The reservoir is an adaptable combination of the HDR model and an EGS. The fluids circulating between the re-injection well and the production well are cooling down the hot rock gradually. This depends on the thermal properties of the rocks and the fluid, the geometry of the flow paths and most dominant by the flow rate of the circulating fluid. The parts of the fluid which are not circulating but are produced from and re-injected into the far field of the aquifer system are not affected by this thermal drawdown. The equations describing the HDR model have been developed by Heuer (1988). The combination of HDR and EGS models to an enhanced analytical heat-exchanger are explained in detail by Heidinger et al. (2006). For the following calculations, the internal surface of the heat-exchanger hooked up by two wells was chosen to be 3.4 km². This surface is modeled by three horizontal oriented “penny-shaped” fracs, each with a radius of 600 m. The fracs are coupled by conductive heat flow. This setting is derived from the stimulated volume between GPK2 and GPK3; see Fig. 2 and results from flow logs performed in the open-hole sections of these wells. The lateral distance between the open parts of the wells is 600 m; the connectivity to the far field is set to 50%. Tracer experiments indicate even connectivity to the far field up to 80% (Sanjuan et al., 2006). The small thermal drawdown for such a reservoir in 5 km depth at a low circulation rate of 25 L/s is shown in Fig. 3 (temperature at inlet of production well). For higher flow rates or lower connectivity values to the far field, the thermal drawdown can affect the production temperature significantly after relatively short times (∼ years). Hydraulic and chemical stimulation together with the reservoir are fixed costs of 1 M€. Dependent of the reservoir depth, the initial temperature of the reservoir is defined by the undisturbed temperature profile at Soultz-sous-Forêts; the profile was measured down to 5 km depth, below it is extrapolated, see Fig. 4.

The drilling costs of wells are rising exponentially with depth; this empirical behavior is described by Garnish (1987), and by Legarth and Wohlgemuth (2003). “Steel prices” and energy costs have boomed (drilling rigs are equipped with fuel oil generators) during the last years and the costs to drill a borehole to a specific depth increased significantly. Depth dependent costs for mobilizing a rig and to drill two boreholes with casing, used in the following calculations, are shown in Fig. 5. The costs for two wells to 5 km depths would be actually ∼ 17 M€, whereas to 3 km depth only ∼ 6 M€.

The power demand of pumps and the temperature change development of the fluid during its flow in the wells are a nice example of complex dependencies within the EGS. When the produced fluid ascends in the well, it is cooled down by the surrounding rocks; with time these rocks get heated itself and the cooling of the ascending fluid decreases. Thus, the temperature of the fluid at the wellhead increases with time. The “flow depending” temperature evolution of the geothermal fluid during its transit up and down the wells was described with an analytical approach by Ramey (1962). Together with a thermal drawdown of the reservoir, this leads in most calculations to a peak of energy production which is reached after several years. This temperature change does not only affect the energy production of the plant but also the “parasitic” power demand of the pumps (the energy demand of the pumps and the self-consumption of the heat-to-power unit are necessary to run the plant and are not a by-side effect, therefore this negative contribution to the energy balance of the plant is called parasitic). The electric power needed for the pumps to maintain the fluid circulation depends on several factors, these are: the flow rate, the efficiency of the pumps (different for production, here 50% and injection pumps, here 65%) and the total dynamic head (TDH) of the pump which itself again depends on: the flow rate, the productivity or injectivity index of the well, friction losses and the buoyancy effect. The buoyancy effect is driven by density differences between the water column responsible for the hydrostatic pressure in the reservoir and the water column in the well and supports the circulation. The density of the fluid is pressure, temperature and “chemical composition” dependent (Champel, 2006) and based on the database of ASPEN (1988) computations. Nevertheless, the “chemical composition” dependency is considered constant over the lifetime of the plant. The friction losses are calculated after Stelzer (1974). The fluid pressure in the surface piping system from the production pump outlet to the injection pump inlet is kept at 16 bars to prevent scaling, corrosion and pump cavitation by “degassing”. See evolution of power demand for GPK2 and GPK3 for actual characteristics at Soultz-sous-Forêts in Fig. 6. The pump chamber of the production pump is situated at 400 m depth; the pump can be either a line-shaft or a submersible pump; both types are difficult to maintain and lifetime is set to 10 years and investment costs are set to 800 000 €. The re-injection pump is located on the surface, easier to maintain than production pump but requires fine filtration to avoid erosion of injection pump impeller by mineral particles; there is no lifetime limitation and investment costs are set to 100 000 €.

