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Theoretical Modelling of The Effect of Temperature on Co2
Injectivity in Deep Saline Formations.
Yen Adams Sokama-Neuyam*,a , Francis Adu-Boaheneb , Patrick Boakyeb , Jann Rune Ursinc
aDepartment
of Petroleum Engineering, Kwame Nkrumah University of Science and Technology, PMB Kumasi, Ghana.
of Chemical Engineering, Kwame Nkrumah University of Science and Technology, PMB Kumasi, Ghana.
cDepartment of Energy and Petroleum Engineering, University of Stavanger, 4036 Stavanger, Norway
bDepartment
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Abstract
Well injectivity and storage capacity defines the storage potential of a CCUS facility. Formation
temperature have high impact on the phase behaviour and flow properties of CO2 such as density
and viscosity. The effect of temperature on CO2 injectivity, especially in the wellbore injection
inlet is not well understood. We investigated the thermal behaviour of CO2 from the wellhead to
the reservoir using simple theoretical models that capture the major heat transfer mechanisms. The
effect of CO2 injection flow rate and injection time on the temperature of CO2 were studied. The
findings provide vital understanding of the effect of temperature on CO2 injectivity especially in
the wellbore vicinity.
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Keywords: CO2 Temperature; Well injectivity; CCUS; Temperature effects; CO2 storage.
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1. Introduction
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CO2 Capture, Utilisation and Storage (CCUS) is a promising technique to reduce CO2 emission for
mitigation of climate change [1]. The storage potential of a CCUS candidate depends on its storage
capacity and well injectivity [2–4]. In terms of storage capacity, deep saline aquifers have high
potential [5–7]. However, to attain optimal plausibility, adequate well injectivity is required to
inject the target volumes of CO2 through a minimum number of wells. Therefore, a threshold well
injectivity is required to achieve both technical and economic viability of CCUS operations.
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The temperature distribution of reservoir fluids in the well during oil production have been
previously investigated [26–29]. Hasan and Kabir [30] developed analytical models to study
temperature distribution along the well during two-phase flow of oil, assuming a linear temperature
distribution in the formation. Alves et al. [28] derived a unified model for 36 describing and
predicting thermal behaviour of both oil and gas in production and injection wells and pipelines at
different inclinations. More recently, Dong et al. [31] presented a two38 phase flow model for
predicting thermal response of fluids in both open-hole and perforated completion horizontal wells.
Although most of these analytical models have been developed for production of oil and gas, they
*
Corresponding Author:
Email: asokama@knust.edu.gh
Tel: +233 502 568 729
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can be adapted to investigate the thermal behaviour of fluids in injection wells. Several correlations
have also been developed to predict CO2 properties under different temperature and pressure
conditions [32–34]. If the temperature distribution of injected CO2 from the wellhead to the
reservoir is properly modelled, the effect of temperature changes on CO2 injectivity can be
investigated.
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In the present work, analytical models were developed to track the temperature profile of injected
CO2 from the wellhead to the reservoir. The evolution of CO2 temperature around the injection
inlet of the wellbore was then investigated. The impact of injection time and injection flow rate on
the temperature of CO2 around the injection area were also studied. The work begins with
description of the modelling process followed by analysis of results. The findings are then
discussed and some practical implications of the results are suggested, leading to conclusions that
are very fundamental to understanding CO2 injectivity impairment.
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2. Modelling Work
2.1 Model Description
Schematics of the injection well used in the study and associated completion facilities are
presented in Figure 1. CO2 is injected into the vertical well centred in a cylindrical reservoir at a
TVD of 5500 ft. The formation consists of 5000 ft of impermeable shale and 500 ft of clean sand.
The well is cased-hole completed and perforated through the sand. Injected CO2 flows into the
well through the production casing.
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Figure 1. Schematic of the injection well and its associated facilities
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Liquid CO2 is injected into the well at injection flow rate of 𝑤𝐶𝑂2 . The sandstone formation is
assumed to be a saline aquifer fully saturated with formation water. In the reservoir, injected CO2
removes water from the formation through immiscible CO2 – brine displacement. At irreducible
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brine saturation, water is removed through vaporization until complete dryness is attained. A dryout zone is then created around the injection inlet where CO2 flows as single-phase fluid into the
formation. We assume negligible salt precipitation in the dry-out zone.
