M Abuaisha

B Loret

Permeability enhancement of HDR reservoirs by hydraulic fracturing

Permeability enhancement of HDR reservoirs by hydraulic fracturing

Murad S. Abuaisha, B.

INTRODUCTION

The exploitation of the geothermal energy has become a world strategy since 1975. However, geothermal energy exploitation has been limited to certain areas on the planet where it was feasible and easy to extract, for instance areas near tectonic plate boundaries. Modern technologies such as hydraulic fracturing and chemical enhancement were recently deployed to extract geothermal energy from specific geological sites, if cost effective [START_REF] Turcotte | Geodynamics[END_REF].

Geothermal energy is produced by pumping cold fluids into Hot Dry Rock (HDR) reservoirs where temperature gradients are favorable. Deep in the ground at the level of the reservoir, the thermoporoelastic mechanisms that are taking place will be controlling the development of reservoir fluid pressure, the effective stresses, the rate of fluid losses, the thermal recovery progress and hence the economic viability of the entire geothermal process [START_REF] Bruel | Heat extraction modelling from forced fluid flow through stimulated fractured rock masses: Application to the Rosemanowes hot dry reservoir[END_REF]. One of the most important factors affecting thermal recovery from HDR reservoirs is the permeability of the fractured medium. Natural HDR reservoirs have quite low permeability; the process of injecting geothermal fluids is always endangered by large amounts of fluid loss and frustratingly inefficient thermal recovery. Modern geothermal projects are nowadays focusing on enhancing the permeability of the geothermal reservoirs which has given rise to the terminology of Enhanced Geothermal Systems (EGS). This enhancement is implemented by pumping geothermal fluids at considerable flow rates which will eventually lead reservoir fractures to evolve and connect (Hydraulic Fracturing (HF)). Representation of thermal recovery from a single fracture embed-ded in a geothermal reservoir has been outlined by [START_REF] Cheng | Integral equation solution of heat extraction from a fracture in hot dry rock[END_REF]. The same approach has been addressed by [START_REF] Zhou | A threedimensional integral equation model for calculating poro-and thermoelastic stresses induced by cold water injection into a geothermal reservoir[END_REF]) with investigating the thermoelastic and poroelastic effects of cold water injection.

Studies that are addressing the evolution of HDR reservoir permeability under thermo-poroelastic conditions are scarce. For instance, [START_REF] Lee | Thermoporoelastic analysis of injection-induced rock deformation and damage evolution[END_REF] considered HDR reservoirs consisting of a single fracture and adopted empirical relations to relate permeability to the effective stresses. Such studies, despite being indicative, do not address the effect of HF on the stability of geothermal boreholes, nor do they study the dependence of HF process on the geostatic conditions of the HDR reservoirs.

This paper provides a fracturing model which is integrated into a fully coupled thermo-poroelastic framework. This fracturing model is capable of tracking the fracture evolution at any geometrical point and in all possible fracture orientations. The new fracture properties namely, fracture radius and aperture, are used to calculate local fluid velocity fields using Navier-Stokes equation for laminar flow. The macroscopic velocity field is deduced by a directional averaging over the local velocities. An anisotropic permeability tensor, that describes the hydraulic connectivity of the hydraulically fractured medium, is then calculated by applying Darcy's law for laminar flow.

HYDRAULIC FRACTURING (HF)

In a poroelastic medium, HF can be defined as the process of causing fractures to propagate by using pressurized fluid. Normally the process of HF is suppressed by the confining pressure coming from the surroundings. HF is practically done by reducing the effective stress by pumping pressurized fluid to a point the minimum principal stress (in algebraic sense) becomes tensile and exceeds the tensile strength of the rock. HF is henceforth synonymous to tensile failure of rock material.

Thermal effects on HF

Thermally induced fracturing is a phenomenon observed while injecting cold water into hot rock layer. Rock matrix shrinks and thus reduces the compressive geologic stresses that confine the borehole. Let us consider the stress equation which describes the thermo-mechanical behavior of a saturated porous medium subjected to a temperature change ∆T :

σ ij + κ p δ ij = E ijkl (ε kl -ε T kl ), (1)
σ ij is the total stress tensor, p is the pore fluid pressure, κ is the Biot's coefficient, δ ij is the Kronecker delta, E ijkl is the elasticity tensor, ε kl is the mechanical strain tensor, ε T kl is the thermal strain tensor defined as ε T kl = (α s /3) ∆T δ kl and α s is the cubical thermal expansion coefficient.

If the porous medium was sufficiently permeable to a point the diffusion of fluid happens much faster than the diffusion of heat (the common case when simulating real EGS reservoirs), the term κ p δ ij could be assumed constant while cooling. Thus, while cooling ∆T becomes negative and contractive mechanical strains (ε kl ) are needed in equation ( 1) to keep the equilibrium condition ∇ j σ ij = 0. Contractive mechanical strains develop positive tensile stresses, imagine some degree of restrain at the boundaries, which in turn means reduction of the confining compressive geologic stresses.

Hydraulic Fracturing Model (HFM)

This section is aimed at providing a fracturing model which is capable of ensuring a directionally stable mode I of fracture evolution.

Fracture initiation

To illustrate the concept of fracture initiation, let us consider the following situation: a vertical borehole penetrating a rock formation which is homogeneous and isotropic in its elastic and transport properties. The far field stresses are such that -σ v > -σ H > -σ h . As the injection starts, the rock formation cools and the wellbore pressure p w increases. The effective tangential stress σ ′ θ in the rock material will correspondingly decrease, see figure (1).

The condition for HF initiation reads: where T c is the material tensile strength. In the presence of a mud cake, the wellbore pressure required to create the hydraulic fracturing in the direction of σ H is expressed as in equation ( 3):

σ ′ θ = T c , (2)
p HF w = -(3σ h -σ H ) + p f - E α s ∆T 3(1 -ν) -T c . (3)
In the absence of a mud cake and if the pressurization rate was slow enough to ensure steady state conditions during pumping, the pressure required to create hydraulic fracturing is given by1 :

p HF w = -(1 -ν)(3σ h -σ H ) + (1 -2ν)p f - E α s ∆T 3 -(1 -ν)T c . (4)
Note that the pressurization of impermeable media (permeability < 10 -18 m 2 ) is equivalent to the presence of a mud cake. Meanwhile all porous media with permeability > 10 -18 m 2 are assumed permeable and the limit for pressurization without a mud cake shall apply.