For heat-to-power conversion, the temperature of the produced geothermal fluid is low and far from ideal. The maximum possible efficiency of an ideal heat-to-power conversion in the power station is defined by the Carnot efficiency, but in reality the efficiencies are lower. Due to the high mineralization of the formation water, a closed loop for circulation is required and binary systems for heat-to-power conversion are used. These are mainly organic-rankine-cycles (ORC) or Kalina-cycles. This module uses specific characteristics of the conversion (coolant temperature 20 °C, pinch-point temperature differences at condenser 15 °C and vaporizer 15 °C, efficiency of turbine 85%, re-injection temperature 70 °C) to calculate production temperature dependent efficiencies (Milora and Tester, 1976). This process can be adapted to the model of the conversion unit. With this implementation, a location-specific decision of the type and model of the power station type can be done. The costs of the unit are specific costs linked to the maximum producible electric gross power output; the value used for the following calculations is 1.5 M€/MW_el. Inflow temperature dependent gross efficiencies for the above given set of characteristics are shown in Fig. 7. The self-consumption of the conversion unit amounts to 10% of the gross energy production. The load factor of the plant is set to 95%.

The rock permeability in each well determines the productivity and injectivity indexes of the well (PI and II). These indexes may exhibit great variations from one well to another, even when they are very close to each other. The individual characteristics of all wells define the maximum possible circulation rate as well as the energy consumption of pumps. The financial revenues are directly linked to both effects and the productivity and injectivity indexes easily decide about success or failure of a project. The indexes cover magnitudes, from nearly 0 to 30 L/s/MPa at the geothermal site at Landau, Germany (BMU, 2008), yielding circulation rates from 4 L/s to 70 L/s; in the Molasse of Bavaria even 150 L/s (BMU, 2008) was reached. The great range of these indexes is explained with the fractal characteristics of the fluid flow paths and no reliable predictions of the well indexes before drilling them are possible today. Generally permeability decreases with increasing pressure (Rummel, 1990). Extrapolating results from the upper (best value found in Evans et al., 2005) and lower reservoir (average of GPK2, GPK3 and GPK4, Nami et al. (2008) at Soultz-sous-Forêts, a depth dependent well index profile was compiled, see Fig. 8. Generally, the naturally found productivity/injectivity well index can be improved by artificial hydraulic and/or chemical stimulations. In the following, the stimulation process of the reservoir was set to fixed costs (independent from depth) of 1 M€.

The revenue of the geothermal plant for the generated electric power differs in France and Germany and depends also on various other parameters: the size of the plant, when it was constructed, operation time or some bonus if thermal energy is sold too. Generally, the net present value (NPV), which is the sum of all discounted cash flows, is an indicator of how much value a project adds to an investment and is widely used throughout economics as criteria for evaluating projects. Here, it may not be the appropriate method, because the NPV is not related to the investment sum and the investment costs of a deep geothermal power plant vary strongly because of the depth dependent drilling costs. In this case, better criteria are the prime costs. These prime costs are the total effective costs to generate 1 kWh of electricity. These costs are composed by all costs, including the investment costs and are independent from the feed-in tariff. This sum in relation to the sum of the product (here the electricity, which can be sold), yields the total effective costs. But regulations defining the electricity, which can be feed-in, are different in France and Germany. In France, only the net resulting energy is sold (net scheme, generated energy minus parasitic energy consumption of plant). Whereas in Germany, all generated power is fed to the electric grid (gross scheme), the power to maintain the pumps and the heat-to-power conversion unit is bought in at lower prices. Therefore, effective costs are quite different for the same type of plants located in France and in Germany. This conclusion is only slightly dependent from an optional sale of heat.

The most important remaining input parameters are listed here. A summary of all input parameters can be found in the Appendix A of this article.

