Patent Description:
A well used for reaching a geological formation usually extends between a first end located towards the surface level, or "wellhead", and a second end opposed to the first end.

Immediately after drilling, a well consists in a borehole in the geological formation, with at most the first end cased, the cased portion being usually referred to as "shoe" of the well, the rest of the well not being cased and being usually referred to as "borehole" portion of the well. Such a configuration is usually referred to as "open-hole" configuration.

After it has been drilled, and before considering incurring the costs of casing the well, the well undergoes well testing operations in order to determine if this well will be used for hydrocarbon recovery or abandoned as a dry hole.

If the well testing operations determine that the well may be used for hydrocarbon recovery, then it is cased, from the first end to the second end, in order to e.g. prevent it from closing upon itself.

Well testing operations usually use tools that are inserted into the well in order to measure and evaluate physical properties of the geological formation along the length of the borehole portion of the well.

In particular, the depth pressure profile and depth permeability profile of the geological formation are of interest.

The depth pressure profile of the geological formation corresponds to the variation of the pressure of the geological formation (a. the natural pressure or pore pressure) along the length of the borehole portion of the well, i.e. the pressure of each layer of the geological formation passed through by the the borehole portion of the well. Similarly, the depth permeability profile corresponds to the variation of the permeability of the geological formation along the length of the borehole portion of the well.

For instance, document <CIT> describes a solution for well testing operations. In document <CIT>, a tube is inserted down to the second end of the well. The tube defines two spaces inside the well: an inner space inside the tube, and an annular space surrounding the tube, between the outer surface of the tube and the inner surface of the well. The inner space and the annular space are in fluidic communication towards the second end of the well. Then the well is filled with two fluids and an interface between the two fluids is moved in the annular space, by injecting a second fluid in the inner space at the first end of the well, and by extracting a first fluid from the annular space at the first end, and vice versa. Hence, the fluids are circulated inside the well, from the first end to the second end via the inner space and from the second end to the first end via the annular space, and vice versa. By disturbing the hydraulic balance of the fluids inside the well, and by measuring effects of said disturbance of the hydraulic balance, the solution proposed enables to estimate physical properties of the borehole portion of the well. These estimated physical properties may be used to determine whether the well should be cased or not.

A drawback of the solution described by document <CIT> lies in the fact that it can be computationally demanding in some cases, because there are many different physical properties that need to be determined. Many computer simulations need to be performed in order to find an optimum set of values for the physical properties that is consistent with the measurements.

The present disclosure aims at improving the situation. In particular, the present disclosure aims at overcoming at least some of the limitations of the prior art discussed above, by proposing a solution for estimating a depth pressure and/or permeability profile of a geological formation that reduces the computational complexity while maintaining accuracy.

According to a first aspect, the present disclosure relates to a method for estimating a depth pressure and/or permeability profile of a geological formation, a well extending in the geological formation between a first end and a second end, said method comprising equipping the well with an inner tube extending between the first end of the well and towards the second end of the well, said tube defining an inner space and an annular space in fluid communication towards the second end of the well, wherein said method further comprises:.

Hence, the estimating method uses an inner tube that is inserted in the well, as in document <CIT>.

Then the estimating method performs at least two well closing phases. A well closing phase corresponds to a phase during which the well, initially filled with a first fluid at least in a bottom portion of the annular space, is progressively filled with a second fluid having a higher viscosity than the first fluid, the second fluid being injected in the inner space at the first end of the well while the first fluid is extracted from the annular space at the first end of the well. Each well closing phase is performed while maintaining the pressure substantially constant in the annular space at the first end of the well, and the estimating method uses different constant pressure values for the at least two well closing phases. Each well closing phase uses the same first and second fluids, i.e. the first fluid used has the same physical properties (density, viscosity, compressibility) during both well closing phases and the second fluid used has also the same physical properties during both well closing phases.

During each well closing phase, the injection flowrate, the extraction flowrate and the pressure in the inner space at the first end of the well are measured continuously. Hence, the estimating method may rely only on measurements performed at the wellhead, without requiring inserting sensors at the bottom of the well.

