#### Stationary state

In preparation for dynamic reservoir simulation, initial reservoir conditions have to be determined. These are the initial hydraulic heads, the initial temperature field and the distribution of total dissolved solids. For this purpose, we modeled the steady state condition of the natural reservoir without any injection and production and set the initial hydraulic head to *h*(*x*_{i},*t*_{0}) = −185 m for the total domain. The initial temperature *T*(*x*_{i},*t*_{0}) was set at 137.5°C for the total domain, representing the temperature at the top of the reservoir. For the top layer we applied a constant temperature of *T*(*x*_{i},*t*) = 137.5°C for the total time of simulation. A terrestrial heat flow of *q*_{nT}(*x*_{i},*t*)=72 mW m^{−2} was applied to the bottom surface. For the mass concentration, we used 265 g l^{−1} as a starting value.

As described above, the thermal conductivity depends on reservoir temperature and the fluid density depends on temperature, pressure and concentration. As these adjustments are dynamic, steady state conditions must be calculated with a transient model. After approximately 40 000 years quasi-stationary conditions were achieved. The resulting temperature profile is shown in Fig. 5 and is consistent with measured data. The modeled static water level (*h* = −191 m at the injection well) matches the measured one (*h* = −182.8 to −196.3 m) very well (Huenges & Hurter 2002).

#### Transient state

We started the transient model by applying calculated values for initial hydraulic head, temperature and concentration from the results of the stationary model. We removed the Dirichlet boundary condition at the top layer, which was a constant temperature of *T*(*x*_{i},*t*)=137.5°C, and added a constant temperature of *T*(*x*_{i},*t*)=70°C along the injection well. This boundary condition represents the temperature of the injected fluid. The final simulation time was set at 30 years according to the expected life cycle of geothermal utilization. We applied a constant injection rate of *Q*(*x*_{i},*t*)=75 m^{3} h^{−1} at the top of the Elbe base sandstone II unit, which corresponds to the top of the multifrac. A constant production rate of *Q*(*x*_{i},*t*)=−75 m^{3} h^{−1} was set at the intersection between the production well and the second gel-proppant frac, which is at the top of the Elbe base sandstone II. We set the mass concentration to *C*(*x*_{i},*t*) = 265 g l^{−1} at the injection point because the extracted fluid is scheduled to be reinjected after passing a heat exchanger.

The simulation results for the total domain show that the temperature perturbation due to injection does not reach the boundaries of the model. By contrast, pressure perturbations reach the north-east and south-west borders of the model. At the north-east border a pressure build-up of 28 m due to injection was simulated. At the farther south-west border a drawdown of 4 m due to production was simulated. At the borders in the north-west and south-east no pressure perturbation was simulated.

The cold-water front propagates away from the injection well. Figure 6 shows propagation of the 130°C isosurface during the 30 years (10 950 days) of operation time. Figure 8 shows the final state of the hydraulic head, temperature and velocity field after 30 years of production.

Highest fluid velocities occur within the induced fractures (Fig. 8C) and can result in pressure equalization. Due to the finite fracture conductivity (FCD), significant pressure gradients develop along the fractures (Fig. 8A), and their effective length is reduced. The fact that the flow lines in Fig. 7 intersect the multifrac at low angles away from the injection well indicates a combination of linear and radial flows. This results in a nonradial pressure field around the injection well. By contrast, the presence of the multifrac does not have a strong effect on the temperature field, and the temperature drawdown contours around the injection well have predominantly radial symmetry (Figs 6 and 8B).

Due to its high permeability, the Elbe base sandstone is the preferred rock for matrix infiltration. After passing through the rock matrix, the injected fluid reaches the second gel-proppant frac (308 m away from the injection well). Due to the high hydraulic conductivity of the induced fracture, the fluid is directly channeled to the production well before the cold-water front interferes with the production well. After approximately 3.6 years, the cold-water front reaches the second gel-proppant frac, and after roughly 5 years reaches the first gel-proppant frac (352 m away from the injection well). At the waterfrac (448 m away from the injection well) cooling starts after approximately 10 years. The injected cold water arrives somewhat earlier, having heated up along the way. Figure 7 shows the flow field and the travel time of the injected water. After approximately 2.5 years, the first injected water reaches the second gel-proppant frac. At this point no significant change in production temperature was simulated.

In addition to simulated results for the total domain, we recorded detailed observations of four single points during the simulation. The first observation point (OP1) is located at the top of the multifrac in the injection well and the other three (OP2–4) are at the intersections of the production well and the induced fractures (Figs 6 and 7). The three hydraulic fractures at the production well are fully connected by the production well, yielding cumulative values of hydraulic head, temperature and concentration at OP2–4. Observation point 4 represents the production well at the conglomerates, OP3 measures the additional influx of the two Elbe base sandstone units and OP2 gives values for the cumulative flux from the volcanic rocks through the Elbe alternating sequence.

