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Environmental Earth Sciences ISSN 1866-6280 Environ Earth SciDOI 10.1007/s12665-013-2402-3

Modelling of fractured carbonate reservoirs:outline of a novel technique via a case studyfrom the Molasse Basin, southern Bavaria,Germany

Mauro Cacace, Guido Blöcher, NorihiroWatanabe, Inga Moeck, Nele Börsing,Magdalena Scheck-Wenderoth, OlafKolditz & Ernst Huenges

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SPECIAL ISSUE

Modelling of fractured carbonate reservoirs: outline of a noveltechnique via a case study from the Molasse Basin,southern Bavaria, Germany

Mauro Cacace • Guido Blocher • Norihiro Watanabe •

Inga Moeck • Nele Borsing • Magdalena Scheck-Wenderoth •

Olaf Kolditz • Ernst Huenges

Received: 15 November 2012 / Accepted: 7 March 2013

� Springer-Verlag Berlin Heidelberg 2013

Abstract Fluid flow in low-permeable carbonate rocks

depends on the density of fractures, their interconnectivity

and on the formation of fault damage zones. The present-

day stress field influences the aperture hence the trans-

missivity of fractures whereas paleostress fields are

responsible for the formation of faults and fractures. In

low-permeable reservoir rocks, fault zones belong to the

major targets. Before drilling, an estimate for reservoir

productivity of wells drilled into the damage zone of faults

is therefore required. Due to limitations in available data, a

characterization of such reservoirs usually relies on the use

of numerical techniques. The requirements of these math-

ematical models encompass a full integration of the actual

fault geometry, comprising the dimension of the fault

damage zone and of the fault core, and the individual

population with properties of fault zones in the hanging and

foot wall and the host rock. The paper presents both the

technical approach to develop such a model and the

property definition of heterogeneous fault zones and host

rock with respect to the current stress field. The case study

describes a deep geothermal reservoir in the western cen-

tral Molasse Basin in southern Bavaria, Germany. Results

from numerical simulations indicate that the well produc-

tivity can be enhanced along compressional fault zones if

the interconnectivity of fractures is lateral caused by

crossing synthetic and antithetic fractures. The model

allows a deeper understanding of production tests and

reservoir properties of faulted rocks.

Keywords Fractured carbonate geothermal reservoirs �Fault core and damage zone � In situ stress field �3D mesh generator � OpenGeosys � Well productivity

Introduction: general

Recent advances in hardware and software capabilities

have led to an increased use of numerical operations for the

scientific study of processes occurring in natural systems

(Oreskes et al. 1994; Turner 2006). A natural system

should be regarded as the final product of several inter-

acting components and coupled processes. What makes the

problem challenging is the need for a unified description

linking and grasping the coupling between different scales

and related physical phenomena involved.

Modelling of such complex systems as represented by

fractured reservoirs becomes increasingly important for

groundwater, petroleum, gas or geothermal utilization. The

prominent role played by faults and fractures on reservoirs’

productivity and recovery has been long recognized (Cacas

M. Cacace (&) � G. Blocher � M. Scheck-Wenderoth �E. Huenges

Helmholtz Centre Potsdam GFZ German Research Centre

for Geosciences, Telegrafenberg, 14473 Potsdam, Germany

e-mail: cacace@gfz-potsdam.de

URL: http://www.gfz-potsdam.de

N. Watanabe � O. Kolditz

Helmholtz Centre for Environmental Research UFZ,

Permoserstrasse 15, 04318 Leipzig, Germany

I. Moeck

Department of Earth and Atmospheric Sciences,

University of Alberta, Alberta, Canada

N. Borsing

University of Potsdam, Am Neuen Palais 10,

14469 Potsdam, Germany

O. Kolditz

Dresden University of Technology, Helmholtzstrasse 10,

01069 Dresden, Germany

123

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DOI 10.1007/s12665-013-2402-3

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et al. 2001; Hickman et al. 1998; Muller et al. 2010). Fluid

flow is likely to occur along open fractures giving rise to

secondary permeability and porosity which may drastically

modify the hydrogeologic conditions and the flow

dynamics of the reservoir. In a typical carbonate fractured

reservoir rock, matrix permeability is low, whereas an

enhanced permeability is given through fractures and faults

(e.g. Ferrill et al. 2009; Wibberley 2008 and references

therein; Anderson 1951; Anderson and Fairley 2008).

Fractures and faults permeability depends on the inter-

connectivity of fractures and the characteristic of damage

zone and core of a fault with respect to the host rock.

The definition of the relevant hydraulic properties of

existing major fault zones is particularly crucial to estimate

the range of reservoir productivity from such fractured rock

under the current stress field. It follows that an analysis of

such systems should be estimated by numerical models of

the reservoir behaviour. The use of computer modelling in

the planning and management of the development of geo-

thermal reservoirs has become a standard practice during

the last two decades (O’Sullivan et al. 2001 and references

therein).

This study deals with a novel workflow for modelling

fractured geological reservoir. The approach comprises the

building of the conceptual model, its migration into a

coherent structural geological model and an automatized

conversion of the latter into a dynamic process simulation.

In the present study, these concepts are described by

taking a field application as a natural working example for

a rather complex carbonate fractured reservoir. The model

area describes the geothermal reservoir Mauerstetten

(south German Molasse Basin) where a well has been

drilled into Upper Jurassic carbonate rock. The existing

well has been drilled along a fault dip into the hanging wall

without penetrating its damage zone as indicated by

hydraulic tests. This newly developed model should pro-

vide quantitative answers to the following two issues:

(a) whether and to which degree the damage zone can

influence the long-term production from the reservoir, and

(b) whether and to which extent the productivity can be

increased by drilling directly inside the damage zone.

Although the general behaviour of these scenarios could

even be expected (rather qualitatively though) without a

proper modelling of the system, the adopted simulation

enables to quantify these predictions in terms of reservoir

performance.

Therefore, the novelty and merits of the manuscript does

not stem only from an improved technique to model frac-

tured reservoirs by which to simulate the interaction

between flow within fractures and fault zones and

throughout the host porous matrix. At the same time, by its

application to the Mauerstetten geothermal reservoir, the

modelling approach enables to reveal the impact of the

permeability structure and geometry of fault zones on the

nearby reservoir productivity. On the one hand, the

approach outlines in the manuscript has added values for a

wide range of geoscientific topics including CO2 seques-

tration issues, shale gas extraction and enhanced heat or oil

recovery. On the other hand, the study via its direct

application already provides important insights in under-

standing reservoir scale permeability structure in a frac-

tured carbonate geothermal reservoir.

Introduction: geologic setting, in situ stress field

and fault characteristics

Throughout the manuscript, depths are indicated as nega-

tive with respect to the reference level they are calculated

from, i.e. -3,000 m TDVSS (true vertical depth subsea) is

used to indicate a depth position which is 3,000 m below

mean sea level and -3,000 m TVD (true vertical depth)

indicates the depth position of a point in the well which is

3,000 m below the ground surface. To avoid any possible

misinterpretation, both values are always given.

Geological setting and permeability structure

The South German Molasse Basin (SGMB) is a part of the

North Alpine Foreland Basin (NAFB) which evolved from

Upper Eocene to Upper Miocene in response to Alpine

tectonics and accompanied erosion and uplift (Kuhlemann

and Kempf 2002). The basement of the SGMB consists of

Upper to Middle Jurassic carbonate rocks which are

ongoing to be explored and utilized for geothermal energy

production. The basin-wide permeability structure of these

carbonate rocks is heterogeneous and varies with the

regional difference of permeability controls from facies

and faults (Wolfgramm et al. 2009; Birner et al. 2011). In

particular, the causes for the changing permeability struc-

ture of the Upper Liassic Malm aquifer are still under

debate. The temperature distribution could provide some

indications (Energiegewinnung 2010). The temperature in

the east of the basin is higher than in the west indicating a

larger recharge of meteoritic water through permeable rock

than in the western part in the Allgau region, SW of

Stanberg Lake. High-porous reef limestone could be one

reason for this enhanced permeability. However, in the

eastern part of the basin, platy micritic limestones are

described (Wolfgramm et al. 2009), indicating that faults

may play a major role for fluid and heat transport. Towards

the southwestern part of the SGMB, the Malm lithofacies

change to fine-grained limestone and marl (referred as

Helvetian facies) which is considered as low-permeable

rock (Wolfgramm et al. 2009). Temperatures are higher in

the Malm aquifer of the southwestern basin part, indicating

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that faults might be low permeable in this region or that

fluids heated up through their migration.

