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Abstract
Concern about global warming is generating interest in reducing the emissions of greenhouse gases such as CO2. One way of reducing CO2 emissions is to replace conventional (hydrocarbon fuels) energy sources for heating buildings by geothermal energy. Recently it was suggested to co-inject carbon dioxide with cold water for simultaneous geothermal energy production and subsurface carbon dioxide storage. Our data correspond to a geothermal energy project proposed for heating the buildings of the Technical University of Delft. After injection of the water/CO2 mixture a complex interaction between physical transport and the phase redistribution of the components, i.e., water and CO2, occurs. This redistribution is usually described in terms of local thermodynamic equilibrium. There are no published complete analytical solutions for 1-D problems involving complex thermodynamics that include CO2 and heat effects in the flow. We take into account the heat effects related to the cold fluid injection and related to the dissolution of CO2.

We give an analytical solution for the model equations for the temperature and for the flow of CO2, vapor and water after combined injection of a cold carbon dioxide-water mixture in a geothermal reservoir. Due to high pressures and temperatures, CO2 is in a supercritical state and it is necessary to determine the phase equilibrium for non-ideal gases. We used a modification of the Peng-Robinson equation of state and an activity coefficient based mixing rule for the thermodynamic calculations. A volume shift procedure is applied to obtain an accurate liquid density. The structure of the solution depends strongly on the injection and initial reservoir conditions. The application of the work is in the effective recovery of heat from geothermal reservoirs with simultaneous CO2 storage. Moreover, the theory provides fundamental understanding of non-isothermal flow of mixtures undergoing mass transfer between phases. The advantage of the analytical model is that it provides a simple methodology to screen injection conditions for optimal geothermal recovery or maximal storage of carbon dioxide.

Introduction
Concern about global warming is generating interest in reducing the emissions of greenhouse gases such as CO2. There is a large body of literature concerning the injection of carbon dioxide in aquifers. Practical examples are the injection of the separated carbon dioxide produced in the Sleipner gas field (Kongsjorden, Kårstad et al. 1998; Zweigel, Arts et al. 2004) and the Salah field in Algeria (Riddiford, Wright et al. 2004). One way of reducing CO2 emissions is to replace conventional (hydrocarbon fuels) energy sources for heating buildings with geothermal energy. An important aspect is the transfer rate of carbon dioxide to the water phase, because the storage volume of dissolved carbon dioxide is much lower than gaseous carbon dioxide (R. Farajzadeh 2010; Gmelin's Handbuch). The use of high quality energy to heat buildings has aroused recent interest in geothermal energy, which has low quality but can be used equally well for space heating. In the Netherlands, there is a geothermal gradient of about 30oC/km leading to a temperature of around 80oC at a depth of 2000 m. There are numerous papers that describe injection of cold water in geothermal reservoirs and here we only mention the classical paper of Lauwerier (Lauwerier 1955).