Thanks to the fact that at least two well closing phases are performed under substantially the same conditions (same fluids used) except for the constant pressure value maintained in the annular space at the first end of the well, the measurements made can be used to estimate the depth pressure and/or permeability profile of the geological formation in the bottom portion of the well. Indeed, for each layer of the geological formation, the measurements may be used to derive a non-linear system having substantially two equations for two unknows, which can be solved with a reduced computational complexity with respect to the prior art.

In specific embodiments, the estimating method can further comprise one or more of the following features, considered either alone or in any technically possible combination.

In specific embodiments, the geological formation is decomposed in a plurality of layers, and estimating the depth pressure and/or permeability profile comprises, for each of the first well closing phase and the second well closing phase:.

and a pressure value and/or a permeability value of the geological formation is determined for each layer of the geological formation, based on the injectivity variation and on the well pressure value of each layer of the geological formation, thereby obtaining the depth pressure and/or permeability profile of the geological formation.

In specific embodiments, the first constant pressure value P<NUM> and the second constant pressure value P<NUM> are such that: <MAT> wherein α is higher than or equal to <NUM>, or higher than or equal to <NUM>.

In specific embodiments, the first fluid has the same density as the second fluid.

In specific embodiments, the second fluid is a gel and/or the first fluid is water or brine.

In specific embodiments, the estimating method comprises performing at least a third well closing phase under a third constant pressure value in the annular space at the first end of the well, said third constant pressure value being different from the first and second constant pressure values, and the depth pressure and/or permeability profile of the geological formation is estimated based on the measurements performed during the first, second and third well closing phases.

According to a second aspect, the present disclosure relates to a computer program product comprising code instructions which, when executed by a processor, cause said processor to carry out the step, of the estimating method according to any one of the embodiments of the present disclosure, whereby the depth pressure and/or permeability profile of the geological formation is estimated based on the measurements performed during at least the first well closing phase and the second well closing phase.

According to a third aspect, the present disclosure relates to a computer-readable storage medium comprising code instructions which, when executed by a processor, cause said processor to carry out the step, of the estimating method according to any one of the embodiments of the present disclosure, whereby the depth pressure and/or permeability profile of the geological formation is estimated based on the measurements performed during at least the first well closing phase and the second well closing phase.

According to a fourth aspect, the present disclosure relates to a system for estimating a depth pressure and/or permeability profile of a geological formation, a well extending in the geological formation between a first end and a second end, said well being equipped with an inner tube extending between the first end of the well and towards the second end of the well, said tube defining an inner space and an annular space in fluid communication towards the second end of the well, wherein the system comprises means configured for implementing an estimating method according to any one of the embodiments of the present disclosure.

In specific embodiments, the well comprises a cased portion at the first end and a borehole portion towards the second end.

The invention will be better understood upon reading the following description, given as an example that is in no way limiting, and made in reference to the figures which show:.

In these figures, references identical from one figure to another designate identical or analogous elements. For reasons of clarity, the elements shown are not to scale, unless explicitly stated otherwise.

As discussed above, the present disclosure relates inter alia to a method and system for estimating a depth pressure and/or permeability profile of a geological formation having a well <NUM>.

The present disclosure relates more specifically to well testing operations, for measuring and evaluating physical properties of the geological formation in order to determine e.g. whether the well <NUM> can be used for hydrocarbon recovery. Hence, the present disclosure finds a main and preferred application in case of well <NUM> having an open-hole configuration.

However, the present disclosure may also be applied to other configurations, including a well having a cased-hole configuration.

Also, the present disclosure is not limited to a specific geometric configuration for the well <NUM>, and can be applied to wells comprising vertical, slanted or horizontal portions, or any combination thereof (provided that a tube <NUM> may be inserted inside the well <NUM>)
In the following description, the case of a vertical well <NUM> having an open-hole configuration is considered, as a non-limitative example.

<FIG> represents schematically a cross-sectional view of a well <NUM> made in a geological formation <NUM> for which a depth pressure and/or permeability profile is to be estimated.

As illustrated by <FIG>, the well <NUM> extends between a first end <NUM> located towards the surface level (or "wellhead"), and a second end <NUM>, opposed to the first end <NUM> and located underground (or "well bottom").

As illustrated by <FIG>, a cemented casing, which may comprise an internal metal cylinder, forms the internal lining of a cased portion <NUM> of the well <NUM> towards the first end <NUM>. This cased portion <NUM> is also referred to as "shoe" of the well <NUM>. This cased portion <NUM> is substantially seal-tight to the various fluids that can circulate in the well <NUM>. The bottom of the cased portion <NUM> is situated at a depth z<NUM>.