Summing up the foregoing strategies, HF technique in EGS can be summarized following figure (2). As the injection of cold water begins, the geostatic stresses start to decrease. Temperature change (cooling) helps mitigating the compressive geostatic stresses as well. If pressurization and cooling continue to a point the effective stresses become tensile and exceed the tensile strength of the rock material, fracturing takes place.

Fracturing criterion

Let us consider again the vertical borehole of figure (1) with a group of cracks of average radius r and arbitrary normal direction n in the horizontal plane (x, y). If the borehole pressure is gradually increased to a point the effective stress σ ′ n (at the crack tip) becomes tensile and exceeds the limit of material tensile strength, the group of cracks starts propagating and consequently the average aperture of cracks increases.

The following model, equation ( 5), has been suggested to track the evolution of average radius r of a group of cracks in direction n:

F (σ ′ n , r) = f (r) σ ′ n √ πr -K Ic , (5)
where K Ic is the material toughness for mode I of fracturing. The normal effective stress applied to the crack (σ

′ n ) is expressed as: σ ′ n = n i σ ′ ij n j . (6)
f (r) is a positive scalar valued function which controls the kinetics of crack propagation. f (r) is expressed as:

f (r) =    η r f r , r < r f η, r ≥ r f (7)
with r f denoting the critical crack radius for accelerated coalescence of microcracks, and η being the crack growth stabilizing parameter. f (r) decreases as the crack begins to propagate denouncing the relaxation of local tensile stresses as the cracks grow away from the zone of stress concentration: this feature ensures the stable growth of cracks. As the cracks start to coalesce, the function f (r) reaches an asymptotic value: this feature marks the onset of damage localization and macroscopic failure. The loading-unloading condition for a propagating crack of normal direction n is defined according to the Kuhn-Tucker relations:

ṙ ≥ 0, F (σ ′ n , r) ≤ 0, ṙ F (σ ′ n , r) = 0. (8)
Authors like (Klimczak et al. 2010) and [START_REF] Shao | Coupling between anisotropic damage and permeability variation in brittle rocks[END_REF] have related the normal increment of crack aperture to crack face mismatch and local grain matrix interaction during crack growth. Thus, the normal crack aperture increment is proportional to the average crack radius increment, that is to say:

δw δr = β, (9)
where β is the proportionality coefficient. (Klimczak et al. 2010) have performed experiments and collected data from literature on 15 types of rocks. They have found that β ranges from 0.0005 to 0.5.

Permeability tensor

Knowing the new fracture radius r(n) and aperture w(n) of arbitrary direction n, the local velocity field is calculated by implementing Navier-Stokes equation for laminar flow between two parallel plates. The macroscopic velocity field is deduced by a directional averaging over the local velocities. An anisotropic permeability tensor, that describes the fracture hydraulic connectivity, is then calculated by applying Darcy's law for laminar flow:

k c = N Ω 1 48 S R(n) w(n) 3 r(n) 2 (δ δ δ -n ⊗ n) dS, (10)
where N/Ω is the fracture density. The connectivity coefficient R(n) is given by:

R(r(n)) = t 1 r(n) -r 0 r f -r 0 t 2 , 0 ≤ R(n) ≤ t 1 , (11)
where r 0 is the initial crack radius. R(r(n)) involves two dimensionless positive constants, t 1 and t 2 , to be determined. The value of this coefficient depends on the microstructure of the damaged material. It indicates that connectivity between cracks increases as the cracks grow in size, which contributes to the crack permeability tensor k c . The overall permeability tensor of the cracked medium is composed of two parts: the initial permeability tensor denoted as k 0 due to the initial porosity, and the crack induced permeability tensor denoted by k c . The flow in the two cavities is assumed to take place in parallel and the total permeability tensor is obtained by summation, i.e. k = k 0 + k c .

HYDRAULIC STIMULATION

The HDR reservoir of Soultz-Sous-Forêts is chosen to be hydraulically enhanced by our HFM model discussed above. To perform the stimulation process, the HFM is integrated into a domestic Fortran 90 finite element code that simulates thermo-poroelastic transient BVPs.

Geometry and material properties

Due to symmetry, only a quarter of the reservoir volume is to be simulated, figure (3). Initial and boundary conditions are also highlighted on the graph. The horizontal finite element mesh is composed of 300 Q4 elements, 10 elements in y-direction and 30 elements in x-direction. The simulations are conducted under a 2D plane strain conditions.

Cold water is injected from the well (GPK1) and left to travel through the geothermal reservoir before it is retrieved via the production well (GPK2). Injection pressure is increasing at GPK1 linearly; pumping starts with 58 MPa and terminates, after 15 years, with 82 MPa. The material properties of Soultz-Sous-Forêts reservoir are shown in Tables (1) and(2). The crack growth stabilizing parameter η is determined based on the threshold of HF by equation (4). Circulation tests for a time period of 1 year with and without standing for HF are reported below.

Results and simulations

The high fluid gradients near the injection well traveling mainly in y-direction (the shorter dimension of the reservoir) cause fast cooling and lead cracks to propagate and thus permeability to increase in this direction, figures (4) and ( 5).

Since the reservoir is constrained in x and y directions due to roller displacement, near the injection well y = x = 0 m, cooling creates tensile stresses which mitigate geologic stresses and contribute to crack propagation in these directions, figures (9) and (10).

In the case when HF is utilized, the distribution of effective stress is much more irregular following the preferential cooling derived by the new paths created by the HF, see figures ( 9) and ( 10) and compare with figure (4).

In the regions where HF is active, formation pressure distribution tends to be spatially uniform before it starts to decline considerably in the regions of low permeability, figures ( 7) and ( 8). This pattern of pressure distribution was also noticed by [START_REF] Lee | Thermoporoelastic analysis of injection-induced rock deformation and damage evolution[END_REF]. Figure (11) shows the space distribution of the longitudinal permeability component k x at year 10 of HF. The reservoir is being enhanced equally in x and y directions. This is due to the isotropic geologic stress state applied on the reservoir, see figure (3). If the applied geologic stress state is not isotropic, which is the common case in field, fractures will evolve in the direction of maximum geologic stress. The permeability will, therefore, be enhanced in that direction (AbuAisha 2014).

