cased lateral).

Fig. 11. Temperature profile at different times for the “10/5” geometry (with cased lateral).

50 min, the MPO system starts to increase the surface backpressure to
avoid evaporation. Due to the increased backpressure and the resulting
compression of the water, the outlet flow rate is decreased after thistime. As steady-state approaches, the outlet flow rate converges to thepump rate value. When the inlet pump rate changes at 780 and 960
minutes, the outlet flow rate converges to the inlet pump rate and thewellbore reaches steady-state again.
The generated thermal power depends on the outlet temperature andoutlet flow rate. During the initial stages of circulation, the hightemperature water that initially stays at bottomhole is circulated to­wards surface, increasing the outlet temperatures and the resulting
thermal powers. Thereafter, the temperature and power slowly decrease
with time due to the cooling of the heat-supplying rock, with somevariations in the generated power caused by the varying outlet flow rate.
At 780 min (300 m3/h), the outlet temperature and net thermal power
for the “7/7” geometry are 128 ◦ C and 30.6 MW (168 ◦ C and 44.0 MW
9A. Fallah et al.

Energy Conversion and Management 236 (2021) 114056

sufficient SBP to avoid evaporation and maintain well control. A
maximum SBP of 2.5 MPa and 4.5 MPa is applied at 75 min for the “7/7”
and “10/5” geometries, respectively. As the temperature and boilingpressure decrease, the choke is slowly opened to reduce the excessive
SBP, while maintaining a safety margin of 1 MPa (assuming in this casethat no excess safety margin is needed for open-hole stability control in
the horizontal lateral). Varying the pump rate will affect the outlet
temperature, and the choke is automatically adjusted to maintain the 1
MPa safety margin while the boiling pressures vary.
3.1. Effect of cementing the lateral section
While cementing and casing problems can be avoided through openhole completion of the lateral, it may not always be feasible to drill andmaintain long open-hole lateral sections. In this case, the lateral section

Fig. 12. Outlet temperature and thermal power versus time for both geometries(with cased lateral).

for the “10/5” geometry). With the pump rate increasing at 780 min, thenet thermal power is increased to 40.0 and 60.2 MW for the “7/7” and“10/5” geometries, respectively. However, as the higher pump rate ismaintained, the outlet temperature slowly decreases due to the reduced
heat transfer time, thus reducing the generated thermal power. At 960
min, the pump rate drops to 350 m3/h, which reduces the net thermal
power. However, as the circulation is continued, wellbore temperatures
are recovered due to the improved heat transfer time at lower fluid
velocities, increasing the outlet temperature and thermal power. At
1200 min, the outlet temperature is 109 ◦ C and the resulting net thermal
power is 28.1 MW for the “7/7” geometry. (142 ◦ C and 41.4 MW for the“10/5” geometry).
Fig. 9 shows the SBP and choke opening versus time. As the outlet
temperature increases between 0 and 170 min (Fig. 8), the boilingpressure increases according to Equation (18). The automated controller
calculates the boiling pressure, adjusts the choke opening, and applies

Fig. 14. Comparison of the outlet temperature and the generated power fordifferent pump rates.

Fig. 13. Comparison of the temperature profiles for different pump rates.
10

A. Fallah et al.

Energy Conversion and Management 236 (2021) 114056

Fig. 15. Comparison of temperature profiles for uninsulated versus insulated wellbores.