In the present disclosure, the depth of a given point along the well <NUM> corresponds to the length measured along the well <NUM> between said given point of the well <NUM> and a reference point of the well <NUM>, for instance located towards the surface level. For instance, the reference point may be the first end <NUM> of the well <NUM>. The depth considered herein is sometimes referred to as measured depth or MD in the literature. Hence, in the present disclosure, the depth injection flowrate profile to be estimated is a function of the depth (MD) measured along the well <NUM>. In most cases (e.g. if the well <NUM> is not completely vertical), the depth (MD) of a given point of the well <NUM> is different from the actual depth of this given point, which corresponds to the distance measured vertically between the surface level (or the sea level) and said given point of the well <NUM>. This actual depth is sometimes referred to as true vertical depth or TVD in the literature.

Under the cased portion <NUM>, the well <NUM> comprises a borehole portion <NUM> which extends from the bottom of the cased portion <NUM> to the second end <NUM> of the well <NUM>. In this borehole portion <NUM>, the internal surface of the well <NUM> consists in the geological formation <NUM> itself. In the example illustrated by <FIG>, the borehole portion <NUM> passes through a succession of N geological layers denoted C<NUM>, C<NUM>,. These geological layers are made of materials that are substantially homogeneous in their mineralogical composition. The first geological layer C<NUM> is situated under the cased portion <NUM> and adjacent to the latter. The geological layer CN is situated close to the second end <NUM>. These geological layers C<NUM>-CN of materials are represented as horizontal around the well <NUM>, but they can of course be arranged otherwise.

Each geological layer Cn (<NUM> ≤ n ≤ N) is delimited by a top surface and a bottom surface. The bottom surface of a geological layer Cn corresponds to the top surface of the next geological layer Cn+<NUM>. The bottom surface of the last geological layer CN can be considered to be situated at the second end <NUM> of the well <NUM>, which is situated at a depth z<NUM> (MD).

The respective depths (MD) of the surfaces between the geological layers C<NUM>-CN may have been determined by known subsoil imaging techniques, notably by seismic techniques implemented before the drilling of the well <NUM> or by diagraphic techniques implemented during the drilling of the well <NUM>. These techniques make it possible to be informed of the geometry of the geological layers C<NUM>-CN forming the subsoil.

Each geological layer Cn can be characterized by physical properties such as a permeability, a porosity or a pressure (sometimes referred to as natural pressure or pore pressure). The present disclosure aims at determining at least one among the pressure and the permeability for each geological layer Cn (<NUM> ≤ n ≤ N) but may also be used to estimate other physical properties.

By estimating the "depth pressure profile" of the geological formation <NUM>, we mean estimating the pressure for each geological layer Cn (<NUM> ≤ n ≤ N) in the borehole portion <NUM> of the well <NUM>, each geological layer having a predetermined thickness associated thereto. Similarly, by estimating the "depth permeability profile" of the geological formation <NUM>, we mean estimating the permeability for each geological layer Cn (<NUM> ≤ n ≤ N) in the borehole portion of the well <NUM>.

It is also emphasized that the present disclosure may also be applied by considering arbitrary layers in the borehole portion <NUM> of the well <NUM> instead of geological layers Cn (<NUM> ≤ n ≤ N). For instance, it is possible to consider successive layers having a same predefined thickness along the well <NUM>, from the bottom of the cased portion <NUM> to the second end <NUM> of the well <NUM>, without requiring any knowledge on the actual configuration of the geological layers Cn. In such a case, the estimated depth pressure and permeability profiles may be used to identify the adjacent layers having substantially the same physical properties and which can be considered to belong to a same geological layer.

<FIG> shows also components of a system <NUM> for estimating the depth pressure and/or permeability profile of the geological formation <NUM> in the borehole portion <NUM> of the well <NUM>.

As can be seen in <FIG>, the system <NUM> for estimating the depth pressure and/or permeability profile comprises a tube <NUM> inserted in the well <NUM>, extending from the first end <NUM> of the well <NUM> to substantially the second end <NUM> of the well <NUM>. This tube <NUM> defines two different spaces inside the well <NUM>:.

