Patent Description:
Such a method is used for example to determine the exponent coefficient n of the brine saturation Sw in Archie's law. The porous sample is for example a rock sample recovered from a sub-soil formation.

When drilling a well, it is known to recover solid samples from the formations through which the well is drilled, in particular rock samples.

In the same well, measurement tools can be conveyed in order to perform various measurements at various depths. This process is called logging. The result of this process is a continuous measurement of properties (porosity, resistivity. ) as a function of depth.

Rock samples are used to measure properties in laboratory and to calibrate the logs.

The log is generally obtained by visual inspections of the samples recovered at the surface, and/or by physical measurements carried out along the well.

In a logging operation, electrical conductivity is often measured. Electrical conductivity can be related to significant parameters of the formations, including in particular porosity and saturation.

For example, an empirical law such as Archie's law relates the electrical conductivity of a porous sample of formation to its porosity and to its brine saturation. In a fluid saturated rock, the brine saturation is then related to hydrocarbon saturation, providing extremely relevant information about the location and potential of hydrocarbon reservoirs after the well is drilled.

Archie's law, reformulated for electrical resistivity reads as follows: <MAT> in which Rt is the sample resistivity, Rw is the resistivity of the brine (which depends on salinity and temperature), Φ is the sample porosity, and a is a constant.

The formation factor a x Φ-m is related to the resistivity of the porous sample saturated only with brine by the equation R<NUM> = a x Φ-m X Rw. Consequently, a resistivity index RI can be determined following the following equation: <MAT>.

In order to use Archie's law, the exponent coefficient n associated with the brine saturation Sw has to be experimentally determined for a particular porous sample.

Experimental determination of Archie's law exponent coefficient n is generally a long and tedious process.

A porous sample containing water is inserted in a cell. Oil under pressure is injected in the porous sample, at one end of the porous sample, and another end of the porous sample is equipped with a porous plate from which only water is able to be extracted.

After a long time, generally in the order of a month, a steady state is reached in the porous sample. An average saturation Sw in water of the porous sample is measured.

In parallel, the resistivity Rt of the porous sample is measured by placing electrodes at the ends of the porous sample when the steady state is reached.

A first point of the curve connecting the logarithm of the saturation with the resistivity index is thus obtained. The capillary pressure is here equal to the pressure at which the oil is injected and a first point of the curve of the capillary pressure versus saturation is obtained.

Then, the oil pressure is increased at the porous sample inlet. The experiment is stayed until a steady state is reached. When the steady state is reached, a second measurement of the resistivity and of the capillary pressure is carried out to obtain a second point of the above mentioned curve.

The previously described operations must then be repeated several times until an adequate number of points is determined.

Consequently, the measurement of the determination of the exponent coefficient n of Archie's law and of the pressure of the capillary pressure Pc versus saturation takes several months. This significantly delays the log interpretation and the resultant business decisions for the operations.

In order to speed up the experimental determination of the Archie's law coefficient, <CIT> discloses a method of the above-mentioned type, in which a steady state profile of a second fluid is established in the porous sample by centrifugation. The article "<NPL>, also discloses a method of the above-mentioned type.

After the steady state is obtained, the porous sample is extracted from the centrifuge and a measurement of resistivity and of water saturation is carried out in a plurality of regions along the porous sample. Based on the corresponding values of local resistivity and water saturation obtained in each region, a correlation is made to determine Archie's law exponent.

Such a method is much faster than the traditional measurement process. However, it still requires a lot of sample handling, first to load the sample in the centrifuge, then to unload the sample from the centrifuge, and thereafter, to transfer the sample to a resistivity measurement apparatus and to a saturation measurement apparatus such as a nuclear magnetic resonance system.

The need for measuring the sample in at least two very different devices for obtaining resistivity and saturation values also delay the provision of the results.

<CIT> discloses a method of measuring a global resistivity and a global saturation of a sample.

One aim of the invention is to obtain a robust method for determining a representative parameter of a porous sample and associated relationships correlating physical quantities of the porous sample, the method being very fast to operate, with minimal sample handling.

To this aim, the subject matter of the invention is a method according to claim <NUM>.

The method according to the invention may comprise one or more of the features of claims <NUM> to <NUM> or of the following feature, taken solely, or according to any technical feasible combination:.

The invention further concerns a system according to claim <NUM> or <NUM>.

Advantageously, the first profile is a first steady state profile.

