domain: spi phys

text:
J-P Parmantier
email: jean-philippe.parmantier@onerafr

S Bertuol

C Guiffaut

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 

Keywords: Transmission-lines, Multiconductor, Thin wire model, Field-to-Transmission-Line, Cable bundles, Cable networks

This paper presents an application of a modified field-to-transmission-line-model inspired from Agrawal's model. In this model the field applied as a source term includes the tangential incident electric field as well as surrounding tangential scattered electric fields due to the current induced on the transmission-line. This weak domain decomposition approach allows one to calculate currents accounting for the reaction of those currents on the EM incident fields. The theoretical development is made on the basis of a two-wire transmission line; it is then extended to any transmission-line geometry. A numerical validation is made on several configurations of excitations of single wire transmission line networks. Particularly the results show that this model is able to predict the EM radiation of the cable. The paper concludes on future possible applications of this modified field-to-transmission-line approach in real applications of cable bundles in 3D structures of industrial complexity.

I. INTRODUCTION

ield-to-Transmission-Line (FTL) [START_REF] Tesche | EMC Analysis Methods and Computational Models[END_REF] is a well-known approach to model cables in 3D structures. The main interest of this model is to be easily extended to Multiconductor Transmission Line Network (MTLN) models [START_REF] Baum | On the Analysis of General Multiconductor Transmission-Line Networks, Interaction Notes[END_REF] and to make possible MTLN calculations separately from 3D calculations. Nowadays, in the related numerical modelling process, the incident EM fields are collected on the routes of cable bundles (but in the absence of the bundles in the 3D model) and are then introduced as source terms for the MTLN model. The calculation time for the MTLN models is significantly smaller compared to the 3D full-wave calculation for determining the MTLN incident field source terms. Several formulations of FTL exist but Agrawal's formulation [START_REF] Agrawal | Transient Response of Multiconductor-Transmission-Line Excited by a Non Uniform Electromagnetic Field[END_REF] based on incident electric tangential fields is the most appropriate for 3D numerical applications. The main interest of Agrawal's model is that the source terms are tangent to the cable routes which avoids the constraint of having to define transverse field components like in the two other FTL models, Taylor [START_REF] Taylor | The Response of a Terminated Two-Wire Transmisison Excited by a Nonuniform Electromagnetic Field[END_REF] and Rachidi [5]. This approach has been the subject of several applications of EM-coupling-on bundles in 3D structures ( [START_REF] Paletta | Susceptibility analysis of wiring in a complex system combining a 3-D solver and a transmission-line network simulation[END_REF], [START_REF] Ferrières | Application of Hybrid Finite Difference / Finite Volume to Solve an Automotive problem[END_REF], [START_REF] Arianos | Evaluation of the Modeling of an EM Illumination on an Aircraft Cable Harness[END_REF]). It is now well generalized in laboratories and industry for system-level modelling and has been successfully demonstrated on many complex wiring configurations ( [START_REF] Paletta | Susceptibility analysis of wiring in a complex system combining a 3-D solver and a transmission-line network simulation[END_REF], [START_REF] Ferrières | Application of Hybrid Finite Difference / Finite Volume to Solve an Automotive problem[END_REF], [START_REF] Arianos | Evaluation of the Modeling of an EM Illumination on an Aircraft Cable Harness[END_REF]). This approach is suitable for cable bundle design and installation, to optimize parameters such as cable types, cable shields, segregation distances, etc… This is particularly true in the perspective of the certification regulation on wiring installation [START_REF]Certification of Electrical Wiring Interconnection Systems on Transport Category Airplanes[END_REF]. Nevertheless, one of the main limitations of the FTL model is that it does not take into account the reaction of the currents induced by transmission-lines (TLs) onto the incident EM fields. EM coupling thereby results of incident fields only but coupling with scattered fields is not made. Several TL models have been proposed to overcome this limitation ( [START_REF] Haase | Transmission-Line Super Theory: a New Approach to an Effective Calculation of Electromagnetic Interactions[END_REF], [START_REF] Rachidi | Electromagnetic Field Interaction with Transmission-lines[END_REF]) but their implementation for real complex cable bundle configurations in 3D structures does not seem yet to be as operatory as regular FTL models. Of course such a current reaction can be obtained with meshed models of multiconductor wires or MTL models embedded in 3D full-wave models [START_REF] Berenger | A multiwire formalism for the FDTD method[END_REF] but again those models are not mature enough to offer the same level of flexibility as FTL for system level modelling. Besides wire models currently applied in 3D models are generally limited to single thin wire models [START_REF] Holland | Finite-Difference Analysis of EMP Coupling to Thin Struts and Wires[END_REF] or their derived-oblique models [START_REF] Edelvik | A new technique for accurate and stable modeling of arbitrarily oriented thin wires in the FDTD method[END_REF]- [START_REF] Guiffaut | Insulated oblique thin wire formalism in the FDTD method[END_REF]. The idea of this paper is therefore to investigate how both MTL and thinwire 3D-modeling approaches can be combined in order to solve this current-on-scattered EM-field reaction issue. Section II of this paper establishes an analogy between a usual TL model made of two wires illuminated by an incident EM field and the thin wire model as currently used in 3D modelling; the modified FTL model is then obtained. In Section III, numerical verifications of the modified MTL model are made on several configurations of single-wire networks for both EM field illumination and lumped voltage source application. Finally Section IV concludes on the relevance of the modified FTL model for future applications on complex and realistic cable-bundle configurations. A. Problem to solve Our theoretical development starts from a reminder of the demonstration of the first TL equation applied on the same two-wire transmission line geometry as in [START_REF] Tesche | EMC Analysis Methods and Computational Models[END_REF]. We call the two parallel wires of the TL, "signal wire" and "return wire", each of them having a length ℓ and radiuses a s and a r respectively (Fig. 1). The distance between the two wires is d. In this paper, we do not make any restriction on a s and a r with respect to d since we do not explicitly need to calculate the per unit length (p.u.l.) inductance and capacitance parameters of the TL. The signal wire has a p.u.l. resistance R signal and the return wire has a resistance p.u.l. R return . x represents the longitudinal direction of the wires, y represents their transverse direction and z represents the direction normal to x and y passing by the two wires. The electrical current in the wires, I(x), is in the x direction and is supposed to be uniformly distributed around the cross-section of the two wires.

 

x V tot TL is the voltage between the wires. We will see later in this paper that the "tot" subscript accounts for the total electromagnetic fields. The objective of the problem is to calculate I(x) on the signal wire.