7.5 × 10 -6 (1/ • C) Volumetric thermal expansion of the fluid α f 1 × 10 -3 (1/ • C)

CONCLUSION

Hydraulic fracturing in a thermo-poroelastic framework has been studied in the context of thermal recovery from large scale geothermal systems. A fracturing model which is capable of tracking the directional evolution of fractures has been presented. This fracturing model has been integrated into a domestic Fortran 90 FEM code which is able to solve thermoporoelastic transient BVPs.

Figure 1 :

 1 Figure1: Vertical wellbore with vertical cracks. Wellbore wall can/can not be lined with a mud cake.

Figure 2 :

 2 Figure 2: Mohr circles and failure line: the effect of increasing pore pressure and decreasing temperature on HF.

Figure 3 :

 3 Figure 3: Modeling of HF process at Soultz-Sous-Forêts. Figure is not to scale.

Figure 4 :Figure 5 :Figure 6 :

 456 Figure 4: Space distribution of longitudinal permeability component k x at year 1 of HF.

Figure 7 :

 7 Figure 7: Pressure space distribution at year 1 with HF.

Figure 8 :

 8 Figure 8: Pressure space distribution at year 1 without HF.

Figure 9 :

 9 Figure 9: Space distribution of longitudinal effective stress σ ′ x at year 1 with HF.

Figure 10 :

 10 Figure 10: Space distribution of longitudinal effective stress σ ′ x

Figure 11 :

 11 Figure 11: Space distribution of longitudinal permeability component k x at year 10 of HF.

Table 1 :

 1 Material properties of Soultz-Sous-Forêts reservoir,[START_REF] Evans | Studies and support for the EGS reservoirs at Soultz-Sous-Forêts[END_REF]).

	Property	Value
	Drained Young's modulus E Drained Poisson's ratio ν	54 × 10 9 (Pa) 0.25
	Bulk modulus of solid grains K s Bulk modulus of fluid K f Dynamic viscosity of the fluid µ Porosity φ	50 × 10 9 (Pa) 2.2 × 10 9 (Pa) 3 × 10 -4 (Pa.s) 0.1003
	Initial permeability k 0 Solid thermal conductivity χ s	6.8 × 10 -15 (m 2 ) 2.49 (W/m • C)
	Fluid thermal conductivity χ f	0.6 (W/m • C)
	Solid heat capacity at constant volume c s,v	1000 (J/kg • C)
	Fluid heat capacity at constant volume c f,v	4200 (J/kg • C)
	Density of solid ρ s	2910.2 (kg/m 3 )
	Unit weight of water γ f	9800 (N/m 3 )
	Volumetric thermal expansion of the solid α s

Table 2 :

 2 Parameters used in the application of the HFM. References: 1.[START_REF] Shao | Coupling between anisotropic damage and permeability variation in brittle rocks[END_REF], 2.[START_REF] Atkinson | Fracture mechanics of rock[END_REF]) and 3.[START_REF] Evans | Studies and support for the EGS reservoirs at Soultz-Sous-Forêts[END_REF]).

		Parameter	Value	Reference
	Damage parameters	Initial radius of cracks r 0 (cm)	15.0	3
		Final radius of cracks r f (cm)	55.0	3
		Initial aperture of cracks w 0 (cm) Material tensile strength T c (MPa) Material toughness K Ic (MPa √ m)	3.111 × 10 -3 8.3 1.87	Calculated 2 2
		Crack growth stabilizing parameter η	0.04	Parameterized
	Crack density (1/m 3 ) Hydraulic connectivity t 1	2 × 10 6 0.0001	1 1
	parameters	t 2	1.0	1

To understand the role of thermal stresses in equations (3) and (4), the reader is advised to check (AbuAisha

2014) and[START_REF] Fjaer | Cubic law with aperture-length correlation: Implications for network scale fluid flow[END_REF]).


The kingdom of Pontic Kappadokia -which was not known as 'Pontus' until Eupator's time 1 -was founded in the beginning of the third century BCE by Mithridates Ktistes . Mithridates was born into the Persian family that, according to Greek sources, 'ruled' the Greek city of Kios in Propontis under the Achaemenids . The last of the "masters of Kios", who had maintained the city's rule under the Diadochi, was assassinated by Antigonus I Monophtalmus in 301 BCE; his nephew Mithridates (later known as Ktistēs) 2 subsequently fled to Pontic Kappadokia, where he founded a "kingdom of which he declared himself King (basileus)" in 281 or 280 BCE . 3 The new dynasty, usually referred to by historians as the 'Mithridatids', rapidly integrated into the Hellenistic monarchies through intermarriage with the Seleukid house: Mithridates II (266-220) married Laodike, Seleukos II's sister 4 , and presented his daughter Laodice to Antiochos Hierax -she finally became Achaios's wife 5 . Her daughter, also called Laodike, married Antiochos III in 222 BCE .

THE MITHRIDATIC DYNASTY AND REFERENCES TO THE "SEVEN"

Polybius, describes the wedding, informs us of the Mithridatids' genealogical claims:

(Antiochos) was joined by Diognetos, the admiral from Kappadokia Pontica, bringing Laodice, the daughter of Mithradates, a virgin, the affianced bride of the King. Mithradates claimed to be a descendant of one of those seven Persians who had killed the Magus, and he had preserved in his family the government on the Pontus originally granted to them by Darius .

1

On this name see Reinach (1988) p . 161 . 2

The surname 'Ktistes' can only be found only in textual sources: see, e . g ., Strabo 12, 3, 41; Lucian, Makrobioi 13. It is unknown whether Mithridates adopted it officially or not. 3

For this date, see Reinach (1888) . The tale of the Mithradatids' origins, very largely hypothetical, is a reconstitution obtained mainly through the combination of several source texts (Diodorus Siculus 20,111,4;Strabo 12,3,41;Plutarch,Demetrius 4;Lucian,Makrobioi 13) . It has been established by Ed . Meyer (1879) and admitted by all the scholars; later it was shown that Ktistes was the nephew, and not the son, of Mithridates of Kios (see Olshausen (1978) . However, it raises many questions; one can wonder, for instance, which kind of 'rule' the Mithridatids family could exercise on Kios -we have no other example of a Persian family 'ruling' a Greek city in Achaemenid times . Briant (1996) p . 1051-1052 is quite skeptical about this 'domination', which seems to be an anachronic projection . 4