The invention will be better understood, upon reading of the following description, given only as an example, and made in reference to the following figures, in which:.

A method for determining a representative parameter of a porous sample <NUM> shown in <FIG> is carried out in the measuring system <NUM> schematically illustrated on <FIG> and <FIG>.

The representative parameter is a parameter in an equation relating at least two physical quantities associated with the porous sample <NUM>, such as resistivity and/or conductivity on the one hand, and saturation in a first fluid of the porous sample <NUM>, on the other hand.

Preferably, the representative parameter is the exponent saturation coefficient n in an empirical equation relating conductivity and/or resistivity to saturation in a first fluid of the porous sample <NUM>.

The equation is for example Archie's law as defined above. In a variant, the equation is chosen among Waxman-Smits's law, Poupon-Leveaux's law, Simandoux's law, Clavier-Coates Dumanoir's Dual-Water law and/or the effective Spalburg's medium model law.

Simultaneously to determining the representative parameter, the method according to the invention advantageously allows a determination of the relationship relating capillary pressure to saturation in a first fluid for the porous sample <NUM>.

The porous sample <NUM> is for example a formation sample extracted from a sub-soil. The formation sample is in particular a rock sample having an internal porosity.

Typically, the porous sample <NUM> has for example a volume comprised between <NUM><NUM> and <NUM><NUM>. It is advantageously cylindrical, with a circular cross-section.

The diameter of the porous sample <NUM> is generally comprised between <NUM> and <NUM>. Its length is for example comprised between <NUM> and <NUM>.

In a variant, the porous sample <NUM> is a parallelepiped.

The measuring system <NUM> comprises a cell <NUM> receiving the porous sample <NUM> filled with a first fluid (see <FIG>), and an apparatus <NUM> for establishing at least a profile, in particular a steady state profile, of a second fluid content in the porous sample <NUM> by applying a first mechanical load and for measuring a volume Vp of first fluid produced from the porous sample <NUM>, when establishing the profile.

As shown in <FIG>, the apparatus <NUM> is thus able to create, in the porous sample <NUM>, a plurality of regions <NUM> having different second fluid contents in the porous sample <NUM> and to measure, in each of the plurality of regions <NUM>, a corresponding local electrical resistivity Rt (i) and/or conductivity Ct(i).

The measuring system <NUM> further comprises a calculator <NUM> for estimating a value of the total volume VT<NUM>,est of first fluid in the porous sample <NUM> from the local resistivities Rt (i) and/or conductivities Ct(i) measured in each region <NUM> and for determining the representative parameter n, based on minimizing the difference between the estimated volume VT<NUM>,est and a measured volume VT<NUM>,mes of first fluid in the porous sample <NUM> obtained from the measured volume Vp of first fluid produced from the porous sample <NUM> when establishing the steady state profile.

An example of cell <NUM> is shown schematically in <FIG>. It comprises a closed enclosure <NUM> defining a volume <NUM> for receiving the porous sample <NUM>, an upstream chamber <NUM>, for injection of the second fluid in the porous sample <NUM>, and a downstream chamber <NUM> for receiving fluids collected when a mechanical load is applied to the porous sample <NUM>.

The cell <NUM> delimits at least an inlet <NUM> for feeding the second fluid into the upstream chamber <NUM>. It extends along a longitudinal axis X-X' which is coaxial with the longitudinal axis of the porous sample <NUM>.

The inlet <NUM> is able to be closed to seal the enclosure <NUM>. Chambers <NUM> and <NUM> are able to fluidly communicate to equilibrate pressures when fluid is produced from the porous sample <NUM> in either of the chambers <NUM>, <NUM> as will be described below.

The cell <NUM> defines at least a transparent window in the downstream chamber <NUM> and/or in the upstream chamber <NUM>.

Advantageously, the enclosure <NUM> of the cell <NUM> comprises an assembly of a centrifuge cup containing the porous sample <NUM> and of a transparent test tube delimiting the downstream chamber <NUM>.

As shown in <FIG> and <FIG>, the apparatus <NUM> comprises a centrifuge <NUM>, a sensing control system <NUM> and a control unit <NUM>.

The centrifuge <NUM> comprises an outer enclosure <NUM> defining an inner volume <NUM>, and a centrifuge rotor <NUM> equipped with electrically powered sensors <NUM> to measure at least a property of the porous sample in regions <NUM> of the porous sample.