The inner space <NUM> and the annular space <NUM> are in fluid communication towards the second end <NUM> of the well <NUM>, such that a fluid moving downwards in the inner space <NUM> may arrive at the second end <NUM> of the well <NUM> where it can be injected into the annular space <NUM> and move upwards to the first end <NUM> of the well <NUM>, and vice-versa.

The system <NUM> for estimating the depth pressure and/or permeability profile comprises means for injecting fluids in the tube <NUM> at the first end <NUM> of the well <NUM> and means for extracting fluids from the annular space <NUM> at the first end <NUM> of the well <NUM>. The system <NUM> comprises also means for measuring and controlling continuously, at the first end <NUM> of the well <NUM>:.

In the non-limitative example illustrated by <FIG>, the extracting means comprise a valve <NUM>, a line <NUM> and a pump <NUM> with a tank <NUM> adapted for containing a first fluid <NUM> extracted from the annular space <NUM> at the first end <NUM> of the well <NUM>. Similarly, the injecting means comprise a valve <NUM>, a line <NUM> and a pump <NUM> with a tank <NUM> adapted for containing a second fluid <NUM> to be injected in the inner space <NUM> at the first end <NUM> of the well <NUM>.

In the example illustrated by <FIG>, the measuring means comprise a flowmeter <NUM> in the line <NUM>, for measuring the extraction flowrate of the first fluid <NUM> from the annular space <NUM> of the well <NUM>, and a pressure sensor <NUM> for measuring the pressure in the annular space <NUM> at the first end <NUM> of the well <NUM>. The measuring means comprise also a flowmeter <NUM> in the line <NUM>, for measuring the injection flowrate of the second fluid <NUM> in the inner space <NUM> of the well <NUM>, and a pressure sensor <NUM> for measuring the pressure in the inner space <NUM> at the first end <NUM> of the well <NUM>.

It should be noted that the injecting, extracting and measuring means illustrated in <FIG> correspond to a non-limitative examplary configuration. It is emphasized that other configurations may be used, as long as they enable:.

In particular, and as will be discussed below, the injecting, extracting and measuring means need to enable continuously injecting a second fluid <NUM> in the inner space <NUM> and simultaneously extracting a first fluid <NUM> from the annular space <NUM>, while maintaining a constant pressure value in the annular space <NUM> at the first end <NUM> of the well <NUM>.

The estimating system <NUM> comprises also means for estimating the depth pressure and/or permeability profile of the geological formation <NUM> in the borehole portion of the well <NUM> based on the measurements performed by the measuring means.

These estimating means (not represented in the figures) correspond for instance to a processing circuit comprising one or more processors and storage means (magnetic hard disk, solid-state disk, optical disk, or any type of computer-readable storage medium) in which a computer program product is stored, in the form of a set of program-code instructions to be executed in order to estimate the depth pressure and/or permeability profile. Alternatively, or in combination thereof, the processing circuit can comprise one or more programmable logic circuits (FPGA, PLD, etc.), and/or one or more specialized integrated circuits (ASIC), and/or a set of discrete electronic components, etc., adapted for implementing all or part of the operations for estimating the depth pressure and/or permeability profile of the geological formation <NUM>.

<FIG> represents a flow chart illustrating the main steps of a method <NUM> for estimating a depth pressure and/or permeability profile of the geological formation in the borehole portion <NUM> of the well <NUM>.

As illustrated by <FIG>, the estimating method <NUM> comprises first a step <NUM> of equipping the well <NUM> with the tube <NUM>, as represented in <FIG>.

As illustrated by <FIG>, the estimating method <NUM> comprises two main phases during which fluids are circulated inside the well <NUM>. These main phases are referred to as "well closing phases".

The estimating method <NUM> comprises a step <NUM> of performing a first well closing phase which may start when the well <NUM>, or at least the annular space <NUM> in the borehole portion <NUM> thereof, is filled with a first fluid <NUM>.

The step <NUM> of performing the first well closing phase comprises a step <NUM> of injecting a second fluid <NUM> into the inner space <NUM> at the first end <NUM> of the well <NUM>, while extracting the first fluid from the annular space <NUM> at the first end <NUM> of the well <NUM>. The second fluid <NUM> is injected continuously into the well <NUM> until the well <NUM> is filled with said second fluid <NUM>, or at least the annular space <NUM> in the borehole portion <NUM> of the well <NUM>.

