A NOVEL TECHNIQUE FOR EXTRACTION OF GEOTHERMAL ENERGY FROM ABANDONED OIL WELLS

A NOVEL TECHNIQUE FOR EXTRACTION OF GEOTHERMAL ENERGY FROM ABANDONED OIL WELLS Seyed Ali Ghoreishi-Madiseh McGill University 3450 University St., Room 125 Montreal, QC, Canada H3A2A7 e-mail: seyed.ghoreishimadiseh @mail.mcgill.ca Mohammed J. Al-Khawaja Qatar University P. O. Box 2713 Doha, Qatar e-mail: khawaja@qu.edu.qa Ferri P. Hassani McGill University 3450 University St., Room 109 Montreal, QC, Canada H3A2A7 e-mail: ferri.hassani@mcgill.ca ABSTRACT This paper investigates the possibility of design and construction of a geothermal heat exchanger suitable for installation in abandoned oil wells. Based on the insitu data collected, an amenable heat transfer numerical model is developed with which the performance of the underground geothermal heat exchanger is assessed. Using a finite volume descretization method, the transient three-dimensional temperature and flow fields in the ground and within the fluid flowing through the heat exchanger are assessed. The model is capable of controlling the rate of heat extraction through continuous adjustment of the inlet water temperature. Sustainable rate of heat extraction is calculated under different heat load variations and for various operational life cycles. Effects of geometrical dimensions and the thermal properties of the medium on the performance of the geothermal heat exchanger are examined. It is found that thermal conductivity of ground plays an important role on the performance of the system. The results of the research suggest that effect of natural convection cannot be always neglected and depending on the hydraulic conductivity of the porous ground medium, an estimation of the significance of natural convection is given. The term sustainable rate of heat extraction is introduced and a substantial study of how the geometrical and the thermo-physical properties of the geothermal system affect the sustainable rate of heat extraction is carried out. Eventually, this study aims to create the engineering infrastructure required for the design of underground heat exchangers suitable for extraction of geothermal heat from abandoned oil wells. 1. INTRODUCTION Abandoned oil wells are usually regarded as enduring liabilities, which can evolve significant costs for decades after the oil reservoir is deplenished. However, due to its access to deep geothermal resources, an abandoned oil well provides an exceptional opportunity for geothermal heat extraction. Installing a geothermal heat exchanger in an abandoned oil well is a novel technique for harvesting the geothermal heat content of the well. Applying this method, a U-tube heat exchanger is placed in the well prior to filling the well with a cemented material with a desirable thermal conductivity. This filling material is usually regarded as backfill. In this newly proposed geothermal system, a working fluid circulated inside the closed loop of the U- tube heat exchanger extracts the geothermal heat from the underground reservoir and conveys this energy to the surface. Since the working fluid is circulated in a closed loop heat exchanger, this method does not require excessive pumping power, as opposed to open loop geothermal systems which are usually associated with considerable pumping powers. Also, the fact that the proposed system involves little or no drilling and excavation costs implies its considerable economic advantages compared to convectional closed loop geothermal systems. To investigate the possibility of design and construction of such geothermal heat exchangers installed inside the oil well, this paper follows presents the preliminary findings of a multidisciplinary research work carried out in Qatar and Canada. The study includes the development of an amenable heat transfer numerical model capable of assessing the performance of the underground geothermal heat exchanger. The existing models proposed for assessing the performance of 1

ground coupled heat exchangers are conduction-based models mechanism (Kavanaugh and Rafferty 1997), (Zeng, Diao et al. 2003), and (Omer 2008). These models result in reliable results for shallow applications of closed loop geothermal cycles. However, the applicability of these models for the case of U-tube heat exchangers installed in deep oil wells may be rejected. This is mainly due to the fact that in deep applications of U-tube heat exchangers, buoyancy driven natural convection in the porous heat exchange medium may play an important role in heat exchange between the working fluid of the U-tube and the medium. Neglecting this naturally convected heat component, will lead to underestimation of the performance of the heat exchanger and therefore overestimation of the length of the U-tube heat exchanger and the associated