Porphyry FGrH260F . 32 = Eusebios, Chron . I, p . 251 Schoene; see also Justin 38,5,3 . 5 See Polyb . 5,74,5 and 8,22 . See also the commentary by McGing (1986), p . 21-23 . ὁ δὲ Μιθριδάτης εὔχετο μὲν ἀπόγονος τῶν ἑπτὰ Περσῶν ἑνὸς τῶν ἐπανελομένων τὸν μάγον, διατετηρήκει δὲ τὴν δυναστείαν ἀπὸ προγόνων τὴν ἐξ ἀρχῆς αὑτοῖς διαδοθεῖσαν ὑπὸ Δαρείου παρὰ τὸν Εὔξεινον πόντον. 6 This text shows that the Kings of Pontic Kappadokia claimed to be descendants of one of the seven noble Persians that assassinated the usurper Smerdis in 522 at the instigation of Darius, and thus enabled him to take royal power (this well-documented episode is described by Greek sources, beginning with Herodotos, as well as by Darius' engraved inscription at Behistun) . 7 Not only the Mithridatids placed the Seven at the root of their family tree: two other Hellenistic dynasties that claimed Persian descent, namely, the Ariarathids of Kappadocia and the Orontids of Armenia, did likewise . 8 Even though some scholars accept the idea that all these dynasties actually descended from one of the Seven, these genealogical assertions cannot be proven and are generally considered as false 9 . Even if one of these Hellenistic rulers was linked to one of the Seven, it is very doubtful that this link would still be remembered three centuries after the murder of Smerdis .

This tendency to link themselves to the Seven should probably not be understood as the remnant of an Achaemenid custom: nothing indicates that it became customary in the Achaemenid world to distinguish dignitaries by recalling their descent from one of the seven conspirators . 10 The idea that Darius had given a 6

Polybius 5, 43, 1-2 . I chose to translate the word dunasteia as 'government' instead of 'kingdom', which appears in the LCL: dunasteia is a more neutral term . 7

Greek and Latin sources: Aesch ., Ktesias F 13,[11][12][13][14][15][16][17][18]; Justin 1 .9 .0 . A transcription and German translation of the Behistun inscription of Darius by Weissbach (1931), p . 9-74, can be consulted at achemenet .com; the English translation by King and Thompson (1907) (1996) . 10 On this point, see Lerouge-Cohen (2013) .

dunasteia on the shore of the Pontus to the Mithridatids' ancestor in order to thank him for his help should not be accepted by historians: of course, it is well known that Darius felt gratitude towards his (six) accomplices, as mentioned on to the Behistun inscription 11 ; moreover, Herodotus tells us that Darius granted them some privileges not because of their courage, but because they recognized him as King: the Seven had the right to enter the Royal Palace without an 'introductor', and the King was obliged to choose his wives from among their families 12 . However, it is not mentioned here that a dunasteia was given to them . One cannot imagine, in any case, that the Achaemenid King would present a dunasteia to one of his friends: as P . Briant has shown, when the King gave estates or even cities, they were above all fiscal presents, and did not necessarily imply a political domination 13 . The story told by the Mithridatids (and the Ariarathids) about Darius and their ancestors must be considered as invention 14 .

It is evident why they would forge such a tale . Firstly, it legitimized their dynasty's power in Pontic Kappadokia: namely, it showed that the kingdom was not a recent creation (while in fact it was) but that it had already existed in Achaemenid times, and that the Mithridatids were its legitimate rulers because they had received it from Darius . In addition, the link with the Seven, gave prestige to the dynasty: we know from Darius and Herodotus that the Seven all came from very high-born families of the Achaemenid kingdom .

This leads to the following question: When the Mithridatids (and the Ariarathids) presented themselves as descendants of one of the Seven, did they try to please a Persian 'audience'? Many scholars insist on the fact that old Persian families from the Pontic kingdom (as well as Ariarathid Kappadokia) that had been installed in Anatolia by the Achaemenids remained very powerful in the kingdoms that emerged after the fall of the Persians and the Macedonian conquest . Did their dynastic genealogical claims target these Persian aristocratic families, whose support the Kings needed and whose 'Iranian' pride they tried to exalt 15 ? In the eyes of the Persian nobles, however, this genealogical discourse would counter-balance the real and deep Hellenization of the Kings, who spoke Greek, struck coinage 11 See the Behistun inscription par . 69 : Darius invites his successors to keep protecting the Seven and their descendants . 12 Hdt 3, 84 . 13 Briant (1985a) . 14 See Meyer (1879) p . 31-38 ;McGing (1986) p . 13 . For an analysis of this reference to the Seven by the Mithridatids and Ariarathids, see Panitschek (1987)(1988); Lerouge-Cohen (2014) (they should be understood in a Hellenistic context) . 15 See MgGing (1996) p . 10: genealogical claims of the Mithridatic dynasty show 'how important the Iranian element was in Pontic society' .

copying Hellenistic models 16 , and practiced euergetism in the main Greek religious centers 17 . This interpretation is problematic . Historians have indeed often emphasized the power of the Persian families in the kingdom of Pontic Kappadokia, but this is not confirmed by the sources: in fact, the genealogical claims of the reigning dynasties represent one of the most important proofs of this alleged power . The Kings seem to have met no opposition to their Hellenizing policies from these families, and there is no proof that it would have been necessary for them to give 'pledges of Persianism' to render them docile . The sources do not reveal any tension between the Persian element of Pontic Kappadokia's population and the sovereigns that ruled it .

Moreover, there is no indication that the Seven were even remembered in the Iranian world: the Arsakids never referred to them, and neither did the Sasanids that succeeded them .

In contrast, the story of the Seven was famous throughout the Greek world, and had very positive connotations: Greek sources describe the murder that they accomplished as a noble and courageous act 18 . The tale of a group of people killing an usurper was popular because it could easily evoke tyrannicide, and recalled Greek (and Roman) ideals of freedom 19 . Notably, Polybius also calls to mind the origins of Mithridates II at the time of his daughter's wedding to Antiochos III, and those origins clearly gave prestige to the bride 20 . If it was prestigious for a Seleukid to marry a descendant of one of the Seven, we can deduce that the references to these historical figures were not confined to an Iranian audience.