B. Notations for the application of the Faraday law

The theoretical developments presented in this paper all start from the Faraday Law on an open surface S. In homogeneous free space medium, we have in the frequency domain:

         S C S dS H j dl E ds E rot    0  , ( 1
)
where S is the open surface bounded by a contour C. We classically decompose the total EM fields {E tot , H tot } as the sum of the incident EM fields {E inc , H inc } (fields in the absence of the signal wire but in the presence of the return wire) and the EM scattered fields {E sca , H sca } (fields due to the induced currents on the signal wire). We can thereby respectively write the electric and magnetic fields as:

𝐸 𝑡𝑜𝑡 = 𝐸 𝑖𝑛𝑐 + 𝐸 𝑠𝑐𝑎 𝐻 𝑡𝑜𝑡 = 𝐻 𝑖𝑛𝑐 + 𝐻 𝑠𝑐𝑎 (2)
The EM field notations will be generalized as 𝐸   (𝑥, 𝑦)

and 𝐻   (𝑥, 𝑦) for the electric and magnetic fields respectively, in which the subscript  stands either for "tot", "sca" or "inc" and  for either x, y or z. In Fig. 1's geometry we remind the incident problem includes the return wire. In the following, we choose the integration surface S with a rectangular contour along the x axis, between x and x+x, and the z axis, between positions z 1 and z 2 (Fig. 2). Then, the limit x  0 is considered.

With those conditions, the Faraday law in (2) applies either on total, incident or scattered EM fields writes as:

        1 2 , 0 0 , , . , lim 2 1 2 1 z x E z x E dx dV x dx dz z x H j x x z z x x x z z y x                                    (3)
In which we define an equivalent voltage by:

    dz z x E x V z z z z z     2 1 2 1 , ,   (4)

C. Formulation of the TL equations

The application of (3) for the total fields gives the first TL equation based on Taylor's model [START_REF] Tesche | EMC Analysis Methods and Computational Models[END_REF]. According to Fig. 2 we take z 1 = 0 and z 2 = d. The voltage to be considered is the total voltage and the source term is expressed in terms of the incident transverse magnetic field in S:

                                        x dx dz z x H j dx x dV x I L j R x x x d inc y x tot TL TL TL . , lim 0 0 0   (5)
where

      dx dz z x H x I L x x x d sca y x TL . , lim 0 0                (6)
and R TL represents the p.u.l. resistance of the transmission line, classically equal to the sum of the p.u.l. resistances of the signal wire and the return wire. We have:

return signal TL R R R   (7) where     d x E x I R tot x signal ,  , (8)
    0 , x E x I R tot x return   , (9)
    dz z x E x V d tot z tot TL     0 , . (10)
The application of (3) for the incident fields gives:

          0 , , . , lim 0 0 0 x E d x E dx x dV x dx dz z x H j inc x inc x inc TL x x x d inc y x                                (11)
with

    dz z x E x V d inc z inc TL     0 , . (12)
The application of (3) for the scattered fields gives:

        0 , , x E d x E dx x dV x I L j sca x sca x sca TL TL      , (13)
with

    dz z x E x V d sca z sca TL     0 , , (14)
generally defined as the "scattered voltage" [START_REF] Tesche | EMC Analysis Methods and Computational Models[END_REF]. In [START_REF] Rachidi | Formulation of the field-to-transmission-line coupling equations in terms of magnetic excitation field[END_REF] we can introduce the following property:

      x V x V x V sca TL inc TL tot TL   .
(15) Then combining ( 5) and ( 11), we find the well-known Agrawal-formulation for which we remind that the voltage to be considered is the scattered voltage and the source term is expressed in terms of tangential incident electric fields at the level of the signal and return wires:

          0 , , x E d x E dx x dV x I L j R inc x inc x sca TL TL TL      (16)
The 2 nd transmission line equation is obtained in a way entirely similar to the one presented in [START_REF] Tesche | EMC Analysis Methods and Computational Models[END_REF]. The introduction of the scattered voltage in the 2 nd transmission line equation formulated according to Taylor's model provides an equation without any right hand-side. We have then:

      0    dx x dI x V C j G sca TL TL TL  ( 17
)
where:

-G TL is the TL p.u.l. conductance, -C TL is the TL p.u.l. capacitance The demonstration will not be reported in this paper since the focus is on the 1 st TL. From an application point of view, it is important to remember that even if the Agrawal-formulation involves only a scattered voltage which has no real existence, the current I(x) remains the "real" electrical current and the real voltages (total voltage) at the ends can always be obtained by applying the Ohm-law as far as end impedance loads are known, which is the case for EM simulation applications.

D. Signal wire in fictitious enveloping return contour

We consider the same geometry as the one in Fig. 1 with the signal wire parallel to the return wire and a separation distance d between the wires. Now we as well consider a small fictitious cylinder with an arbitrary cross-section surface of contour C, extending in the x direction around the whole signal wire path (Fig. 3). Similarly to the way to generate a unified TL model of a shielded cable with respect to a common reference conductor [START_REF] Degauque | Chapitre 2 : Couplage aux structures filaire[END_REF], we define three different TLs. We call:

-"Inner TL", the TL made of the signal wire with respect to the cylinder.

-"Outer TL", the TL made by the cylinder with respect to the return wire. -"Reference TL", the TL made by the signal wire with respect to the return wire (the TL defined in the previous paragraph). The TL model of the Inner TL is of particular interest in real 3D geometrical configurations since it is independent from a reference taken on the 3D structure. As for [START_REF] Guiffaut | Insulated oblique thin wire formalism in the FDTD method[END_REF], we start the derivation from the application of Faraday's law in its infinitesimal formulation [START_REF] Agrawal | Transient Response of Multiconductor-Transmission-Line Excited by a Non Uniform Electromagnetic Field[END_REF]. For this we define 3 reference points: a point of origin O s on the signal wire and a point O r on the return wire, both of them at the position x and a point M taken on the contour C of the cylinder at the same The application of (3) is made on the total EM fields marching on the integration contours made by the two S int (M) and S out (M) surfaces. Similarly to the derivation of ( 16), we find:

                            0 , , , , lim , , , , lim 0 ,
, 0 0 0 0 0 0 0                                                                              z x E d z x E x dx d p x H x dx dh h h x H j x d x E x x E x dh h x E h x x E z x E d z x E inc x inc x x x x d n sca x x x d n sca x d sca sca d sca h sca h x tot x tot x p h h              (18)
where two specific voltages terms can be defined:

        x dh h x E h x x E dx x dV h d sca h sca h x sca out           0 0 , , lim , ( 19
)
the p.u.l. variation of the scattered voltage in the outer TL.

        x d x E x x E dx x dV d sca z sca z x sca               0 0 int , , lim (20)
the p.u.l. variation of the scattered voltage in the inner TL. From (3), we have also:

          0 , , , lim 0 0 0 x E d h x E dx x dV x dx dh h h x H j sca x h sca x sca out x x x d n sca x h                        (21)
Fig. 3. The modified TL model made by the signal wire inside the fictitious cylinder together with its local cylindrical system By introducing ( 21) in ( 18), we finally obtain:

            h sca x inc x sca x x x d n sca x wire d h x E d z x E dx x dV x dx d x H j x I R                      , , , lim int 0 0 0        (22)
Now the last step is to integrate [START_REF] Andrieu | Multiconductor Reduction Technique for Modeling Common Mode Current on Cable Bundles at High Frequency for Automotive Applications[END_REF] over the whole contour C. For this, we introduce a curvilinear coordinate u allowing positioning point M anywhere over the contour. We note that:   C P du [START_REF] Parmantier | Simplification Method for the Assessment of the EM Response of a Complex Cable Harness[END_REF] where P is the perimeter of C. A particular application is when the cylinder has a circular section of radius R c . In this case, the u variable becomes: du  R c .dΦ and P  2πR c . We obtain:

            P du d h x E d z x E P du x dx d x H j x I R P du dx x dV C h sca x inc x C x x x d n sca x wire C sca                            , , , lim 0 0 0 int        (24)
In which we can introduce the definitions:

-The average scattered voltage in the inner TL defined by:

    P du x V x V C sca sca    int int (25)
-The p.u.l. inductance of the inner TL defined by:

      P du x dx d x H x I L C x x x d n sca x TL                        0 0 0 int , , lim   (26)
-The average scattered field on the C contour:

    P du d h x E x E C h sca x sca x     , (27)
In [START_REF] Parmantier | The test-wiring method[END_REF] we can also define an "equivalent total tangential electric field" at the level of the signal wire as the sum of the incident field at wire level and the average of the scattered tangent electric fields on the contour C:

      x E d z x E x E sca x inc x tot x    , ( 28
)
With those definitions, we can now write [START_REF] Parmantier | The test-wiring method[END_REF], in the following compact form:

          x E dx x x V d x I L j R tot x sca TL signal      int int ,  (29)
In (29), note that the equation does not depend anymore of the return conductor. Similarly to [START_REF] Degauque | Chapitre 2 : Couplage aux structures filaire[END_REF], the second TL equation writes:

      0 int int ,     dx x dI x x V C j sca TL  ( 30
)
where C TL,int is the p.u.l. capacitance of the inner TL. This formalism can be applied to any types of full wave solvers together with their specific meshed geometrical models. ( 29) is obtained a contour averaging for the sake of clarity of this paper but it can be recovered with an averaging over an area as well. The averaging process with many electric field component contributions increases accuracy as for oblique thin wire configurations for which the 2D symmetry observed for regular thin wires does not exist anymore and leads to non-uniform distribution of scattered electric field components around C [START_REF] Guiffaut | New oblique thin wire formalism in the FDTD method with multiwire junction[END_REF]. In this paper we are particularly interested by the FDTD method when it is coupled with Holland's formalism [START_REF] Holland | Finite-Difference Analysis of EMP Coupling to Thin Struts and Wires[END_REF] and its extensions for oblique thin wires [START_REF] Edelvik | A new technique for accurate and stable modeling of arbitrarily oriented thin wires in the FDTD method[END_REF]- [START_REF] Guiffaut | Insulated oblique thin wire formalism in the FDTD method[END_REF]. In all cases for which regular thin-wire models are included along a Cartesian direction, the tangential fields along the wire result of an averaging of the electrical fields obtained by the FDTD method close to the wire. Note that each field component calculated by the FDTD method is an average field flux through a quad area. The average process leading to (29) applies even when the wire is located along a FDTD grid edge. Moreover, the total field quantity in (28) calculated by the FDTD method and located along the wire does not need to be zero as expected by the theory on a PEC wire because it must be understood as an average of fields around the wire. Finally, the above whole theoretical development has been made with a two-wires TL as described in Fig. 1. However, as done in [START_REF] Tesche | EMC Analysis Methods and Computational Models[END_REF] for the derivations of Taylor's and Agrawal's FTL models, (29) and (30) can be extended to any geometrical configuration of the return conductor. In the following of this paper, the return wire will be replaced by a reference structure, standing for example for a wire, a ground plane, a 3D surface etc...

E. Modified FTL formulation based on an equivalent "total" tangential electric field

We observe that (16) (for the reference TL) and (29) (for the inner TL) have TL equation forms. We have to remember that both equations are derived from an application of Faraday's law of the same problem. The difference in both equations is that the TL approximation (i.e. TEM mode) is required in the whole domain in [START_REF] Guiffaut | Insulated oblique thin wire formalism in the FDTD method[END_REF] whereas it is required in the cylinder domain only in (29) which makes this formulation less restrictive and particularly adapted for 3D full-wave techniques with the possibility to update EM fields in the 3D model at the level of C. Hereafter we want to make an analogy between the two equations in order to generalize (29) to a TL formulation of the reference TL as in [START_REF] Guiffaut | Insulated oblique thin wire formalism in the FDTD method[END_REF]. The objective is to overcome the usual FTL limitation consisting in not having the reaction of the current induced on the wires on the total field.

For this purpose we introduce the k L coefficient defined as the ratio between the p.u.l. inductances of the reference TL and the inner TL respectively:

int , TL TL L L L k  (31)
From (31) we derive the transformation of the p.u.l. capacitance:

L TL TL L TL TL k C L k v L v C int , int , 2 2 . 1 . 1
   (32)
Then we multiply (29) by the k L coefficient. We obtain:

        x E k dx x dV x I L j R k tot x L eq TL TL signal L       (33)
If we introduce (32) in (30), we obtain:

    0     dx x dI x V C j eq TL TL  (34)
In both (33) and (34) we introduce a new equivalent TL voltage definition:

      x x V k x V sca L eq TL int  (35)
In an analogous way as what is done in Agrawal's model in ( 16) and ( 17) which involve a scattered voltage,

 

x V sca TL , the system of equations ( 33) and ( 34) involve an equivalent voltage definition,   x V eq TL , which is not the real voltage. However both models provide the real current solution, I(x). Besides, compared to ( 16) which uses the incident electric fields (namely

    0 , , x E d x E inc x inc x



) as the right hand side term, (33) uses an analogous (

  x E k tot x L term.

III. VALIDATION

A. Numerical methods used

In this section, the modified FTL method is validated on simple configurations of lossless one-wire networks over a PEC ground plane. As far as our validations are concerned the main advantage of these configurations is that we know that the wire networks will behave as antennas and that EM radiation of EM fields will be observed in a large frequency band which requires being able to model the reaction of EM fields scattered by induced currents. All validation problems are solved with 3 methods:

-Method 1: with a full 3D calculation in which the wires under test are present. This calculation is considered to provide reference results. -Method 2: with the classical Agrawal's FTL approach based on Agrawal's model in which the 3D calculation does not include the wire under test and provide incident electric fields along the route -Method 3: with the modified FTL model developed in this paper in which the 3D calculation includes the wire under test and provide total electric fields along the route All the field calculations in the 3 methods are performed with the TEMSI-FD solver developed by the XLIM Institute [START_REF]Time ElectroMagnetic Simulator -Finite Difference software[END_REF]. Fig. 4 represents the geometry of the problem as it is depicted by TEMSI-FD. The calculations of the MTLN responses in methods 2 and 3 are made using the CRIPTE code based on the resolution of the BLT equation in frequency domain [START_REF] Baum | On the Analysis of General Multiconductor Transmission-Line Networks, Interaction Notes[END_REF] and developed by ONERA [START_REF] Parmantier | CRIPTE : Code de réseaux de lignes de transmission multiconducteur -User's guide -Version 5[END_REF]. In both FTL methods (2 and 3), note that the field source terms must be applied on the horizontal wire as well as on the two vertical wires connecting the horizontal wires on the PEC ground planes.