The injection / extraction is performed while maintaining the pressure constant in the annular space <NUM> at the first end <NUM> of the well <NUM>, equal to a first constant pressure value P<NUM>, for the duration of the first well closing phase, or at least for the duration required to fill the annular space <NUM> in the borehole portion <NUM> of the well <NUM> with the second fluid <NUM>. The second fluid <NUM> has a higher viscosity than the first fluid <NUM>, thereby resulting in a "closing" of the borehole portion <NUM> of the well <NUM>.

For instance, the first fluid <NUM> is a non-viscous fluid such as water and/or brine, and the second fluid <NUM> is a viscous fluid such as a gel. For instance, the viscosity of the first fluid <NUM> is lower than <NUM> centipoises (cP, one cP being equal to one millipascal-second - mPa·s), and the viscosity of the second fluid <NUM> is higher than <NUM> cP. Preferably, the ratio between the viscosity of the second fluid <NUM> and the viscosity of the first fluid <NUM> is equal to or higher than thirty (<NUM>), for instance around fifty (<NUM>). Preferably, the first fluid <NUM> and the second fluid <NUM> have the same density, in order to e.g. stabilize the interface <NUM> between the second fluid <NUM> and the first fluid <NUM>. However, it is emphasized that the second fluid <NUM> is not necessarily viscous, and the first fluid <NUM> and the second fluid <NUM> need only to have contrasted viscosities and to be immiscible.

The step <NUM> of performing the first well closing phase comprises also a step <NUM> of measuring continuously:.

The estimating method <NUM> comprises also a step <NUM> of performing a second well closing phase which may start when the well <NUM>, or at least the annular space <NUM> in the borehole portion <NUM> thereof, is filled with the first fluid <NUM>.

Of course, although not represented, this implies that a well opening phase is performed between both well closing phases, in order to re-fill the well <NUM> with the first fluid <NUM>, or at least the annular space <NUM> in the borehole portion <NUM> thereof. This may be accomplished, for instance, by injecting the first fluid <NUM> in the inner space <NUM> at the first end <NUM>, or by circulating the fluids in the other direction, i.e. by injecting the first fluid <NUM> in the annular space <NUM> at the first end <NUM> while extracting the second fluid <NUM> from the inner space <NUM> at the first end <NUM>.

The step <NUM> of performing the second well closing phase comprises a step <NUM> of injecting the second fluid <NUM> into the inner space <NUM> at the first end <NUM> of the well <NUM>, while extracting the first fluid <NUM> from the annular space <NUM> at the first end <NUM> of the well <NUM>. The second fluid <NUM> is injected continuously into the well <NUM> until the well <NUM> is filled with said second fluid <NUM>, or at least the annular space <NUM> in the borehole portion <NUM> of the well <NUM>.

The injection / extraction is performed while maintaining the pressure constant in the annular space <NUM> at the first end <NUM> of the well <NUM>, equal to a second constant pressure value P<NUM>, for the duration of the first well closing phase, or at least for the duration required to fill the annular space <NUM> in the borehole portion <NUM> of the well <NUM> with the second fluid <NUM>. The second constant pressure value P<NUM> is different from the first constant pressure value P<NUM>, and preferably significantly different. For instance, the first constant pressure value P<NUM> and the second constant pressure value P<NUM> are such that: <MAT> wherein α is higher than or equal to <NUM>, or higher than or equal to <NUM>, or preferably higher than or equal to <NUM>.

The step <NUM> of performing the second well closing phase comprises also a step <NUM> of measuring continuously:.

As illustrated by <FIG>, the estimating method <NUM> then comprises a step <NUM> of estimating the depth pressure and/or permeability profile of the geological formation <NUM> in the borehole portion <NUM> of the well <NUM> based on the measurements performed during the first well closing phase and the second well closing phase, i.e. the first and second temporal injection flowrates profiles, the first and second temporal extraction flowrate profiles and the first and second temporal pressure profiles. The first and second constant pressure values P<NUM> and P<NUM> are also used during step <NUM>.

<FIG> represents schematically cross-sectional views of the well <NUM> during a well closing phase.