3.2. Effect of pump rate
For a given well geometry, the generated power can be controlled byadjusting the pump rate. In this section, the effects of three different
pump rates (i.e., 250, 350, and 450 m3/h) on the power generation of
the “7/7” well geometry are compared. In each case, the pump rate ismaintained for 20 h until steady-state is reached. Fig. 13 shows thewater temperature profile of the three different pump rates. The higher
flow rate for the case of 450 m3/h pump rate results in a lower output
temperature compared to the other two cases with lower pump rates.
This is because at higher pump rates, the water has less time flowing
through the inlet and lateral sections, thus less time to absorb the heatfrom the surrounding formation. Fig. 14 shows the outlet temperatureand the net thermal power during the first 20 h of pumping. The
maximum outlet temperature is reached at 194, 132 and 99 min for the
250, 350 and 450 m3/h cases, respectively. The outlet temperatures at
1200 min are 128, 109 and 96 ◦ C for the three cases, correspondingly. Itshould be noted that the generated power slightly increases with therising pump rate despite a lower outlet temperature. This is due to theincreased mass flow rate through the well which carries more thermalenergy per unit time to the surface and compensates for the lower output
temperature. After 1200 min, the generated thermal powers of the 250,
350 and 450 m3/h cases are 25.5, 27.9 and 29.3 MW, respectively.
Varying pump rate, and associated SBP changes controlled by the MPO
system, is therefore an effective way to deal with an ever-changing
commercial power demand, which can also reduce the thermal deple­
tion and improve the life-time performance of the well.

Fig. 16. Comparison of the outlet temperature and the generated power foruninsulated versus insulated wellbores.

needs to be cased and cemented to ensure wellbore integrity. Figs. 10–12
show the temperature profiles and the generated thermal power forcased lateral sections for both geometries. The outlet temperatures at
1200 min (where the pump rate is 350 m3/h) are 110 ◦ C and 142 ◦ C for
the “7/7” and “10/5” geometries, respectively. The outlet temperatures
result in net thermal powers of 28.2 MW and 41.4 MW for the “7/7” and“10/5” geometries, respectively. These values are similar to the caseswith open-hole lateral, showing that the heat transfer is mostly limitedby the slow heat conduction in the rock formation.

3.3. VIT insulation effectFigs. 15 and 16 show the effect of insulating the outlet section of thewell using VIT. In this section, the geometry of the “7/7” geometry isused with a constant pump rate of 350 m3/h. Two cases are compared:(1) using a conventional casing string and cement sheet similar to theinlet section of the well (referred to as the “original case”) and (2)insulating the near surface parts of the return section of the well where11

A. Fallah et al.

Energy Conversion and Management 236 (2021) 114056

the rock temperature is lower than the fluid temperature (referred to as
the “insulated case”). In this case, the optimum insulated depth is 2 km,
where the remaining parts of the return section are cased and cemented.
Fig. 15 shows the temperature profile of the two cases at different
times. Temperature profiles are similar along the inlet and lateral sec­
tions of the well for both cases due to the same external conditions.
However, the heat loss to the near-surface surrounding rock in theoriginal case results in a temperature drop along the top 2 km of theoutlet section of the well. This effect is more pronounced at around 100
min due to the larger temperature difference between the water and therock formation behind the cement sheet, resulting in more heat loss. At
1200 min, a temperature drop of about 2 ℃ is observed in this case,while the temperature in the outlet section of the well near surface forthe insulated case remains relatively unchanged. This effect would be
more pronounced in deeper wells that produce higher outlet
temperatures.
Fig. 16 compares the outlet temperature and thermal power gener­
ation for the two cases. At 1200 min, the thermal power of the insulatedcase is about 0.6 MW higher than that of the non-insulated case,indicating the importance of insulating the outlet section of the well.
The maximum observed surface temperature is 221 ◦ C and 203 ◦ C for
the insulated case and the original case, respectively.

Validation, Formal analysis, Writing - original draft, Visualization.
Qifan Gu: Methodology, Software. Dongmei Chen: Conceptualization,
Methodology, Writing - review & editing, Supervision. Pradeepkumar
Ashok: Conceptualization, Methodology, Writing - review & editing,
Supervision. Eric van Oort: Conceptualization, Methodology, Writing review & editing, Supervision, Project administration, Funding acqui­sition. Michael Holmes: Methodology, Validation.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Acknowledgements
The authors would like to thank the members of the Rig Automation
and Performance Improvement in Drilling (RAPID) group at The Uni­
versity of Texas at Austin, United States for the financial support pro­vided for this project.
Appendix A. Model validation