B. One-wire validation test-case 1) Presentation of the test-case

The first geometrical configuration is made of a thin victim wire of radius 0.1 mm and length 2 m, called "victim wire", running in parallel in the x direction over a PEC and finitedimensions ground plane (1.5 m x 1.5 m) at a 10-cm height (Fig. 4). Two vertical wires of similar radiuses connect it to the ground plane at which level two lumped resistances equal to 1 Ohm have been applied. On the lower side of the PEC plane, in the same x-z plane as the victim wire, another wire, called "excitation wire", with the same radius and height as the victim wire is running in the x direction; it is connected to two vertical wires as above the ground plane but this time with a resistive load of 50  on the left hand side (low x-value end) and a short-circuit on the right hand side (large x-value end). In this geometry, a lumped voltage generator can be applied at the level of the ground plane on either the left-hand-side extremities of the victim wire or the excitation wire. In the MTLN model of the victim wire, the model of the TL is approximated as a wire over an infinite ground plane and the vertical wires have the same p.u.l. electrical parameters as these of the horizontal line (usual conic antenna approximation [START_REF] Vance | Shielding Cables[END_REF]). The cell-size in the FDTD model has been chosen equal to 2 cm and Perfectly Matched Layers (PML) absorbing conditions surround the useful calculationdomain box of size 3.4 m x 3.4 m x 0.4 m. Time domain calculations have been made by applying on one of the two wires a lumped voltage generator with a Gaussian waveform of a frequency content up to 1 GHz. Then all currents induced on the victim wire and calculated either directly in Method 1 or by FTL and modified FTL approaches in Methods 2 and 3 (through tangential electric fields computed in the 3D simulation) have been Fourier transformed. All currents obtained by the 3 methods have been normalized to the Gaussian waveform.

The objective is to observe the current on the victim wire at two positions: at the left hand side extremity ("I 1 ") and in the middle ("I middle "). The excitation wire is always included in the 3D model.

2) Field illumination configuration

In this configuration, the lumped generator including the 50  resistive load is applied on the left-hand-side extremity of the excitation wire at the level of the ground plane; the incident field applied on the victim wire is generated by the current developed on this excitation wire. The results of currents obtained at the two observation test points on the victim wire are presented in Fig. 5. On the one hand, we observe that the classical Agrawal FTL method perfectly works from DC up to about 20 MHz, i.e. for quasi-static regime but not in the resonance regime of the wire. In the resonance regime, the FTL model does not capture properly the amplitude of the resonance peaks observed in the reference results, even if the resonance frequencies are well predicted. On the other hand, the modified FTL entirely predicts the reference results on the whole frequency band. The comparison is almost perfect at the left hand side extremity (I 1 ) since the modified approach results fully overlap the reference calculated current. We do not observe such a perfect matching in the middle of the wire (middle) but we note that this discrepancy also appears in Agrawal's classical FTL. We attribute this discrepancy to the fact that the TL approximation does not perfectly work outside the extremities of the line certainly due to so-called "common antenna mode currents" as explained in [START_REF] Tesche | EMC Analysis Methods and Computational Models[END_REF].

3) Victim wire voltage excitation configuration

A lumped generator including a 1  resistive load is now applied on the left-hand-side extremity of the victim wire at the level of the ground plane. This configuration is more challenging for our validation since no incident field is applied on the victim wire: especially the response of the victim wire can be directly obtained from a straightforward unique TL model exciting the victim wire with a 1V voltage generator. Nevertheless, we can also apply the modified FTL model and see the effect of the equivalent total field source terms (here equal only to the average scattered tangential electric field around the wire). The conclusions are the same as for the former field illumination configuration; especially in this configuration the modified FTL approach allows taking into account the EM radiation of the wire. We even observe that the current at the center is better predicted than in the illumination configuration, certainly because a pure differential mode is excited on the TL and no common antenna mode currents is generated, which does not mean that this configuration does not radiate EM fields. Fig. 5: Field illumination configuration (local voltage generator on the excitation wire) -Comparisons of currents obtained at the left-hand-side extremity (I1, above) and in the center of the wire (middle, below) between full-3D (Method 1 -label "Full FDTD"), classical Agrawal's method (Method 2 -Label "FTL (with incident E field)") and modified FTL method (Method 3 -label "FTL with Total E field"). On the left hand side full frequency range. On the right hand side, high frequency range.

C. Branched network configuration

The previous test-case concerned only one TL but it is important to evaluate the robustness of the modified FTL model for branched network configurations, even if the previous single-TL test-case already included network aspects because of the connection of the two vertical wires to the horizontal wire. The PEC ground plane dimensions are 2.3 m x 1.7 m. Other main dimensions are reported in Fig. 7. A straight wire of radius 5 mm is connecting two metal boxes at the level of two connection points called "connector A" and "connector B" and a transverse wire of radius 5 mm connects this straight wire to a connector C at the level of the ground plane with a vertical wire. As for the previous single TL testcase, an excitation wire is running under the ground-plane in the direction of the straight wire. All wires, including the excitation wire are at a 10 cm height above or below the PEC ground plane. The mesh size in the 3D-model is 2.5 cm. Note that the two metal boxes are meshed in the 3D model as well as the excitation wire.

IV. CONCLUSION AND PROSPECTS

In this paper, we presented an extension of Agrawal's FTL model in a frequency domain formulation that includes the reaction of the induced current on the scattered field. The formulation is obtained by establishing the relationship between two TL models of an electrical wire in a 3D structure. The first TL is made by the wire inside a fictitious surrounding cylinder. The second TL is made by the wire with respect to the 3D structure: this model is directly derived from the first TL model by the multiplication with a k L factor equal to the ratio of the p.u.l. inductances of the first and second TL models. We thereby obtain the modified FTL model, making the analogy with the usual Agrawal's model. As Agrawal's model, the MTLN model is referred to the 3D structure and can run independently from the 3D model. However there are some differences:

-The source term is defined as an equivalent total tangential field made of the usual incident tangential electric field to which a scattered tangential electric field on the surface of a surrounding cylinder is added. This source term is multiplied by the k L factor.

-The p.u.l. resistance of the TL with respect to the 3D structure is also multiplied by the k L factor.