capital costs. temperature will rise linearly from the surface temperature to the bottom-well temperature. The constructed heat transfer simulation model is capable of capturing the effect of conduction, forced underground advection and natural convection heat transfer mechanisms. Using a three-dimensional transient finite volume descretization method, the transient temperature and flow fields in the ground and within the water flowing through the heat exchanger are assessed. The model is capable of controlling the rate of heat extraction through continuous adjustment of the water flow rate. Sustainable rate of heat extraction is calculated under different heat load variations and for various operational life cycles. To address the above mentioned issues, a new approach in the simulation of underground heat exchangers installed in oil wells is proposed in this paper. The present work also discusses effects of various design parameters, such as geometrical dimensions and thermal properties of the medium, on the performance of the geothermal heat exchangers. 2. MODEL SECRIPTION The model is based on a simple geometry indicated in Fig. 1 coordinated in a 3D Cartesian coordinate system. It is comprised of a U-tube heat exchanger placed in the middle of an abandoned oil well. The oil well is then filled with two distinctive materials. At the bottom, the well is filled with a material which has suitable thermal conductance which makes extraction of heat possible. However, due the considerable depth of the well, the ground temperature close to the surface is much lower than the bottom-well temperature. This means that if the well is filled with the same thermally conductive material, part of the heat captured at the bottom of the well will be removed from it while the working fluid is in its way to the surface. In order to preserve the energy content of the working fluid and prevent this undesirable heat removal from it, it is assumed that the upper zone of the well is filled with a material which plays an insulating role. Fig. 1: Geometry of the of the abandoned oil well and the geothermal heat exchanger Using the notion of volume averaged variables, in this paper, the derivation of equations of mass and momentum are based on the (Nield 1991), (Nield and Bejan 1992), (Lage 1993), (Vafai and Kim 1995), and (Alazmi and Vafai 2000), the governing equations of conservation of mass, momentum and energy are expressed by The rock mass of the ground is assumed to have a porous structure which consists of a solid structure and pores saturated by water. Ground source is assumed to exhibit a uniform geo-gradient. Accordingly, ground 2

where,,,,,,,,,,, and are respectively, porosity, permeability, coefficient of thermal expansion of water, porous medium density, water density, specific heat capacity of porous medium, specific heat capacity of fluid, thermal conductivity of porous medium, gravity acceleration vector, dimensionless form-drag constant, and rate of heat generation (or extraction) per unit volume. Also, is the Darcy velocity and is a representative elementary volume of porous medium. Similarly, is the intrinsic average pressure of fluid taken over a volume of the fluid. The term represents the heat exchange between the ground and heat exchanger tube(s). Fig.2 is the illustration of a tube cell and its surrounding control volume. Obviously, is nonzero only in locations where the tubes rest and zero elsewhere. Since the bulk temperature of the water changes along the U-tube length, assuming a constant may lead to unrealistic results. Accordingly, in this paper, is calculated using the local rate of heat exchange between the ground and the U-tube; where,,, and are respectively the bulk temperature of water, mass flow rate of water through the well, and volume of the finite volume cell surrounding the tube cell. Depending on the position, two different set of thermal properties is substituted into equation (2) and (3); as shown in Fig.2, properties of the bore fill material is used for the points located inside the well and properties of porous medium is used elsewhere. where,,, Δ, and are respectively, wall temperature, overall heat transfer coefficient, length of the tube cell and inner diameter of the tube cell. It is important to note that is the ground temperature in the center of the control volume surrounding the tube cell. Integrating the above differential equation over the tube cell length will lead to Δ Therefore, Where,. In other words, equation this formulation relates the temperature of the water flowing inside the heat exchange tube to local bore temperature. The overall heat transfer coefficient is formulated as (Holman 1997). where,,, and are respectively, the convection coefficient of water flowing through the tube, inner radius of the