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Keywords:

  • enhanced geothermal systems;
  • geothermal reservoirs;
  • Groß Schönebeck;
  • thermohaline convection

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Reservoir characterization
  5. Numerical approach
  6. Application – simulation of Groß Schönebeck Site
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. Nomenclature
  11. References

Understanding hydrothermal processes during production is critical to optimal geothermal reservoir management and sustainable utilization. This study addresses the hydrothermal (HT) processes in a geothermal research doublet consisting of the injection well E GrSk3/90 and production well Gt GrSk4/05 at the deep geothermal reservoir of Groß Schönebeck (north of Berlin, Germany) during geothermal power production. The reservoir is located between −4050 to −4250 m depth in the Lower Permian of the Northeast German Basin. Operational activities such as hydraulic stimulation, production (T = 150°C; Q = −75 m3 h−1; C = 265 g l−1) and injection (T = 70°C; Q = 75 m3 h−1; C = 265 g l−1) change the HT conditions of the geothermal reservoir. The most significant changes affect temperature, mass concentration and pore pressure. These changes influence fluid density and viscosity as well as rock properties such as porosity, permeability, thermal conductivity and heat capacity. In addition, the geometry and hydraulic properties of hydraulically induced fractures vary during the lifetime of the reservoir. A three-dimensional reservoir model was developed based on a structural geological model to simulate and understand the complex interaction of such processes. This model includes a full HT coupling of various petrophysical parameters. Specifically, temperature-dependent thermal conductivity and heat capacity as well as the pressure-, temperature- and mass concentration-dependent fluid density and viscosity are considered. These parameters were determined by laboratory and field experiments. The effective pressure dependence of matrix permeability is less than 2.3% at our reservoir conditions and therefore can be neglected. The results of a three-dimensional thermohaline finite-element simulation of the life cycle performance of this geothermal well doublet indicate the beginning of thermal breakthrough after 3.6 years of utilization. This result is crucial for optimizing reservoir management.

Geofluids (2010) 10, 406–421


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Reservoir characterization
  5. Numerical approach
  6. Application – simulation of Groß Schönebeck Site
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. Nomenclature
  11. References

The technical feasibility of geothermal power production from a deep low-enthalpy reservoir will be demonstrated by means of a borehole doublet system consisting of the production well Gt GrSk4/05 and the injection well E GrSk3/90 at the geothermal research site Groß Schönebeck (40 km north of Berlin, Germany).

The intended injection well was tested to investigate enhancing thermal-fluid recovery from roughly −4100-m deep sandstones and volcanics (Legarth et al. 2005; Reinicke et al. 2005; Zimmermann et al. 2005). The doublet system was completed by drilling the production well to a total depth of −4198 m in 2007, which was followed by three stimulation treatments. Hydraulic stimulation is a method of increasing the productivity of a reservoir by inducing artificial fractures through fluid injection. In order to increase the apparent thickness of the reservoir horizon, the production well was inclined by 48° in the reservoir section and drilled in the direction of the minimum horizontal stress (Sh = 288° azimuth) for optimum hydraulic fracture alignment in relation to the pre-existing injection well. Hence, the fractures trend 18° NNE along the maximum horizontal stress (Holl et al. 2005).

An appropriate numerical model is important for planning the well path and fracture design, interpreting hydraulic tests and stimulations, and predicting reservoir behavior during geothermal power production. This model should include: (i) the reservoir geology and structure, (ii) the geometry of wells and fractures and (iii) the hydraulic, thermal, mechanical and chemical (HTMC) conditions of the reservoir and fractures generated due to changes in reservoir conditions.

Various simulation software exists that can handle some of the required parameters, e.g. Eclipse (Schlumberger 2008), Geosys (Korsawe et al. 2003; Wang & Kolditz 2005) and Feflow (Diersch 2005).

For this study, we utilize Feflow, because this software fully supports hydraulic–thermal coupling. However, Feflow cannot be used to simulate mechanical and chemical reservoir behavior, or to represent dipping structures (e.g. natural fault zones).

In the present study, we describe how to set up a thermohaline model for enhanced geothermal systems (EGS). We also discuss: (i) the use of numerical simulations in interpreting the life cycle performance of the particular geothermal research doublet at the drill site Groß Schönebeck and (ii) the general applicability of the Feflow software for geothermal issues, in particular EGS sites. Life cycle performance is defined here as the reservoir response over the scheduled 30 years of production and injection.