-An equivalent voltage is defined along the TL. As for Agrawal's scattered voltage, this voltage is not used as such since its definition is quite complicated. Only the current is practically used in the resolution. Validations have been made on single-wire TL networks over PEC ground planes for both EM field illumination and direct voltage generator application by computing EM source fields with a FDTD model. Results have been compared with full-3D calculations in which the single-wires were parts of the 3D mesh. In these applications with FDTD models, the modified FLT appears as a formulation in the frequency domain of the well-known Holland model (or its derivatives for oblique wires) in which the process of exchange and update of EM fields is now made a posteriori. Despite its theoretical interest, we must admit that the use of this modified model in future applications is not straightforward. The objective of the modified FTL approach is indeed to have an approach similar to Agrawal's FTL model in which field terms are used as a distributed source terms applied in a MTLN model. Actually, the main interest of Agrawal's model (or Taylor's or Rachidi's model) is that the sources terms are based on incident fields, which means that they are calculated with a full-wave calculation in the absence of the cables and any type of multiconductor cable can be used since the same incident field terms can be applied on the wires (provided the wires have the same route as the route on which the incident field have been determined). In the modified FTL model, the wires have to be present in the full-wave calculation. So we can ask ourselves the following question: what is the interest of making another calculation with a TL model when the 3D calculation has already provided the solution of the currents on the wire? As a matter of fact, the foreseen interest of this approach is clearly for MTLN applications. Indeed, as far as Multiconductor TL (MTLs) are concerned, we can anticipate that the scattered fields to be exchanged at the cylinder surface are dominated by the total current generated by all the wires of the MTL. This means that, provided an equivalent wire model of the MTL can be obtained, the scattered EM fields on the cylinder surface can be used and applied as source terms for each equivalent wire of the MTL, as done for usual FTL models. Several references have already investigated this problem of an equivalent wire or MTL models ( [START_REF] Poudroux | A simplified approach to determine the amplitude of transient voltage on the cable bundle connected on non linear loads[END_REF], [START_REF] Andrieu | Multiconductor Reduction Technique for Modeling Common Mode Current on Cable Bundles at High Frequency for Automotive Applications[END_REF]) and could be used for this purpose. Finally, the requirement to have to define a fictitious cylinder could be certainly bypassed applying techniques such as testwires [START_REF] Parmantier | Simplification Method for the Assessment of the EM Response of a Complex Cable Harness[END_REF]. This technique allows the derivation of the source terms to be applied on a TL model thanks to the knowledge of the distribution of currents along the test-wire and the p.u.l. electrical parameters of its TL. From a practical point of view, the test-wire is included in the 3D model and the currents along this wire are collected. Such a technique could be advantageously applied on our problem of the TL in the cylinder. Indeed the source terms obtained from the application of the test-wire method would be directly the ones derived in (28). Another possibility could be to choose appropriately the geometry of the cylinder; namely, a circular cylinder making a coaxial TL would be the simplest choice allowing easy determination of the inner TL p.u.l. electrical parameters, and therefore of the k L factor. All these perspectives will be the subjects of future investigation for determining the scope of practical application of this formalism for real cable bundle configurations.

Fig. 1 .

 1 Fig. 1. Geometry of the two-wires TL problem

Fig. 2 .

 2 Fig. 2. Surface contour of integration in the x, z plane for the application of the Faraday law

Fig. 4 .

 4 Fig. 4. Geometrical configuration used for the validation on a single TL The rectangular box indicates the position of the PML layers

Fig. 6 :

 6 Fig.6: Victim-wire voltage excitation configuration (local voltage generator on the victim wire) -Comparisons of currents obtained at the left-hand-side extremity (I1, above) and in the center of the wire (middle, below), between full-3D (Method 1 -label "Full FDTD"), classical TL model (Method 2 -Label "TL alone") and modified FTL method (Method 3 -label "FTL with Total E field"). On the left hand side full frequency range. On the right hand side, high frequency range.

Fig. 7 .

 7 Fig. 7. Geometrical configuration used for the validation on branched networksFig.8presents the currents obtained at connector A in two loads configurations when all wire ends are either on 50  or on short-circuits. Full 3D FDTD reference results match those obtained with the modified FTL model. Despite some signal processing issues observed at low frequencies, the same conclusions as for the single TL can be drawn. The modified FTL model allows us to reproduce the wire radiation losses in the resonance region. The small shift observed in the shortcircuit configuration are not fully explained up to now but time to frequency signal processing is highly suspected due to time domain signals not fully returned to zero.

Fig. 8 .

 8 Fig. 8. Currents at end A on the branched network configuration when all extremities are loaded on 50  (left) and short-circuit (right)

  x position of O s ; the 𝑂 𝑠 𝑀 ⃗⃗⃗⃗⃗⃗⃗ and 𝑂 𝑟 𝑀 ⃗⃗⃗⃗⃗⃗⃗ vectors are perpendicular to the x direction.We then define a cylindrical coordinate system local to the signal wire with an origin in O

s . In this system the  coordinate defining the position of M on the contour C varies between 0 and d  . The line between point M taken at position x and point M' taken at position x+x allows us to decompose the surface of integration in two plane surfaces: one inner surface, S int (M), and one outer surface, S out (M). The inner surface is defined by the x direction and the 𝑒  ⃗⃗⃗ direction passing through O s and M. The outer surface is defined by the x direction and the 𝑒 ℎ ⃗⃗⃗ direction passing by O s and M. The h coordinate with respect to 𝑒 ℎ ⃗⃗⃗ varies between 0 and d h .  𝑛 ⃗⃗⃗ and ℎ 𝑛 ⃗⃗⃗ vectors define the normal vectors to S int (M) and S out (M) respectively (the reader will pay attention not to make confusion with 𝑒  ⃗⃗⃗ and 𝑒 ℎ ⃗⃗⃗ definitions).

This work was supported by the Direction Générale de l'Armement (D.G.A.),


Jean-Philippe Cueille

Luis De Castro

Pinto Couthino

Jesus F De

Miguel Rodriguez

Denis Babusiaux

Ceg-7 I Cadoret

J.-L Karnik

Ceg-9 A Fauveau

P Chollet

F Lantz

The leading US independent oil companies : features and recent results

Keywords: CEG-1. D. PERRUCHET, J.-P. CUEILLE, Compagnies pétrolières internationales : intégration verticale et niveau de risque . CADORET, P. RENOU, Élasticités et substitutions énergétiques : difficultés méthodologiques. Avril 1991

Les cahiers de l'économie -n° 51

Série Analyses et synthèses

La collection "Les cahiers de l'économie" a pour objectif de présenter des travaux réalisés à l'Institut français du pétrole, travaux de recherche ou notes de synthèse en économie, finance et gestion. La forme peut être encore provisoire, afin de susciter des échanges de points de vue sur les sujets abordés.

Les opinions émises dans les textes publiés dans cette collection doivent être considérées comme propres à leurs auteurs et ne reflètent pas nécessairement le point de vue de l'École du pétrole et des moteurs ou de IFP.