4. Conclusions

In this appendix the validation results of the thermal model against
experimentally-validated models are provided for reference. More de­tails and the parameters used in the validation case can be found else­
where [33]. Since there is a distinct lack of reliable temperature datafrom test wells and actual wells in the field, the temperature results ofthe model are compared against the single-phase steady-state analyticalsolver of Hasan and Kabir [34] as well as a transient commercial soft­
ware that is based on the hydraulic model of Petersen et al. [35].
The validation case consists of pumping drilling mud at a constantrate of 26.12 m3/h and 26.7 ◦ C into a 4200-m vertical well. Temperature
profiles of the drillstring and annulus fluids are compared in Fig. A1.
Results show a great match between the developed model and thevalidation models, with a maximum temperature discrepancy of 2 ◦ C at
the bottom of the wellbore. The difference can be attributed to thedifferent density models used in each model. However, aside from the

A novel concept of integrating an automated managed pressure
operation (MPO) system with a deep closed-loop geothermal system(DCLGS) for scalable power generation is introduced in this paper.
Compared to existing closed-loop designs, the proposed concept con­siders wells at large well depth to access formations at 200 ◦ C− 350 ◦ C
in-situ temperature and includes an open-hole lateral section to avoid
casing expansion/contraction and cement integrity issues at high tem­
perature conditions. The proposed MPO system applies the required
backpressure through an automatically controlled choke placed at thewell outlet to ensure real-time wellbore integrity over the open-holelateral region and control the phase behavior of the circulating fluid.
To demonstrate the concept’s feasibility, a combined thermal andhydraulic model was developed to describe the transient well hydraulics
during the operation and production stages of the DCLGS. Compared toexisting models in the literature, the proposed model uses a fullytransient semi-implicit algorithm that can capture the pressure waves
and fast transients, which are necessary for MPO control. The model can
predict the generated thermal power for operation scenario with various
true vertical well depth and horizontal length, open-hole or cased-holelateral completions, heat insulation or lack thereof of the return flow,
and changing pump rates. Simulation results show that the proposed
integrated DCLGS concept with wells drilled in temperature environ­ments above 200 ◦ C can initially generate net thermal power in therange of 25–50 MW for a wellbore of 31.115 cm diameter and a circu­
lating flow rate in the range of 300–400 m3/h. The MPO control will
enable geothermal wells to support the base load as well as displace thespin reserve.
Simulation results reveal that optimized thermal insulation of the
return flow near surface could improve the power generation of the
DCLGS well. Casing and cementing of the lateral section (e.g., whennecessary for well control and to avoid influx) does not significantly
affect the thermal performance of the well, which is due to the relatively
small thickness of cement and casing layers. It was also observed thatwhile increasing the pump rate reduces the outlet temperature, thegenerated thermal power could be increased by 15%. The maximum
power generation can be achieved by optimally control the flow rate
such that the energy exchange is maximized.

Fig. A1. Steady-state temperature profiles (from Fallah et al. [33]).

CRediT authorship contribution statement
AmirHossein Fallah: Conceptualization, Methodology, Software,
12