Reservoir characterization

  1. Top of page
  2. Abstract
  3. Introduction
  4. Reservoir characterization
  5. Numerical approach
  6. Application – simulation of Groß Schönebeck Site
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. Nomenclature
  11. References

Geology

The reservoir is located within the Lower Permian of the Northeast German Basin (NEGB) between −3815 and −4247 m below sea level. The reservoir rocks are classified into two rock units from bottom to top: volcanic rocks (Lower Rotliegend of the Lower Permian) and siliciclastics (Upper Rotliegend of the Lower Permian) ranging from conglomerates to fine-grained sandstones, siltstones and mudstones. These two main units can be subdivided depending on their lithological properties (Fig. 1, Table 1), which is particularly important for the hydraulic–thermal–mechanical (HTM) modeling.

image

Figure 1.  Geological model developed on the basis of two-dimensional seismic and wellbore data. The production well is directed towards a NE-striking/W-dipping fault. The blue tubes indicate the alignment of the well paths, and the black rectangles show the induced fractures of the doublet system at the Groß Schönebeck site.

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Table 1.   Nomenclature for geological formations of Groß Schönebeck reservoir, including lithology, vertical dimension (below sea level) and numbers of vertical layers used for modeling.
UnitLithologyTop (m)Bottom (m)Thickness (m)Spatial layers
I Hannover formationSilt and mudstone−3815−397415910
IIA Elbe alternating sequenceSiltstone to fine-grained sandstone−3974−4004302
IIB Elbe base sandstone IIFine-grained sandstone−4004−4059554
IIC Elbe base sandstone IFine- to medium-grained sandstone−4059−4111523
III Havel formationConglomerates from fine sandstone to fine-grained gravel−4111−4147363
IV Volcanic rocksAndesite−4147−42471005
Total −3815−424743227

Due to high hydraulic conductivity and porosity, the Elbe base sandstones I and II are the most promising horizons for geothermal power production in a hydrothermal environment like the NEGB. These siliciclastic rocks can generally be characterized as arkosic litharenite and consist mainly of quartz (80 vol%). The quartz grains are often surrounded by iron (III) oxide rims; calcareous and albitic cements are rarely found. The feldspar content is less than 10 vol%. K-feldspar, sometimes partly albitized, is the dominant feldspar. Rock fragments are less than 10 vol% and are mainly of volcanic origin. Accessory minerals are plagioclase, microcline and mica. Illite and chlorite are the dominant clays (Milsch et al. 2009).

Fault zones and natural fractures

The fault pattern interpreted from two-dimensional seismic data is characterized by major NW-striking faults and NNE-striking minor faults. In the current stress field, the NE-striking faults bear the highest ratio of shear to normal stresses, exhibiting a critically stressed state in the sandstones and a highly stressed state in the volcanic layer. As critically stressed faults are described as hydraulically transmissive (Barton et al. 1995, 1996), these NNE-striking faults are expected to be the main fluid pathways in the reservoir (Moeck et al. 2008a). The bottom of the production well, drilled in 2006, is in the direct vicinity of a NE-striking, and W-dipping minor fault (Fig. 1).

The natural fractures in the reservoir are parallel to NW-striking strike-slip faults and NE- to N-striking normal faults (Moeck et al. 2005). Among these structures, the N- to NE-striking fractures are expected to serve as principal flow paths due to their high slip and high dilational tendency in the current stress field (Moeck et al., 2009).

Hydraulically induced fractures

Four induced hydraulic fractures exist in the well doublet (Table 2). At the production well, a waterfrac treatment was applied in the low permeability volcanic rocks, using large amounts of water to create long fractures with a low aperture. Two gel-proppant treatments were used to stimulate the sandstone sections with cross-linked gels and proppants of a certain mesh size. These treatments can be applied in a wide range of formations. At the injection well, two gel-proppant-fracs and two waterfracs were performed and are henceforth referred to as ‘multifrac’ (Zimmermann et al. 2010a).

Table 2.   Dimensions and hydraulic properties of the induced fractures under in situ conditions.
WellTypeLayerDepth (m)Height (m)Half length (m)Kfr(m sec−1)a (mm)
  1. The hydraulic conductivity Kfr was estimated by means of a reference dynamic viscosity of 0.3 mPa sec for the production well and 0.72 mPa sec for the injection well.

Injection2× gel-proppant 2× waterIIB, IIC, III−4004 to −41471431600.0590.228
ProductionWaterIII, IV−4098 to −42431451900.1420.228
ProductionGel-proppantIIB, IIC−3996 to −4099103600.1420.228
ProductionGel-proppantIIA, IIB−3968 to −406395600.1420.228