Another reason for this variable permeability structure

might be a different faulting style with varying fault

damage zone characteristics. A fault zone consists of a

fault core where the major displacement occurred, and a

fault damage zone where increased fracture network

compensated the faulting process towards the non-faulted

host rock. Fault core and damage zone can have either

positive or negative effects on permeability (Wibberley

2008 and references therein). More details on fault zone’s

permeability architecture and induced hydraulic effects

will be given in the following sections (‘‘Fault zone char-

acteristics and fluid flow’’).

The study area Mauerstetten is located in the southwestern

part of the SGMB, east of Kempten and west of the Starnberg

Lake. A well has been drilled into an E–W striking normal

fault to a depth of -3,763 m TVD (-3,052 m TVDSS)

encountering the Malm aquifer (see Fig. 1). The deviated

well path is placed into the hanging wall of the fault zone. A

hydraulic model shall clarify the expected production rates

from this well under the conditions of no flow along the fault

and enhanced permeability through connected fractures in

the hanging wall. Before the model set up is described, an

analysis of the present-day in situ stress field and of the fault

regime shall help to quantify the permeability structure of the

fault core and damage zone.

In situ stress field

The fault system in the Upper Jurassic is dominated by

E–W to NE–SW striking normal faults with offsets of 150–

200 m. Assuming the Andersonian fault–stress concept

(Anderson 1951), such a normal fault system would require

a stress regime with direction of the minimum horizontal

stress ðrhÞ in N–S to NW–SE direction. This faulting style

contrasts the present-day stress field which shows a rh

direction in E–W and a rH direction in N–S as revealed by

borehole breakouts and tensile fracs, Reinecker et al.

(2010) (see Fig. 1). This N–S direction of rH has been

found consistent over the entire Molasse Basin from shal-

low to greater depths (Reinecker et al. 2010) as also

illustrated in the World Stress Map (Heidbach et al. 2010).

In order to determine the magnitude for the horizontal

components of the stress tensor (rh and rH), the approach

as described in Moeck et al. (2009) has been followed.

For the present calculation, a frictional coefficient of

l ¼ 0:85 is assumed according to Byerlee (1978, 1990).

The static water table of the well Mauerstetten is at 300 m

below ground level. By assuming fresh water conditions

(i.e. qfluid = 1 g/cm3), a formation pressure of approxi-

mately Pp = 32.29 MPa at -3,593 m TVD (-2,881 m

TVDSS) has been calculated. The averaged rock density of

the overburden is approximately q = 2.4 g/cm3 leading to

a vertical stress of rV = 84.6 MPa. Normalization of the

Fig. 1 Location of the geothermal well Mauerstetten (red point in

both illustrations) in the South German Molasse Basin, south

Germany. The close up shows the top of the Upper Jurassic (Malm)

around the Mauerstetten geothermal well. 1 Reef and micritic facies

(referred to as Massenfazies); 2 pelagic carbonates (referred to as

Helvetian facies); 3 normal faults (dashed lines stand for ‘‘supposed’’

faults); 4 frontal fault of the Alpine orogenic belt; 5 frontal fault of the

folded tertiary detritus (referred to as Molasse); 6 depth isolines of top

Malm (in meter below sea level); 7 direction of the maximum

horizontal stress direction (rH) extracted from the World Stress Map

(combined from Energiegewinnung 2010 and Reinecker et al. 2010)

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pore pressure at the depth of reservoir leads to the fol-

lowing relationship:

Pp ¼ 0:38� rV ð1Þ

The in situ stress field for the Mauerstetten reservoir can

be then estimated by applying the concept of limiting stress

ratios on frictional sliding on critically stressed faults

(Jaeger et al. 2007) as:

ðr1 � ð0:38� rVÞÞðr3 � ð0:38� rVÞÞ

¼ ðffiffiffiffiffiffiffiffiffiffiffiffiffi

l2 þ 1p

þ lÞ2 ð2Þ

By entering all relevant parameters in Eq. 2 leads to the

following relation:

r1 þ 1:44� rV ¼ 4:68� r3 ð3Þ

Equation 3 finally yields an upper and lower bound of

any possible stress regimes under the described depth, pore

pressure and friction coefficient reservoir conditions as:

rH� 3:24� rV , rh ¼ rv ð4Þrh� 0:52� rV , rH ¼ rV ð5Þ

The upper and lower stress ratio bounds can be

illustrated by a polygon stress graph (Moeck et al. 2009;

Peska and Zoback 1995) as shown in Fig. 2.

The stress polygon depicted in Fig. 2 therefore repre-

sents the potential stress state and respective stress ratios

for the geothermal reservoir rock at -3,592 m TVD

(-2,881 m TVDSS) within the Upper Jurassic succession.

Although the possible state of stress may vary between the

highly tensional stress state (radial tension) and the highly

compressional stress state (radial compression), the

expected in situ stress regime as derived from the World

Stress Map and present-day fault pattern may range

between strike-slip to transpressional (Heidbach et al.

2010), see Fig. 2. However, a reverse faulting stress regime

can be ruled out based on lacking indication of reverse

faulting in the Upper Jurassic layers of the Mauerstetten

reservoir.

From what stated above, a conflict between the fault

kinematic pattern and the in situ stress dynamics becomes

obvious.

One reason for the observed inconsistent faulting to

stress regime ratio might be a ‘‘fossil’’ normal faulting

regime during pre-Tertiary and Upper Jurassic times rep-

resenting paleostress conditions. Another reason might be

normal faulting within a compressional stress field caused

by the Alpine orogenic wedge due to flexural bending and

subsequent stretching, at upper crustal level, caused by

gravitational stresses, increased vertical stresses in the

thickened crust of the orogenic belt and resulting crustal

bending in the foreland (Kuhlemann and Kempf 2002).

Despite the specific cause, the important conclusion

from this observation is that the present-day normal faults

in the Bavarian Molasse Basin are exerted to high stresses

acting on the fault surface caused by rH in N–S direction.

Fault zone characteristics and fluid flow

The style of fault formation depends on the stress state

during slip and on the lithologic and physical properties of

the host rock. Slip on faults usually induces a significant

amount of deformation of the material between the sliding

surfaces or the adjacent wall rock. In addition, as the fault

propagates, the slip on it increases, thus increasing the

deformation. As a result, fully developed fault zones usu-

ally show a complex architecture which consists of two

major components, a zone of brecciated rocks (damage

zone) and a zone of gouge along the fault (fault core), e.g.

Caine et al. (1996).

A fault core consists of very low-permeability rocks

along the surfaces of major slip, in which the host rock’s

tectonic structures and fabrics have been completely

destroyed by cataclastic flow (Wibberley 2008 and refer-

ences therein). From a hydrologic perspective, the fault

core acts as impermeable to fluid flow across the fault

while along-fault flow may still be possible via open and

connected subvertical cracks. In the present case, high

normal stresses that are acting on the fault planes (as

described in ‘‘In situ stress field’’) will result in a fault core

to be a low-permeability rock domain.

Fig. 2 Stress polygon illustrating the possible stress field in depth

within the Mauerstetten reservoir. Dashed ellipse represents the likely

stress regime of the reservoir which might range between strike-slip

(SS) and reverse faulting (RF). Stress ratios are normalized to

reservoir depth and represent stress states typical for certain stress

regimes. I to VII indicate cases of stress regimes defined by specific

stress ratios, methodology after Zoback (2007) as: I radial extension,

II normal faulting, III transition normal-strike-slip faulting, IV strike-

slip faulting, V transition strike-slip-reverse faulting, VI reverse

faulting, VII radial compression. NF normal faulting, SS strike-slip

faulting, RF reverse faulting

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Damage zones are characterized by intensively fractured

(jointed) host rock and dilatation breccias and show a rel-

atively high permeability with respect to both the core and

the unfractured host rock (up to 5–6 orders of magnitude

according to Agosta et al. 2007). Fault-inherited fracture

nucleation and propagation within the damage zone may

give rise to secondary porosity and permeability thus

enhancing fluid flow both within and across the fault itself.

The amount of fluid flow within a damage zone is con-

trolled by different factors of which fracture orientations,

lengths, and level of connectivity are the most important.

Both fault core and damage zones are encompassed by

the host rock, which is characterized by background per-

meability architecture.

All these aspects can cause the hydraulic character of

opposing sides of a fault to differ sharply. This is often the

case for fault zones in carbonate rocks as in the present

study. In these geological settings, fault zones show a

twofold hydrologic behaviour with a highly permeable

damage zone and a tight fault core.

Understanding the hydraulic behaviour of fault zones

(damage zone plus fault core) is important to make feasible

predictions about reservoir productivity from such frac-

tured rocks. Considering a heterogeneous, stratified reser-

voir, it is possible to differentiate three end-member cases

of the hydraulic behaviour of fault zones (Davatzes and

Aydin 2005). These are described as follows, see also

Fig. 3:

1. Fault zone that is transparent to flow (across-fault flow

only depending on the permeability of the host rock),

see Fig. 3a.