16 For the coinage of the Kings of Kappadokia, see Simonetta (2007): from the reign of Ariarathes III (230?-220), the royal coins show the portrait of the King on the obverse, and Athena carrying a Victory in her hand on the reverse . On the few coins struck in the Pontus by the predecessors of Mithridates Eupator, see Callataÿ ( 2009): these coins have specific characteristics (for example, the 'realistic' approach to the portraits as opposed to the idealization of the Greek ones, and the presence on the reverse of the crescent moon and star, which do not belong to Greek iconography) but they are nonetheless closely related to the conventional Hellenistic iconography and have Greek lettering . 17 For a summary on the Hellenization of the Kings of Pontus, Kappadokia (and Armenia), see Bernard (1985), here p . 74-85 . On the euergetism of the Kings of Pontus and Kappadokia, see the Delian decrees in honor of Pharnakes (ID 1497bis (160/159 BCE) and of Mithridates V Euergetes (ID 1557-1558) . In Kappadokia, Ariarathes V (163-130 BCE) was granted Athenian citizenship (IG II2 3781) and was honored, shortly before 130, as was his wife Nysa, in a decree issued by the Athenian Dionysiac Technites (IG II2 1330); see also Le Guen ( 2001) p . 67-74 . 18 See e . g ., Aesch ., Persians v . 774-777; Plato, Laws, 695c and Ep. VII, 332b; Justin 1, 10, 1 . Plato, in particular, strongly idealizes Darius because of the way he took the royal power, and of the kind of relationships he established with his ancient accomplices . P . Briant underlines the legendary dimension acquired by the Seven in the Hellenic world, as early as in the Classical period: see Briant (1996) p . 140-149 . 19 In Hdt 3, 67, Smerdis, seeking the people's support in order to reinforce his power, presents features similar to a Greek tyrant: see Lerouge-Cohen (2014) . 20 See Gabelko (2009) p . 52-53: the marriages between the Seleukids and the other dynasties of Anatolia were researched by the Seleukids for their political aspect and by the 'minor' dynasties for the prestige they bestowed on them; supposedly, however, these marriages were all the more valuable for the Seleukids if the bride was high-born .

Subsequently, I hypothesize that reference to the Seven in the kingdom of Pontic Kappadokia should be understood in a Hellenistic context instead of an Iranian one . The Mithridatids (like the Ariarathids) had probably learnt the story of the Seven from Greek sources; their connections to these glorious characters put them in a favorable light in the Hellenistic world -but not in an allegedly 'Persian' or 'Iranian' context .

This late use and recreation of the Iranian past seem to present a clear example of Persianism . dates VI, following in the footsteps of their neighbors and rivals of Kappadokia, had already attempted to link their dynasty to that of the Achaemenids, even though no sources exist that provide any further knowledge . Panitschek (1987)(1988) emphasizes the rivalry between the two kingdoms . 25 His mother Laodike was allegedly the daughter of Antiochos IV; but this cannot be ascertained with certainty, as it has been deduced from her (dynastic) name only (Ballesteros Pastor (1996), p . 31) . Moreover, the dynasty had been intermarrying with the Seleukid house for a long time, as we have already seen: Mithridates II (266-220) had married the sister of Seleukos While the idea that the Pontic dynasty descended from one of the Seven did not disappear from Greek sources 28 , Mithridates' Achaemenid claim was widely accepted: according to Appian, Mithridates was a descendant of Darius to the sixteenth degree 29 ; Ampelius, the preceptor of Macrinus, presented Darius as the ancestor of Artabazes, "the founder of the kingdom of Mithridates" 30 . Mithridates, King of Bosporos and descendant of Mithridates Eupator through his grand-daughter Dynamis, still maintained that he was the "heir of the great Achemenes" (prole magni Achaemenis) during the reign of Claudius . 31 In contrast, the sources never mention the 'Macedonian' claim -except in the speech transmitted by Justin .

Eupator's claims to Achaemenid ancestry may be associated with the fact that he chose to depict Pegasus, Perseus' winged horse, on the obverse of the coinage of the first part of his reign 32 : Perseus was reputed to be the heroic founder of the Persian race 33 . This clearly underlines the assumption that Mithridates intended to link himself closely to the Persian world (albeit not precisely, in the case of Pegasus, to the Achaemenids) 34 .

Once again, as was the case with the "Seven" claim, the question is whether this choice should be understood, on Eupator's part, as a pledge to his kingdom's Persian aristocracy, as is often assumed in scholarly literature: by introducing himtext and translation of the Nemrud Dagh inscriptions, see K . Dörner in Sanders (1996), vol . 1, chapter 5, p. 254-355; specifically for the ancestors' inscription p. 323; see also Facella (2006), p . 87 and270 . On Nemrud Dagh andKommagene, see Facella (2006); Wagner (2012); and most recently Brijder (2014); on the 'ancestors' galleries' see in particular Jacobs (2012) and Messerschmidt (2012); also Strootman (in press) . 28 Panitschek (1987)(1988) self as a descendant of both the Achaemenids and Alexander, the King would try to court his two main 'audiences', the Persians on the one side, and the Greeks on the other side 35 . The Persian aristocracy would have been proud to have an heir of Cyrus as King, whereas Greeks in the kingdom and beyond would identify with a man connected to the memory of Alexander and the Seleukids . These two separate threads of propaganda would lead to the same result: the desire to take the power in Asia Minor back from Rome . This interpretation of a dualistic speech contains several flaws. Firstly, it postulates not only that the kingdom's population was made up exclusively of Persians and Greeks, which ignores the specific Anatolian population that constituted the majority of the demography, but also that the Greeks and Persians would have developed in completely distinct directions, thus entailing the elaboration of two different genealogical traditions, which is not plausible . Is it truly plausible to think that at the heart of a kingdom in the first century BCE where a strong familiarity with Greek culture was essential if one wished to serve the King -and thereby belong to the elite -the Persians remained so viscerally attached to their Persian past that they required a specific discourse to differentiate themselves from the discourse that the 'Greeks' recognized themselves in? Moreover, Eupator does not establish any links between the proclamation of his Achaemenid origins and a Persian sense of solidarity in his speech . He never encourages the Persians as Persians to unite around him to chase the Romans out of Asia . The existence of a 'Persian feeling' in the Pontic kingdom that was directed against Greek cultural hegemony is highly doubtful . If, however, such a sentiment could be acknowledged, nothing in Mithridates' speech indicates that the King made use of it, by proclaiming himself a descendant of Cyrus and Darius, in reference to the war he was about to wage on Rome .