In part a) of <FIG>, the well <NUM> is assumed to be initially completely filled with the first fluid <NUM>. In part b) of <FIG>, the injection of the second fluid <NUM> in the inner space <NUM> at the first end <NUM> has started, and the first fluid <NUM> is extracted from the annular space <NUM> at the first end <NUM> while maintaining a constant pressure value (P<NUM> or P<NUM>) in the annular space <NUM> at the first end <NUM>. The second fluid <NUM> and the first fluid <NUM> have different viscosities and are immiscible, such that an interface <NUM> between the second fluid <NUM> and the first fluid <NUM> appears inside the inner space <NUM> of the well <NUM>. The interface <NUM> travels downwards inside the tube <NUM> from the first end <NUM> of the well <NUM> towards the second end <NUM> as the second fluid <NUM> is injected into the inner space <NUM> of the well <NUM>. In part c) of <FIG>, the interface <NUM> has reached the second end <NUM>. The tube <NUM> is completely filled with the second fluid <NUM>. In part d) of <FIG>, the interface <NUM> travels upwards in the annular space <NUM> of the well <NUM>, in the borehole portion <NUM> of the well <NUM>. This corresponds to the actual "closing" of the well <NUM>, since the borehole portion <NUM> of the well <NUM> is the only portion where fluids can penetrate into the geological formation <NUM>, and since the second fluid <NUM> has a higher viscosity than the first fluid <NUM> and is therefore less likely to penetrate into the geological formation. In part e) of <FIG>, the interface <NUM> has continued to move upwards such that the annular space <NUM> in the borehole portion <NUM> of the well <NUM> is completely filled with the second fluid <NUM>. In part f) of <FIG>, the interface <NUM> has continued to move upwards and both the inner space <NUM> and the annular space <NUM> of the well <NUM> are completely filled with the second fluid <NUM>.

<FIG> represents schematically examples of the temporal evolution of the pressures and of the apparent injectivity (see below) obtained for the first well closing phase. More specifically, part a) of <FIG> represents the temporal evolution of the pressure <MAT> in the inner space <NUM> at the first end <NUM> and of the pressure <MAT> in the annular space <NUM> at the first end <NUM>, and part b) of <FIG> represents the temporal evolution of the apparent injectivity q<NUM>(t). As can be seen in part a) of <FIG>, the pressure <MAT> remains substantially equal to the first constant pressure value P<NUM> during all the time interval considered. In turn, the pressure <MAT> tends to decrease slightly before the first well closing phase, and then increases during the first well closing phase, especially when the second fluid <NUM> reaches the borehole portion <NUM> of the well <NUM>, due the higher viscosity of the second fluid <NUM>. As can be seen in part b) of <FIG>, the apparent injectivity q<NUM>(t) is substantially constant before the first well closing phase, and then decreases during the first well closing phase, especially when the second fluid <NUM> reaches the borehole portion <NUM> of the well <NUM>, due the higher viscosity of the second fluid <NUM>.

<FIG> represents schematically the main steps of a preferred embodiment of the estimating step <NUM> of the estimating method <NUM>.

As illustrated by <FIG>, the estimating step <NUM> comprises, for each of the first well closing phase and the second well closing phase:.

Then the estimating step <NUM> comprises a step <NUM> of determining a pressure value and/or a permeability value for each geological layer Cn of the geological formation <NUM>, based on the injectivity variation and on the reference well pressure value in the well <NUM> for each geological layer Cn, thereby obtaining the depth pressure and/or permeability profile of the geological formation <NUM> in the borehole portion <NUM> of the well <NUM>.

During step <NUM>, the temporal evolution of the position in the well <NUM> of the interface <NUM> between the first fluid <NUM> and the second fluid <NUM> is determined. The position of the interface <NUM> is denoted by xj(t), wherein the j = <NUM> for the first well closing phase and j = <NUM> for the second well closing phase. It should be noted that the position xj(t) takes into account the presence of the tube <NUM> inside the well <NUM>, and the fact that the interface <NUM> travels first in the inner space <NUM> and second in the annular space <NUM> of the well <NUM>. Hence the position xj(t) is for instance measured from the first end <NUM> of the well <NUM>, in the inner space <NUM>, to the first end <NUM> of the well <NUM>, in the annular space <NUM>, over a length that is substantially twice the actual length of the well <NUM>. Basically, the position xj(t) makes it possible to determine whether the interface <NUM> is in the inner space <NUM> or in the annular space <NUM>, and more specifically whether the interface <NUM> is in the annular space <NUM> of the borehole portion <NUM> of the well <NUM>.