A. Fallah et al.

Energy Conversion and Management 236 (2021) 114056

influx [36].
The same concept could be implemented for the proposed deep
closed-loop geothermal system (DCLGS) concept. The MPO system will
(1) maintain the pressure within the open-hole region to avoid any
reservoir influx and fluid contamination and to ensure wellbore stabil­ity; and (2) control the phase behavior of the working fluid by ensuring
the downhole or pipe pressure is above the evaporation pressure in realtime.
References[1] Watson A. Geothermal engineering. New York: Springer-Verlag; 2016.
[2] Tester J, Anderson B, Batchelor A, Blackwell D, DiPippo R, Drake R, et al. The
future of geothermal energy. Massachusetts Inst Technol 2006:358.
[3] Tester J, Blackwell D, Petty S, Richards M, Moore M, Anderson B, et al. The futureof geothermal energy: an assessment of the energy supply potential of engineered
geothermal systems (EGS) for the United States. Proceedings, Thirty-Second Work
Geotherm Reserv Eng 2007. 2007.
[4] Rybach L. “The Future of Geothermal Energy” and Its Challenges. World Geotherm
Congr 2010:1–4.
[5] Winsloe R, Richter A, Vany J. The Emerging (and Proven) technologies that could
finally make geothermal scalable. Proc. World Geotherm. Congr. 2020;2:1–11.
[6] Polsky Y, Blankenship D, Mansure AJ, Swanson RJ, Capuano LE. In: Enhanced
geothermal systems well construction technology evaluation; 2009. https://doi.
org/10.1190/1.3255790.
[7] Lu SM. A global review of enhanced geothermal system (EGS). Renew Sustain
Energy Rev 2018;81:2902–21. https://doi.org/10.1016/j.rser.2017.06.097.
[8] Olasolo P, Juárez MC, Morales MP, Damico S, Liarte IA. Enhanced geothermal
systems (EGS): a review. Renew Sustain Energy Rev 2016;56:133–44. https://doi.
org/10.1016/j.rser.2015.11.031.
[9] Pan SY, Gao M, Shah KJ, Zheng J, Pei SL, Chiang PC. Establishment of enhanced
geothermal energy utilization plans: barriers and strategies. Renew Energy 2019;132:19–32. https://doi.org/10.1016/j.renene.2018.07.126.
[10] Schulz S-U. Investigations on the improvement of the energy output of a closed
loop geothermal system (CLGS). Technische Universität Berlin; 2008.
[11] Hu Z, Xu T, Feng B, Yuan Y, Li F, Feng G, et al. Thermal and fluid processes in aclosed-loop geothermal system using CO2 as a working fluid. Renew Energy 2020;
154:351–67. https://doi.org/10.1016/j.renene.2020.02.096.
[12] Amaya A, Scherer J, Muir J, Patel M, Higgins B. GreenFire energy closed-loop
geothermal demonstration using supercritical carbon dioxide as working fluid. In:
45th Work. Geotherm. Reserv. Eng.,; 2020. p. 1–19.
[13] Eavor. Eavor-Loop. <https://eavor.com/about/eavor-loop-basics>; 2020.
[14] Yu H, Li Q, Sun F. Numerical simulation of CO2 circulating in a retrofitted