The dimensions (height, half length and aperture, see Table 2) of all four induced fractures were computed with the 3D fracture simulator fracpro (Cleary 1994) and verified by field experiments (Zimmermann & Reinicke 2010; Zimmermann et al. 2010a). fracpro software allows the integration of geological background information and takes wellhead pressures, friction and near-wellbore tortuosity into account. The multifrac at the injection well ranges vertically from the Elbe base sandstone II to the Havel formation. The first gel-proppant frac at the production well ranges from the Elbe base sandstone II to the Elbe base sandstone I. The second gel-proppant frac ranges from the Elbe alternating sequence to the Elbe base sandstone II, and the waterfrac ranges from the Havel formation to the volcanic rocks (Fig. 1). The horizontal distances from the second gel-proppant frac, first gel-proppant frac and waterfrac at the production well to the multifrac at the injection well are 308, 352, and 448 m respectively. Microseismicity was monitored by a three-axis geophone installed in the injection well at −3735 m during waterfrac treatment in the production well. The orientation of the seismic events is similar to the maximum horizontal stress direction SH = 18.5 ± 3.7° (Kwiatek et al. , 2008, 2009). This implies that the induced waterfrac is mainly tensile, with the aperture direction along the minimum principal stress and strike direction along the maximum principal stress.

The hydraulic properties of the fractures were computed with fracpro, and the transmissibility TRfr of the multifrac at the injection well was verified by a long-term injection experiment in 2004 (Zimmermann et al. 2009). From this experiment a fracture transmissibility (TRfr) of approximately 1 Dm ≈ 9.9E−13 m3 was determined. This transmissibility value was applied to the other fractures based on the fracpro simulations. The fracture transmissibility depends strongly on pore pressure (see the Transient state section) and is related to fracture permeability kfr and aperture a:

  • image(1)

Under the assumption of laminar flow between parallel plates, the fracture permeability is related to fracture aperture by kfr=a2/12 and a hydraulic aperture of 0.228 mm was determined by:

  • image(2)

Based on the hydraulic aperture the corresponding fracture permeability can be calculated. The fracture hydraulic conductivity Kfr defined in the simulation (Table 2) was determined by means of the gravitational acceleration g (m sec−2), reference density of the fluid ρ (kg m−3) and dynamic viscosity of the fluid μ (kg msec−1):

  • image(3)

Due to different temperatures, a dynamic viscosity of 0.3 m Pa sec was used for the production well and 0.72 m Pa sec was used for the injection well.

Wells

The arrangement of the two wells must fulfill two important conditions. First, the pressure in the reservoir must not drop significantly below the initial formation pressure during production. Second, a temperature drop in the production well must be minimized. The two wells are 28 m apart at the surface. As both wells start from the same drill site and the injection well is vertically orientated, the production well had to be deviated to ensure a distance of 500 m between wells within the reservoir. At the top of the reservoir (−3815 m), the inclination is 18° and it increases progressively to 48° at −4236 m. Therefore, the distance between the two wells increases from 241 to 470 m between the top and bottom of the reservoir (Fig. 1).

Mechanical properties

Moeck et al. (2008b) and Moeck et al. (2009) have presented a stress state determination for the Lower Permian (Rotliegend) reservoir using an integrated approach of 3D structural modeling, 3D fault mapping, stress ratio definition based on frictional constraints, and slip tendency analysis. The results that the minimum horizontal stress Sh is greater or equal to 0.55 times the vertical stress SV (Sh≥ 0.55SV), and that SH≤ 0.78 to 1.00SV for the maximum horizontal stress, which collectively indicates stress regimes from normal to strike slip faulting. Thus, stresses acting in the 4035-m-deep reservoir are SV = 100 MPa, Sh = 55 MPa and SH = 78–100 MPa. These stress ratios are supported by analysis of borehole breakouts in the injection well (Moeck & Backers 2006).

Holl et al. (2005) determined a horizontal stress direction of SH = 18.5 ± 3.7° in the Rotliegend at Groß Schönebeck. This stress direction correlates to the world stress map (Zoback 1992) and is supported by further analysis of borehole breakouts in the NEGB (Roth & Fleckenstein 2001).

The pore pressure of the reservoir is pp = 43.8 MPa, as determined by p, T-logs under stationary conditions at the geothermal target horizon (Legarth et al. 2005). According to the stress relation for normal faulting (SV=S1), the effective vertical stress is SVeff = S1pp = 56.2 MPa and the effective mean stress is Smeff = (S1+S2 + S3)/3−pp = 41.2 MPa.

The elastic moduli for homogeneous isotropic materials were determined by ultrasonic and density logs. Young's modulus (E) for both the sandstone and the volcanic rocks is 55 GPa, and Poisson's ratio (ν) is 0.18 and 0.2 respectively (Zimmermann et al. 2010a).