The time history of the four observation points with respect to hydraulic head and temperature are shown in Fig. 9. The hydraulic head build-up at the injection well is equivalent to the drawdown at the production well, but the absolute value of drawdown (388 m) is lower than the value for build-up (448 m). By means of the measured productivity index PI=15 m^{3} h^{−1} MPa^{−1} and an injection/production rate of 75 m^{3} h^{−1}, a head change equivalent to 5 MPa can be calculated. From to the density of the fluid, which is 1100 and 1145 kg m^{−3} at the production and injection wells, respectively, water level changes of −463 m in the production and +445 m in the injection well are calculated. The lower simulated values for drawdown result from full connection between well, fracture and reservoir matrix without any skin effects. Therefore, the productivity index inside the Feflow model represents a potential value that is higher than the initial one. We recalculated the productivity index on this basis and determined a PI of 17.9 m^{3} h^{−1} MPa^{−1} for the production well and a PI of 14.9 m^{3} h^{−1}MPa^{−1} for the injection well.

At the beginning of the simulation, OP2–4 show different temperatures according to the geothermal gradient calculated by the stationary model (Fig. 9). After production begins, hotter water from the volcanic rocks (OP4) passes OP3 and OP2. Therefore, an initial increase in temperature is observed at the two gel-proppant fractures. An increase in production temperature (OP2) from 144.7 to 146.3°C can be achieved during the first 10 days of production. After this point, production temperature remains nearly constant until the cold-water front reaches the second gel-proppant frac after 3.6 years. A significant drop in production temperature to 125.8°C at the final simulation time follows. At this point, temperatures at the first gel-proppant frac and in the volcanic rocks are still 133.8 and 145.6°C respectively.

It is well known that the hydraulic conductivity of induced fractures depends strongly on pore pressure. Although this relation is not implemented in Feflow, we reduced and increased the dimensionless FCD (Economides & Nolte 2000) of the induced fractures by an order of magnitude. This mimics to some degree the effects of fracture closure and opening. The dimensionless FCD is defined as:

- (15)

where *k*_{fr}, *a*, *l*_{fr} and *k* denote fracture permeability, aperture, half length and matrix permeability respectively. Fracture half length and matrix permeability were kept constant during these simulations. The results, including the fractional influx from the induced fractures, are summarized in Table 5. The time history of the production and injection wells with respect to hydraulic head and temperature are shown in Fig. 10.

Table 5. Simulated fractional influx at the induced fractures for three different fracture conductivities with corresponding pressure response and PI of the production and injection wells. | Fractional influx | Build-up/drawdown (MPa) | PI (m^{3} h^{−1} MPa^{−1}) |
---|

m^{3} h^{−1} | % |
---|

FCD = 0.1 × FCD0 |

Injection well | 74.4 | 100.0 | 8.6 | 8.7 |

Second gel-proppant frac | 25.9 | 34.7 | | |

First gel-proppant frac | 34.3 | 46.0 | | |

Waterfrac | 14.5 | 19.4 | | |

Production well | 74.6 | 100.0 | −12.6 | 5.9 |

FCD = FCD0 |

Injection well | 73.8 | 100.0 | 5.0 | 14.7 |

Second gel-proppant frac | 26.5 | 35.8 | | |

First gel-proppant frac | 28.9 | 39.1 | | |

Waterfrac | 18.6 | 25.1 | | |

Production well | 74.0 | 100.0 | −4.2 | 17.7 |

FCD = 10 × FCD0 |

Injection well | 74.0 | 100.0 | 3.1 | 24.2 |

Second gel-proppant frac | 27.1 | 36.7 | | |

First gel-proppant frac | 28.2 | 38.1 | | |

Waterfrac | 18.6 | 25.1 | | |

Production well | 73.9 | 100.0 | −2.9 | 25.6 |

In general, for low FCD (FCD/FCD0 = 0.1) the pressure response of the reservoir is more pronounced. This results in a decrease in the productivity index from 17.7 to 5.9 m^{3} h^{−1} MPa^{−1}. Thus, the waterfrac becomes less effective, and its fractional influx decreases from 25.1% to 19.4%. The initial temperature increase due to the influx of hot water from the volcanic rocks is less pronounced than in the other scenarios. The reduced influx from the volcanic rocks is compensated by an increased influx from the Elbe base sandstone units (first gel-proppant frac). For high FCD (FCD/FCD0 = 10), the productivity index increases from 17.7 to 25.6 m^{3} h^{−1} MPa^{−1} at the production well. In comparison with the reference simulation, the fractional influx of the induced fractures stays roughly the same. The chronological behavior of the production temperature is similar to the reference results.