1 2 3 4 5 6 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 7 8 9 10 11 12 13 14 15 16 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. 17 18 Keywords: CO2 Temperature; Well injectivity; CCUS; Temperature effects; CO2 storage. 19 1. Introduction 20 21 22 23 24 25 26 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. 27 28 29 30 31 32 33 34 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 35 36 37 38 39 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. 40 41 42 43 44 45 46 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. 47 48 49 50 51 52 53 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. 54 55 56 Figure 1. Schematic of the injection well and its associated facilities 57 58 59 Liquid CO2 is injected into the well at injection flow rate of π€πΆπ2 . 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 60 61 62 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. 63 64 65 Under steady-state flow conditions the temperature of injected CO2,ππΆπ2 at any section of the vertical well, βπΏ can be derived from the mass, momentum and energy balance equations [28] 2.2 Wellbore Temperature Model βπΏ 66 βπΏ ππΆπ2 = (πππ + πΊπ βπΏ) + (ππΆπ2π − πππ )π − π΄ + πΊπ π΄ [π − π΄ − 1] (1) 67 68 69 In Eq. (1), friction effects have been neglected. We have also assumed a linear temperature variation in the formation given by: 70 πππ = πππ + πΊπ βπΏ (2) 71 72 73 74 75 Where in Eq. (1) and (2), πππ is the temperature of the surrounding formation at intake, πππ is the temperature of the formation at the section of the well under consideration, ππΆπ2π is temperature of injected CO2 at intake, πΊπ is the thermal gradient of the surrounding formation and π΄ is the thermal relaxation distance given by: π΄= 76 ππΆπ2 πΆπ πππ·π (3) 77 78 In Eq. (3), ππΆπ2 is the mass flow rate of CO2, πΆπ is the heat capacity of CO2 at constant pressure, π·π is the diameter of the production casing andπ is the overall heat transfer coefficient defined as: 79 π π πππ ln πππ πππ ln ππ€ π 1 πππ ππ ππ ππ = + + + π(π‘) π βπΆπ2 πππ ππππ ππππ ππ 80 81 82 83 84 85 (4) In Eq. (4), βπΆπ2 is the individual heat transfer coefficient inside the production casing, πππ andπππ is the inner and outer radii of the production casing respectively ππ€ , is the radius of the well, ππππ , ππππ , and ππ are the thermal conductivity of the production casing, cement and formation, respectively and π(π‘) is the dimensionless transient heat conduction time function of the formation given by [30]: πππ ≤ 15, π(π‘) = 1.1281√πππ (1 − 0.3)√πππ 86 87 88 πππ > 1.5, π(π‘) = 0.4063 + 0.5 ln( πππ ) (1 + In Eq. (5), πππ is the Fourier number defined as: 0.6 ) πππ (5) πππ = 89 90 91 92 πΌπ‘ ππ€2 (6) Where, πΌis the thermal diffusivity coefficient of the surrounding formation, and π‘ 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. 93 94 95 96 97 98 99 100 101 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, π΄. CO2 is injected at the formation intake temperature, 70β. Equation (1) was used to compute ππΆπ2 iteratively at every βπΏ = 1ππ‘ from the wellhead to the bottomhole. The temperature difference between CO2 in the well and the surrounding formation at every section of the well, ( πππ − ππΆπ2 ) 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. 102 103 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 104 105 106 Symbols TVD πππ ππΆπ2π πππ πππ ππ€ ππππ ππππ ππ πππ ππ βπππ ππΆπ2 πππΆπ2 πΌπ πππ πΌπ βπππ ππΆπ2 ππΆπ2 πΊπ π πππ πΊπ π βπππ π 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 β β in in in Btu/hr-ft-β Btu/hr-ft-β Btu/hr-ft-β Btu/hr-ft-β Btu/hr-ft-β Btu/lbm-β ft2 /hr ft2 /hr lbm/ft-hr lb/ft3 β/ft β/ft psia 107 108 109 110 111 112 113 114 115 116 117 2.3.1 Effect of injection flow rate on the temperature profile At the same intake and initial CO2 temperature of 70β, 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. 118 119 Figure 2. The effect of injection flow rate on the temperature of injected CO2 120 121 122 123 124 125 126 127 128 129 130 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. 131 132 Figure 3. Effect of CO2 injection time on temperature profile 133 134 135 136 137 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. 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 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, π under laminar flow conditions where the velocity and temperature profiles are fully-developed. If the surface of the tube of length βπΏ is set to a constant temperature ππ and CO2 is assumed incompressible with constant mass flow rate, the mean temperature of CO2 in the tube, πππΆπ2 can be derived from Newton’s Law of Cooling as [37]: πππΆπ2 = ππ − [ππ − πππ ]ππ₯π (− 2βπΏβ ) π£ππππ (7) 155 156 157 158 159 160 161 162 163 164 165 166 167 168 In Eq. (7), πππ is the mean CO2 entry temperature, π£ is the flow velocity, π is the density of CO2, ππ is the specific heat capacity of CO2 and β 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, πππΆπ2 increases along the length of the tube until it attain a maximum πππΆπ2 = ππ . 2.4.2 Heating of CO2 in a Bundle-of-tubes For a cylindrical core, radius π and length πΏ reconstructed into a bundle of parallel, non-interacting capillary tubes with varying radii (π1 , π2 , π2 … . ππ ) it can be shown that, the total number of capillary tubes in the core is given by [38]: 3 π 2 π = ∅( ) 4 αΉπ (8) Eq. (8) shows that the total number of capillary tubes depend on the porosity of the core, ∅, average pore size, αΉπ , and the core radius, π . Berea Sandstone core has average pore size of about 6ππ and average coordination number between 4 and 8 and lognormal pore size 185 distribution as shown in Figure 4. 169 170 Figure 4. Pore size distribution of Berea Sandstone Rock used in the study. 171 172 173 Applying Eq.(7) for the bundle-of-capillary-tubes, the mean CO2 temperature, πππΆπ2 at every βπΏ = 1ππ‘ of flow distance from the wellbore into the formation can be estimated from a weighted average of the mean CO2 temperature in each tube: 174 175 176 177 πππΆπ2 2 ∑π π=1 ππ πππΆπ2π = 2 ∑π π=1 ππ (9) Where πππΆπ2π is the mean CO2 temperature in tube with radius ππ for a total of π capillary tubes. Thus, Eq. (10) can be used to compute the mean CO2 temperature in the core with increasing length until πππΆπ2 is equal to the reservoir temperature. 178 179 180 181 182 183 184 185 186 187 188 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,π π between 3 and 10, where: π π = π ππ·π π΄ 1 π 1−∅ (11) In Eq. (11), π·π is the average grain diameter and π΄ 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 π π values within the Darcy flow regime. Forπ π = 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 π π . At higher π π , the fluid flows faster through the formation and attains thermal equilibrium deeper into the formation. 189 190 Figure 5. Evolution of CO2 temperature in the formation 191 192 193 194 3. Discussion and Practical Application 195 196 197 198 199 200 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 201 202 203 204 205 206 207 208 209 210 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. 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 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: ο· ο· ο· ο· 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. 242 243 244 245 246 247 ο· 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. 248 249 250 251 5. Acknowledgements The authors would like to thank the College of Engineering and especially the Department of Petroleum Engineering, KNUST, for their support. 252 253 6. References 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 1. EA. Technology roadmap - Carbon capture and Storage. 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