The centrifuge <NUM> further comprises a motor <NUM> able to drive the rotor <NUM> in rotation around a rotation axis A-A', a hood <NUM> able to close the inner volume <NUM>, and an electrical power source <NUM> able to power the motor <NUM>.

The centrifuge <NUM> also comprises a contactless power and signal transmission system <NUM> able to transmit power from the source <NUM> to the electrically powered sensors <NUM> and to transmit information from the electrically powered sensors <NUM> to the control unit <NUM> during rotation of the rotor <NUM> around the rotation axis A-A'. It further comprises an electrical connection <NUM> connecting the electrically powered sensors <NUM> to the contactless power and signal transmission system <NUM>.

The enclosure <NUM> and the hood <NUM> remain static in rotation around the rotation axis A-A' when the rotor <NUM> rotates around the rotation axis A-A'. They will be referred to as the "static" part of the centrifuge <NUM> in the following description. More generally, the term "static" should be understood as static in rotation around the axis A-A' when the rotor <NUM> rotates. It does not prevent a movement to occur, for example of the hood <NUM> with regards to the enclosure <NUM> to allow access to the inner volume <NUM>.

The centrifuge rotor <NUM> comprises a support <NUM> defining at least a housing <NUM> for receiving a porous sample <NUM> housed in a cell <NUM>.

The support <NUM> also holds the electrically powered sensors <NUM> and the electrical connection <NUM>, at least when the cell <NUM> is received in the housing <NUM>.

In the example shown in <FIG>, the support <NUM> comprises a bowl <NUM>, mounted rotatable in the inner volume <NUM> around the axis A-A', a central hub <NUM> connecting the motor <NUM> to the bowl <NUM> and a rotatable holder <NUM> for holding a first part of the contactless power and signal transmission system <NUM>.

The bowl <NUM> has a bottom wall <NUM> and a lateral wall <NUM> defining a central cavity <NUM> around axis A-A'. The bowl <NUM> is driven by the motor <NUM> to rotate around axis A-A' at a speed comprised between <NUM> rpm and <NUM> rpm.

The central cavity <NUM> receives at least a frame <NUM> defining each housing <NUM>. The frame <NUM> preferentially comprise arms with protrude radially from the central hub <NUM>.

Each housing <NUM> extends radially with regards to the rotation axis A-A'. When received in the housing <NUM>, in particular during rotation of the rotor <NUM>, the axis X-X' of each porous sample <NUM> extends radially with regards to the rotation axis A-A'.

The electrically powered sensors <NUM> are mounted in the cell <NUM> around the sample <NUM>. In the example of <FIG>, the sensors <NUM> comprise at least two plate electrodes <NUM>, mounted at the ends of the porous sample <NUM> and intermediate electrodes <NUM> each formed of at least a coil of wire, which are distributed along the length of the porous sample <NUM>.

Each plate electrode <NUM> and an adjacent electrode <NUM>, and each electrode <NUM> and another adjacent electrode <NUM> define between them a successive region <NUM> of the porous sample <NUM> in which a local resistivity Rt(i) and/or conductivity Ct(i) is measured by determining the tension arising between two successive adjacent electrodes <NUM>, <NUM>, or <NUM> when a current circulates in the sample <NUM>. It may comprise a supplementary radial electrode.

In the example of <FIG> and <FIG>, the successive regions <NUM> are slices of the porous sample <NUM> taken in succession longitudinally along the length of the porous sample <NUM>. Each slice is delimited by two parallel transverse planes which are perpendicular to the longitudinal axis X-X' of the porous sample <NUM>. The number of regions <NUM> is for example comprised between <NUM> and <NUM> preferably between <NUM> and <NUM>. The length of each region <NUM>, taken along the axis is preferably smaller than <NUM>% of the total length of the porous sample <NUM>.

Advantageously, the electrically powered sensors <NUM> comprise a further sensor <NUM> measuring the sealing of the cell <NUM>, for example by a resistivity measurement at the interface of the cell <NUM> to check that no leak occurs during centrifugation.

The electrical connection <NUM> comprise wires or leads connecting the electrically powered sensors <NUM> to the contactless power and signal transmission system <NUM> along the frame <NUM>.

For example, the electrical connection <NUM> has at least a conductor with a first section running radially along the arms and a second section which runs axially to the rotatable holder <NUM>.