If the permeability of the geological formation <NUM> is low and if the second fluid <NUM> has a high viscosity, then the position xj(t) may be estimated based on the following equation: <MAT> wherein:.

If the injectivity of the second fluid <NUM> into the geological formation <NUM> cannot be neglected, then the following equation may be used: <MAT> wherein:.

At each instant, the apparent injectivity qj(t) may be computed by using the following equation: <MAT>.

Preferably, the apparent injectivity qj(t) may be instead computed by using the following equation: <MAT> wherein: <MAT> <MAT>.

If we denote by <MAT> the maximum apparent injectivity (i.e. when the annular space <NUM> in the borehole portion <NUM> is filled with the first fluid <NUM>) and by <MAT> the minimum apparent injectivity (i.e. when the annular space <NUM> in the borehole portion <NUM> is filled with the second fluid <NUM>), then <MAT> (in principle χ is the same for both the first and second well closing phases).

Hence, the above equations may be used to determine the temporal evolution of the position xj(t) of the interface <NUM> and the apparent injectivity qj(t) as a function of xj(t) during both the first well closing phase and the second well closing phase.

For illustration purposes, <FIG> represents a graph illustrating an example of apparent injectivities determined for different positions of the interface <NUM> during a first well closing phase and a second closing phase. In this example, the borehole portion <NUM> of the well <NUM> is located between a depth z<NUM> (MD) of <NUM> meters and a depth z<NUM> (MD) of <NUM> meters. As can be seen in <FIG>, the apparent injectivity qj(t) decreases as the interface <NUM> moves upwards (from the depth z<NUM> to the depth z<NUM>). Also, the second constant pressure value P<NUM> is assumed to be higher than the first constant pressure value P<NUM>, such that the apparent injectivity q<NUM>(t) is higher than the apparent injectivity q<NUM>(t).

During step <NUM>, the variation of injectivity is determined for each geological layer Cn.

At this stage, it is recalled that it is also possible, in other embodiments, to consider arbitrary layers instead of geological layers, such as layers having all the same predefined thickness along the borehole portion <NUM> of the well <NUM>.

The variation of injectivity may be determined based on the temporal injection flowrate profile of the second fluid <NUM>, on the temporal extraction flowrate profile of the first fluid <NUM> and on the temporal evolution of the position in the well <NUM> of the interface <NUM>.

For instance, given the thickness en and depth for each geological layer Cn (<NUM> ≤ n ≤ N), it is possible to use the temporal evolution of the position xj(t) to determine an input time <MAT> and an output time <MAT>, which correspond respectively to the time when the interface <NUM> has entered the geological layer Cn during the well closing phase of index j (i.e. first or second well closing phase) and to the time when the interface <NUM> has exited said geological layer Cn during said well closing phase of index j. The input time <MAT> and the output time <MAT> are such that <MAT>.

Then the variation of injectivity Δqn,j, for the geological layer Cn and the well closing phase of index j, may be computed based on the apparent injectivity qj(t) (which may be computed based on <MAT> and <MAT> as discussed above), for instance by using the following equation ; <MAT>.

It is emphasized that the variation of injectivity Δqn,j relates mainly to the injectivity of the first fluid <NUM>, since the injectivity of the second fluid <NUM>, due to its higher viscosity, is lower than that of the first fluid <NUM>.

During step <NUM>, the temporal evolution of the pressure in the annular space <NUM> of the well <NUM>, at least along the borehole portion <NUM>, is determined. In other words, this step <NUM> aims at determining the pressure in the well <NUM> in a plurality of positions in the annular space <NUM> in the borehole portion <NUM>, and their variations over time, denoted <MAT>, wherein:.

For instance, the well pressure <MAT> may be computed by determining the pressure losses inside the well <NUM>, and their variations over time.

The pressure losses may be computed e.g. by using the well-known Darcy-Weisbach equation, and depends on the considered position inside the well <NUM>, on the characteristics of the well <NUM> at the considered position (e.g. dimensions and shape - e.g. disk in the inner space <NUM> or ring in the annular space <NUM> - of the cross section at the considered position), of the physical properties of the fluids (e.g. viscosity and density) and their types (Newtonian or non-Newtonian), on the current position of the interface <NUM>, on the flowrate at the considered position (which may be obtained based on the measured injection and extraction flowrates), etc..