2. Fault zone that acts as a high-permeability conduit to

fluid flow (preferential along-fault flow and minor

across-fault flow), see Fig. 3b.

3. Dual permeability fault zone with a high-permeability

damage zone and a low-permeability fault core (three-

dimensional flow in the damage zone and neither

across- and along-fault flow in the fault core), see

Fig. 3c.

From the above description, it follows that depending on

the porosity–permeability architecture of the fault zone,

different flow regimes are possible. Therefore, each end-

member scenario will have a distinct impact on the pro-

ductivity of a geothermal reservoir drilled in the proximity

of such a fault zone. In order to characterize these differ-

ences, numerical simulations have been carried out for

each permeability architecture and the results have been

analysed and compared in terms of pressure evolution of a

production well drilled nearby the major fault zone. Those

simulations, modelling set up, parameterization and results,

are discussed in detail in the remaining of the manuscript.

Description of the modelling workflow

3D geological model of the reservoir

To integrate the geometry of the Mauerstetten reservoir in

the numerical simulator, an available structural model has

been used. This model has been generated using the

commercial software PETREL (� Schlumberger) and it

includes the two major reservoir units, i.e. Upper Jurassic

(Malm) and Middle Jurassic (Dogger). The topology of the

reservoir units are given by their corresponding top surface

layers, i.e. top Malm, top Dogger and top basement. Fur-

thermore, two wells were integrated within the PETREL

model, the no longer existing well GT1 and the current

existing well GT1a (see Fig. 4a). Therefore, well GT1a

Fig. 3 End member hydraulic behavior for a fault zone embedded in

a stratified geological layer, modified after Davatzes and Aydin

(2005). a Fault zone which is transparent to fluid flow along its plane.

Only across-flow is possible depending on the permeability of the

surrounding rocks. b Fault zone which is highly permeable (compared

to the host rocks). Due to the permeability contrast between fault and

surrounding rock, fluid preferentially flow along the fault, while a

minor across-fault flow is still possible. c Fault zone consisting of an

impermeable fault core and a highly permeable damage zone. Three

dimensional flow occurs within the damage zone but no across-fault is

possible

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will be used as production well during the upcoming

simulations (Fig. 6). An additional feature of the geologi-

cal model is represented by the presence of an ENE–WSW

striking major fault zone which cuts through and separates

the two major geological units.

All surfaces in the original PETREL model were defined

as the two-way travel time of the seismic wave (TWT)

which does not directly equate to their depths. Therefore, to

use the existing PETREL model for simulation purposes, a

time-depth conversion has been performed. To achieve this

step, the entry points of both wells into the geological units

have been used as major depth constraints. From the dril-

ling report of GT1 and GT1a, the depths of these entry

points have been determined. For GT1, the depths of top

Malm and top Dogger are -3,464 and -3,931 m TVD

(-2,753 and -3,220 m TVDSS), respectively. For GT1a,

the depth of the top Malm was determined to be -3,249 m

TVD (-2,718 m TVDSS) (Fig. 4a). Based on the location

of these two entry points, a sonic velocity model for the

two major units has been calculated. The sonic velocity for

the Malm unit has been determined to be 4,010 m/s and

that of the Dogger unit to be 4,647 m/s. These values are in

good agreement with known measurements (sonic velocity

of limestone 3,962–5,639 m/s, Hyne 2001). Using the

above-determined velocities, the complete model has been

converted from travel times to depth (Fig. 4b). The accu-

racy of this conversion has been validated by minimization

of the difference between the depth of the measured and

calculated entry points of the wells.

Based on the depth-converted model, the thickness of

the two major units has been determined. The thickness of

Malm and Dogger are approximately 480 and 210 m,

respectively. To use the depth-converted model as input

structure for the numerical simulation, all relevant geo-

metric entities, i.e. top and bottom surfaces of the geo-

logical units plus geometry of the fault zones, have been

converted as point data and exported to (xyz)-coordinate

files (Fig. 5).

(a) Original PETREL model of the reservoir (s TWT) (b) Depth converted model

Fig. 4 Steps for generating the model geometry. a Available geo-

logical model of the Mauerstetten reservoir as generated from the

PETREL software in s TWT. Also shown are the geometry of the two

wells (abandoned GT1 in light blue colours, and GT1a in light greencolours) together with the locations at depth of the points which were

used to perform the time-depth conversion, see ‘‘ Numerical

simulations–—results and discussion’’ for more details. b Depth

converted geological model of the reservoir. Different colourshighlight the different top surfaces for each geological unit in the

model. The geometry and location of the major fault zone is also

shown by the light blue surface cutting through the different layers

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3D meshing of the geologic model

The generation of a detailed geological model to represent

the specific geological information of the study area is the

first step in the pre-simulation work-flow, the pre-process-

ing phase (Kalbacher et al. 2005). Additional efforts are

then required to migrate this information onto the numerical

simulator, i.e. to ‘‘divide’’ the continuous domain into grids

of elements. Numerical methods rely on approximate

solutions of a physical process or of a system of coupled

problems as defined by proper governing equations (partial

differential equations, PDEs) with corresponding initial and

boundary conditions. Despite inherent differences, all

methods share the requirement of a discrete regular or

piecewise regular topological structure, a mesh of nodes, to

support the local approximations. The nature of the mesh is

of particular importance since it determines both the accu-

racy and stability of the numerical method as well as the

type of problem that can be solved. Given the rule that the

quality of the resulting model predetermines the quality of

the numerical outcomes, it follows that each degree of

simplification in the representation of the system will

inevitably affect the reliability of the final solution.

The problem of boundary mesh generation has been

widely discussed both for two- and three-dimensional

applications (e.g. Marshall and Eppstein 1992). Current

available, state of the art meshing algorithms rely on the

existence of specific geometric objects describing the

geometry of the domain to be discretized, so called

‘‘Piecewise Linear Complexes’’ or PLC’s (Si 2010 and

Cheng et al. 2012). By definition, a PLC can be regarded as

a set of elementary geometric objects—nodal vertices, line

segments, and planar facets—which must obey strict

topological relations. Indeed, each pair of elementary

geometric objects of the complex must be close under

taking intersection. In other words, two line segments can

intersect only at a shared nodal vertex and two planar facets

must be either completely disjointed or they must intersect

at shared nodal vertices and/or line segments. In addition,

the piecewise requirement forces all facets to be coplanar.

Due to these geometric restrictions, the generation of a

PLC for practical applications often presents a non-trivial

problem. This is especially the case with real-case geo-

logical applications, which consist of an assemblage of

non-planar, curved, and intersecting surfaces representing

either geological interfaces or fault planes that need to be

considered in the geometric reconstruction. At the same

time, a computational mesh must meet additional require-

ments (quality criteria) dictated by modelling issues.

Briefly stated, the task of mesh generation is to find a

proper balance between two generally conflicting criteria,

that is geometry adaptation and element shape.

Fig. 5 Point data extracted from the depth converted PETREL

geological model describing the geometry of the different surfaces

and of the major fault zones (light blue colours) which has been used

to constrain the actual geometry of the simulation domain. Differentcolours indicate different surface horizons

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An automated approach has been developed by the first

two authors which provides a practical solution to the

aforementioned issues. The approach takes advantage of

existing state of the art meshing algorithms which have

been combined in an efficient and robust software frame-

work to solve common problems and limitations lying at

the heart of geometric modelling of complex fractured

reservoirs. In following sections, some basic information is

provided concerning the application of the novel meshing

technique to the study presented here. Details about the

theory behind the methodology are the subject of a separate

manuscript under preparation.

The workflow consists of different steps to generate an

unstructured, boundary conforming, Delaunay tetrahedral

mesh of the input geological model.

The available input data are files of points scattered in

3D space delineating the geometry of the interfaces

between neighbouring geological units as well as the

geometry of the fault zones (see Fig. 5). Points which

belong to the input ensemble do not bear any topologic

relationship to each other, i.e. no shaped surfaces are

delineated by the input points at this stage. The first task is

now to recover the internal point–point relations by means

of a surface reconstruction from the scattered points. By

approximating each internal and boundary geologic surface

as a two-dimensional mesh of triangles, the missing

information among all points on an intra-surface level can

be recovered. In addition, the conditions of co-planarity of

all elementary facets can be equally satisfied, i.e. each facet

is a planar triangle.

In a second stage, inter-surface connections are calcu-

lated. This step is required because of the piecewise line-

arity of the final complex, as no blind intersection among

its constitutive geometric objects should be allowed.