The rotatable holder <NUM> preferentially has a surface which extends perpendicular to the rotation axis A-A'.

The motor <NUM> of the centrifuge <NUM> is able to be actuated by the control unit <NUM> to rotate the rotor <NUM> and jointly the cell <NUM> containing the porous sample <NUM> and the electrically powered sensors <NUM> at a speed of rotation ranging from <NUM> rpm to <NUM> rpm.

A mechanical load in the form of a centrifugal force applies on the porous sample <NUM> and on the fluid contained in the porous sample <NUM>. This leads to impregnation of the porous sample <NUM> with the second fluid contained in the upstream chamber <NUM> and to first fluid production in the downstream chamber <NUM>.

The power source <NUM> is for example an electrical connection to an electrical network or to a generator.

The sensing unit <NUM> comprises a rotation speed sensor <NUM> able to detect the speed of rotation of the rotor <NUM> and a fluid production sensor <NUM>.

The fluid production sensor <NUM> is able to monitor the rate of fluid production of the fluid sample <NUM> during rotation of the cell <NUM> around the rotation axis A-A'. In the example shown in <FIG> and <FIG>, the fluid production sensor <NUM> comprises at least a stroboscope 92B and a camera 92A able to take images of the content of the downstream chamber <NUM> and/or of the upstream chamber <NUM> along time.

The control unit <NUM> is able to analyze the fluid production from the images taken in the camera 92A and to relate it to a rate of production of fluid and to a volume of produced fluid Vp in the downstream chamber <NUM> and/or in the upstream chamber <NUM> by image analysis.

The hood <NUM> comprises a door <NUM> able to close the inner volume <NUM> of the enclosure <NUM>, and a stand <NUM> for receiving a second part of the contactless power and signal transmission system <NUM>.

In this example, the hood <NUM> has a trough opening 86A provided through the door <NUM> to let the camera 92A take images of the content of the downstream chamber <NUM> and/or of the upstream chamber <NUM> along time.

In the example shown in <FIG>, the stand <NUM> comprises a lower static plate <NUM> which protrudes transversally and perpendicularly to axis A-A', when the door <NUM> closes the inner volume <NUM>.

In that position, the lower plate <NUM> faces the rotatable holder <NUM> of the centrifuge rotor <NUM>, parallel to the upper surface of the holder <NUM>.

An air gap <NUM> is defined between the lower plate <NUM> and the rotatable holder <NUM>. The gap <NUM> for example has a height of at least <NUM>,<NUM>, in particular comprised between <NUM> and <NUM>.

Thus, the rotatable holder <NUM> is able to rotate coaxially to the lower plate <NUM> around the rotation axis A-A', facing the lower plate <NUM>, without contact with the lower plate <NUM>.

As shown in <FIG>, the contactless power and signal transmission <NUM> comprises a static contactless power transmitter <NUM> held by the lower plate <NUM> and a rotatable contactless power receiver <NUM> held by the rotatable holder <NUM>.

In addition, the contactless power and signal transmission system <NUM> further comprises a rotatable contactless signal transmitter <NUM> held by the holder <NUM> and a static contactless signal receiver <NUM> held by the lower plate <NUM>.

The contactless power transmitter <NUM> comprises a static antenna made of a coil of wires <NUM> and a first electronic card <NUM> able to inject electrical power from the source <NUM> to the static coil of wires <NUM>.

The contactless power receiver <NUM> comprises a rotatable antenna made of a coil of wires <NUM>, able to receive electrical power from the static coil of wires <NUM> by contactless power transmission and a second electronic card <NUM> able to receive electrical power from the rotatable coil of wires <NUM> and to distribute it to the electrically powered sensors <NUM>.

The contactless power transmission is carried out preferentially by inductive coupling during rotation of the rotor <NUM> around the rotation axis A-A'.

Thus, electrical power is continuously fed to the electrical connection <NUM> and to the electrically powered sensor <NUM> during rotation of the centrifuge rotor <NUM> around axis A-A', without electrical contact between the rotor <NUM> and the static parts of the centrifuge <NUM>. The electrical power is also provided without having to place a battery in the centrifuge rotor <NUM>.

In this example, the contactless signal transmitter <NUM> comprises the same rotatable coil of wires <NUM> as the contactless power receiver <NUM> and a third electronic card <NUM> able to transmit electrical signals conveying measurements made by the electrically powered sensors <NUM>.