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Under steady-state flow conditions the temperature of injected CO2,𝑇𝐶𝑂2 at any section of the
vertical well, ∆𝐿 can be derived from the mass, momentum and energy balance equations [28]
2.2 Wellbore Temperature Model
∆𝐿
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∆𝐿
𝑇𝐶𝑂2 = (𝑇𝑓𝑖 + 𝐺𝑓 ∆𝐿) + (𝑇𝐶𝑂2𝑖 − 𝑇𝑓𝑖 )𝑒 − 𝐴 + 𝐺𝑓 𝐴 [𝑒 − 𝐴 − 1]
(1)
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In Eq. (1), friction effects have been neglected. We have also assumed a linear temperature
variation in the formation given by:
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𝑇𝑓𝑖 = 𝑇𝑓𝑖 + 𝐺𝑓 ∆𝐿
(2)
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Where in Eq. (1) and (2), 𝑇𝑓𝑖 is the temperature of the surrounding formation at intake, 𝑇𝑓𝑖 is the
temperature of the formation at the section of the well under consideration, 𝑇𝐶𝑂2𝑖 is temperature
of injected CO2 at intake, 𝐺𝑓 is the thermal gradient of the surrounding formation and 𝐴 is the
thermal relaxation distance given by:
𝐴=
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𝑊𝐶𝑂2 𝐶𝑃
𝜋𝑈𝐷𝑖
(3)
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In Eq. (3), 𝑊𝐶𝑂2 is the mass flow rate of CO2, 𝐶𝑃 is the heat capacity of CO2 at constant pressure, 𝐷𝑖
is the diameter of the production casing and𝑈 is the overall heat transfer coefficient defined as:
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𝑟
𝑟
𝑟𝑐𝑖 ln 𝑟𝑐𝑜 𝑟𝑐𝑖 ln 𝑟𝑤 𝑟
1
𝑟𝑐𝑖
𝑐𝑖
𝑐𝑖
𝑐𝑜
=
+
+
+ 𝑓(𝑡)
𝑈 ℎ𝐶𝑂2 𝑟𝑐𝑖
𝑘𝑐𝑎𝑠
𝑘𝑐𝑒𝑚
𝑘𝑓
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(4)
In Eq. (4), ℎ𝐶𝑂2 is the individual heat transfer coefficient inside the production casing, 𝑟𝑐𝑖 and𝑟𝑐𝑜
is the inner and outer radii of the production casing respectively 𝑟𝑤 , is the radius of the well, 𝑘𝑐𝑎𝑠 ,
𝑘𝑐𝑒𝑚 , and 𝑘𝑓 are the thermal conductivity of the production casing, cement and formation,
respectively and 𝑓(𝑡) is the dimensionless transient heat conduction time function of the formation
given by [30]:
𝑁𝑓𝑜 ≤ 15,
𝑓(𝑡) = 1.1281√𝑁𝑓𝑜 (1 − 0.3)√𝑁𝑓𝑜
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𝑁𝑓𝑜 > 1.5,
𝑓(𝑡) = 0.4063 + 0.5 ln( 𝑁𝑓𝑜 ) (1 +
In Eq. (5), 𝑁𝑓𝑜 is the Fourier number defined as:
0.6
)
𝑁𝑓𝑜
(5)
𝑁𝑓𝑜 =
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𝛼𝑡
𝑟𝑤2
(6)
Where, 𝛼is the thermal diffusivity coefficient of the surrounding formation, and 𝑡 is time. With
appropriate data, Eq. (1) can be used to estimate and track the temperature profile of injected CO2
from the wellhead to the bottomhole.