Internal coherence between all surfaces is achieved in two

separate steps. First, points of intersection between trian-

gles belonging to intersecting surfaces are calculated and

ordered in piecewise linear polylines. Those intersection

lines are then used to perform a Constrained Delaunay

Triangulation of the respective surfaces.

After completing the generation of the PLC, a final

three-dimensional tetrahedralization is performed and

subjected to quality criteria on element size (see Fig. 6).

The final mesh adopted for the present study consists of

225,438 nodal points arranged to form 1,173,477 tetrahe-

dral elements. Local refinement has been enforced along

the boundaries between intersecting internal surfaces, at

fault-layer intersection (see Fig. 6). Faults cutting the

geological succession have been discretized in terms of

two-dimensional triangle-shaped surfaces sharing faces

with adjacent matrix tetrahedra. All tetrahedra belonging to

a closed geological domain as well as all triangles of a fault

share a common ID which is used to define different

fracture and rock properties for the numerical simulations,

see ‘‘Matrix and fault parameter settings’’. As seen from

Fig. 6, domains characterized by different IDs parallel

the major fault. These have been integrated to simulate the

presence of a damage zone along the surroundings of the

fault core, the latter being discretized as a 2D surface.

Following this approach, it is then possible to define dif-

ferent material properties for each domain and to correctly

simulate different physical scenarios in terms of flow

characteristics (see ‘‘ Numerical simulations–—results and

discussion’’).

Description of the numerical simulator

Numerical simulations are conducted using the open source

finite element method (FEM)-based simulator OpenGeosys

(OGS http://www.opengeosys.org/; Wang and Kolditz

2007; Watanabe et al. 2010; Kolditz et al. 2012). The

simulator offers a hybrid approach combining discrete

fracture and continua models for simulating flow and

transport processes in fractured rocks. Following this

approach, discrete fractures are superimposed on a contin-

uous volume representing homogenized porous media

under the assumption that groundwater dominantly flows

along the permeable fractures. The approach is particularly

applicable when single fractures dominate the system

behaviour, although influences of rock blocks are still not

negligible (Segura and Carol 2004; Dietrich et al. 2005).

Details on the governing equations used in OGS and applied

numerical schemes are described in Watanabe et al. (2012).

The PDEs describing fluid flow and heat transport in

fractured porous media are mathematically initial value and

boundary value (IVBV) problems with primary variables

pressure (p) and temperature (T). With given initial and

boundary conditions, approximated solution of the problem

can be obtained by applying the Galerkin FEM for spatial

discretization with linear interpolation functions and the

first-order finite difference schemes for temporal discreti-

zation (Wang and Kolditz 2007). Domains composed of

discrete fractures and porous media can be discretized by

combination of multiple element types. Discrete fractures

are idealized as lower-dimensional geometric objects so

that they can be represented by, e.g., lines in two-dimen-

sional space and triangles in three-dimensional space.

Since solutions are assumed to be continuous over domains

of the fractures and porous media, the discrete fracture

elements must be located along boundaries of porous

medium elements and both kinds of elements share the

same nodes (Segura and Carol 2004).

Initial conditions such as pore pressure distributions

can be specified either by giving analytical formulas such

as linearly depth-dependent hydrostatic/conductive condi-

tions or by taking pre-computing simulation results, i.e.

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results from simulating steady-state conditions of the

natural reservoir without any production. For real-site

studies, the latter approach is preferred because it can take

into account fault zones and complex geological structures

having inhomogeneous distributions of material properties

as well as fluid density variation due to geothermal gra-

dient. Dirichlet and Neumann boundary conditions can be

assigned along reservoir boundary surfaces to constrain

hydraulic (e.g. in situ pressure or regional groundwater

flow) and thermal state (e.g. temperature or terrestrial heat

flux). The surface geometry may be non-planar but can be

represented with triangulated irregular network (TIN) data

which OpenGeoSys accepts. TIN data can be easily

extracted from the meshing process (details about the

boundary and initial conditions setting adopted for the

present study are given in ‘‘Boundary and initial

conditions’’.

Although OpenGeoSys is equipped with several pre-

conditioners and iterative linear solvers, the linear solver

part is replaced by a more robust library, namely Lis

(a Library of Iterative Solvers for linear systems,

http://www.ssisc.org/) (Nishida 2010). This is because very

low-permeable rocks and high-permeable discrete fractures

coexist in the same domain (e.g. permeability roughly

varies from 1 9 10-18 to 1 9 10-14 m2, see also ‘‘Matrix

and fault parameter settings’’ below), and it results in ill-

conditioned matrices in linear equations obtained after the

discretization. In this study, GMRES solver combined with

the ILU preconditioner has been chosen for solving for

both the hydraulic and the heat component.

Matrix and fault parameter settings

According to the description of the fault zone characteris-

tics (see ‘‘Fault zone characteristics and fluid flow’’), three

end-member cases in terms of the hydraulic behaviour of

fault zones can be defined. These end members are based

on the model geometry shown in Fig. 6. Figure 7 illustrates

the derived scenarios: (1) a fault zone that is transparent to

flow (Fig. 7a); (2) a fault zone that acts as a high-perme-

ability conduit (Fig. 7b) and (3) a dual-permeability fault

zone with a high-permeability damage zone and a low-

permeability fault core (Fig. 7c). These three end-member

scenarios provide the settings for the dynamic simulations.

In the following, a description of the parameters adopted

for the three different cases is outlined. For the sake of

clarity, a simplify nomenclature is observed to which the

remaining of the manuscript conforms. We will refer to the

three cases investigated as case 1 (no fault), case 2 (highly

permeable fault) and case 3 (tight fault and permeable

damage zone).

For all simulation scenarios, the thickness of the damage

zone has to be defined. The latter is calculated by the

projection of the fault core onto the reservoir layer thus

leading to a damage zone thickness ranging between 200

and 250 m.

Given the differences in the fluid dynamics simulated,

each model run needs to have a proper set of (non-frac-

tured) matrix and fault zone parameters.

Measured permeability for the Malm aquifer has been

found to vary in a range between k = 2.5 9 10-14 m2 and

Fig. 6 Cut out of the 3D model

showing the geometry of the

fault zone (damage zone plus

fault core) and the depth

location of the producing well

implemented in the numerical

simulations. Different coloursindicate different material IDs

which are used to identify the

geological compartments of

interest. The fault core is

implemented as a triangle

shaped surface (dark greycoloured) to which relative low-

permeability values are assigned

to inhibit flow along its plane.

The damage zones flanking the

latter are integrated as three

dimensional domains (dark blueand dark orange coloured) to

which relative high permeability

(higher than the host rock) are

assigned. The production well is

implemented as a point source

(production point)

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k = 6 9 10-12 m2 according to Fritzer (2010). Because of

the karstification process, the eastern part of the Bavarian

Molasse basin shows a more conductive hydraulic behav-

iour than the western basinal domain. A permeability range

representative for the western part is given by Birner et al.

(2009) to lie between k = 1 9 10-18 m2 and k =

1 9 10-13 m2. Unfortunately, such a wide range cannot be

directly applied for setting up a numerical simulation. In

order to find a proper permeability spectrum for these

rocks, data from a more detailed study by Homuth et al.

(2011) have been used. In their study, Homuth et al. (2011)

investigated analogue outcrops of the Franconian facies

and the Swabian facies, similar to the facies analysed

around the well GT1a, obtaining values ranging between

k = 5 9 10-18 m2 and k = 1 9 10-14m2. To complement

the permeability value from the literature, permeability

measurements at analogue outcrops samples were per-

formed. Specifically, in these studies, samples of the Pur-

beck formation, Siliceous sponge facies and reef facies

were investigated. The measured permeability was found in

a range between k = 5 9 10-18 m2 and k = 1 9

10-15 m2. In addition, two airlift tests were performed in

the well GT1a. By assuming an average reservoir thickness

of 480 m, a permeability range between k = 3 9 10-17 m2

and k = 9 9 10-16 m2 may be assumed. For the present

study, the values of the laboratory measurements and the

field tests were combined and used as parameter for the

simulation, as summarized in Table 1.

For the Dogger aquifer, which acts as a lower non-

conductive constrain for the Malm aquifer, a permeability

of k = 5 9 10-18 m2 was used for all simulations (Clauser

et al. 2006).

According to Agosta (2006), the permeability of the

damage zone could be five orders of magnitude higher than

in the surrounding matrix. However, this measure was

made for low-porosity rocks (about / = 0.01) which does

not reflect reservoir rocks conditions under investigation.