The presence of Pegasus on his coinage is indeed a sign of the royal desire to recall the Persian origins of his dynasty, but it is also proof of his knowledge of Greek sources: only Greeks, or at least those who knew Greek culture, could understand this reference to Perseus as the founder of the Persian race, as it was told by Herodotus 36 and does not appear in Persian sources . Notably, Perseus was 35 See, e . g ., McGing (1986) p . 10; ibidem p . 107, where he distinguishes between the Greek subjects and the 'eastern subjects and prospective eastern subjects' whom the King addressed when emphasizing his Achaemenid lineage . Panitschek (1987)(1988), p . 95, states that the Mithridatids' Persian claims not directed to the Greeks but toward the 'Kleinasiaten und Iranier Anatoliens' . Both P . Panitschek and B . McGing, conclude that the target audience of the 'Achaemenid' part of Mithridates' propaganda included Persians and Anatolians, in short, all those that were not Greek, and that this created a problem of definition: why would the Anatolians be open to Persian themes, and if they were, why should the Greeks not be equally receptive? We can also cite Reinach (1890), p . 299-300: Mithridate 'sut jouer de l' Olympe et de l' Avesta, des souvenirs d'Alexandre et des reliques de Darius, du despotisme et de la démagogie, de la barbarie et de la civilisation, comme autant d' instruments de règne, autant de moyens de séduire et d' entraîner les hommes … ' See also ibidem p . 35-37 . 36 According to Herodotus (7, 150-152), certain accounts say that Xerxes would have sent ambassadors to the Argians to demonstrate they had a common ancestor with the Persians, since the latter descended from Perses, the son of Perseus and Andromeda; it would therefore be also an extremely popular figure in the Hellenistic era in the Greek cities of Asia that referred to him as their founder, most famously Tarsus 37 , which was a way for them to emphasize their Hellenism, namely, by proving their link to the ancient Greek city of Argos 38 . The same is true for the dynasty of Philip and Alexander of Macedonia, who were called the Argeads . For this reason, the reference to Perseus is rather ambiguous .

As far as the specific Achaemenid connections in Hellenistic times are concerned, it is clear that being an heir to the ancient Persian Kings bestowed a royal prestige that was not confined to an Iranian context. Diodorus Sicilus, for instance, described the ties uniting Cyrus to the Ariarathides at length, thereby showing that, for him, those ties augmented the glory of Ariarathes V, a King whom he valuated very much 39 . Similarly, Josephus reveals that Princess Glaphyra of Kappadokia, who had married one of Herod's sons between the years 15-17 CE, never ceased to brag about her royal origins in front of her in-laws, recalling her descent from Temenos on one side and from Darius on the other -an attitude that made her hated by the other women at the court . 40 In a Jewish kingdom, this claim would certainly not be meant to entice the Persian population .

Notably, the Persian Kings that appear in the genealogy during the Hellenistic era are Cyrus and Darius I, who both were positively portrayed in the Greek tradition, as opposed to their successors, Kambyses and Xerxes 41 . More generally, Herodotus as well as the IV th century Persika testify that the Greek writers from the Classical era had real interest in the Persian Kings: the Greeks had real knowledge of the Achaemenids and did not systematically deny them, as might be assumed 42 . In contrast, the Achaemenids, like the Seven, seem to have been entirely forgotten in the Arsacid and Sassanid kingdoms 43 . natural for them to ally themselves with the Persians . Either Herodotus replicates a purely Greek tradition, or Xerxes was sufficiently aware of Greek mythology to use this account to diplomatic ends . In either case, the link between Perseus and the Persians does not originate from Persian culture . 37 See Robert (1977), here p . 96-132 . 38 For the ambiguous quality of the reference to Perseus and for a list of the cities claiming a link to this hero, see Briant (1985b), here p . 185-187 . 39 Diodorus Siculus 31, 19, 1-2 ; 31, 19, 7-8: Ariarathes 'received a Greek education' (παιδείας τε Ἑλληνικῆς μετασχεῖν) and made Kappadokia 'unknown to the Greeks', 'a place of sojourn to men of culture' (τοῖς πεπαιδευμένοις ἐμβιωτήριον) . 40 Jos ., Bell . 1, 228-229: Glaphyra boasted about her origins and mocked the other women in the palace that had been chosen not for their birth, but for their beauty . 44 It is commonly assumed that these references to Alexander had a strong anti-Roman signification: 45 according to Claudia Bohm, to recall Alexander's name -which was not a new attitude among the later Hellenistic rulers at all 46 -began to sound dangerous to Roman ears after Eupator 47 . Admittedly, the King does not use the trope of the conqueror in a 'nationalist' Greek sense in his speech to his troops . He does not use the name of Alexander to appeal to the unification of the Greeks and the necessary protection of the latter, nor does he try to encourage them by calling to mind the exploits of his glorious predecessor -in fact, further on in the speech, Alexander's qualities are even presented as inferior to those of the Pontic King . 48 The mention of Alexander remains unique and does not diverge towards an exposition of a particular policy aimed at the Greeks . This does not mean that another, more loaded use of the Macedonian conqueror trope was not available to support Mithridates' actions; it quite simply does not appear in this particular speech .

Just as searching the speech for any appeal to a Persian sentiment would be in vain, the reference to Alexander and Seleukos is not mixed with political philhellenism directed against the Romans . Mithridates does not establish any link behistorical summary written about them by Ammianus Marcellinus (23, 6, 1-9), who established no distinction whatsoever between Parthians and Persians) that it seems imprudent to use it as a reliable source: see Lerouge (2007) [17][18][19]18,6,in particular . 48 Just . 38 .7 .2: Mithridates is the only one that conquered Kappadokia, Paphlagonia, Pontus or Bithynia: 'none of these peoples had even been reached by the famous Alexander, who subdued the whole of Asia, nor by anyone who succeeded or preceded him' .

tween his origins and the self-ordained mission he might have followed among the Greeks . In fact, by presenting himself as a descendant of the Achaemenids, on the one hand, and of Alexander and Seleukos, on the other, Mithridates seems to aim most of all to add prestige to his dynasty not simply in front of two different audiences, but before the eyes of the entire population of the Hellenistic world. His first aim is to humiliate the Romans, who had low origins . Obviously, he mentions his Achaemenid lineage for the same reason: the fact that he descended from two royal families and not just from one was important in order to debase the Romans . Moreover, the two lineages that Mithridates attributed to himself were complementary .

The King focused the glory that each of them provided on his unique person and thus profited from two different sources of prestige and political charisma.