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2.3 Temperature Profile of Injected Co2
The well and injection data used to simulate the temperature profiles are shown in Table 1. A
constant mass flow rate was used in the calculation of the thermal relaxation distance, 𝐴. CO2 is
injected at the formation intake temperature, 70℉. Equation (1) was used to compute 𝑇𝐶𝑂2
iteratively at every ∆𝐿 = 1𝑓𝑡 from the wellhead to the bottomhole. The temperature difference
between CO2 in the well and the surrounding formation at every section of the well, ( 𝑇𝑓𝑖 − 𝑇𝐶𝑂2 )
was then calculated and plotted as a function of depth. The objective is to study the temperature of
injected CO2 in the well compared to the formation temperature.
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Table 1. Well and injection data used in the simulation
Parameter
Well vertical depth below seabed
Formation intake temperature
Initial CO2 injection temperature
Casing inner radius
Casing outer radius
Wellbore radius
Thermal conductivity of casing
Thermal conductivity of cement
Thermal conductivity of sandstone
Thermal conductivity of shale
Thermal conductivity of CO2
Specific heat capacity of CO2
Thermal diffusivity of sand
Thermal diffusivity of shale
Viscosity of liquid CO2
Density of liquid CO2
Geothermal gradient for sand
Geothermal gradient for shale
Average reservoir pressure
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Symbols
TVD
𝑇𝑓𝑖
𝑇𝐶𝑂2𝑖
𝑟𝑐𝑖
𝑟𝑐𝑜
𝑟𝑤
𝑘𝑐𝑎𝑠
𝑘𝑐𝑒𝑚
𝑘𝑠𝑎𝑛𝑑
𝑘𝑠ℎ𝑎𝑙𝑒
𝑘𝐶𝑂2
𝑐𝑝𝐶𝑂2
𝛼𝑠𝑎𝑛𝑑
𝛼𝑠ℎ𝑎𝑙𝑒
𝜇𝐶𝑂2
𝜌𝐶𝑂2
𝐺𝑓
𝑠𝑎𝑛𝑑
𝐺𝑓
𝑠ℎ𝑎𝑙𝑒
𝜌
Values
5500
70
70
2.446
2.750
4.0
26
0.42
1.06
0.7
0.0536
0.846
0.04
0.02
0.1396
45
0.0083
0.015
3100
Units
ft
℉
℉
in
in
in
Btu/hr-ft-℉
Btu/hr-ft-℉
Btu/hr-ft-℉
Btu/hr-ft-℉
Btu/hr-ft-℉
Btu/lbm-℉
ft2 /hr
ft2 /hr
lbm/ft-hr
lb/ft3
℉/ft
℉/ft
psia
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2.3.1 Effect of injection flow rate on the temperature profile
At the same intake and initial CO2 temperature of 70℉, after 24 hours of CO2 injection, the
temperature difference between injected CO2 and the surrounding formation increases from the
wellhead to the bottomhole (Figure 2). In the well, CO2 is heated by thermal energy transmitted
from the surrounding formation to the well infrastructure. As formation temperature increases with
depth, heat transmitted from the production casing to CO2 in the well also increase with depth.
However, because of the low thermal conductivity of CO2, the injected fluid in the well is heated
at a lower rate compared to the temperature of the formation. Thus, at any point in the well,
formation temperature is higher than the temperature of CO2, even though CO2 was injected at the
formation intake temperature.
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Figure 2. The effect of injection flow rate on the temperature of injected CO2
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2.3.2 Effect of injection time on CO2 temperature profile
The impact of injection time on the temperature profile is shown in Figure 3. CO2 was injected at
a constant injection flow rate of 100 ft3 /hr, the injection time was varied from 2 hours to 1 week
and the temperature difference was computed. Figure 3 shows that the temperature difference
increases with injection time as more CO2 is injected into the well. At start-up of CO2 injection,
only small amount of CO2 is present in the well to be heated. As more CO2 is injected, the
amount of fluid present in the well per time to be heated by the same amount of heat from the
surrounding formation increases. Thus, the effective temperature of CO2 in the well is low and
the temperature difference is increased.