Therefore, to derive permeability values for the damage

zone of our reservoir rock, we performed laboratory

experiments at fractured outcrop samples under in situ

conditions. Permeability of such fractured rocks was found

to range between k = 8 9 10-15 m2 and k = 1.4 9

10-14 m2 at 40 MPa effective pressure, which is a 3–10

times higher than the permeability of the non-fractured

(a) Case 1: no fault (b) Case 2: highly permeable fault

(c) Case 3: tight fault and permeable damage zone

Fig. 7 Figure showing the set up (geometry and parameterization) of

the different simulation cases investigated. The three scenarios have

been decided based on the end-members fault related groundwater

dynamics as described in ‘‘Fault zone characteristics and fluid flow’’.

a represents a fault zone that is transparent to flow (referred to as case

1); b a fault zone that acts as high-permeability conduit (case 2); and

c a dual permeability fault zone with a high-permeability damage

zone and a tight fault core (case 3)

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rocks under the same in situ conditions. In addition, an

injection test in the abandoned well GT1 was performed. In

the reservoir section, this well is located within the damage

zone. The field test indicated a permeability of the damage

zone to range between k = 2.9 9 10-15 m2 and

k = 1.6 9 10-14 m2, which gives an excellent agreement

with the laboratory tests. Therefore, a damage zone per-

meability, ten times higher than the permeability of the

non-damaged area, was used (compare Table 1). Both for

the damage zone and the non-damaged area, a vertical to

horizontal permeability ratio of 1:2 has been used.

Various studies analysed the porosity of the Malm

aquifer. The effective porosity of the western Bavarian

Molasse basin was constrained around a value of / =

0.025. The transition to the Helvetian facies reflects a

slightly decrease in the effective porosity down to / =

0.02 (Fritzer 2010). Clauser et al. (2006) measured 50 core

samples of the Malm and the Muschelkalk and found the

effective porosity to be about / = 0.03 (the measured

range was between / = 0.01 and / = 0.06). Furthermore,

Homuth et al. (2011) analysed the Franconian facies and

the Swabian facies and determined their porosity to be in a

range from / = 0.002 to / = 0.097 and from / = 0.008

to / = 0.108, respectively. The values derived from the

literature has been quantified for the present case by per-

forming porosity measurements at outcrop samples by

weighting the dry and wet samples, by mercury injection

method and by nano-pycnometry. Again, the Purbeck for-

mation, Siliceous sponge facies and reef facies were

investigated. For the Purbeck formation, the porosity val-

ues are in a range between / = 0.1 and / = 0.33 (average

value of / = 0.18). For siliceous sponge facies, the

porosity values are in a range between / = 0.02 and / =

0.09 (average value of / = 0.05), and for reef facies, the

porosity values are in a range between / = 0.02 and / =

0.11 (average value of / = 0.06). Based on the

aforementioned discussion, an averaged porosity of / =

0.07 for the Malm aquifer and / = 0.12 for the Dogger

formation has been adopted.

Depending on the simulation scenario, the fault core is

assumed either to behave as a conductive plane in which

case the same flow parameter as used for the damage zone

are adopted (case 2) or as a tight internal no flow boundary

domain (case 3). To quantify the impact of a fault trans-

parent to across-flow on the pressure evolution at the

production well, a reference model was simulated in which

neither the damage zone nor the fault core have been

considered (case 1).

All simulations consider heat transport by advective

fluid. However, given the focus of the study, that is to

investigate the effect of different fault zone configuration

of the productivity of the geothermal well, values adopted

for the thermal rock properties (i.e. heat capacity and heat

conductivity) are not discussed. In a similar fashion, we

avoid to enter details of the temperature fields while dis-

cussing the modelling results (‘‘ Numerical simulations–—

results and discussion’’).

Boundary and initial conditions

For all three scenarios, a steady state and a transient sim-

ulation have been performed. Under steady-state condi-

tions, the PDE is a classical boundary value problem, the

solution of which requires proper distributions of the rel-

evant field variables, i.e. pressure and temperature gradi-

ents, to be specified along the reservoir boundaries

(boundary conditions). Based on the imposed boundary

values, the distribution of the field variables at any point

within the reservoir can be computed. Resulting pressure

and temperature do not change with time and reflect the

internal state of the model domain due to the applied

boundary conditions only.

From a computational point, a transient simulation

should be seen as a boundary and initial value problem.

Therefore, apart from setting pressure and temperature

boundary conditions, values of these field variables are to

be specified at all points within the reservoir at a particular

initial time t0 (initial conditions). Initial conditions describe

the whole internal state of the system at the beginning of

the simulation and therefore should provide a physically

consistent starting point for calculating its evolution

through time, i.e. solving for the field variables at each

internal point at times t [ t0. To assure a proper set of

initial conditions, both with respect to the boundary setting

and to the model configuration, the pressure and tempera-

ture field as computed from the steady-state simulations

were used as initial condition for the transient simulations.

The model domain is constrained by isohypsic surfaces

(surfaces of constant hydraulic head level) along the NE

Table 1 Summary of the applied permeability and porosity for the

matrix, damage zone and fault core during the three simulations

Case Matrix Damage zone Fault core

k (m2) / k (m2) / k (m2) /

Malm (1st

simulation)

3 9 10-15 0.07 3 9 10-15 0.07 – –

Dogger (1st

simulation)

5 9 10-18 0.12 5 9 10-18 0.12 – –

Malm (2nd

simulation)

3 9 10-15 0.07 3 9 10-14 0.07 3 9 10-14 1

Dogger (2nd

simulation)

5 9 10-18 0.12 5 9 10-17 0.12 3 9 10-17 1

Malm (3rd

simulation)

3 9 10-15 0.07 3 9 10-14 0.07 No flow –

Dogger (3rd

simulation)

5 9 10-18 0.12 5 9 10-17 0.12 No flow –

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and the SW domains (Frisch and Huber 2000). Following

the same study, a constant hydraulic head level of 400 m of

430 m above sea has been imposed along the NE and SW

borders, respectively. For both the steady state and the

transient simulations, these constant-level surfaces have

been converted to pressure values as:

p zð Þ ¼ p0 � q � g � zð Þ ð6Þ

In Eq. 6, z is the vertical depth subsea, p0 is the

corresponding pressure of the water column at z = 0, q is

the density of water (assumed constant at q = 1,000 kg/m3)

and g is the gravitational acceleration (g = 9.81 ms-2).

Given the hydraulic head values adopted, a pressure of

p0 = 3.92 MPa and of p0 = 4.22 MPa has been calculated

for the NE and SW borders, respectively. Therefore, the

applied vertical pressure gradient across the NE and SW

border reads as p zð Þ ¼ 3:92 ½MPa� � ðq � g � zÞ and

p zð Þ ¼ 4:22 ½MPa� � ðq � g � zÞ, respectively (Fig. 8a).

In order to determine the in situ temperature field, we

applied the natural temperature gradient of TðzÞ ¼

282:8 ½K� � 0:0426 Km�z

h i

at all external and internal sur-

faces of the model domain (Fig. 8b).

For the transient simulations, the same pressure

boundaries at the NE and SW borders as used for the

steady-state counterparts have been adopted. Initial con-

ditions were set accordingly to the resulting temperature

and pressure fields computed from the steady-state

simulations.

In order to investigate the hydraulic impact of the fault

domain (damage zone plus fault core), we implemented a

production point in the Malm section of the GT1a well.

The production rate of well GT1a was set to w = 100 m3/h

for all transient simulations. The adopted value should be

considered as being representative for the region (Energi-

egewinnung 2010; Schultz 2007). The shortest distance of

the production point to the damage zone and the fault core

is approximately 100 and 350 m, respectively. No bound-

ary conditions for the thermal field have been set for all

transient simulations conditions. Therefore, the tempera-

ture development is influenced by the production rate only.

Numerical simulations: results and discussion

According to the distinction made above, a total of three

scenarios have been simulated: (1) a fault zone that is

transparent to flow (case 1), (2) a fault zone that acts as a

high-permeability conduit (case 2), and (3) a dual-perme-

ability fault zone with a high-permeability damage zone and

a low-permeability fault core (case 3). Case 1 represents an

intact (i.e. non-faulted) rock where only the rock’s matrix

permeability controls the flow. It is simulated in order to

provide a reference state to compare the results from the

different simulations in terms of the parameterization of the

fault domain. Simulation cases 2 and 3 represent a faulted

rock setting which differs for the properties of the fault core

only. Case 2 (permeable fault core and damage zone) rep-

resents a karstified fault core with a (permeable) damage

zone. Case 3 (impermeable fault core plus permeable

damage zone) represents a ‘‘fossil’’ normal fault with fault

gouge, mineralization or cement sealing the fault core. For

both cases 2 and 3, the damage zone around the fault core is

considered to be still permeable due to pre-existing conju-

gated fractures formed under a normal faulting paleo-stress

field. Although these fractures could be closed under recent

stress field conditions, the intersection of these conjugated

fractures would serve as preferential fluid channels. Within

the Mauerstetten reservoir, both scenarios are possible

under the current stress field and taking the fossil fault

regime into account. Given the present day direction of rH,

newly generated faults would predominantly strike NE–SW

and NW–SE acting as strike-slip faults forming vertical to

subvertical intersection lines inducing vertical flow. How-

ever, such fault patterns are not observed in the seismic

sections from the Mauerstetten field and therefore they are

not considered in the present study.