Hydraulic properties

During geothermal power production using a borehole doublet the reservoir conditions will change. In addition to a temperature decrease at the injection well, which will result in a thermoelastic response, the pore pressure will vary. The initial pore pressure of the reservoir is pp = 43.8 MPa. Assuming a productivity index PI = 13–15 m3 h−1 MPa−1 as determined from well testing (Zimmermann et al. 2010a,b) and a target injection/production rate of 75 m3 h−1, a pore pressure change of ≈5 MPa can be calculated. This leads to a poroelastic response of the reservoir rocks that depends on effective pressure peff (the difference between confining pressure pc and pore pressure pp). Poroelastic responses will result in a change in permeability k (Al-Wardy and Zimmermann, 2004) and porosity φ (Carroll & Katsube 1983; Zimmerman 1991). Although the minimum horizontal stress Sh is 55 MPa, the confining pressure pc was approximated by the mean stress Sm = 85 MPa. According to peff=pcpp, an effective pressure change of peff≈5 MPa can be assumed.

To explore the poroelastic response of Rotliegend sandstone, we investigated porosity and permeability dependence on effective pressure with laboratory experiments (Blöcher et al. 2009). During the laboratory experiments, the porosity decreases by 6.2% as peff increases from 5 to 37 MPa, and the permeability decreases by 21.3% as peff increases from 3 to 30 MPa. The most significant changes occur at low effective pressures up to 20 MPa (Fig. 2). At effective pressures above 20 MPa, the porosity changes by less than 0.8%, and the permeability changes by less than 2.3% as peff changes by 5 MPa. Therefore, the porosity and permeability dependence on effective pressure can be excluded from our numerical investigation.

image

Figure 2.  Measured porosity and permeability dependence on effective pressure for a Rotliegend sandstone (Flechtinger sandstone, an outcropping equivalent of the reservoir rock).

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The initial hydraulic condition of the injection well was tested with a production test of the entire open-hole section between −3815 and −4236 m in 2001 (Legarth et al. 2005; Zimmermann et al. 2009), and a productivity index of 0.97 m3 h−1 MPa−1 at maximum pressure drawdown was determined. From the shut-in period, a transmissibility TR between 4E−14 and 6E−14 m3 was derived. The coefficient of transmissibility is equivalent to the coefficient of permeability k multiplied by the thickness of the aquifer. A flow log showed outflow only in the conglomerates and the volcanic sections; the sandstone section was not permeable, perhaps due to mud infiltration during the long standstill period of the well. Therefore, the transmissibility value may reflect the transmissibility of the conglomerates and volcanic rocks only. As the rock matrix of the conglomerates and the volcanic rocks is nearly nonconductive, nearly all fluid flow occurs in the natural fracture system. For the sandstone layer, the influence of the natural fracture system on the rock conductivity is less pronounced, and matrix flow is the dominant process. The total thickness of conglomerates and volcanic rocks is 136 m, so that a permeability k of 2.9E−16 to 4.4E−16 m2 is obtained (compare Table 3).

Table 3.   Hydraulic and thermal properties of the reservoir rocks under in situ conditions.
Unitk (m2)K (m sec−1)φ (%)T (°C)λs (W mK−1)VHCs (MJ m−3 K)
  1. The hydraulic conductivity K was estimated by means of a reference dynamic viscosity of 0.3 mPa sec (at T = 150°C and C = 265g l−1).

I4.9E−171.6E−91138.21.92.4
IIA2.0E−156.4E−83141.71.92.4
IIB4.0E−151.3E−78143.22.92.4
IIC7.9E−152.6E−715145.22.82.4
III9.9E−173.2E−90.1146.53.02.6
IV9.9E−173.2E−90.5147.42.33.6

Neutron porosity measurements from Reservoir Saturation Tool (RST) logs were also used to estimate permeability by applying the empirical formula by Pape et al. (2000), which is based on a fractal approach. This results in minimum permeability of 3.9E−17 m2 for volcanic rocks and maximum permeability of 1.1E−13 m2 for Elbe base sandstone. This calculation was repeated with porosity data from density and sonic measurements and led to transmissibilities of 2.5E−13 to 6.9E−13 m3 for the 107-m-thick sandstone layer (−4004 to −4111 m). From the determined transmissibility and the thickness of the sandstone layers, permeability ranging from 2.3E−15 to 6.5E−15 m2 was calculated (Table 3). These porosity φ and permeability k data were verified by abundant porosity (290 samples) and permeability measurements (109) on cores (Trautwein & Huenges 2005), and the derived physical parameters assigned to the stratigraphic layers are listed in Table 3. A ratio between vertical and horizontal permeability of kz/kxy=0.25 was determined by the core measurements and was assigned to the reservoir model.

Feflow software requires hydraulic conductivity K (m sec−1) values of the solid rock (Table 3). Hydraulic conductivity is related to permeability tensor k (m2), gravitational acceleration g (m sec−2), reference density of the fluid ρ (kg m−3) and dynamic viscosity of the fluid μ (kg ms−1):

  • image(4)

The dynamic viscosity of the fluid is commonly regarded as a function of mass concentration C of one or more species (here the value of total dissolved solids or TDS was used) and temperature T (Diersch 2002):

  • image(5)

with mass fraction and relative temperature coefficient

  • image(6)

Fluid density is also related to temperature T, pressure p and concentration C:

  • image(7)

with thermal expansion coefficient β=β(T,p), compressibility γ=γ(T,p) and density ratio α=α(T,p,C) all related to temperature, pressure and concentration (Magri et al. 2005). The flow and transport equations for thermohaline convection are nonlinear and strongly coupled as temperature, pressure and salinity control the fluid density.

