In the absence of convincing evidence that passing injected water along km-scale planar interfaces to ＆mine＊ heat from crustal rock (e.g., Tester 2006; Sutter et al 2011), EGS attention has turned to circulating water between wellbores within hot crustal volumes (e.g., DOE 2004; USGS 2008; Wang, Horne & McClure 2009). As with all EGS heat extraction schemes, wellbore-to-wellbore heat transport is subject to heat supply by conduction rather than by advection. The impact of a conductive rather than a convective heat flow boundary is, however, not widely recognised. This omission can be remedied via a simple 2D steady-state radial analytic heat transport solution that expresses wellbore-centric EGS heat extraction performance in terms of appropriate Peclet parameters. Radial flow heat transport solutions in 2D and 3D are analogues of the Bredehoeft & Papadopulos (1965) temperature distribution derived from conservation of heat energy in 1D groundwater heat transport. The planar temperature field defines a (dimensionless) Peclet parameter 汕 = v0L/D in terms of Darcy fluid velocity v0 in a crustal layer of thickness L with effective thermal diffusivity D √ 老C/K for the water-rock system (老C = heat capacity of water in J/m3, K = thermal conductivity of rock). Solutions for 2D cylindrical and 3D spherical radial flow define Peclet parameter 污 = v0r0/D for respective radial fluid velocity fields v(r) √ v0r0/r and v(r) √ v0r0^2/r^2 centred on inner radius r0 with temperature boundary conditions T0 and T1 at inner and outer radii r0 and r1. Generalising the wellbore-centric steady-state 2D radial temperature distribution to a two-layer concentric heat transport analytic model of constant heat flux at inner, intermediate, and outer radii r0 less than r1 less than r2 defines inner and outer layer Peclet parameters. The injection of heat-depleted fluid of temperature T0 at a central wellbore of radius r0 defines the inner Peclet number 污0. Crustal heat supply Q2 [W/m] of temperature T2 at radius r2 defines the outer Peclet parameter 污2. For robust advective wellbore inflow (inner Peclet number 污0 more than ~ 10), the steady-state temperature T1 of fluid extracted at intermediate radius r1 is T1 ~ (2 每 (r1/r2)^污2)∙T2 每 (1 每 (r1/r2)^污2)∙Q2/K污2, where the outer Peclet number 0 less than 污2 less than 5 can range from purely conductive to substantially advective. For 污2 more than ~ 3 corresponding to advective heat supply to the heat exchange area, T1 ~ 2T2 每 Q2/K污2. For 污2 less than ~ 0.3 corresponding to largely conductive heat inflow from the crust, the outflow fluid temperature is three times smaller, T1 ~ 1/3 (2T2 每 Q2/K污2). The constant-heat-flux analytic wellbore-centric heat transfer temperature distribution for 2D radial flow admits of expressions for time-evolving heat extraction in terms of the rate 污2 at which the crust supplies heat to the heat exchange section. Time-evolving advective heat extraction per unit wellbore length from crustal sections of characteristic radius r2 is expressed by modulating the thermal conduction time-evolution expression exp(每r2^2/4Dt)/4Dt with weighting function (r2^2/4Dt)^(污2/2). For r2 ~ 50m, a Peclet parameter 污2 less than ~ 0.3 corresponding to largely conductive heat inflow from the crust yields a nominal heat extraction lifetime ~ 30 years. For 污2 more than ~ 3 corresponding to advective heat supply from the crust the nominal heat reservoir lifetime is less than 10 years. Peclet parameters for wellbore-to-wellbore radial advection systems of plausible dimension (r2 ~ 50m) thus show that commercial heat extraction rates cool off crustal heat exchange volumes dependent on thermal conduction recharge only. Moeck & Beardsmore (Stanford GW 2014) give empirical evidence consistent with this result in noting that 187 commercial geothermal systems sustained by advective flow in active magmatic and rift environments generate ~ 5GW of electrical power, while 10 (quasi-)commercial geothermal systems sustained by conduction only contribute perhaps 20MW of electrical power. Similarly, Wagner, Bayer & Blum (WGC2015) illustrate well-known effects of groundwater advection on ground source heat pump performance.

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