Steady-state initial state

For all three scenarios, steady-state simulations have been

first calculated. The results of the steady-state simulations

(initial point of the pressure curve in Figs. 9 and 10a)

indicate an in situ reservoir pressure of 32.8 MPa at the

production point which corresponds to a hydraulic head of

417.5 m (case 1), 415 m (case 2), and 414.7 m (case 3).

Due to the moderate natural hydraulic gradient (as imposed

via the flow boundary conditions) and without any artificial

flow disturbance due to production, the calculated

hydraulic heads from the three scenarios are similar. The

measured water table of GT1a is approximately 300 m

below the surface. The well head is situated at 711.71 m.

Therefore, the measured hydraulic head of GT1a is around

411.71 m, which is in excellent agreement with the

obtained simulation results (Table 2).

Well GT1a: production point outside the damage zone

The resulting pressure and temperature distributions have

been integrated as initial conditions for the transient runs.

For the latter, a computing time of 10 years has been set

up, considered long enough to assure the system to reassert

stable conditions under groundwater production. A con-

stant production rate of w = 100 m3/h at the well GT1a

has been applied. The resulting pressure response expres-

sed as hydraulic head is given by Fig. 9.

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(a) Pressure boundary conditions

(b) Temperature boundary conditions

Fig. 8 Pressure (a) and temperature (b) boundary conditions applied

during the steady state simulation. Pressure values are consistent with

the values calculated based on reservoir averaged depth, fluid and

rock parameters as described in details in ‘‘In situ stress field’’. A

linear temperature gradient (approximately 42.6 K/km) has been

imposed throughout the model domain. For the transient simulations,

the temperature gradients were removed at all surfaces and a

production well (red dot) was implemented

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Starting from the initial state, a transient draw down

phase of the water table characterized all three model

realizations. The observed draw down is due to the

starting of the (constant) production at the well. In the

very early stages (up to 3 h of simulation time), a very

similar hydraulic head evolution can be observed for all

cases. At this time step, the computed absolute draw down

is around 500 m or 4.9 MPa. From this point in the time

evolution of the system, the results of the three simulation

scenarios start to differ as visible by comparing the tran-

sient part of the draw down curve for the three cases.

Though showing a similar trend in the hydraulic head

evolution, each run is characterized by different magni-

tudes of computed draw down. At the final stage, after

10 years, the draw down calculated for case 1 (no damage

zone and no fault core) is found to be the highest and the

draw down calculated for case 2 (damage zone but no

fault core) to be the lowest. The absolute draws down of

the three simulations are 892 m (case 1), 713 m (case 2)

and 828 m (case 3). Accordingly, the corresponding

pressure drops are 8.75 MPa (case 1), 6.99 MPa (case 2)

and 8.12 MPa (case 3). For longer simulation times (i.e.

time above 5 years), pressure draw down keeps constant

in all simulations.

A better way to quantify the impact of the different

fault zone permeability scenarios on the productive

capacity of the simulated geothermal well is to describe

the outcomes in terms of computed productivity index

(PI). By definition, PI is given by the total mass flow

rate (w) per unit pressure draw down (Dp), i.e. PI = w/

Dp. Based on the pressure drops as calculated from the

three simulations, a corresponding productivity index of

PI = 11.4 m3/(h MPa) for case 1, of PI = 14.3 m3/

(h MPa) for case 2, and of PI = 12.3 m3/(h MPa) for

case 3 can be determined, respectively. The results

described above indicate that the presence of a highly

conductive damage zone as well as of a non-conductive

fault zone can significantly influence reservoir produc-

tivity. The maximum difference in the productivity index

(25 %) is observed between case 1 (where no damage

zone has been integrated) and case 2 (damage zone). The

reason behind such a big difference can be explained as

follows.

Until 3 h of simulation time, the calculated draw down

from the three scenarios is almost identical. Since the well

GT1a is situated within the non-damaged area, it can be

concluded that the draw down radius has yet to reach the

damage zone. Between 3 h and 1.5 days of simulation

time, case 1 shows a higher draw down compared to the

other scenarios. This last aspect indicates that the draw

down radius has now reached the damage zone. Therefore,

the differences observed in the calculated PIs can be related

to the different permeability architecture considered for the

fault domain in the three simulations. In this regard, it is

worth to mention that while case 1 does not integrate a

damage zone (i.e. there is no permeability contrast between

the domain flanking the major fault and the non-fractured

rock matrix), cases 2 and 3 do integrate such a domain of

increased permeability. Therefore, it can be assumed that

for these last two simulations, the inflow from the existing

damage zone becomes dominant within this time interval

thus resulting in the observed minor draw down with

respect to case 1.

The relative difference in the PIs for cases 2 and 3 can

be understood by inspecting the well pressure history at

longer times. For simulation times above 1.5 days, the

draw down of case 3 starts to deviate from that computed

from case 2, the former being higher. This difference in

the pressure history is maintained for the remaining of the

simulations thus explaining the difference between the

productivity indexes calculated from the two model real-

izations (PI for case 2 is higher than the PI from case 3).

Once again, this discrepancy can be related to the perme-

ability architecture of the fault domain considered, no fault

core (simulation 2) and a tight fault core (case 3) inte-

grated. The presence of a tight fault core implies the

existence of an internal no flow boundary which inhibits

any hydraulic connection among the two domains along

both sides of the fault core. This could be caused by fault

gouge due to intensive tectonic movement along the major

normal fault (offset around 200 m) or by cementation and

mineralization through migrating fluids along the fault. For

the present case, this hydraulic setting prevents water from

the NE block of the model domain to be accessible to the

production well (case 3). Under constant production rates,

this requires higher amounts of water to be taken from the

domain nearby the well thus resulting in an increased draw

down and in a lower PI.

From the above discussion, it can be concluded that the

presence of a highly conductive damage zone as well as of

Fig. 9 Evolution through time of calculated hydraulic head during

production from well GT1a

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a non-conductive fault core can significantly alter the

productivity of a well drilled nearby such a fault domain.

Moreover, the same results point to an influence which is

localized to areas in between the fault zone and the pro-

duction well. This implies that the draw down radius must

enter these domains of heterogeneous permeability condi-

tions in order to start being effective. This last aspect in

turn explains the reason why no differences in the pro-

ductivity could be observed during the very early stages

(before 3 h of simulation time) among the three

simulations.

(a) Geometry of the model considering a production well within the damage zone

(b) Hydraulic head evolution through time

Fig. 10 Well path and location of the production point used for the

second group of numerical simulations (upper figure). In comparison

with the first set of simulations (Fig. 7a–c), the production point is

now set inside the damage zone. Numerical results in terms of the

evolution through time of calculated hydraulic head during produc-

tion (lower figure)

Table 2 Summary of productivity index values (PI) as obtained from

the different simulations

PI at well GT1a

[m3/(h MPa)]

PI at well GT1

[m3/(h MPa)]

Case 1

No fault 11.4 6.5

Case 2

Damage zone only 14.3 42.1

Case 3

Damage zone and tight fault

core

12.3 26.4

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Well GT1: production point inside the damage zone

The results described so far have been obtained by

assuming a well which was considered to be located close

to but not inside the damaged area. Whether similar con-

clusions could be derived for a well drilled directly inside

this domain has been ascertained via a second group of

simulations in which the production well has been placed

inside the damage zone (Fig. 10a). In order to locate the

production point, the well path of the abandoned well GT1

has been used. This was done because this well enters the

damage zone in the Malm section. For those simulations,

the minimum distance between the production point and

the non-conductive fault core is approx. 75 m (compared to

350 m of the previous case). The same kind of simulations

in terms of the permeability architecture of the fault zone

as described above have been considered. The results in

terms of pressure draw down curves at the well location are

shown in Fig. 10b.