During geothermal power generation, a production temperature of 150°C and an injection temperature of 70°C are scheduled. To include the viscosity dependence on temperature and concentration, we adjusted the hydraulic conductivity K as follows: for the matrix, the hydraulic fractures at the production well and the production well itself, a dynamic viscosity of 0.3 mPa sec (at T =  50°C and C = 265 g l−1) was estimated, and for the cooler injection well and the hydraulic fracture a dynamic viscosity of 0.72 mPa sec was estimated (at T = 70°C and C = 265 g l−1).

To calculate the dynamic change of fluid density during geothermal power generation, we implemented Eqn 7 into the Feflow environment. The reference values were concentration C0 = 0 g l−1, CS = 350 000 mg l−1, pressure p0 = 100 kPa and temperature T0 = 0°C. The density equation of state was adjusted by means of sodium chloride concentration, but, as shown in Section 8, the reservoir fluid is composed of a mixture of calcium and sodium chloride. Therefore, we compared density and viscosity of calcium and sodium chloride brine at various state points (C = 0–292 g l−1; T = 20–80°C). Due to the fact that the density relation takes only the total dissolved solids (TDS) into account, the calculated data match the measurements very well. We calculated the viscosity and density dependence on pressure, temperature and concentration as shown in Fig. 3.

image

Figure 3.  Calculated dynamic viscosity (left) and density (right) of the fluid depending on temperature, pressure and total dissolved solids (TDS). The viscosity and density are significantly different at the injection and production wells.

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Thermal properties

According to the continental geothermal gradient at this site, the temperature of the reservoir increases from Hannover formation at 137.5–150°C in the volcanic rocks (Henninges et al. 2005). Thermal conductivity λ and volumetric heat capacity (VHC) differ between fluid (f) and solid (s) phases and the bulk (b) property can be calculated by volume fraction-weighted sum as follows:

  • image(8)

Due to the low porosity of the reservoir rocks, the properties of the solid fraction are similar to the bulk properties.

The thermal properties of the NEGB are well investigated: Lotz (2004) and Scheck (1997) give values for the thermal conductivity, Magri (2005) for the heat capacity and Norden et al. (2008) for the surface heat flow. The results of the latter investigations are summarized in Table 3.

Values of the thermal conductivity were determined by laboratory experiments at 20°C and corrected for temperature dependence. Somerton (1992) has developed the following correlation equation based on experimental data for fully saturated sandstones:

  • image(9)

where λ20 denotes the thermal conductivity measured at 20°C by laboratory experiments.

Using Eqn 9, we calculated the thermal conductivity of the solid at any point of the reservoir.

McDermott et al. (2006) have shown that changes in fluid heat capacity at dynamic conditions similar to those of the Groß Schönebeck reservoir are marginal. Therefore, a constant value was chosen. The heat capacity of the solid was kept constant as well.

Norden et al. (2008) determined a heat flow of q=75 ± 3 mW m−2 for the Permo-Carboniferous formation at the bottom of the reservoir. By means of a stationary simulation (see the Introduction section), we compared measured and calculated in situ temperature fields. Best results were generated with a constant heat flow value of q=72 mW m−2.

Chemical properties of the formation fluid

The composition of the formation fluid at the injection well was initially measured by downhole sampling before the first stimulation treatment in January 2001. The samples were taken from the zone of main influx located at the transition from volcanics to conglomerates and exhibit a TDS of approximately 265 g l−1. A pH value of 5.7 was determined. As shown in Table 4, calcium and sodium are the main cations (with a dominant share of calcium) and chloride is the main anion. Therefore, the formation fluid is classified as Ca–Na–Cl type, which is a typical Rotliegend fluid (Wolfgramm et al. 2003). The analyzed mass fraction (wt%) of calcium, sodium and chloride corresponds to approximately 150 g l−1 calcium chloride and 100 g l−1 sodium chloride. The influence of the TDS on density and viscosity was necessarily taken into account for the present study.