Then, the well pressure <MAT> may be computed by using the computed pressure losses and the constant pressure value Pj in the annular space <NUM> at the first end <NUM> of the well <NUM>.

During step <NUM>, a reference well pressure value <MAT> is determined for each geological layer Cn of the geological formation <NUM>, based on the well pressure <MAT>, in particular the well pressure values obtained for x ∈ <MAT> and for <MAT>. For instance, the reference well pressure value <MAT> may be computed as a mean value of the well pressure <MAT> over the time interval <MAT> over the positions <MAT>. However, the reference well pressure value <MAT> may be computed differently.

Then the estimating step <NUM> comprises the step <NUM> of determining a pressure value and/or a permeability value for each geological layer Cn of the geological formation <NUM>, based on the injectivity variations Δqn,j and on the reference well pressure values <MAT> obtained for each geological layer Cn and for the first and second well closing phases.

For instance, assuming that the radial flow is established in each geological layer Cn when the interface <NUM> starts to travel in the annular space <NUM> in the borehole portion <NUM> of the well <NUM>, then the injectivity variation Δqn,j may be linked to the permeability kn of the geological layer Cn by the following equation: <MAT> wherein:.

Of course, other equations and models may be used for different assumptions, and the present disclosure may also be used with different equations and models known to the skilled person.

It should be noted that, in the present example, the set of values { <MAT>, <NUM> ≤ n ≤ N} corresponds to the depth pressure profile of the geological formation <NUM>, and the set of values {kn, <NUM> ≤ n ≤ N} corresponds to the depth permeability profile of the geological formation <NUM>.

Also, the well pressure at the level of the geological layer Cn during the well closing phase of index j, present in ΔPn,j, may be considered to be equal to the computed reference well pressure value <MAT>, such that <MAT>. Hence, we may assume <MAT>.

Accordingly, we have then, for each geological layer Cn, a non-linear system of two equations: <MAT> wherein the permeability kn and the pressure <MAT> of the geological layer Cn are the two only unknowns. Hence, this non-linear system of two equations may be solved, for each geological layer Cn, by using solving methods known to the skilled person, thereby obtaining the depth pressure and permeability profiles of the geological formation <NUM> in the borehole portion <NUM> of the well <NUM>.

It is emphasized that the present disclosure is not limited to the above exemplary embodiments. Variants of the above exemplary embodiments are also within the scope of the present invention.

Claim 1:
- Method (<NUM>) for estimating a depth pressure and/or permeability profile of a geological formation (<NUM>), a well (<NUM>) extending in the geological formation between a first end (<NUM>) and a second end (<NUM>), said method comprising equipping (<NUM>) the well with an inner tube (<NUM>) extending between the first end of the well and towards the second end of the well, said tube defining an inner space (<NUM>) and an annular space (<NUM>) in fluid communication towards the second end of the well, wherein said method further comprises:
- the annular space of the well being filled with a first fluid (<NUM>): (<NUM>) performing a first well closing phase by injecting, into the inner space at the first end, a second fluid (<NUM>) having a higher viscosity than the first fluid while extracting, from the annular space at the first end, the first fluid under a first constant pressure value in the annular space at the first end, wherein the first well closing phase comprises measuring (<NUM>) a first temporal injection flowrate profile of the second fluid, a first temporal extraction flowrate profile of the first fluid, and a first temporal pressure profile in the inner space at the first end;
- the annular space of the well being filled with the first fluid: (<NUM>) performing a second well closing phase by injecting, into the inner space at the first end, the second fluid while extracting, from the annular space at the first end, the first fluid under a second constant pressure value in the annular space at the first end, the second constant pressure value being different from the first constant pressure value, wherein the second well closing phase comprises measuring (<NUM>) a second temporal injection flowrate profile of the second fluid, a second temporal extraction flowrate profile of the first fluid, and a second temporal pressure profile in the inner space at the first end;
- (<NUM>) estimating the depth pressure and/or permeability profile of the geological formation based on the measurements performed during the first well closing phase and the second well closing phase.