The contactless signal receiver <NUM> comprises the same static coil of wires <NUM> as the contactless power transmitter <NUM>, able to receive the signals which are transmitted without contact by inductive coupling from the rotative coil of wire <NUM> to the static coil of wire <NUM> and a fourth electronic card <NUM>.

Thus, the electrical signals produced by the electrically powered sensors <NUM> conveying information on the sensed physical properties of the porous sample <NUM> are transmitted to the contactless signal transmitter <NUM> through the electrical connection <NUM>, to the contactless signal receiver <NUM>, and then to the control unit <NUM>.

In the present case, the signals include in particular tension and current information measured between each pair of adjacent electrodes <NUM>, <NUM> around the porous sample <NUM> and advantageously at the sealing sensor <NUM>.

Advantageously, the control unit <NUM> is able to submit the porous sample <NUM> to a plurality of successive mechanical load levels to establish successive profiles, in particular successive steady state profiles of second fluid content in the porous sample <NUM>.

In particular, it is able to submit the porous sample <NUM> to a first mechanical load at a first speed of rotation of the porous sample <NUM> around the rotation axis A-A' until a first steady state is reached, when the rate of fluid extraction measured by the fluid production sensor <NUM> becomes zero.

Then, the control unit <NUM> is able to submit the porous sample <NUM> to a second mechanical load at a second speed of rotation of the porous sample <NUM> around the rotation axis A-A' until a second steady state is reached when the rate of fluid extraction measured by the fluid production sensor <NUM> again becomes zero. The second rotation speed is greater than the first rotation speed.

The control unit <NUM> is able to recover resistivity and/or conductivity measurements measured by the electrically powered sensors <NUM> at each steady state profile j corresponding to successive increasing mechanical loads, as well as the fluid produced Vp, until the steady state is reached and to transmit the measured information to the calculator <NUM>.

The calculator <NUM> is for example a computer having at least a processor and at least a memory containing software modules able to be carried out by the processor.

At each steady state profile j corresponding to a given mechanical load, the calculator <NUM> is able to assess an initial value of the exponent coefficient n, and then to calculate, in each region <NUM>, an estimated saturation Sw,est(i,j) of first fluid, based on the measured resistivity Rt(i,j) measured in the region <NUM> at the current mechanical load level j, based on the initial measured resistivity R<NUM> and based on the assessed value of the exponent n.

This calculation is done by using an inverted form of the equation relating resistivity or/and conductivity to saturation in first fluid, whose exponent coefficient is sought. When Archie's law is used, the inverted equation (<NUM>) can be used: <MAT>.

The calculator <NUM> is then able to calculate an estimated volume V<NUM>,est(i,j) of first fluid in the region <NUM> by multiplying the estimated saturation Sw,est(i,j) by an estimated volume of pores Vpo,est(i) in the region <NUM>.

Advantageously, the estimated volume of pores Vpo,est(i) is deduced from the total volume of pores Vpo in the whole porous sample <NUM> divided by the number of regions <NUM> in which an experiment is carried out.

The total volume of pores Vpo of the sample is determined for example via pycnometry.

Then, the calculator <NUM> is able to estimate an estimated total volume VT<NUM>,est(j) of first fluid in the porous sample <NUM> at the steady state profile j, by summing all the estimated volumes V<NUM>,est(i,j) in the different regions <NUM>.

The calculator is able to calculate a difference D(j) between the estimated volume VT<NUM>,est(j) and the measured volume of first fluid VT<NUM>,mes(j) inside the porous sample <NUM> at level j.

The measured volume of first fluid VT<NUM>,mes(j) inside the porous sample <NUM> at level j is equal to the initial volume VT<NUM>,mes(j-<NUM>) of first fluid contained in the porous sample <NUM> before the steady state profile j is applied minus the volume Vp(j) which has been produced at the level j when the steady state is reached.

The calculator <NUM> is then able to calculate an objective cost function which is here the sum S of the squares of the differences D(j)<NUM>.

The objective cost function here has the following form: <MAT> in which Ne is the total number of regions <NUM>, corresponding to the number of adjacent electrode pairs <NUM>, <NUM> and Nj is the total number of steady states profiles corresponding to the mechanical loads to which the porous sample <NUM> is subjected.