Pour toute information complémentaire, prière de contacter

5

The aim of this article is to examine the leading US independent oil companies, by analyzing a sample of ten companies. Measured by the yardstick of market capitalization, the ten foremost oil groups worldwide, before the recent mergers, are ExxonMobil, Shell, BP, TotalFinaElf, Chevron, Eni, Texaco, RepsolYPF, Conoco and Phillips1 . In the rest of this study, we shall refer to these companies as majors, insofar as they are very big, integrated and international. For our analysis, we have picked the following ten US companies, listed by decreasing order of market capitalization: Anadarko Petroleum, Occidental Petroleum, Marathon Oil, Unocal, Burlington Resources, Amerada Hess, Apache, Kerr-McGee, Devon Energy and Valero Energy 2 . These companies are primarily active in North America and represent players of significant size in this region. Their cumulative oil and gas reserves amount to five times those of Conoco and two and a half times those of Phillips. Note however that our analysis only covers a small part of the US and Canadian petroleum industry, insofar as this industry includes dozens of other smaller companies, attesting to the vitality to the oil and gas sector in this part of the world. In fact, although US oil imports are higher than the production of Saudi Arabia, the US remains the world's second oil producer and the first natural gas producer 3 , and petroleum activity there is still very intense. The headquarters of the companies examined are located in Texas, at Houston (Anadarko, Apache, Burlington Resources, Marathon Oil) and San Antonio (Valero Energy), in Oklahoma, at Oklahoma City (Devon Energy, Kerr-McGee), in California at Los Angeles (Occidental) and El Segundo (Unocal), and in New-York (Amerada Hess), and this geographic arrangement reflects the principal producing regions of the country, with the exception of Alaska.

Presentation of the sample

Most of the companies examined are old, some formed in the 19th century, and have participated in the US and international petroleum history. The privileged links of Armand Hammer, the founder of Occidental, with the ex-communist countries, the presence of this company in Libya in the early 1970s, Unocal which made the first natural gas discovery in Alaska, and Kerr-McGee which drilled the first offshore well invisible from the shore, illustrate the importance and dynamism of these companies. The spectrum of their current activities accordingly stems from a long history, as well as the occasional more or less recent abandonment of areas deemed unstrategic. The strong competitive environment of the last fifteen years has led to drastic reassessments of the quality of the assets and led to major repositionings: one example, among others, is the case of Unocal, which, shortly after having filed patents for the manufacture of reformulated gasolines, still today the subject of numerous legal battles in the US courts, decided in 1997 to sell its downstream division to Tosco 4 in order to focus on the upstream oil and gas industry.

The ten companies of our sample are not all, like the majors, integrated companies. Some of them have decided to be present only in a single sector and to develop a strategy of concentration (in the sense of Michael Porter). These include Anadarko, Apache, Burlington Resources, Devon Energy and Unocal, which are only active upstream, and Valero Energy which focuses downstream. Others, like Amerada Hess and Marathon, are both producers and refiners, while Kerr-McGee and Occidental also have chemical assets 5 , in addition to exploration and production. Note however that upstream activity is generally predominant: thus for example, the distribution of capital employed by Amerada Hess in 2001 privileges exploration and production, with more than 70% of investments devoted to this segment.

Besides, some companies have activities downstream in the gas chain and sometimes produce electricity by cogeneration. Figure 1 shows the mainly upstream positioning of the large independents, with nine companies out of ten in this sector. To varying degrees, these produce both oil and natural gas.

Figure 1: Segments of activity and independents

Relative situation of the independents examined and the majors

If we compare the smallest of the majors, ConocoPhillips, with the biggest independent, Anadarko, in terms of reserves and production and with Occidental in terms of results, a large difference in size exists between them, as expected (Figure 2). The reserves of ConocoPhillips amount to three and a half times the reserves of Anadarko and nearly three times its production. In terms of results, Occidental, the independent with the highest results in 2001, earns three times less than ConocoPhillips, and in May 2002, the market capitalization of Anadarko, was three times smaller than that of ConocoPhillips. This leads us first to analyze the features of the nine companies currently active upstream. The world's leading ten oil groups (from ExxonMobil to Phillips) are primarily oil companies, although the proportion of natural gas in total oil and gas production is close to 50% for some of them. The same cannot be said of several companies of our sample, which are primarily gas companies. Figures 3 and4 which show the proved reserves and oil and gas production, demonstrate that this is clearly the case for Burlington Resources and Unocal, as well as Anadarko, Devon and Apache to a lesser degree.

Explo. and Production

Refining

Comparison between majors and independents

Growing globalization, generally focused on few key areas

A limited level of globalization, with an activity base strongly focused on North America, is a feature traditionally associated with the independents, although historically speaking, some of these companies have made significant discoveries outside the North American continent Occidental in Libya, in Colombia, Unocal in Thailand). Figure 5, which shows the location of the reserves, illustrates this situation. However, some companies have oil and gas reserves mainly located outside North America (Amerada Hess, Unocal) and the general international orientation is clear if we consider the distribution of production zones (Table 1). Table 1: Oil and gas production outside North America Amerada Hess, Kerr-McGee and Unocal produce at least 2/5 of their gas and gas outside North America. The weight of oil production outside the North American continent is significant for nearly all the companies 6 , representing values of 20 to 75 %. Contrary to the majors, which produce in a large number of countries, these companies make most of their international production in a given area, the North Sea for Amerada Hess (11 Mtoe/year, or 50% of the total produced) and Kerr-McGee (5 Mtoe/year, or nearly 40% of the total produced), Algeria for Anadarko (1.1 Mtoe/year, or 1/3 of international production), again attesting to the concentration strategy. Only Occidental has a more diversified portfolio of activities (Qatar, Yemen, Russia, Colombia, Ecuador, Oman, Pakistan), but the quantities produced are generally small by country. Since natural gas is an energy more difficult to market, the independents are less active on the whole in production abroad: Amerada Hess and Unocal, present respectively in the North Sea (4 Gm3/year) and the Far East (8.5 Gm3/year), are the main two players in this area. The globalization of the independents is hence quite genuine and would be even more evident if we analyzed the areas where they conduct exploration activities, foreshadowing future production.

Full fledged players

The independents are not only minority partners, leaving the conduct of the operations to the majors. Thus it is not rare to find independents in charge of operations (Unocal in Thailand, Occidental in Colombia). Some companies also specialize in very technology intensive slots, like deep offshore (Kerr-McGee is the operator of Neptune and Baldpate, American reservoirs located in more than 1650 ft of water), the resumption of old fields to revive their production by enhanced recovery (Occidental, Amerada) and natural gas from coal mines (Devon, Marathon). Another illustration is the participation of Occidental and Marathon in one of the gas consortiums in Saudi Arabia (Core Venture No.2). Table 2 lists some of the upstream assets of the companies examined and reveals their weight on the international scene.

Table 2: Examples of upstream assets owned by the independents

To conclude the presentation of our sample, we may observe the predominance of the upstream sector in the activities of these US independents. It also appears that these ten companies, although they may not have the world scale of the ten international majors, represent significant competitors of the majors in the areas of activity where they concentrate. This illustrates the relevance of the niche strategy that they have adopted and the name of super-independents that they are sometimes given.

Few independents are integrated

The ten biggest US independent oil companies therefore display a strong upstream orientation of their activities, but some of them are nonetheless involved in the downstream sector of the petroleum chain: this is the case of Amerada Hess, Marathon and Valero7 (Figure 5). Thus with seven refineries, Marathon Ashlands Petroleum (62% controlled by Marathon) accounts for nearly 6% for US refining capacity. Valero Energy controls a dozen refineries and Amerada Hess has a smaller presence, since it is only active on two refining facilities (50% stake in the Hovensa Complex in the US Virgin Islands and Port Reading catalytic cracker in New Jersey). Figure 6 compares the levels of production and refined crude and shows that Valero Energy and Marathon are exclusively or chiefly downstream companies, while Amerada Hess has a balanced structure.