geothermal well. J Pet Sci Eng 2019;172:217–27. https://doi.org/10.1016/j.
petrol.2018.09.057.
[15] Bu X, Ma W, Li H. Geothermal energy production utilizing abandoned oil and gas
wells. Renew Energy 2012;41:80–5. https://doi.org/10.1016/j.
renene.2011.10.009.
[16] Ebrahimi M, Torshizi SEM. Optimization of power generation from a set of lowtemperature abandoned gas wells, using organic Rankine cycle. J Renew Sustain
Energy 2012:4. https://doi.org/10.1063/1.4768812.
[17] Oldenburg CM, Pan L, Muir MP, Eastman AD, Higgins BS. Numerical simulation ofcritical factors controlling heat extraction from geothermal systems using a closedloop heat exchange method. In: 41st Work Geotherm. Reserv. Eng.; 2016. p. 1–8.
[18] Blackwell D, Richards M, Frone Z, Batir J, Ruzo A, Dingwall R, et al. Temperatureat-depth maps for the conterminous U. S. and geothermal resource estimates. Trans- Geotherm Resour Counc 2011;35(2):1545–50.
[19] Kozlovsky Y. The World’s deepest well. Sci Am 1984;251:98–105.
[20] Emmermann R, Lauterjung J. The German continental deep drilling program KTB:
overview and major results. J Geophys Res Solid Earth 1997:102. https://doi.org/
10.1111/j.1365-246X.1991.tb00816.x.
[21] Gupta VP, Yeap AHP, Fischer KM, Mathis RS, Egan MJ. Expanding the extended
reach envelope at Chayvo Field, Sakhalin Island (Russian). Soc Pet Eng - SPE Annu
Casp Tech Conf Exhib 2014;1:1–23.
[22] Ma T, Chen P, Zhao J. Overview on vertical and directional drilling technologies
for the exploration and exploitation of deep petroleum resources. Geomech
Geophys Geo-Energy Geo-Resources 2016;2:365–95. https://doi.org/10.1007/
s40948-016-0038-y.
[23] Rosneft. The World’s Longest Well Was Drilled in Sakhalin; 2017.
[24] Shadravan A, Amani M. HPHT 101-what petroleum engineers and geoscientists
should know about high pressure high temperature wells environment. Energy Sci
Technol 2012;4:36–60. https://doi.org/10.3968/j.est.1923847920120402.635.
[25] Rehm B, Schubert J, Haghshenas A, Paknejad AS, Hughes J. Managed Pressure
Drilling. Elsevier; 2008.
[26] Sun F, Yao Y, Li G. Literature review on a U-shaped closed loop geothermal energy
development system. Energy Sources, Part A Recover Util Environ Eff 2020;42:
2794–806. https://doi.org/10.1080/15567036.2019.1618990.
[27] Sun F, Yao Y, Li G, Li X. Geothermal energy development by circulating CO2 in a Ushaped closed loop geothermal system. Energy Convers Manag 2018;174:971–82.
https://doi.org/10.1016/j.enconman.2018.08.094.
[28] Sun X, Wang Z, Liao Y, Sun B, Gao Y. Geothermal energy production utilizing a Ushaped well in combination with supercritical CO2 circulation. Appl Therm Eng
2019;151:523–35. https://doi.org/10.1016/j.applthermaleng.2019.02.048.