Preferentially, Ne ranges from <NUM> to <NUM>, notably from <NUM> to <NUM>. Preferentially, Nj ranges from <NUM> to <NUM>, notably from <NUM> to <NUM>.

Then, the calculator <NUM> is able to adjust the value of the estimated representative parameter n and repeat the previous calculation steps to minimize the above-mentioned objective cost function. The representative parameter n for the porous sample <NUM> corresponds to the value of n for which the objective cost function is minimized.

Similarly, based on the position of each region <NUM> along the porous sample axis, and on the rotation speed, the calculator <NUM> is able to calculate the capillary pressure Pc applied in each region using the following equation: <MAT> in which ω is the rotation speed, Δρ is the difference of density between the first fluid and the second fluid, rs is the radius separating the region <NUM> from the axis of rotation A-A', and r<NUM> is the radius separating the axis of rotation A-A' from the surface of the porous sample <NUM> farthest (in drainage) or closest (in imbibition) to the axis of rotation A-A'.

The calculator <NUM> is then able to determine a plot of the capillary pressure Pc as a function of the saturation in the first fluid Sw, calculated in each region from the above mentioned equation (<NUM>).

A method for determining a representative parameter of a porous sample <NUM> using the system <NUM> will now be described.

Initially, a dry porous sample <NUM> is provided. The volume of pores Vpo in the sample is evaluated by pycnometry.

The porous sample <NUM> is then saturated with a first fluid, in particular with a water-based fluid such as brine.

Then, the porous sample <NUM> filled with the first fluid is inserted into the porous sample reception volume <NUM> of the cell <NUM>.

The cell <NUM> is introduced in the housing <NUM> of the centrifuge rotor <NUM>, with the axis X-X' of the porous sample <NUM> extending radially with regards to the axis of rotation A-A' of the rotor <NUM>.

A second fluid is introduced in the upstream chamber <NUM> located closer to axis A-A'. The second fluid is for example oil, or gas (for example air).

The electrically powered sensors <NUM> are powered by transmitting power from a static part of the centrifuge <NUM> to the rotor <NUM> via the contactless power and signal transmission system <NUM>.

The resistivity Ro of the porous sample <NUM> saturated with the first fluid is then measured, for example using the tension measured between the end electrodes <NUM>.

Then, the control unit <NUM> of the centrifuge <NUM> is activated to actuate the motor <NUM> and rotate the rotor <NUM> jointly with the porous sample <NUM> contained in the cell <NUM> around the rotation axis A-A'. A first mechanical load applies on the porous sample <NUM> due to the centrifugal force applying on the porous sample <NUM>.

The axis X-X' of the porous sample <NUM> extending radially with regard to the rotation axis A-A', the second fluid contained in the upstream chamber <NUM> progressively penetrates into the porous sample <NUM> to generate a profile of saturation in the second fluid which is represented schematically with curve <NUM> in <FIG>. In <FIG>, the rotation axis A-A' of the porous sample <NUM> is located on the right of the porous sample <NUM>.

The fluid production sensor <NUM> of the sensing unit <NUM> is activated to measure the rate of fluid extraction from the porous sample <NUM> collected in the downstream chamber <NUM> and the volume of produced fluid Vp.

In a time period comprised generally between <NUM> hour and <NUM> days, a second fluid content steady state profile establishes in the porous sample <NUM>, when the rate of fluid extraction measured by the fluid production sensor <NUM> becomes zero.

In the steady state profile, the porous sample <NUM> comprises successive regions <NUM> along the longitudinal axis X-X', the successive regions <NUM> having different local average values of saturation Sw, in particular increasing values of saturation in the first fluid Sw along the length of the porous sample <NUM>, taken from the end of the porous sample <NUM> located closer to the axis A-A' (on the right in <FIG>) to the end of the porous sample <NUM> located further away from the axis A-A' (on the left in <FIG>).

During the measurement, and at the steady stage, power is supplied to the electrical sensors <NUM>, during rotation of the rotor <NUM> through the contactless power transmitter <NUM>, by contactless transmission to the contactless power receiver <NUM>, and then to the electrical connection <NUM>.

The power in particular feeds the electrodes <NUM>, <NUM>, to allow measurement of the resistivity in each region <NUM> located between an electrode <NUM> and the adjacent electrode <NUM>, or between two adjacent electrodes <NUM>.