Some independents have chemical activities. Kerr-McGee, wishing to focus on its key areas, sold its refining and coal related assets in the 1990s, but retained the proprietary chemicals segment (pigments etc), which contributed in 2000 to about 10% of income from operations (7% in 2001). The same applies to Occidental, which has a significant chemical branch, focused on the vinyl chloride chain. Moreover, the presence in the gas logistics (midstream) and in the downstream gas sector through the installation of power generation and marketing structures, particularly by cogeneration, are development guidelines of certain companies. Thus Marathon recently acquired Enron's delivery rights at the regasification terminal of the Isle of Elba and seeks to promote the installation of import gasline between Norway and the United Kingdom.

These few examples are nonetheless exceptions which confirm the rule of the upstream concentration of the activities of most of the independents examined. The existence of big independents downstream is possible, but rare.

Valero Energy is the only company of our sample exclusively specialized in refining and distribution. This Texan company, headquartered in San Antonio, now has twelve refineries, in Texas, Louisiana, New Jersey, Oklahoma, Colorado, California and Canada, with a combined capacity of nearly 2 Mb/d (Table 3), and a distribution network spread over thirtyfour American states and Canada. Its refining capability is highly sophisticated, with considerable operational flexibility enabling it to process a whole range of heavy feedstocks and convert them to gasolines and diesels meeting the most stringent specifications, such as those of the California Air Resources Board (CARB). Valero Energy has adopted a strategy of concentration (sale of its natural gas activities in 1996 for 1.5 G$) and intense external growth: thus five years ago, it had only one 170 000 b/d refinery.

In 2001, moreover, the company virtually doubled in size, following its acquisition of Ulltramar Diamond Shamrock, an operation which received the green light from the Federal Trade Commission on 18 December 2001. Yet it is still the smallest company of our sample.

Hence it appears more difficult for an independent to grow and survive downstream than upstream. It is very likely that the high investments needed to manufacture high grade products demanded by the US market penalize or jeopardize the existence of smaller companies in this sector. Besides, the margins are often narrow and the rates of return on capital employed (ROCE) are generally much lower downstream than upstream.

A dynamic external growth strategy

The optimization of the activity portfolio accordingly represents a significant concern of the independents. Thanks to abundant financial resources, large scale projects have been completed, leading to major reinforcements: doubling of size for Anadarko, sharp growth of Occidental in California and Texas, for example. Most of the operations listed in Table 4 illustrate the quest for reinforcement in areas where the companies are already active (North America) in order to benefit from new synergies, to spread fixed cost over a broader base, and to achieve critical size in certain regions. The possibility of acquiring assets which the majors abandon, for reasons of streamlining or because they are forced to do so in the United States by the Federal Trade Commission, the attractions of Canada as a natural area of expansion and a zone of future growth, explain the numerous acquisitions of onshore reserves and refining assets.

Furthermore, since the number of interesting companies likely to be acquired is shrinking, the competition between the different players has led to a rapid succession of mergers and acquisitions. This was especially true in 2000 and early 2001 insofar as, thanks to the high prices of oil and natural gas, the financial situation of the companies was excellent and many operations were conducted not by trading shares, but by cash outflows (Devon Energy, Marathon in 2001). The many acquisitions should not obscure the fact that the amounts involved are high, often in the range of several billion dollars, representing large scale operations for these companies.

It is also important to note that many disinvestments have taken place, in order to focus on the most promising assets and to release liquidities designed to minimize debt. Thus at their scale and in their field of activity, the independents appear to display the same behavior as the majors, in their wish for external growth and optimization of activities. Yet the financing of these mergers and acquisitions generally leads to a much higher debt level for the independents than for the majors.

Developments in reserves

These overall acquisitions explain a good share of the growth of reserves of the companies of our sample (Figure 7). With the exception of Marathon, all the companies have increase their reserves very significantly in four years (threefold increase for Devon Energy, doubling of Anadarko and Apache). Table 5 shows the anticipated lifetime of the proved oil and gas reserves of the companies examined, at the present rate of production (end of year reserves divided by production of the year), with a comparison with the situation of the majors. If we only consider the specific cases of Repsol YPF and Marathon, the R/P ratio of the majors generally ranges from twelve to fifteen years, while that of the independents displays a wider dispersion over a range of nine to fourteen years. Despite the sharp increases, the independent companies of our sample hence possess smaller proved oil and gas reserves than the majors, not only in absolute value, but also generally in terms of lifetime8 . The results for the years 2000 and 2001 for the independents were exceptionally good. In 2000, the companies benefited from the high prices of oil and natural gas, as well as higher refining margins for the companies active downstream. Prices fell in 2001, affecting the performance of certain companies. However, the increases in production often help to offset the price effect. Thus the reserves for the year 2001 of our group of independents are often comparable to those of the year 2000, despite the drop in price per barrel (about 15%) from one year to the next, and in the price of gas in the United States (-20%). The rise in production in 2001, often associated with mergers and acquisitions of Amerada Hess (+16%), Anadarko (+ 78 %), Apache (+ 32 %), and Devon Energy (+ 12 %) and Unocal (+ 8 %) explain the trend in the results of these companies. The selling price coverage operations of some of these companies conducted on forward markets also diminished the impact of the lower prices.

Total reserves totales

The comparison of the results between different companies must nonetheless be made with caution, insofar as the accounting methods employed are not always rigorously comparable. Two methods of accounting for exploration expenditures9 exists in particular and are accepted by the Securities Exchange Commission (SEC): the successful-efforts method and the full cost method. The former consists in considering geology, geophysics and dry well expenditures as expenses, while positive wells are capitalized and depreciated according to the production rate. By contrast, with the full cost method, all the exploration expenditures, (geology, geophysics and drilling) are capitalized and depreciated. Both approaches are justified: the first naturally treats as expenses any unsuccessful exploration, which effectively has no value for the future. The second amounts to interpreting the entire exploration activity as an investment which must therefore be depreciated. Anadarko, Apache and Devon use the full cost method while Amerada Hess, Burlington Resources, Kerr-McGee, Marathon Oil, Occidental and Unocal employ the successful-efforts method.

Moreover, depending on the conditions in which a merger is completed between two companies, it was possible, up to 30 June 2001, to consider the operation from an accounting standpoint as a pooling of interests or as an acquisition (purchase method). We saw earlier that the independents completed several mergers and acquisitions in recent years, and these differences in accounting make comparisons difficult over several years and could require retreatment, in order to make a detailed analysis of performance. The American accounting authorities now require all mergers and operations to be considered as acquisitions (Statements of Financial Accounting Standards No.141), which will introduce more uniformity in the presentation of the financial statements. Figure 8 shows that Occidental is the leading independent in terms of net earnings. In 2001, chemical operations posted a loss, so that its entire profit is derived from its upstream activities. Through its size and variety of countries where it produces, the company is close to the majors, but it retains a feature of the independents, namely its very strong US involvement (60% of its oil and gas production). Occidental's good performance is explained by a sharp growth in its upstream operations earnings (associated partly with the acquisition of Altura Energy, which significantly boosted its oil production in the United States).