tube, and thermal conductivity of the tube. The convection coefficient,, is obtained using the relation developed by Dittus and Boelter (Dittus and Boelter 1930);, for laminar U-tube flow ( ).., for turbulent U- tube flow ( ) where,,,,, and are respectively, the Nusselt number, Reynolds number, Prandtl number, thermal conductivity of water, and dynamic viscosity of water. The physical interpretation of this technique is better understood by examining the following extreme cases: Case1) 1 or 1 (associated to 1) leads to Δ 0; meaning that if, the overall heat transfer coefficient is low or the fluid flow rate is high, the fluid temperature at the outlet of the tube cell will be the same as its inlet temperature. Fig.2: Demonstration of the U-tubes heat exchanger, filling material and its surrounding porous medium To guarantee the satisfaction of energy balance, the rate of enthalpy change in water must be equal to the rate of heat transferred through the tube cell; Case2) 1 or 1 (associated to 1) leads to Δ ; meaning that if the overall heat transfer coefficient is high or the fluid flow rate is low, the temperature of the fluid at the outlet of the tube cell will approach the ground temperature at the location of the tube cell. It is assumed that; 1- there is no initial underground water flow and 2- initial ground temperature field is the 3

geo-gradient. As for boundary conditions it is considered that; 1- there no underground water flow on the boundary walls and 2- all the boundaries are isothermal walls except the adiabatic surface boundary. Finite volume method was employed to solve the equations (Patankar 1980). Based on the Mark and Cell (MAC) scheme developed by Harlow and Welch (Harlow and Welch 1965), equations were descritized over a staggered mesh while fully explicit descritization was used for energy equation. A computer FORTRAN program code, named Convective Geothermal Solver (CGS), was devised to carry out the numerical calculations. Fig.3 shows the block diagram this computer program. imposed by the buoyancy force in the ground. The properties of this test case are given in TABLE1. Rate of heat extraction is assumed to be 20kW for this test case. As shown in Fig.4, after 10 years of operation, buoyancy force has created a natural circulation of water through the ground pores. In order to examine the performance of the U-tube heat exchanger, Fig.5 indicates the resulting outlet temperature of the system over 10 years of its operation. As shown in Fig.5, gradual heat extraction from the geothermal reservoir decreases the resource temperature leading to a lower outlet temperature of the working fluid. For example, initially, the outlet fluid temperature exhibits 6.3 C decrease over 10 years of operation. To simulate the seasonal variations of heat load demand, a Heat Exchanger Flow Controller Subroutine was developed in the computational code. This controller scheme takes advantage of Newton-Raphson method to adjust the flow of the heat exchanger(s) in a way that the extracted heat power would match the heat load demand power. The dynamic adjustment of flow in the heat exchanger(s) provides the opportunity to match the rate of heat extraction with the seasonal heat load variation. This method, also, provides a more realistic approach for the simulation of heat load in heat exchangers, compared to the existing heat transfer models which assume a uniform heat flux over the U- tube length. Fig.4: Velocity and temperature field of the U-tube heat exchanger after 10 years of operation Effect of rate of heat extraction on the outlet temperature of the heat exchanger is shown in Fig.6. As can be seen, extracting heat at a higher rate will result in significantly lower outlet temperature values. Thus, the minimum outlet temperature would be criterion according to which the proper rate of heat extraction should be opted. Fig.3: Flow chart diagram of the flow control scheme applied in the simulation 3. RESULTS AND DISCUSIONS The first illustration of the results is given in Fig.4 which shows the underground water velocity field 4

T( o C) 35 34 33 32 31 30 29 28 27 T outlet ( o C) T inlet ( o C) Fig.8 is an illustration of the effect of ground hydraulic conductivity on the performance of the U-tube heat exchanger. According to Fig.8, results associated to thermal conductivity values smaller than 10-5 m/s are identical. However, it is also observed that after 10 years of operation, the resulting outlet temperature for a ground thermal conductivity of 10-4 m/s is 8 percent higher than the outlet temperature of a ground medium with thermal conductivity of 10-5 m/se. The findings of this research suggest that the thermal conductivity of the heat exchange medium is significantly important in evaluation of the effect of natural convection on the performance of U-tube heat exchangers installed in oil wells. 