The simultaneous reference to the Achaemenids and the Seleukids in Mithridates' speech probably had a second use . It provided the King a source of legitimacy for the domination of the whole of Asia, whereas the presence of Romans in Asia Minor could only be explained by their greed (Justin 18 .6 .8) . According to Hellenistic ideas, it was a legitimate claim for a King to take territories that one of his ancestors had conquered by force as his own property . 49 The fact that he was a descendant of both the Achaemenids and Alexander and Seleukos, who had all been empire-builders, doubly justified Mithridates' claim to Asia.

CONCLUSION

The Mithridatic dynasty, as well as the Ariarathids of Kappadokia, established a link with the Persian past early in their history: they claimed to be descendent from one of the Seven that killed the usurper . Later, Eupator abandoned the reference to the Seven, choosing instead to emphasize his Achaemenid ancestors, namely, Cyrus and Darius . He added a Macedonian heritage (Alexander and Seleukos) to this glorious ancestry, thus forging a double genealogy for himself . These Pontic references to the Seven and the Achaemenids should be understood, in my opinion, as examples of Persianism . The Kings selected Persian events and individuals (the Seven, Cyrus and Darius) that were well-known across the Greek world and enjoyed a very good reputation: the Persian past was probably known from Greek sources . Their Persian identity was not transmitted from a remote past through the centuries, but was consciously recreated in Hellenistic times instead . The claim to Persian or Achaemenid roots was not targeted to an Iranian audience: it was a deliberate way to gain prestige and legitimacy, which could be combined with Macedonian claims, in a world that was not 'Greek' or 'Iranian', but simply 'Hellenistic' .

  23 21 For this part of the paper see alsoLerouge-Cohen (forthcoming), where I express similar views . 22 Justin 38 .3 .10 . Trogus disapproved of the insertion of direct speech in historical works and it is therefore usually accepted that Justin accurately reproduced this speech from Trogus' original text, cf . e .g .,Jal (1987), p . 196 . R . Develin in Develin & Yardley (1994), p . 5, however, questioned the assumption that Justin was faithful to Trogus' version; according to Ballesteros Pastor (2013), the speech was invented entirely by Justin and did not originally feature in Trogus' narrative . 23 Justin 38 .7 .1 . Some doubts have been raised about the authenticity of the speech . Even if it was re-written by Trogus, it is undeniable that the contents must be at least partially faithful to the historical reality . For further discussion on the authenticity of the speech, see, e . g ., McGingMithridates is not the first Hellenistic King to link himself to the Achaemenids: Diodorus tells us that the Ariarathids of Kappadokia had already done so from the time of the reign of Ariarathes V (163-130 BCE), claiming that the founder of their dynasty, Anaphas, was of the Seven and a cousin of Cyrus on his mother's side 24 . Mithridates, however, is the first King to underline his dual origins in all accounts. His double genealogy is partially based on historic fact: Eupator was indeed a descendant of the Seleukid dynasty through political inter-dynastic marriages25 , but naturally not of Alexander the Great, as Seleukos was not related to Alexander by blood . His Achaemenid connections can neither be proved nor disproved: Mithridates was of Persian origin and his family was possibly linked to the Achaemenid line, 26 but the precise nature of this connection, if it even existed, was long forgotten in Mithridates' time . Another King, Antiochos I Theos of Kommagene (c . 69-40 BCE), whose reign began before Mithridates' death, would in turn claim both Achaemenid (through his father) and Macedonian (through his mother) ancestry 27 a few decades later . Ciceronian reminiscences . Ballesteros Pastor (2006): 581-596, here p . 595, notes the occurrence in the speech of geographic terms, such as 'Bithynia and Pontus', or 'Lesser Armenia', which are associated with Roman expressions coined at the time of Augustus . 24 Diod . Sic . 31, 19, 1 . Nothing prevents us from surmising that the predecessors of Mithri-

	THE DOUBLE GENEALOGY OF MITHRIDATES EUPATOR: REFERENCES TO THE ACHAEMENIDS 21
	The Mithridatids' genealogical claims underwent a major change during the reign
	of Mithridates Eupator (111-63 B .

C .) . Eupator apparently made no mention of the Seven: instead, he boasted about his descent from Cyrus and Darius on one side, and from Alexander and Seleukos on the other . We know this from the famous speech attributed to him by Pompeius Trogus in his Historiae Philippicae, and from an indirect speech transmitted by Justin 22 . As he addresses his troops on the eve of his first war against Rome, Eupator first justifies his decision to wage war by explaining that the Romans attacked him first, and then gives proof that the latter are far from invincible. He then clarifies why the Romans are acting so unjustly towards him: they loathe and envy Kings, since their own first Kings were of low birth (38 .6 .7-8) . Mithridates subsequently brags about his own noble origins, as opposed to those of the Roman Kings .

Suppose, he continued, that he was compared with the Romans in terms of breeding . He was superior to that motley rabble of refugees since he could trace his line back on his father's side to Cyrus and Darius, the founders of the Persian empire, and on his mother's side to Alexander the Great and Seleukos Nikator, founders of the Macedonian empire .

Se autem, seu nobilitate illis comparetur, clariorem illa conluvie convenarum esse, qui paternos majores suos a Cyro Darioque, conditoribus Persici regni, maternos a magno Alexandro ac Nicatore Seleuco, conditoribus imperii

Macedonici, referat . (1986), 154-162, most notably 160-162; Ballesteros Pastor (1996), 391; Ballesteros Pastor (2006)

; the speech is fully analyzed in Ballesteros Pastor (2013) . On the traces of revision after the event, see

Yardley (2003)

: 21-23. Trogus seems to have been greatly influenced by Livy, and Mithridates' speech in particular contains many Livian reminiscences; see also 89-90 for

  II, Antiochos III had married Laodike of Pontus, and Pharnakes I (200-169 BCE) had married Nysa, the daughter of Laodike and Antiochos III . Mithridates could therefore legitimately claim to be a