The measurement of the local resistivity Rt(i) carried out between each pair of electrodes <NUM>, <NUM> or <NUM>, <NUM> is transmitted from each pair of electrodes <NUM>, <NUM> or <NUM>, <NUM> through the electrical connection <NUM> to the contactless signal transmitter <NUM> and without contact to the contactless signal receiver <NUM>, before reaching the control unit <NUM>.

At each steady state profile j, the calculator <NUM> assesses an initial value of the exponent coefficient n, and then calculates, in each region <NUM>, an estimated saturation Sw,est(i,j) of first fluid, based on the measured resistivity Rt(i,j) measured in the region <NUM> at the current mechanical load level j, based on the initial measured resistivity R<NUM> and based on the assessed value of the exponent n.

This calculation is done by using an inverted form of the equation relating the resistivity to the saturation, as explained above.

The calculator <NUM> then calculates an estimated volume V<NUM>,est(i,j) of first fluid in the region <NUM> by multiplying the estimated saturation Sw,est(i,j) by an estimated volume of pores Vpo,est(i) in the region <NUM>, as determined above.

Then, the calculator <NUM> estimates an estimated total volume VT<NUM>,est(j) of first fluid in the porous sample <NUM> at the steady state profile j, by summing all the estimated volumes V<NUM>,est(i,j) in the different regions <NUM> and calculates a difference D(j) between the estimated volume VT<NUM>,est(j) and the measured volume of first fluid VT<NUM>,mes(j) inside the porous sample <NUM> at level j, as explained above.

The calculator <NUM> is then calculates an objective cost function which is here the sum S of the squares of the differences D(j)<NUM>, as defined above.

Then, the calculator <NUM> adjusts the value of the estimated representative parameter n to minimize the above-mentioned objective cost function.

The representative parameter n for the porous sample corresponds to the value at which the objective cost function is minimized.

The method according to the invention therefore allows a very simple and effective determination of the exponent coefficient n representative of a porous sample <NUM> by applying successive mechanical loads in a centrifuge <NUM> and by measuring the produced first fluid volume and the resistivities or/and conductivities in different regions <NUM> along the porous sample <NUM>.

The latter measurement is carried out continuously when operating the method, advantageously by powering the electrically powered sensors <NUM> in a contactless manner and by receiving data from the electrically powered sensors <NUM> in a contactless manner.

The method does not require a handling of the porous sample <NUM> during the experiment, even if successive increasing levels of mechanical load are applied to the porous sample <NUM>. The porous sample <NUM> remains in the centrifuge <NUM> during the whole experiment.

There is no need to use external techniques to determine the saturation in first fluid in the porous sample <NUM>.

The timeline and cost for carrying out the method according to the invention are therefore greatly reduced, while still obtaining a very wide range of data.

In a variant, only one level of mechanical load is applied to the sample.

In another variant, the information generated by the electrically powered sensors <NUM> carried by the rotor <NUM> is transmitted by a wireless transmitter independent of the contactless power transmission to the sensors <NUM>.

In a further variant, the method is carried out using a centrifuge <NUM> having a rotatable electrical connector, having for example brushes, between the rotor <NUM> and the static part of the centrifuge <NUM>.

Claim 1:
Method for determining a representative parameter of a porous sample (<NUM>) in an equation relating the resistivity or/and conductivity of the porous sample (<NUM>), with a saturation of the porous sample (<NUM>) in a first fluid, the method comprising :
- providing a porous sample (<NUM>) containing a first fluid ;
- feeding a second fluid in the porous sample (<NUM>) and establishing at least a first profile of second fluid content in the porous sample by applying a first mechanical load ;
- measuring a resistivity or/and conductivity in a plurality of regions (<NUM>) having different second fluid contents in the porous sample (<NUM>); characterized by:
- measuring a volume of first fluid produced from the porous sample (<NUM>) when establishing the first profile;
- calculating a measured total volume of first fluid remaining in the porous sample (<NUM>) after establishing the first profile ; and
- repeating the following steps :
*determining an estimated local volume of first fluid contained in each region (<NUM>) from the resistivity or/and conductivity measured in the region (<NUM>) and from an estimated value of the representative parameter;
* calculating a estimated total volume of first fluid in the porous sample (<NUM>) from each estimated local volume of first fluid contained in each region (<NUM>);
* modifying the value of the estimated representative parameter to minimize the difference between the estimated total volume and the measured total volume,
the representative parameter of the porous sample being the estimated representative parameter minimizing said difference.