The economics of a geothermal power plant are affected significantly by the parasitic power consumption of the pumps. The power consumption of such well pumps is in first approximation proportional to the square of the flow rate. The pumps are located on ground surface or close from it but the pressure for production and re-injection are needed at the intersection of the open hole to the reservoir. Therefore, the different densities between the water column in the well and the water column responsible for the hydrostatic pressure in the reservoir have to be accounted in the calculations. At production, the fluid is warmer and has a lower density, than the fluid column on the underground reservoir, which helps the pump; at injection, the fluid is soon colder than the fluid in the formation and has a relatively higher density, which again helps the pump. In both cases, the buoyancy effect supports the pump. In the beginning of the circulation, the temperature of the fluid changes much while flowing in the wells; by time the surroundings of the wells are influenced by the temperature of the fluid and this effect decreases. This temperature evolution again affects the density and therefore the buoyancy effect. Even more important is this effect for calculating the wellhead temperature of the production well. This temperature is the intake temperature to the heat-to-power conversion unit and directly affects the amount of produced electric energy. The evolution of the fluid temperature (and pressure) during their flow in the boreholes was well constrained by adaptation of the model (diffusivity value of 1.25 × 10^–6 m²/s of the surrounding rocks) to the data from the injection experiment into GPK3 in June, 2007, where down hole measurement instruments have been installed.

The parasitic power demand of the pumps in Fig. 6 was calculated with a flow rate of 23.6 L/s. This is the only flow rate where the power consumption of the actual installed pumps at Soultz-sous-Forêts is known. Without further calibration, the results fit already quite well with the known values after ∼ 10 days of circulation: injection pump 110 kW and production pump 88.4 kW. Also shown is the temperature evolution at the wellhead of GPK2. During these first two years, the parasitic power demand of the pumps only amounts to ∼ 12.5% of the gross energy generation. Regarding the self-consumption of the heat-to-power unit also, the total parasitic power demand requires ∼ 22.5%; this is nearly one quarter of the gross energy generation. The results shown in Fig. 3 reveal that even after some years of production, a temperature difference from the reservoir to the production wellhead of ∼ 14 °C is remaining. Then after ∼ 12 years, the reservoir starts to cool down slowly; decreasing temperatures at the inlet and, with some delay, decreasing temperatures at the wellhead are the consequence. The gross and net power generation of the plant are closely related to the wellhead temperature, which can be seen in Fig. 3.

For this actual existing doublet system a flow rate dependent sensitivity analysis was performed. The flow rates are varying from 5 to 35 L/s; a higher flow rate is not possible because otherwise the pressure in the pump chamber of the production pump would be too low (< 16 bars). No investment costs at all are assumed, the maintenance costs are higher then in the previous calculations and set to 1 M€ per year due to reduced lifetime of pumps. The calculation system for the generated power is the net scheme, the feed-in tariff accounts to 12 Cents/kWh; both cash flows: the maintenance costs and the feed-in tariff are increasing by 1.5% per year. The lifetime of the project was shortened to 15 years. The heat-to-power conversion unit shall not be limited to a maximum power. The results of this calculation are shown in Fig. 10. For circulation rates lower than 20 L/s the system has a negative economical balance. At 20 L/s the system starts to make profit. Then, growing circulation rates increase not only the generated net energy of the plant, but have significant positive effects to the NPV. The conclusion of this analysis is clear: to operate the doublet system at highest possible production rate. In reality, the production rate is not only limited by the production pump, but also by the heat-to-power conversion unit and the behavior of GPK3 during re-injection to avoid seismic events.

As a future development, the multi well system will be implemented as another configuration of modules within the Euronaut software. For this system, GPK2 and GPK4 will be used for production and GPK1 and GPK3 for re-injection. Actually, this task is not yet completed, but similar simplified calculations about the power balance of this multi well system were performed already with the antecessor program HDRec v6.2. In 2006, the idea was still to use only GPK2, GPK3 and GPK4 as a triplet system with GPK3 as the only re-injection well. But due to the low injectivity index of GPK3, the power demand for higher circulation rates would have been very high and seriously affecting the energy balance, also it would heighten the risk of seismic events. At that time, the idea emerged to use GPK1 as an additional re-injection well. The distribution of the re-injection in the calculations was chosen dependent on the individual injectivity indexes in order to get the lowest possible power consumption of both pumps. The additional use of GPK1 for re-injection allowed raising the production rate without excessive increase of the parasitic pumping power consumption. The effect to the energy balance and the generated electricity is significant. To get new qualitative and quantitative results, the calculations will be repeated with actual data of the multi well system at Soultz-sous-Forêts.