	Seleukid descendant .
	26 Reinach (1890), p . 3-4 does not entirely exclude this tradition . It is rejected more often than
	included: see for instance Meyer (1879) p . 32; McGing (1986) p . 10; Panitschek (1987-1988)
	p . 73-95; Ballesteros Pastor (1996), p . 24 and p . 290 . Regarding the Seven (see n . 8), the dif-
	ferent hypotheses described by A . B . Bosworth and P . V . Wheatley that aim to justify the reality
	of this claim (see Bosworth and Wheatley (1998)) are not convincing enough to end the debate .
	Very recently, L . Ballesteros Pastor went back on his previous statements and tried to prove that
	the Mithridates line descended from Achaemenid origins: see Ballesteros Pastor (2012) . He
	reminds us that Pharnabazos, the satrap of Hellespontine Phrygia in the early 4th century, mar-
	ried Apama, daughter of King Artaxerxes II, and also claims that the ancestors of Mithridates
	Ctistes belonged to the same line as Pharnabazos. Nevertheless, filiation between Pharnabazus
	and the Mithridatids does not appear probable . McGing (1986) p . 15 does not include Pharna-
	bazus among Ctistes' ancestors .
	27 On each of the two monumental terraces of the sanctuary of the Nemrud Dagh, which was
	consecrated to Antiochos' cult, a series of stelae displayed the King' s ancestors; on both ter-
	races, the ancestors are divided into two series: those of the maternal side and those of the pa-

ternal side; each ancestor was identified by a relief and an inscription. 'King of Kings Darius the Great, son of Hystaspes' (βασιλέα βασιλέων μέγαν Δαρεῖον τὸν Ὑστάσπ[ου]) features as the first ancestor on the paternal side; 'Alexander the Great, son of Philip' (μέγ[αν Ἀλέ]ξανδρον τὸν ἐκ [βασιλέ-]ως Φιλίππου) is the first of the maternal ancestors. For the

  Ann., 12, 18, 4 . With these words, Mithridates aims at convincing Eunones, King of the Aorsi, to receive him in his kingdom after a military defeat . 32 SeeCallataÿ (1997), p . 8-27 and pl . 1-15: Pegasus appears on the reverse of the tetradrachms minted between 96 and 85 BCE in the 'realist' style . Pegasus is strongly reminiscent of the Greek hero Perseus (see e . g ., McGing (1986) p . 97), who appears on many coins issued by the Pontic cities; these coins faithfully reflect royal propaganda and show how important this hero was for the King (ibidem, p . 94-95) . 33 See Callataÿ (1997) p. 63-86, with figs. 32-38 on p. 76. 34 One could add the fact that a famous inscription found in the city of Nymphaion shows that

	underlines the non-unified aspect of the Mithridatid dynasty's genea-
	logical traditions . See also Ballesteros Pastor (2013) p . 275-277 .
	29 App ., Mith., 540 .
	30 Ampelius 30, 5: 'It is from (Darius) that Artabazus descends, he who was, according to Sallus-
	tius Crispus, the founder of the kingdom of Mithridates' . (Darius […], a quo Artabanes origi-
	nem ducit, quem conditorem regni Mithridatis fuisse confirmat Sallustius Crispus) . On Artaba-
	zus see Ballesteros-Pastor (2012) .
	31 See Tac ., Mithridates had taken the Achaemenid title of 'King of Kings' in 102/101 (see Vinogradov
	1990); and also that he installed 'satraps', again an Achaemenid reminiscence, in the conquered
	Greek world (see Appian Mithridatic Wars 3, 21; 5, 35; 7, 46) . However, only one is still here
	in the frame of "genealogical claims" . Moreover, these Achaemenid references are questiona-
	ble: 'King of Kings' may evoke the Parthian Kings, who adopted the title from the reign of
	Mithridates II (123-188), instead of the Achaemenids (the Persian King is never called 'King

of Kings' in classical Greek sources; the title does not appear in Greek and Roman sources before the 1 st century B . C .) . The Seleukids made use of the 'satraps' even after the reign of Antiochos III, who is supposed to have replaced satraps with strategoi : see Capdetrey (2007) p . 283 .

  41 For Cyrus see, of course, Xenophon' s Cyropaedia; Cyrus and Darius are presented as examples of good Persian Kings: see Plato, Laws 694a-695e; Darius: Plato, Ep . 7, 332 b . After these Kings, the Achaemenids degenerated: on this topic seeBriant (1989) . 42 About the Persika, see recentlyLenfant (2014) . 43 A certain number of historians base themselves on a passage from the Byzantine historian George Syncellus (ed.Niebuhr, Bonn, 1829, 539, 14) stating that the first Arsacids, Arsaces and Tiridates, 'descended from the Persian Artaxerxes' in order to bolster the idea that the Parthians tried to pass themselves off as the descendants of the Achaemenids . See e . g .,Tarn (1923);Neusner (1963), here p . 43; see alsoWiesehöfer (2001) p . 133 . However, this source is so late and the history of the Arsacids has been so much transformed over time (see for example the The King's claim to a Persian identity (through Pegasus/Perseus) is therefore transmitted through a common Hellenistic cultural background; the selective claim to Achaemenid ancestry seems likewise related to the cultural Greek world: once again, Eupator's genealogical claims very clearly give evidence of Persianism .What does the reference to Alexander and Seleukos tell us? This question is of course less important in a paper devoted to Persianism than the previous question was . However, it is important to underline one particular point .Various sources, apart from this genealogical claim, show Mithridates' intention to attach himself to the figure of Alexander.

	THE DOUBLE GENEALOGY OF MITHRIDATES EUPATOR:
	THE MACEDONIAN KINGS

  p . 191 note 48 . 44 See all the attestations in Bohm (1989) p . 153-187 . 45 See Bohm (1989) p . 115: 'eine antirömische Komponente gewann das Alexanderbild erst in späterer Zeit, als Mithridates VI . Eupator die Alexanderangleichung programmatisch in seinem Machtkampf gegen Roms Herrschaft im Osten einband' . 46 First, King Pyrrhus comes to mind; Bohm (1989) analyzes the cases of Alexander of Megalopolis, of Seleukid pretenders to the throne, like Alexander Balas, Diodotos Tryphon and Alexander Zabinas, and of Ptolemaic Kings like Ptolemy X and Ptolemy XI . 47 In the age of Augustus, Greeks with strong anti-Roman sentiments referred to the name of Alexander and spread the idea that, if the Macedonian King had met the Roman armies, he would have defeated them: see Liv . 9,

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On this topic, see especiallyMa (2000): Antiochos III based his policy of the re-conquest of Asia Minor on the idea that he was recapturing an inheritance that was his right . On Antiochos III, see also Polyb . 18, 51, 3-6 . Another reference is the analysis of Fowler (2005), p . 126 .This material is under copyright. Any use outside of the narrow boundaries of copyright law is illegal and may be prosecuted. This applies in particular to copies, translations, microfilming as well as storage and processing in electronic systems. © Franz Steiner Verlag, Stuttgart 2017