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Figure 3. Effect of CO2 injection time on temperature profile
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High CO2 injection rates are required to meet the global CO2 emission reduction targets [35]. With
typical CO2 injection rates between 0.5 and 2.0 Mt/year, characterized by long injection time, the
temperature difference between CO2 and the surrounding reservoir at bottomhole is expected to be
even higher than the scenarios presented in Figure 2 and Figure 3.
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2.4 Evolution of CO2 Temperature in the Reservoir
A core-scale bundle-of-tubes model is calibrated to track the evolution of CO2 temperature from
the bottomhole into the formation. Although such a model oversimplifies the problem, it captures
the linear flow of fluid and transmission of heat between the rock and the flowing fluid which are
the major mechanisms. The model also offers computational advantage and useful insight of heat
transfer in the reservoir.
2.4.1 Heating of CO2 in a single tube
Assuming CO2 is flowing through a capillary tube of constant radius, 𝑟 under laminar flow
conditions where the velocity and temperature profiles are fully-developed. If the surface of the
tube of length ∆𝐿 is set to a constant temperature 𝜃𝑆 and CO2 is assumed incompressible with
constant mass flow rate, the mean temperature of CO2 in the tube, 𝜃𝑚𝐶𝑂2 can be derived from
Newton’s Law of Cooling as [37]:
𝜃𝑚𝐶𝑂2 = 𝜃𝑆 − [𝜃𝑆 − 𝜃𝑚𝑖 ]𝑒𝑥𝑝 (−
2∆𝐿ℎ
)
𝑣𝑝𝑟𝑐𝑝
(7)
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In Eq. (7), 𝜃𝑚𝑖 is the mean CO2 entry temperature, 𝑣 is the flow velocity, 𝜌 is the density of CO2, 𝑐𝑝
is the specific heat capacity of CO2 and ℎ is the average thermal diffusivity of CO2 in the tube.
Heat is transferred from the walls of the tube to the flowing CO2. The mean CO2
temperature, 𝜃𝑚𝐶𝑂2 increases along the length of the tube until it attain a maximum 𝜃𝑚𝐶𝑂2 = 𝜃𝑆 .
2.4.2 Heating of CO2 in a Bundle-of-tubes
For a cylindrical core, radius 𝑅 and length 𝐿 reconstructed into a bundle of parallel, non-interacting
capillary tubes with varying radii (𝑟1 , 𝑟2 , 𝑟2 … . 𝑟𝑁 ) it can be shown that, the total number of
capillary tubes in the core is given by [38]:
3 𝑅 2
𝑁 = ∅( )
4 ṝ𝑖
(8)
Eq. (8) shows that the total number of capillary tubes depend on the porosity of the core, ∅, average
pore size, ṝ𝑖 , and the core radius, 𝑅. Berea Sandstone core has average pore size of about 6𝜇𝑚 and
average coordination number between 4 and 8 and lognormal pore size 185 distribution as shown
in Figure 4.
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Figure 4. Pore size distribution of Berea Sandstone Rock used in the study.
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Applying Eq.(7) for the bundle-of-capillary-tubes, the mean CO2 temperature, 𝑇𝑚𝐶𝑂2 at every
∆𝐿 = 1𝑓𝑡 of flow distance from the wellbore into the formation can be estimated from a weighted
average of the mean CO2 temperature in each tube:
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𝑇𝑚𝐶𝑂2
2
∑𝑁
𝑖=1 𝑟𝑖 𝜃𝑚𝐶𝑂2𝑖
=
2
∑𝑁
𝑖=1 𝑟𝑖
(9)
Where 𝜃𝑚𝐶𝑂2𝑖 is the mean CO2 temperature in tube with radius 𝑟𝑖 for a total of 𝑁 capillary tubes.
Thus, Eq. (10) can be used to compute the mean CO2 temperature in the core with increasing length
until 𝑇𝑚𝐶𝑂2 is equal to the reservoir temperature.