Table 4.   Composition of Rotliegend fluid at the injection well before first stimulation treatment in 2001.
Cationsmg l−1mEq l−1Anionsmg l−1mEq l−1
Ca2+54 0002694.61Cl167 30047 18.92
Na+38 4001670.29Br3003.75
K+290074.17SOinline image1402.91
Sr2+190043.37HCOinline image18.90.31
Mg2+43035.38   
Mn2+2709.83   
Fe2+2007.16   
Li+20429.39   
Pb4+1803.48   
NHinline image754.16   
Zn2+742.26   
Ba2+340.50   
Cu2+70.22   
Cd2+1.80.03   
As3+1.40.06   
Total98 677.24574.91 167 758.94725.90
Error of ion balance = inline image=−0.016
Dissolved SiO2=80 mg l−1
Total dissolved solids (TDS)=266.5 g l−1
pH=5.7

Numerical approach

  1. Top of page
  2. Abstract
  3. Introduction
  4. Reservoir characterization
  5. Numerical approach
  6. Application – simulation of Groß Schönebeck Site
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. Nomenclature
  11. References

Governing equations

Feflow fully implements the governing equation of thermohaline convection in a saturated porous media (Diersch 2002). These equations are derived from the conservation principles for linear momentum, mass and energy (e.g. Bear & Bachmat 1990; Kolditz et al. 1998), and the resulting system is given by the following set of differential equations:

  • image(10)

where Ss, qfi and Q denote specific storage coefficient, Darcy velocity vector and source/sink function of the fluid respectively. The Darcy velocity vector can be expressed in terms of the hydraulic conductivity tensor Kij, fluid viscosity relation function fμ and fluid density ρf:

  • image(11)

Without adsorption of the solute at the solid surface, the source/sink of the solute mass QC can be calculated as the sum of mass storage, convection and diffusion (Fickian law):

  • image(12)

where C is the mass concentration, D the hydrodynamic dispersion and φ the porosity. The heat supply QT is the sum of heat storage, convection and conduction (Fourier's law) and is determined by means of heat capacity c of the fluid and solid and the thermodispersion tensor λij (conductive and dispersive) at temperature T:

  • image(13)

with

  • image(14)

Spatial discretization

The horizontal extent of the model is defined by the dimension of the maximum hydrothermal–mechanical influence of stimulation treatments, reservoir utilization by production/injection during power production and geological boundary conditions. Structural geological data are integrated into the model through two north-west-striking faults along the north-east and south-west borders of the reservoir. These faults are no-flow boundaries, qnh(xi,t) = 0 m sec−1, due to a frictional blockade in the current stress field (Moeck et al., 2008b). We defined a model area of 5448 m in an east–west direction by 4809 m in a north–south direction. The vertical extent of a maximum of 594 m is given by geological boundaries, the Zechstein salt at the top and underlying Carboniferous at the bottom. Both rock units are hydraulically nonconductive.

In order to avoid excessive numbers of elements, we refined the model in areas of hydraulically induced fractures and the near-wellbore region. Consequently, each layer was filled with 18 133 six-nodal triangular prisms. Due to the refinement, the edge length of the prism front surface varies between 2.5 and 400 m in the xy direction. To keep the ratio between xy and z length close to 1, we performed vertical refinement by subdividing each geological layer into 2–10 sub-layers (Table 1), resulting in an average thickness of 16 m. Altogether, 27 spatial layers consisting of 489 591 prism elements and 254 744 nodes define the model area (Fig. 4).

image

Figure 4.  Unstructured reservoir grid consisting of 27 vertical layers, each with 18 133 triangular prisms. Together, these 27 vertical layers represent the six geological formations.

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The induced fractures are represented by 2D quadrilateral vertical elements. These quadrilateral vertical elements are consistent with the side surfaces of the six-nodal triangular prisms. Therefore, their vertical extent is 16 m, and the horizontal extent is between 2 and 3 m.

To represent the vertical injection well, 1D linear vertical elements with a cross-sectional area of 126.7 cm2 (diameter d=5 inch) were chosen. As the production well is deviated, and Feflow only supports 1D linear vertical elements, we achieved a short circuit of the three production fractures by arbitrary 1D linear elements. By means of these special 1D elements, nodes of different layers and horizontal positions can be connected without any interaction with the surrounding matrix elements. For the production well, a cross-sectional area of 126.7 cm2 (diameter of d = 5 inch) was implemented. With Hagen–Poiseuille's law we estimated the hydraulic conductivity of both wells as 6867 m sec−1 for the injection well and 16 480 m sec−1 for the production well. The discrepancy in hydraulic conductivity results from a contrast in dynamic viscosity, 0.72 mPa sec at 70 °C for the injection well and 0.3 mPa sec at 150°C for the production well.

Time discretization

Feflow provides two automatic temporal discretization techniques: automatic time step control based on a predictor–corrector scheme of first-order accuracy (forward Euler/backward Euler) and a scheme of second-order accuracy (forward Adams–Bashforth/backward trapezoid). The forward Euler/backward Euler time integration scheme was applied in our study. For mass transport, we chose Feflow’s full upwinding option.