Net

For reasons of an accounting nature, net income figures can be affected by the volatility of crude oil and natural gas prices. In fact, at the end of each quarter, the companies have to evaluate their onshore reserves using the price on the last day of the quarter. If the discounted value of the future production flows is lower than the accounting value of the assets, a provision must be set aside for depreciation (impairments). This is an exceptional nondisbursable accounting expense, which has no impact on the cash flows, but which reduces net income. The latter may therefore not faithfully represent the performance for the year. In 2001, this was the case for Anadarko, which posted an accounting loss of 188 M$ (compared with income of 1389 M$, including this provision) and for Devon, whose net income in 2001 dropped sharply for the same reason. These two companies, as we showed earlier, made acquisitions in recent years and valorized them in their books in agreement with accounting rules, using the "fair value" of the reserves estimated on the basis of the price forecasts that the company management considers realistic over the medium term. Due to the sharp recent fluctuations, the closing prices of certain quarters in 2001 were substantially lower than the Source: annual reports values employed and hence led to the setting aside of these provisions. It is conceivable that in a context of high price volatility, with depressed or exaggeratedly high prices, this accounting necessity could effect the faithful image of the accounts, leading to an underestimation of the value of the company's reserves.

In terms of operational performance, the second company of our example is therefore Anadarko, a company that has slightly bigger oil and gas reserves than Occidental. Through its external growth strategy and increasing the production of its reserves, Anadarko has the largest oil and gas production (27 Mtoe/year) of our sample, followed by Unocal and Occidental.

Marathon recorded exceptional expenses in 2001, associated with the separation of the oil and steel activities (Marathon is controlled by USX Corporation, a steel holding company). Without these one-time items, Marathon will be the third company in terms of results, thanks in particular to the excellent contribution of refining and distribution activities (about 50% of income from operations).

The only downstream independent of our sample, Valero Energy, also significantly increases its profits, while the two mainly gas companies Unocal and Burlington Resources, are affected by the drop in gas prices on the North American market.

Market capitalization

Our sample consists of the ten US companies trailing the eight international majors, according to the yardstick of market capitalization. The world contains many other oil companies which are bigger, but which are fully or mainly owned by public capital and are not listed on the stock exchange for the time being. Some public companies have part of their capital listed and their market value is estimated by publications like Business Week and the Financial Times. Considering the companies elected by these two publications and the private non-American companies, the following companies can be added between the eight majors and the companies of our sampling10 : Petrobras (27 G$), Statoil (18.9 G$), Yukos (18.7 G$), Gazprom (17.4 G$), BG Group (15.3 G$), EnCana (14.7 G$), Norsk Hydro (13.4 G$). Anadarko Petroleum, the first company of our sample, then falls to sixteenth position in terms of market capitalization worldwide, but it is clear that this type of classification has its limits with regard to the evaluation of certain companies (for example Gazprom) which is sharply biased by the fact that their floating capital (listed on the stock exchange) is very limited.

The drop in crude prices in second half of 2001 reduced the market values, but did not overall change the classification between the different companies. Anadarko thus takes first place in terms of market value, trailed far behind by Occidental in second place (Figure 9).

Conclusion: a glance at 2002 results

Performance in 2002 is below that of 2001, due to the low prices at the start of the year. Crude prices rose during the year, while natural gas prices remained substantially below their 2001 value. The companies present in the refining sector (Amerada Hess, Marathon, Valero) have suffered from the small refining margins. Some exceptional expenses (associated with the depreciation of assets: impairments) also tended to reduce the net income of Amerada Hess, Devon and Kerr-McGee. Thus due to a less favorable price and margin environment, the financial results of our sampling of companies should be slightly lower in 2002, after two exceptional years (2000 and 2001). The groups generally hope for a recover of natural gas prices in the United States to stimulate their results in the coming years. Performance in 2003 will also obviously depend on the price of crude, which is at a relatively high level today due to international pressures. This level is not necessarily sustainable over the long term, but the invasion of Iraq, if it materializes, could bring new pressures on short-term prices.

Net

5

  Kerr-McGee's chemical operations are in fact almost exclusively concerned with the production of a specific product, titanium dioxide, which is a base for pigments. Kerr-McGee is the world's third producer of titanium dioxide.

Anadarko

  chemical activities for Kerr-McGee and Occidental

Figure 2 :

 2 Figure 2 : Comparison between majors and independents

Figure 4 :

 4 Figure3: Oil and natural gas reserves(December 2001)

Figure 5 :

 5 Figure 5 : Location of oil and gas reserves (December 2001)

Figure 6 :

 6 Figure 6: Oil and refined crude production in 2001

Figure 7 :

 7 Figure 7: Total reserves since 1998

Figure 8 :

 8 Figure 8: Net income 1999-2000-2001

Figure 11 :

 11 Figure 11: Net income for the first nine months of 2002

Rounded off values 2001 in % Weight of oil production outside North America Weight of gas production outside North America

				Weight of oil + gas
				production outside
				North America
	Amerada Hess	74	48	67
	Unocal	40	45	44
	Kerr-McGee	61	11	43
	Marathon Oil	35	35	35
	Occidental	42	8	33
	Apache	40	19	28
	Anadarko	24	0	11
	Burlington	12	9	9
	Devon Energy	23	2	8

Table 3 :

 3 Capacity and location of Valero Energy refineries

Table 4 :

 4 Examples of acquisitions and mergers completed by the independents

These companies were discussed in the previous article, published in September

in Cahiers de l'Economie, No. 46, Institut Français du Pétrole.2 In fact, the tenth US independent company by market capitalization is EOG Resources and not Valero Energy.We nonetheless decided to select Valero for its downstream positioning and its merger with Ultramar Diamond Shamrock, which will lead to a significant increase in its size. EOG Resources is only active upstream. 3 Source BP statistical review, June

 4 The same Tosco was acquired by Phillips in 2000, demonstrating the constant recomposition of the American petroleum landscape.

with the exception of Burlington Resources, which is nearly exclusively a gas company tightly focused on North America.Source: annual reports

only active downstream.

Some companies have abnormally high or low figures for the life of their reserves, due to the opposing variations during the year in the level of their reserves and their production. This applies in particular to Repsol YPF, which registered a 20% increase in its reserves in 2001 with a concomitant drop of 3% in its production. Marathon registered a drop in its reserves over the last four years, explaining its low R/P ratio.Source: annual reports

and dry development wells.Source: annual reports

Market capitalization on 1 April 2002 according to Business Week, for Statoil, BG Group, EnCana, Norsk Hydro. Market capitalization on 1 January 2002, according to the Financial Times for Petrobras, Yukos, Gazprom.