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2.4.3 Heat gained by CO2 as it flows into the formation
Ergun [39] observed that, for flow in porous media, transition from Darcy to non-Darcy flow
occurs at a critical modified Reynold’s number,𝑅𝑒 between 3 and 10, where:
𝑅𝑒 =
𝑞
𝜌𝐷𝑝 𝐴 1
𝜇 1−∅
(11)
In Eq. (11), 𝐷𝑝 is the average grain diameter and 𝐴 is the cross-sectional area of flow. Figure 5
shows the mean CO2 temperature as a function of the length of the core for different 𝑅𝑒 values
within the Darcy flow regime. For𝑅𝑒 = 0.2, CO2 will attain thermal equilibrium with the
formation at a flow distance of about 600 ft. Figure 5 also shows that the thermal equilibrium
distance increases with 𝑅𝑒 . At higher 𝑅𝑒 , the fluid flows faster through the formation and attains
thermal equilibrium deeper into the formation.
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Figure 5. Evolution of CO2 temperature in the formation
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3. Discussion and Practical Application
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Well injectivity impairment is both a technical and economic challenge in CCUS projects. The
transport properties of CO2 are highly dependent on temperature and pressure. The effect of
pressure on well injectivity has been attracted a chunk of research attention over the past years.
However, the thermal behaviour of CO2 during injection and transport into the formation has
not been given the required attention. It has always been assumed that injected CO2 will attain
supercritical state at wellbore and reservoir conditions. We have investigated the thermal
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behaviour of CO2 under wellbore and reservoir conditions using simplified models that capture
important mechanisms from the wellhead to bottomhole. This section discusses the major
findings and identifies some practical implications. Depending on temperature gradient, the
depth of the formation, injection flow rate and injection time, the temperature of CO2 in the
well is lower than the surrounding formation temperature even if CO2 is injected at the
formation intake temperature (Figure 2 and Figure 3 ). Although the injected CO2 may attain
supercritical condition at bottomhole, CO2 flows into the reservoir at a temperature lower than
the reservoir temperature (Figure 5). At high injection flow rate and long injection time, the
temperature difference increases significantly. To ensure faster thermal equilibrium in the
formation, the CO2 injection flow rate could be optimized to maximize heating in the well.
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4. Conclusion
CO2 Capture, Utilization and Storage (CCUS) is a viable option to reduce global CO2
emission and transition from fossil energy to green economy in the long term. Storage
capacity, well injectivity and containment efficiency have been identified as prerequisites
for CCUS operations. Adequate well injectivity is required to inject large volumes of CO2
through a minimum number of wells. Important injectivity parameters such as density and
viscosity are affected by formation pressure and temperature. The effect of pressure on
CO2 injectivity has been investigated in the past years. However, the effect of temperature
on CO2 injectivity has not been thoroughly investigated.
We developed theoretical models to investigate the thermal behaviour of injected CO2 from
the wellhead to the reservoir. The effect of injection flow rate and injection time on the
temperature of CO2 were also investigated. Some highlights of the study include the
following:




With the same initial CO2 injection temperature and formation intake temperature, the
temperature of CO2 in the well is lower than the surrounding formation temperature
from the wellhead to the bottomhole.
The temperature difference between injected CO2 and the formation increases with
injection time and injection flow rate.
Injected CO2 flows into the reservoir at temperature lower than the reservoir
temperature. The results suggest that CO2 may attain thermal equilibrium with the
formation at a flow distance of about 600 ft into the formation depending on the
injection flow rate and the reservoir temperature.
The resulting thermal instability of CO2 in the wellbore vicinity where fluxes are high
could change CO2 injectivity until thermal equilibrium is attained.
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
The thermal instability of CO2 could also impact viscosity of CO2 and consequently
the mobility of CO2 during CCUS and EOR operations.
The findings provide fundamental understanding of the behaviour of CO2 with temperature in the
reservoir and the consequences on CO2 injectivity especially in the wellbore vicinity. The insight
gained could also serve as a foundation for advanced geochemical and numerical modelling of
CO2 injectivity.
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5. Acknowledgements
The authors would like to thank the College of Engineering and especially the Department of
Petroleum Engineering, KNUST, for their support.
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6. References
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