Fig. A2. Bottomhole temperature versus time (from Fallah et al. [33]).

small deviations, the comparisons show a good match both for the
drillstring and annulus temperatures.
Fig. A2 shows the bottomhole temperature versus time for thedeveloped model and commercial software (note that the Hasan and
Kabir model is a steady-state solver and cannot predict transient effects).
The maximum discrepancy is 2 ◦ C, which is observed at 200 min into thesimulation.
Appendix B. Managed pressure operation
The automated managed pressure operation (MPO) system proposedin this paper is analogous to the managed pressure drilling (MPD) sys­
tem used in the oil and gas industry to drill challenging wells. The MPD
system consists of a choke (that is preferably automated) on the outlet
side of the wellbore. By adjusting the choke opening, the amount of
backpressure can be adjusted to control the pressure at the bottomhole(or the entire open-hole section). In oil and gas, MPD systems are used tomaintain the bottomhole pressure (BHP) within tight drilling margins
and avoid/control reservoir influx [46–48]. Fig. B1 shows the perfor­
mance of an automated MPD system in controlling the BHP after a gas

Fig. B1. Performance of automated MPD in controlling the BHP. (courtesy of
Ma et al. [36]).

13

A. Fallah et al.

Energy Conversion and Management 236 (2021) 114056[39] Moran MJ, Shapiro HN, Boettner DD, Bailey MB. Fundamentals of engineering
thermodynamics. John Wiley & Sons; 2010.
[40] Lemmon EW, McLinden MO, Friend DG. Thermophysical Properties of Fluid
Systems. In: Linstrom PJ, Mallard WG, editors. NIST Chem. WebBook, NIST Stand.
Ref. Database Number 69. National Institute of Standards and Technology; 2018.
https://doi.org/10.18434/T4D303.
[41] Evje S, Fjelde KK. Relaxation schemes for the calculation of two-phase flow inpipes. Math ComputModel 2002;36:535–67. https://doi.org/10.1016/S0895-7177(02)00182-6.
[42] Zoback MD. Reservoir Geomechanics; 2010. https://doi.org/10.1017/CBO9780
511586477.
[43] Whittington AG, Hofmeister AM, Nabelek PI. Temperature-dependent thermal
diffusivity of the Earth’s crust and implications for magmatism. Nature 2009;458:
319–21. https://doi.org/10.1038/nature07818.
[44] Eppelbaum L, Kutasov I, Pilchin A. In: Applied Geothermics. Springer Berlin
Heidelberg; 2014. https://doi.org/10.1007/978-3-642-34023-9.
[45] Adams BM, Kuehn TH, Bielicki JM, Randolph JB, Saar MO. On the importance ofthe thermosiphon effect in CPG (CO2 plume geothermal) power systems. Energy
2014;69:409–18. https://doi.org/10.1016/j.energy.2014.03.032.
[46] Gu Q, Fallah A, Ambrus A, Ma Z, Chen D, Ashok P, et al. A switching MPD
controller for mitigating riser gas unloading events in offshore drilling. SPE Drill
Complet 2020. https://doi.org/10.2118/194163-PA. Preprint:17.
[47] Gu Q, Fallah A, Feng T, Bakshi S, Chen D, Ashok P, et al. A novel dilution control
strategy for gas kick handling and riser gas unloading mitigation in deepwater
drilling. J Pet Sci Eng 2020;196:107973. https://doi.org/10.1016/j.
petrol.2020.107973.
[48] Kinik K, Gumus F, Osayande N. Automated dynamic well control with managedpressure drilling: a case study and simulation analysis. SPE Drill Complet 2015;30:
110–8. https://doi.org/10.2118/168948-PA.

[29] Song X, Shi Y, Li G, Shen Z, Hu X, Lyu Z, et al. Numerical analysis of the heatproduction performance of a closed loop geothermal system. Renew Energy 2018;
120:365–78. https://doi.org/10.1016/j.renene.2017.12.065.
[30] Cheng WL, Huang YH, Lu DT, Yin HR. A novel analytical transient heat-conduction
time function for heat transfer in steam injection wells considering the wellbore
heat capacity. Energy 2011;36:4080–8. https://doi.org/10.1016/j.
energy.2011.04.039.
[31] Ramey HJ. Wellbore Heat Transmission. J Pet Technol 1962;14:427–35. https://doi.org/10.2118/96-pa.
[32] Fallah A, Gu Q, Ma Z, Karimi Vajargah A, Chen D, Ashok P, et al. An integrated
thermal and multi-phase flow model for estimating transient temperature
dynamics during drilling operations. SPE/IADC Drill. In: Conf., vol. 2019; 2019.
https://doi.org/10.2118/194083-ms.
[33] Fallah A, Gu Q, Ma Z, Vajargah AK, Chen D, Ashok P, et al. Temperature dynamics
and its effects on gas influx handling during managed pressure drilling operations.
J Nat Gas Sci Eng 2020. https://doi.org/10.1016/j.jngse.2020.103614.
[34] Kabir CS, Hasan AR, Kouba GE, Ameen MM. Determining circulating fluid
temperature in drilling, workover, and well-control operations. SPE Drill Complet
1996;11:74–8. https://doi.org/10.2118/24581-pa.
[35] Petersen J, Rommetveit R, Tarr BA. Kick with lost circulation simulator, a tool for
design of complex well control situations. In: SPE - Asia Pacific Oil Gas Conf.; 1998.
p. 25–33. https://doi.org/10.2523/49956-ms.
[36] Ma Z, Karimi Vajargah A, Ambrus A, Ashok P, Chen D, van Oort E, et al. Multiphase well control analysis during managed pressure drilling operations. In: Proc. SPE Annu. Tech. Conf. Exhib., Society of Petroleum Engineers; 2016. https://doi.
org/10.2118/181672-ms.
[37] Ahmed R, Miska S. Advanced Wellbore Hydraulics. In: Aadnoy Bernt S, editor.
Advaned drilling and well technology. USA Society of Petroleum Engineers. SPE;
2009.
[38] Nellis G, Klein S. Heat transfer. Cambridge University Press; 2009.

14