For both the stationary and transient models, we started with an initial time step length of 1E−08 days. The final times of the stationary and transient models were set at 105 years and 30 years respectively. The reasons for this decision are described in detail in the Stationary state and Transient state sections.

Application – simulation of Groß Schönebeck Site

  1. Top of page
  2. Abstract
  3. Introduction
  4. Reservoir characterization
  5. Numerical approach
  6. Application – simulation of Groß Schönebeck Site
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. Nomenclature
  11. References

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(xi,t0) = −185 m for the total domain. The initial temperature T(xi,t0) 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(xi,t) = 137.5°C for the total time of simulation. A terrestrial heat flow of qnT(xi,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).

image

Figure 5.  Observed and simulated reservoir temperature profile.

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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(xi,t)=137.5°C, and added a constant temperature of T(xi,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(xi,t)=75 m3 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(xi,t)=−75 m3 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(xi,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.

image

Figure 6.  Chronological sequence of propagation of the 130°C temperature front after start of injection at the Elbe base sandstone I. Also shown is the projection of the drill site Groß Schönebeck, illustrating the well paths of injection well (blue line), production well (red line) and induced fractures.

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image

Figure 8.  Horizontal cross-section at a depth of −4070 m and vertical cross-section from W to E showing (A) hydraulic head distribution, (B) temperature distribution and (C) velocity field at the final simulation state.

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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).

image

Figure 7.  Simulated flow field and travel time of the injected water after start of injection at the Elbe base sandstone I.

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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 m3 h−1 MPa−1 and an injection/production rate of 75 m3 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 m3 h−1 MPa−1 for the production well and a PI of 14.9 m3 h−1MPa−1 for the injection well.

image

Figure 9.  Simulated hydraulic heads (left) at the injection and production well and temperature (right) at the three production fractures over reservoir lifetime of 30 years.

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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:

  • image(15)

where kfr, a, lfr 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 influxBuild-up/drawdown (MPa)PI (m3 h−1 MPa−1)
m3 h−1%
FCD = 0.1 × FCD0
 Injection well74.4100.08.68.7
 Second gel-proppant frac25.934.7  
 First gel-proppant frac34.346.0  
 Waterfrac14.519.4  
 Production well74.6100.0−12.65.9
FCD = FCD0
 Injection well73.8100.05.014.7
 Second gel-proppant frac26.535.8  
 First gel-proppant frac28.939.1  
 Waterfrac18.625.1  
 Production well74.0100.0−4.217.7
FCD = 10 × FCD0
 Injection well74.0100.03.124.2
 Second gel-proppant frac27.136.7  
 First gel-proppant frac28.238.1  
 Waterfrac18.625.1  
 Production well73.9100.0−2.925.6
image

Figure 10.  Hydraulic heads (left) at the injection and production wells and production temperature (right) during reservoir lifetime for three different dimensionless fracture conductivities (FCDs).

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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 m3 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 m3 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.

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Reservoir characterization
  5. Numerical approach
  6. Application – simulation of Groß Schönebeck Site
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. Nomenclature
  11. References

Compared with measurements from the reservoir, the simulation results revealed some limitations in the modeling procedure. A major limitation may be the restricted implementation of geological structures that are commonly dipping, and thus nonvertical and undulating. During the hydraulic fracture treatments at the production well in 2007, a direct pressure response in the injection well was observed. The software Feflow cannot handle dipping single structures like fault zones. Such fault zones may explain the direct pressure response from one well to the other. A set of north to NE striking faults, known from the 3D structural model and presumably reactivated or dilated by the fluid pressure increase during stimulation, may have acted as connecting structures and causes the instantaneous pressure response in the neighboring well. These structures may act as important hydraulic elements but are not implemented in the current numerical model.

In the present simulation the permeability, porosity and heat capacity were treated as constants. According to laboratory experiments, the changes in these parameters for the rock matrix are small and can be neglected. By contrast, the hydraulic conductivity of the induced fractures depends strongly on the pore pressure. This dependence can be implemented in Feflow by changing the fracture properties using the Feflow InterFace Manager (IFM). Pore pressure changes are caused by production and injection rates, but also by changes in the in situ stress field. This mechanical coupling is not part of Feflow, and its influence has to be examined using other simulation software like Geosys (Wang et al. 2009) or Eclipse (Schlumberger 2008) and verified by field tests.

Using the current Feflow model, we determined that the first arrival of the cold-water front at the production well will occur after 3.6 years. After 30 years of geothermal power production, the predicted temperature of the production fluid is 125.8°C, equivalent to a temperature decrease of approximately 19°C. Franco & Villani (2009) have shown that this temperature decrease will result in a reduction in power provision by 20–30%.