By comparing the results from the two groups of sim-

ulations, it is evident that the biggest difference is found

between the corresponding cases 1 (no damage zone inte-

grated). The absolute draw down computed assuming

production from well GT1 is 1,567 m or 15.4 MPa, which

corresponds to a productivity index of PI = 6.5 m3/

(h MPa). In contrast, in the first simulation stage, the cor-

responding values have been of 892 m or 8.75 MPa for

absolute draw down, PI = 11.4 m3/(h MPa). In both sim-

ulations, the permeability values adopted for representing

the reservoir rock have been kept the same. Therefore, the

reasons behind the computed lower productivity from well

GT1 should be only related to its different location within

the reservoir unit.

A first important aspect is related to the changes in the

reservoir apparent thickness as induced by the offset along

the fault plane. Adopting a unique permeability distribution

for the entire reservoir unit, a change in its thickness

reflects a variation in the transmissivity of the same rock. A

decrease in the reservoir thickness implies a decrease in its

transmissivity. Consequently, a well drilled closer to the

fault will impact a reservoir of reduced thickness and

transmissivity than a well located far away from this

region. In the present study, the offset amounts to 200 m

which in turn corresponds to a reduction in the thickness of

the reservoir from 480 to 360 m and a 25 % reduction of

the reservoir’s transmissivity. By applying the same, pro-

duction rate to a reservoir of a less thickness extent will

induced a higher pressure drop thus resulting in an overall

smaller PI than in the case of a thicker reservoir unit.

In addition, it should be remarked that for the second

group of simulation, the production point is located closer

to the interface between the reservoir and the non-con-

ductive Dogger unit (only 113 m apart). This last aspect

strongly influences the flow field nearby the well raising

the pressure drop around the same well.

More interesting are the results for cases 2 and 3. For

these two simulations, the damage zone has been consid-

ered and due to its high conductivity, a relative minor draw

down could be observed when compared both to case 1 and

to the results obtained by simulating the production from

the well GT1a. The absolute draw dawn for case 2 is now

242 m or 2.37 MPa (before it was 892 m or 6.99 MPa),

which corresponds to a productivity index of PI = 42.1

m3/(h MPa) [before it was PI = 14.3 m3/(h MPa)]. The

absolute draw down for case 3 is 387 m or 3.79 MPa

(before it was 828 m or 8.12 MPa), which corresponds to a

productivity index of PI = 26.4 m3/(h MPa) [before it was

PI = 12.3 m3/(h MPa)].

From the pressure response of an injection test in GT1

and two airlift tests in GT1a, an approximately three times

higher productivity from well GT1 was deduced. Due to the

different pore pressures within the reservoir (injection for

GT1 and production for GT1a) and the unsteady state

conditions during the tests, the field results can provide

indications on the productivity trend only. Nevertheless, the

field data are in excellent agreement with the above-

described simulation results. Though a proper validation of

the modelling results would require additional data, the nice

fit between the simulated and observed productivity trend

clearly confirms the feasibility of the modelling results.

Moreover, a comparison of the two pressure curves

indicates that the draw down radius reaches the non-con-

ductive fault core already after approx. 15 min in the

simulation (as evident by the point at which the two curves

start to deviate in their time evolution). Once again, since

the fault core acts as an internal no flow boundary, the

drawdown of case 3 is more pronounced than the one from

case 2.

Conclusions

A robust and time efficient software framework has been

presented to guide the transfer of 3D geological data to

numerical dynamic simulations of fractured reservoirs with

accurate description of the reservoir geometry, comprising

geological units of interest and heterogeneous fault zones.

The approach has been applied to the Mauerstetten reser-

voir in the South German Molasse Basin as a natural

working example for a rather complex carbonate fractured

reservoir. A fault pattern analysis has been performed to

quantify the possible hydraulic properties across a major

fault zone. The novel part of the approach is the fast

modification of fault geometries and hydraulic character-

istics, and wellbore locations permitting evaluation of

reservoir assessment.

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Different simulations in terms of fault zone permeability

architecture have been carried out to analyse the possible

reservoir productivity. In addition, well positioning was

varied with respect to fault core and damage zone for

further investigation of reservoir productivity. The influ-

ence of the high-conductive damage zone and the non-

conductive fault core on the pressure response has been

proven for all simulations.

The following results were obtained:

• Well GT1a: low productivity outside the damage zone

is less affected by fault properties. Depending on the

hydraulic behaviour of the fault core in the in situ

compressive stress field, different scenarios in terms of

computed PI occur:

– High-permeable damage zone but no fault core

(case 2). The results indicate that productivity

increases by 25 % if the damage zone has a ten

times higher permeability than the host rock.

– Tight fault core and high-permeable damage zone

(case 3). Considering a tight fault core accompanied

with a high-permeable damage zone leads to a

productivity increase of approximately 8 %.

• Well GT1: high productivity within the damage zone is

strongly controlled by fault properties. The hydraulic

properties of the fault core and damage zone strongly

influence well productivity if the well position is within

the highly conductive damage zone.

– No damage zone. The presence of a tight fault core

close to the well without associated damage zone

reduces well productivity by 50 % compared to the

non-faulted case.

– High-permeable damage zone. A well within a

high-conductive damage zone has a two (tight fault

core) up to three (conductive fault core) times

higher productivity than a well outside the damage

zone.

• Characterization of fractured carbonate reservoirs—

implications from the study.

– Well productivity and fault permeability. The

productivity of a fractured reservoir should be

regarded as the result of a dynamic balance between

the permeability architecture of the nearby fault

zone and the well location with respect to this

domain. For such reservoir, no general and ‘‘a

priori’’ guidelines can be proposed regarding opti-

mum drilling locations if not based on a previous

detailed characterization of the permeability of

major existing fault zones in the present-day stress

field.

– Numerical models of reservoir behaviour. By

transferring information gathered about fault geom-

etry and permeability architecture with respect to

the active stress field into numerical models which

integrate all reservoir components, it is then possi-

ble to investigate the response of the system. This

provides a deterministic characterization of the

transient behaviour of the reservoir and contributes

to fast and cost-efficient usage and management of

geothermal resources.

Acknowledgments The authors would like to thank Matthias Kli-

nkmuller for setting up and providing the structural geological

PETREL model of the Mauerstetten reservoir. Personal credits go to

Wasiu Sonnibare for sharing his expertise while carrying out the time-

depth conversion of the geological model and to Dr. David Bruhn for

proofreading some critical parts of the manuscript. The structural

geological data and the hydraulic setting have been investigated as a

part of an ongoing project (0325267B ‘‘Geothermie Allgau 2.0’’)

which has been funded by the German Federal Ministry for the

Environment, Nature Conservation and Nuclear Safety (BMU).

Lastly, a special acknowledgement to the GeoEn project (Grant

03G0671 A/B/C) for providing a working platform cross-linking the

different scientific fields, e.g. exploration, reservoir engineering, and

environmental informatics. Finally, the authors would like to

acknowledge three anonymous reviewers for their helpful criticisms

which help improving the quality of the manuscript.

References

Agosta F (2006) Deformation mechanisms, architecture, and petro-

physical properties of large normal faults in platform carbonates

and their role in the release of CO2from Earth’s interior in

central Italy. PhD thesis, Stanford University

Agosta F, Prasad M, Aydin A (2007) Physical properties of carbonate

fault rocks, Fucino basin (Central Italy): implications for fault

seal in platform carbonates. Geofluids 7(1):19–32. doi:

10.1111/j.1468-123.2006.00158.x

Anderson E (1951) The dynamics of faulting and dyke formation with

application to Britain. Oliver & Boyd, Edinburg

Anderson TR, Fairley JP (2008) Relating permeability to the

structural setting of a fault-controlled hydrothermal system in

southeast Oregon, USA. J Geophys Res 113(B5):B05, 402. doi:

10.1029/2007JB004962

Birner J, Fritzer T, Jodocy M, Schneider M, Stober I (2009) Aufbau

eines geothermischen Informationssystems fur Deutschland.

Final Report, LIAG-Bericht, ArchivNr. 0128452, Hannover,

chap Molassebecken

Birner J, Mayr C, Lutz T, Schneider M, Baumann T, Winkler A

(2011) Hidrochemie und Genese der tiefen Grundwasser des

Malmaquifers im Bayrischen Teil des suddeutschen Molasse-

beckens. Z Geol Wiss 39:291–308

Byerlee J (1978) Friction of rocks. Pageoph 116:615–626

Byerlee J (1990) Friction, overpressure and fault normal compression.