26 25 0 730 1460 2190 2920 3650 t(day) Fig.5: Outlet and inlet temperatures of the U-tube heat exchanger TABLE1: SPECIFICATION OF THE TEST CASE U-tube length 700 m Center to center distance of the U-tube 0.125 m Tube diameter 0.055 m Ground thermal conductivity 1.5 W/m C Ground density 2100 kg/m 3 Ground specific heat capacity 1000 J/kg C Ground hydraulic conductivity 10-6 m/s Ground porosity 0.378 Length of the insulated zone of the U-tube 300 m Bottom-well temperature 50 C Ground temperature at the surface 7 C Fluid velocity in the U-tube 1 m/sec Well diameter 0.254 m Fig.6: Effect of rate of heat extraction on the outlet temperature of the heat exchanger Fig.7 shows how the thermal conductivity of the geothermal resource will affect the outlet temperature of the U-tube heat exchanger working fluid. According to Fig.7, thermal conductivity plays an important role on the performance of the system. For example, increasing thermal conductivity from 1.5 W/m C to 3 W/m C has improved the outlet temperature by 61 percent. This means that the sustainable rate of heat extraction is significantly dependent to the thermal conductivity of the resource. Fig.7: Effect of thermal conductivity on the outlet temperature of the heat exchanger 5

Fig.8: Effect of hydraulic conductivity on the outlet temperature of the heat exchanger 4. CONCLUSIONS A heat transfer model for simulation of heat transfer in U-tube heat exchangers of closed loop geothermal cycles installed in oil well was developed. Using finite volume descritization method, the model was numerically solved to simulate the performance of typical heat exchanger units. The results of the proposed model show good agreement with the results of conduction-based model when hydraulic conductivity of the heat exchange medium was lower than 10-5 m/s. However, as the hydraulic conductivity increases (greater than 10-4 m/s), natural convection cannot be neglected. The findings of this study suggest that for a typical U-tube heat exchanger unit installed in oil wells, if the hydraulic conductivity of the heat exchange medium is smaller than 10-5 m/s, natural convection can be neglected and conduction-based heat transfer models would suffice. However, as the hydraulic conductivity increases from 10-5 m/s to 10-4 m/s, the role of natural convection grows from medium to considerably effective. Also, it was found that natural convection becomes more important in the long term performance of a ground coupled heat exchanger. It is also found that, in addition to the hydraulic conductivity of the heat exchange medium, its thermal conductivity and the rate of heat extraction are the most important parameters which significantly affect the performance of the underground U-tube heat exchangers installed in oil wells. 6. REFERENCE (1) Alazmi, B. and K. Vafai (2000). "Analysis of variants within the porous media transport models." Journal of Heat Transfer 122: 303-326 (2) Dittus, F. W. and L. M. K. Boelter (1930). "Heat transfer in automobile radiators of the tubular type." University of California Publications in Engineering 2(13): 443-419 (3) Harlow, F. H. and J. E. Welch (1965). "Numerical calculation of time-dependent viscous incompresible flow and fluid with free surface." Physics of Fluids 8(12): 2182-2189 Holman, J. P. (1997). Heat transfer. 8th ed. New York, McGraw Hill (4) Kavanaugh, S. P. and K. Rafferty (1997). Groundsource heat pumps, design of geothermal systems for commercial and institutional buildings, American Society of Heating, Refrigerating and Air-conditioning Engineers, Inc (5) Lage, J. L. (1993). "Natural convection within a porous medium cavity: predicting tools for flow regime and heat transfer." International communication of heat and mass transfer 20: 13 (6) Nield, D. A. (1991). "The limitations of the Brinkman-Forchheimer equation in modeling flow in a saturated porous medium and at an interface." International Jounral of Heat and Fluid Flow 12(3): 269-272 (7) Nield, D. A. and A. Bejan (1992). Convection in porous media. New York, Springer-Verlag Inc Omer, A. M. (2008). "Ground-source heat pumps systems and applications." Renewable and Sustainable Energy Reviews 12: 344-328 (8) Patankar, S. V. (1980). Numerical heat transfer and fluid flow, Taylor and Francis (9) Vafai, K. and S. J. Kim (1995). "On the limitations of the Brinkman-Forchheimer-extended Darcy equation." International Jounral of Heat and Fluid Flow 16(1): 11-15 (10) Zeng, H., N. Diao, et al. (2003). "Heat transfer analysis of boreholes in vertical ground heat exchangers." International Journal of Heat and Mass Transfer 46: 4467-4481 5. ACKNOWLEGEMENTS This publication was made possible by NPRP grant # 09-1043-2-404 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the author(s). 6