Wellbore heat transfer in CO2-based geothermal systems (2012)

Geothermal systems utilizing carbon dioxide as the subsurface heat exchange fluid in naturally porous, permeable geologic formations have been shown to provide improved geothermal heat energy extraction, even at low resource temperatures, compared to conventional hydrothermal and enhanced geothermal systems (EGS). Such systems, termed CO2 Plume Geothermal (CPG), have the potential to permit expansion of geothermal energy use while supporting rapid implementation. While most previous analyses have focused on heat transfer in the reservoir and surface components of CO2-based geothermal operations, here we examine wellbore heat transfer. In particular, we explore the hypothesis that wellbore flow can be assumed to be adiabatic for the majority of a CPG facility's lifespan. Introduction Part of the effort to limit CO2 emissions to the atmosphere requires that existing and emerging energy systems shift away from using fossil fuels as primary energy inputs and towards renewable sources that may be used to generate electricity. Renewable sources of primary energy, including geothermal heat, offer the potential to produce electricity with little or no operational CO2 emissions. The transition towards these renewable energy sources will be slow, in part because of embedded infrastructure that naturally turns over on the order of half a century, and in part because the high energy density of hydrocarbons and well-developed hydrocarbon power systems result in produced electricity that is inexpensive relative to other options. Given that CO2 emissions are increasing and unlikely to be abated by sudden and dramatic changes in how societies produce, convert, and use energy, applications that can use CO2 -particularly to produce electricity -may enable transitions to renewables that are not disruptive to economies and the climate. Numerous previous studies have discussed using supercritical CO2 as the subsurface working fluid for geothermal energy capture (e.g., [Brown, 2000], [Pruess, 2006; 2008], [Atrens et al., 2009], [Randolph and Saar, 2010; 2011]). Numerical analyses suggest CO2 transfers heat more efficiently than water, particularly in naturally permeable and porous geologic formations, i.e., in Randolph, Adams, Kuehn, Saar 2 CO2-Plume Geothermal (CPG) systems [Randolph and Saar, 2010; 2011], as a result of its relatively high mobility (inverse kinematic viscosity) and compressibility in deep geologic formations, the latter contributing to a strong thermosyphon [Atrens et al., 2009, Adams et al., in preparation]. Therefore, CO2-based geothermal operations may permit use of lower temperature and lower permeability geologic formations than those currently deemed economically viable. CPG systems involve injecting CO2 -produced by hydrocarbon power systems and/or other industries -into deep, naturally porous and permeable geologic formations where the CO2 displaces native reservoir fluid and is heated by the natural insitu heat and the background geothermal heat flux. A portion of the heated CO2 is piped to the surface, providing energy for electricity production or direct heat utilization, before being returned to the subsurface. Enhanced geothermal systems (EGS) using CO2 as the subsurface heat transfer medium are designed very similarly to water-based EGS but, like CPG, achieve many of the advantages of CO2 over water (e.g., [Pruess, 2006]). With either system, the injected CO2 is ultimately geologically stored, though CPG provides far larger CO2 storage capacities and higher energy electricity production efficiency [Randolph and Saar, 2011]. Previous CPG analyses [Randolph and Saar, 2010; 2011], as well as many CO2-based EGS studies (e.g., [Atrens et al., 2009], [Pruess, 2006; 2008]), have focused on subsurface heat transfer or surface components of the system while assuming minimal or no heat loss or gain in the production or injection wells, respectively, and no wellbore frictional losses. To ensure the accuracy of future CPG studies, wellbore flow and heat transfer assumptions -in particular, that of adiabatic expansion/compression -are examined in detail in the present investigation. In the wells, heat is transferred with surrounding rock, and frictional effects between the flowing fluid and the pipe wall result in pressure loss. Back-of-the envelope calculations reveal Reynolds numbers on the order of 10 for CO2 pipeflow, suggesting large advective heat transfer coefficients. However, this effect may be offset by the low effective thermal conductivity of the subsurface solid-fluid complex. Moreover, the low dynamic viscosity of supercritical CO2, together with the relative smoothness of the nickel-steel pipe generally required for CO2 wells, Figure 1: Several potential implementations of CO2-based geothermal systems (modified after Randolph and Saar [2011]). Randolph, Adams, Kuehn, Saar 3 suggest frictional losses are low. These opposing factors indicate further wellbore analysis is warranted and, thus, is presented below. Heat Transfer Model and Theory A simple, quasi-one-dimensional transient heat transfer model is generated, as shown in Figure 2, representing the buoyant ascent of heated CO2 from the reservoir to the surface. We assume that convective heat transfer outside of the wellbore is negligible. While future studies may allow consideration of convective flow, neglecting it is considered reasonable because reservoir formations chosen for CPG installations will, by necessity, be overlain by large extents of lowpermeability caprock -ensuring injected CO2 is trapped in the reservoir -with minimal potential for fluid flow and, hence, convective heat exchange. We further assume that temperature gradients in the vertical direction are much less than in the radial direction. Thus, vertical heat transfer is assumed negligible compared to radial transfer, permitting the model to be one-dimensional in the radial direction. The model contains 6 radial grid blocks with radii of 0.125m, 2m, 10m, 20m, 40m, and 100m; and 10 grid blocks in the axial direction at even increments of 250m. Finer radial and vertical grid refinements were tested but found to be unnecessary for the purpose of this investigation. We develop the model using Engineering Equation Solver (EES) for its simultaneous equation solving ability in a single axial slice and efficient retrieval of thermodynamic property data, where the latter is based on Span and Wagner [1996]. EES is linked iteratively with MATLAB on a macro-level to process and store axial and time increment results. Heat transfer and frictional losses should be more significant in CPG production wells, as opposed to injection wells, because of higher fluid temperature and flow velocity for relatively low density produced CO2. Thus, we focus here on production well behavior. The CO2 fluid conditions at the bottomhole well inlet are fixed at 25 MPa, 100°C, and 80 kg/s, consistent with the base case of previous investigations [Randolph and Saar, 2010; 2011]. Heat transfer is found for a buoyant CO2 rise of 2.5 km, while the surrounding rock temperature is set initially to a linear geothermal gradient of 35 C/km and a mean annual surface temperature of 12.5 C. The radial temperature boundary condition at grid 6, 100 m from the well, is set equal to this geothermal gradient. The pipe wall is neglected in the heat transfer analysis, Figure 2: One-dimensional heat transfer model schematic (not to scale). Randolph, Adams, Kuehn, Saar 4 as its high thermal conductivity offers little resistance to heat transfer compared to the rock. The rock is assumed to have 10% porosity, and conservatively high thermal conductivity and heat capacity are assumed for the effective, combined water-rock system. For a summary of the nomenclature used in the following analysis, see Table 1, and for a full set of model parameters, see Table 2 (Appendix). Three unique energy balance cases are applied across each axial slice: a fluid convection boundary condition case (for the rock element bounding the wellbore), a center-grid conduction-only case, and a prescribed temperature outer boundary condition. For the convective boundary case, consider the annular volume segment i, with inner radius (the wellbore) ri,inner, outer radius ri,outer, the radius of the next segment ri+1,outer, and having thickness ∆z. An energy balance across the element yields storage conduction out convection in q q q = − , , , where the general forms of each are: dt dT C V q dr dT A k q T A h q rock rock storage tional cross rock conduction surface x convection ⋅ ⋅ ⋅ = ⋅ ⋅ = ∆ ⋅ ⋅ =