Conclusions

  1. Top of page
  2. Abstract
  3. Introduction
  4. Reservoir characterization
  5. Numerical approach
  6. Application – simulation of Groß Schönebeck Site
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. Nomenclature
  11. References

The primary objective of this paper is to understand the hydrothermal processes occurring in an EGS during geothermal power production. Such an understanding is critical to optimal reservoir management and sustainable utilization. Therefore, we simulated the hydrothermal conditions of the geothermal research doublet and related induced fractures at the deep geothermal reservoir of Groß Schönebeck.

A change in the dimensionless FCD of the induced fractures strongly influences the pressure response of the reservoir. For low FCD, the induced fractures become hydraulically ineffective, resulting in a decrease in the productivity index. By contrast, the time and the magnitude of the thermal breakthrough are not greatly affected by the conductivity of the induced fractures. Inclusion of natural fault zones and their pressure-dependent conductivity is the most important issue for further investigations.

In the present study, we captured most of the relevant processes for an EGS by means of a thermohaline simulation including deviated wells and hydraulically induced fractures. The current numerical model displays the reservoir behavior during 30 years of geothermal power production. In particular, the numerical model integrates the known reservoir geometry, structural geology, hydrothermal conditions and the relevant coupled processes. The simulation improves understanding of reservoir behavior, interpretation of the stimulation treatments and prediction of the long-term reservoir characteristics during geothermal power production. The well path design and the importance of induced fractures can be evaluated. Planning a borehole doublet system is a double edged problem: on the one hand, the distance between the wells should be as large as possible to avoid a thermal breakthrough. On the other hand, wells should be close enough to reduce pressure drawdown in the production well and hence the auxiliary power demand.

For the research doublet system at Groß Schönebeck, the simulated thermal breakthrough started after 3.6 years of production, but the temperature decreases less than 19°C during the prospective 30 years of geothermal power production. Our results may guide reservoir management in its early stages and, with additional new measurements and parameters from the reservoir, the model can be progressively updated. Although the current model has some bottlenecks, it has potentially important implications for utilization of geothermal systems for power production.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Reservoir characterization
  5. Numerical approach
  6. Application – simulation of Groß Schönebeck Site
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. Nomenclature
  11. References

We extend our thanks to all participating colleagues at GFZ Potsdam and in particular to Jonathan Banks and James E. Faulds for their valuable contributions. Thanks are also due to the editor Steve Ingebritsen and three anonymous reviewers for editing and reviewing the manuscript. This work was primarily funded by the German Federal Ministry of Education and Research.

Nomenclature

  1. Top of page
  2. Abstract
  3. Introduction
  4. Reservoir characterization
  5. Numerical approach
  6. Application – simulation of Groß Schönebeck Site
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. Nomenclature
  11. References
Greek symbols
α

density ratio (–)

αL, αT

longitudinal and transversal thermodispersivity (m)

β

thermal expansion coefficient (°C−1)

δ

Kronecker delta (–)

γ

compressibility (MPa−1)

λ

thermal conductivity (W m −1 K−1)

μ

dynamic viscosity (kg m−1 sec−1)

ν

Poisson's ratio (–)

ω

mass fraction (–)

φ

porosity (–)

ρ

density (kg m−3)

ς

temperature coefficient (–)

Roman symbols
a

aperture (m)

C

mass concentration (mg l−1)

c

specific heat capacity (J kg−1 K−1)

D

hydrodynamic dispersion

d

well diameter (m)

ej

gravitational unit vector

FCD

dimensionless fracture conductivity (–)

g

gravitational acceleration (m sec−2)

h

hydraulic head (m)

K

hydraulic conductivity (m sec−1)

k

permeability (m2)

L

reference length (m)

l

fracture half length (m)

p

pressure (MPa)

Q

pumping/injection rate of a single well (m sec−3)

q

surface heat flux (mW m−2)

Q , QT, QC

source/sink function of fluid, heat and contaminant mass (s−1)

qfi

Darcy velocity vector (m sec−1)

qnh

normal Darcy flux (m sec−1)

qnT

normal heat flux (mW m−2)

S1, S2, S3

maximum, intermediate and minimum principle stress

Sh, SH, SV

minimum and maximum horizontal stress and vertical stress

Ss

specific storage coefficient (m−1)

T

temperature (°C)

t

time (s)

TR

transmissibility (m−3)

Vfq

absolute Darcy flux (m sec−1)

VHC

volumetric heat capacity (J m−3 K−1)

xi

xj, position vector

Subscript
0

value at initial condition (t = 0) or reference value

20

value at T=20°C

b, f, s

bulk, fluid and solid

c

confining

eff

effective

fr

fracture

i, j

tensor components

meff

effective mean

p

pore

S

at saturation point

x, y, z

coordinates

Superscripts
cond

conductive part

disp

dispersive part

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Reservoir characterization
  5. Numerical approach
  6. Application – simulation of Groß Schönebeck Site
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. Nomenclature
  11. References
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