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Workshop on Geothermal Reservoir Engineering Stanford Univ

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Workshop on Geothermal Reservoir Engineering Stanford Univ ( workshop-geothermal-reservoir-engineering-stanford-univ )

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For CO2 the pressure dependence is weak for liquid- like conditions, but becomes increasingly strong at lower pressures and higher temperatures. For adiabatic (thermally insulated) decompression, thermodynamic conditions will move along isenthalps (lines of constant specific enthalpy). Accordingly, decompression of hot, high-pressure CO2 will be accompanied by substantial temperature decline, while for liquid water there would be a small temperature increase. Figure 3. Specific enthalpy of CO2 (left) and water (right) in units of kJ/kg, as function of temperature and pressure. WELLBORE FLOW The pressure gradient in a flowing well can be represented by a superposition of gravity, frictional, and acceleration terms (Brill and Mukherjee, 1999), ∇P = (∇P)grav +(∇P)fric +(∇P)acc (1) For most applications of interest, the gravitational contribution to the pressure gradient is by far the dominant term, with frictional and inertial pressure gradients contributing typically a few percent or less. In a first effort to evaluate the pressures in HDR injection and production wells, we consider only the dominant gravitational gradient. In an injection well, temperatures will increase with depth, primarily because of heat transfer from the surrounding rocks (Ramey, 1962). Additional temperature changes are expected as a consequence of fluid compression due to pressure increase. The latter effect is very small for water, but could be more significant for the highly compressible CO2. Similarly, in a production well the temperature of a fluid parcel flowing upward will decrease due to heat loss to the surrounding formations. Additional temperature change will occur from decompression, which is expected to be a small effect for water, but could be significant for CO2. The temperature effects from heat exchange with the surroundings are of a transient nature and will diminish over time. For a basic comparison between the pressure behavior of water and CO2 wells, we start from the simplest possible approximation to temperature conditions: we consider an injection well that is entirely at the injection (wellhead) temperature Tinj, and a production well that is entirely at the production (downhole) temperature Tpro. In order to calculate the static pressure profile in a well, the well depth z is divided into N increments, ∆z = z/N. The calculation proceeds recursively from level n∆z to (n+1)∆z by assigning Pn+1 = Pn + ρng∆z, where ρn = ρ(Tn, Pn), and g = 9.81 m2/s is gravitational acceleration. For definiteness, we adopt parameters applicable to the European HDR experiment at Soultz, and take a well depth of 5,000 m, with a downhole temperature of Tpro = 200 ̊C (Baria et al., 2005; Dezayes et al., 2005). Injection temperature is set at Tinj = 20 ̊C. For both water and CO2 we start from an injection wellhead pressure of 57.4 bar, slightly in excess of the CO2 saturation pressure at injection temperature (Psat,CO2 = 57.36 bar at Tinj = 20 ̊C). Corresponding static downhole pressures at 5,000 m depth are 528.7 bar for CO2 and 553.4 bar for water (Fig. 4). Using these downhole pressures as starting values, we then obtain static pressures in the production well by integrating upwards at T = 200 ̊C. This results in production wellhead pressures of 288.1 bar for CO2 and 118.6 bar for water. The difference in wellhead pressures between production and injection wells is 230.7 bar for CO2 and 61.2 bar for water, indicating

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