Geophys Res Lett 17(12):2109–2112. doi:10.1029/GL017i012p

02109

Cacas MC, Daniel JM, Letouzey J (2001) Nested geological

modelling of naturally fractured reservoirs. Petrol Geosci 7(S):

S43–S52. doi:10.1144/petgeo.7.S.S43, http://pg.lyellcollection.

org/content/7/S/S43.abstract

Environ Earth Sci

123

Author's personal copy

Caine JS, Evans JP, Forster CB (1996) Fault zone architecture and

permeability structure. Geology 24(11):1025–1028. doi:10.1130/

0091-7613(1996)024h1025:FZAAPSi2.3.CO;2, http://geology.

gsapubs.org/content/24/11/1025.abstract

Cheng S-W, Dey TK, Shewchuck JR (2012) Delaunay mesh

generation. CRC Press, Boca Raton

Clauser C, Koch A, Hartmann A, Rath V, Mottaghy D, Pechnig R

(2006) Erstellung statistisch abgesicherter thermischer und

hydraulischer Gesteinseigenschaften fur den flachen und tiefen

Untergrund in Deutschland Phase 1—Westliche Molasse und

nordlich angrenzendes Suddeutsches Schichtstufen-land. BMU-

Projekt FKZ 0329985 (Final Report)

Davatzes N, Aydin A (2005) Distribution and nature of fault

architecture in a layered sandstone and shale sequence: an

example from the Moab fault, Utah. In: Sorkhabi R, Tsuji Y

(eds) Faults, fluid flow, and petroleum traps. AAPG Memoir, vol

85, pp 153–180

Dietrich P, Helmig R, Sauter M, Hotzl H, Kongeter J, Teutsch G (eds)

(2005) Flow and transport in fractured porous media. Springer, Berlin

Energiegewinnung BGH (2010) Bayerischer Geothermieatlas—Hyd-

rothermale Energiegewinnung. Bayerisches Staatsministerium

fur Wirschaft, Infrastruktur, Verkehr und technologie

Ferrill DA, Morris AP, McGinnis RN (2009) Crossing conjugate

normal faults in field exposures and seismic data. AAPG Bull

93(11):1471–1488. doi:10.1306/06250909039, http://aapgbull.

geoscienceworld.org/content/93/11/1471.abstract

Frisch H, Huber B (2000) Ein Hydrogeologisches Modell und der

Versuch einer Bilanzierung des Thermalwasservorkommens fur

den Malmkarst im Suddeutschen und im angrenzenden Oberoster-

reichischen Molassebecken. Hydrogeologie und Umwelt 20(25):43

Fritzer T (2010) Bayerischer Geothermieatlas—hydrothermale Energi-

egewinnung: Technik, wirtschaftliche Aspekte, Risiken, hydroth-

ermale Grundwasserleiter in Bayern, Untergrundtemperaturen in

Bayern. Bayern, Staatsministerium fur Wirtschaft Infrastruktur

Verkehr und Technologie. http://books.google.de/books?id=wGA

nygAACAAJ

Heidbach O, Tingay M, Barth A, Reinecker J, Kurfeß D, Muller B

(2010) Global crustal stress pattern based on the World Stress

Map database release 2008. Tectonophysics 482:3–15. http://

www.sciencedirect.com/science/article/pii/S0040195109004132

Hickman S, Zoback M, Benoit R (1998) Tectonic controls on

reservoir permeability in the Dixie Valley, Nevada, geothermal

field. In: Proceedings of the twenty-third workshop on geother-

mal reservoir engineering. Standford University, Standford

Homuth S, Gotz AE, Sass I (2011) Outcrop analogue studies for

reservoir characterization and prediction of deep geothermal

systems in the Molasse Basin, Germany. EGU General Assem-

bly, Wien

Hyne NJ (2001) Nontechnical guide to petroleum geology, explora-

tion, drilling and production, 2nd edn. Pennwell Books, Tulsa

Jaeger J, Cook N, Zimmerman R (2007) Fundamentals of rock

mechanics. Blackwell, Oxford

Kalbacher T, Wang W, McDermott C, Kolditz O, Taniguchi T (2005)

Development and application of a cad interface for fractured rock.

Environ Geol 47(7):1017–1027. 10.1007/s00254-005-1236-z

Kolditz O, Bauer S, Bilke L, Bottcher N, Delfs J, Fischer T, Gorke U,

Kalbacher T, Kosakowski G, McDermott C, Park C, Radu F,

Rink K, Shao H, Shao H, Sun F, Sun Y, Singh A, Taron J,

Walther M, Wang W, Watanabe N, Wu Y, Xie M, Xu W, Zehner

B (2012) OpenGeoSys: an open-source initiative for numerical

simulation of thermo-hydro-mechanical/chemical (THM/C) pro-

cesses in porous media. Environ Earth Sci 67(2):589–599.

10.1007/s12665-012-1546-x

Kuhlemann J, Kempf O (2002) Post-eocene evolution of the North

Alpine Foreland Basin and its response to Alpine tectonics.

Sediment Geol 152(12):45–78. doi:10.1016/S0037-0738(01)00

285-8, http://www.sciencedirect.com/science/article/pii/S003707

3801002858

Marshall B, Eppstein D (1992) Mesh generation and optimal

triangulation. In: Du DZ, Hwang F (eds) Computing on

euclidean geometry. World Scientific Publishing, Singapore,

pp 23–90

Moeck I, Schandelmeier H, Holl HG (2009) The stress regime in a

Rotliegend reservoir of the Northeast German Basin. Int J Earth

Sci 98:1643–1654. doi:10.1007/s00531-008-0316-1

Muller C, Siegesmund S, Blum P (2010) Evaluation of the

representative elementary volume (REV) of a fractured geother-

mal sandstone reservoir. Environ Earth Sci 61(8):1713–1724.

doi:10.1007/s12665-010-0485-7

Nishida A (2010) Experience in developing an open source scalable

software infrastructure in Japan. In: Taniar D, Gervasi O,

Murgante B, Pardede E, Apduhan B (eds) Computational science

and its applications ICCSA 2010, Lecture Notes in Computer

Science, vol 6017, Springer, Berlin, pp 448–462. doi:10.1007/

978-3-642-12165-4_36

O’Sullivan MJ, Pruess K, Lippmann MJ (2001) State of the art of

geothermal reservoir simulation. Geothermics 30(4):395–429

Oreskes N, Shrader-Frechette K, Belitz K (1994) Verification,

validation, and confirmation of numerical models in the earth

sciences. Science 263:641–646. doi:10.1126/science.263.5147.

641

Peska P, Zoback MD (1995) Compressive and tensile failure of

inclined well bores and determination of in situ stress and rock

strength. J Geophys Res 100(B7):12791–12811. doi:10.1029/95

JB00319

Reinecker J, Tingay M, Muller B, Heidbach O (2010) Present-day

stress orientation in the Molasse basin. Tectonophysics

482:129–138. http://www.sciencedirect.com/science/article/pii/

S0040195109004119

Schultz R (2007) Abschatzung des fundigkeitsrisikos erfahrungen mit

projekten. geothermische anforderungen definition:fundigkeit-

srisiko erfolgswahrsheinlichkit beispiel unterhaching ausblick.

Tech. rep., 18. Fachtagung der SVG, Zurich

Segura JM, Carol I (2004) On zero-thickness interface elements for

diffusion problems. Int J Numer Anal Meth Geomech 28(9):

947–962

Si H (2010) Constrained Delaunay tetrahedral mesh generation and

refinement. Finite Elem Anal Des 46(1):33–46

Turner A (2006) Challenges and trends for geological modelling and

visualisation. Bull Eng Geol Environ 65:109–127. doi:10.1007/

s10064-005-0015-0

Wang W, Kolditz O (2007) Object-oriented finite element analysis of

thermo-hydro-mechanical (THM) problems in porous media. Int

J Numer Meth Eng 69(1):162–201

Watanabe N, Wang W, McDermott C, Taniguchi T, Kolditz O (2010)

Uncertainty analysis of thermo-hydro-mechanical coupled pro-

cesses in heterogeneous porous media. Comput Mech

45(4):263–280. doi:10.1007/s00466-009-0445-9

Watanabe N, Wang W, Taron J, Gorke UJ, Kolditz O (2012) Lower-

dimensional interface elements with local enrichment: applica-

tion to coupled hydro-mechanical problems in discretely frac-

tured porous media. Int J Numer Meth Engng 90(8):1010–1034.

doi:10.1002/nme.3353

Wibberley CAJ (2008) The internal structure of fault zones:

implications for mechanical and fluid-flow properties. Special

Publication, Geological Society of London. http://books.google.

de/books?id=ce42jBktYGsC

Wolfgramm M, Obst K, Brandes J, Koch R, Raubbach K, Thorwart K

(2009) Produktivitatsprognosen geothermischer aquifere in Deu-

tschland. In: Der Geothermiekongress 2009 conference proceedings

Zoback M (2007) Reservoir geomechanics. Cambridge University

Press, Cambridge

Environ Earth Sci

123

Author's personal copy