The invention lies in the field of exploitations of reservoirs of deposits of hydrocarbons or gas or for underground storage of compressible fluids, whether natural deposits or artificial storage.
In this field, it is useful to model the geological characteristics of a reservoir as accurately as possible in order to define the best technical and economic exploitation of the reservoir.
By way of example,
Conventionally, the rock formation constituting the reservoir 1 is described using two complementary parameters that are porosity and permeability. Specifically porosity measures the percentage of pores in the rock that are capable of containing hydrocarbons, whereas permeability describes the capacity of the rock to allow fluids to pass horizontally (horizontal permeability Kh) or vertically (vertical permeability Kv), with it also being possible for this capacity to be calculated over the full height of the reservoir (total horizontal permeability or total vertical permeability). These two parameters (permeability and porosity) are thus characteristic of the exploitation performance of a reservoir.
It is known that the porosity φ and the permeability K along a well 2 can be measured by analyzing cores taken from the reservoir-rock, e.g. while drilling the well. A set of discrete porosity and permeability measurements is thus obtained for each well 2.
The capacity to take a measurement on a sample core depends on its consolidation or cementation. In certain reservoirs, levels of low consolidation, corresponding to the greatest permeabilities, cannot be sampled, thereby introducing bias in the representativity of the measurements.
It will readily be understood that the number of wells implemented for a reservoir is limited. In addition, the number of porosity and permeability measurements made along a well in its depth direction is also limited.
That said, in order to be able to use exploitation models or in order to be able to work the reservoir, it is still necessary to have information available about the porosity and the permeability at all points in the reservoir.
Given that measuring permeability is a complicated process, proposals have been made to determine a relationship associating the porosity φ to the permeability K within a reservoir. Such a relationship is generally referred to as a φ-K relationship.
Generally, a φ-K relationship is determined by regression performed on a set of porosity and permeability measurements taken for a set of wells.
That solution is not satisfactory since it is not sufficiently representative of the physical reality of the reservoir.
There therefore exists a need for a simple and effective solution that enables the distribution of permeability within an underground reservoir to be estimated better from a set of porosity and permeability measurements taken within the reservoir.
Consequently, in a first aspect, the present invention provides a determination method for determining a plurality of first relationships associating permeability with porosity within an underground reservoir, e.g. in order to estimate permeability distribution within an underground reservoir, in particular on the basis of a set of porosity and permeability measurements taken within the reservoir. The method comprises:
The method may be performed by a computer system.
The invention thus proposes representing the permeability distribution within an underground reservoir by a set of φ-K relationships representing in simple manner the relationship between permeability and porosity within the reservoir, the relationships in this set being selected, by way of example, as being those relationships for which the result of the counting step exceeds a threshold.
Unlike the solutions in the prior art in which a single φ-K relationship is selected, a plurality of φ-K relationships are obtained that are considered to be properly representative of the reservoir, thus making it possible to estimate the permeability within the reservoir as accurately as possible.
More precisely, the determination method is based on analyzing the ability of a family of φ-K relationships to reproduce a set of porosity and permeability measurements.
The set of measurements may be obtained at the scale of the reservoir, or from a subset of the wells of the reservoir, or indeed from a single well. At reservoir scale, a family of φ-K relationships is obtained for the entire reservoir, whereas with a single well the family of φ-K relationships is representative only of the relationship between porosity and permeability at the scale of a single well. By way of example, it is up to a geologist to segment the reservoir into subsets of wells having the same characteristics in order to calculate different φ-K relationships for each of those subsets.
In the meaning of the invention, a measurement is reproduced by a φ-K relationship when the distance between the point representing the measurement and the curve representing the φ-K relationship is below a threshold, this distance being evaluated in the (φ, K) space or in a space derived therefrom after changing a variable.
By way of example, the threshold may be selected beforehand as a function of the application and of the numbers of φ-K relationships that it is desired to obtain for representing the permeability distribution within the reservoir in more representative manner.
In a particular implementation of the invention, said selected plurality of relationships is selected from the relationships of the family that reproduce at least some minimum number of measurement points of the plurality of measurement points.
In other words, after being normalized relative to one, the function allocating the result of counting the measurement points that are reproduced by the relationship to each of the relationships of the family of relationships is interpreted as a probability distribution.
By setting a cumulative probability threshold, corresponding to a (normalized) number of measurement points that are reproduced, it is possible to define a set of φ-K relationships that represent the most probable pertinent relationships.
In particular, it is possible to select the relationship that is the most representative by selecting a relationship corresponding at least to a maximum of the result of the counting.
In a particular implementation, a counting result is weighted so as to be greater if the measurement points reproduced by the relationship are distributed along the vicinity of the curve representing the relationship. For selection purposes, this makes it possible to give preference to relationships that are corroborated by measurement points over a wider range of values. For example, the result of the counting may be weighted in a manner that is proportional to the product of the variances of the components of the plurality of transformed points.
In a particular implementation, the relationships associating porosity to permeability are determined by at least two parameters.
In a particular implementation of the invention, the relationships of the family of relationships are semi-log relationships or log-log relationships.
Specifically, the inventors have observed that, to a first approximation, the logarithm (base 10) of the permeability is generally correlated either to the porosity φ (semi-log relationship) or else to the logarithm (base 10) of the porosity (log-log relationship). The semi-log or log-log form of the φ-K relationship depends on the intrinsic nature of the rock constituting the reservoir, and the person skilled in the art knows how to select the appropriate form as a function of the rock.
On the basis of this observation, a φ-K relationship may be defined by two parameters A, B for a semi-log relationship defined by log(K)=A·φ+B or for a log-log relationship defined by log(K)=A·log(φ)+B.
It should be observed that polynomial relationships of higher order may also be considered between the variables (log(K), φ) or (log(K), log(φ)).
In a particular implementation of the invention, the relationships of the family of relationships are semi-log relationships defined by two parameters A and B and the counting step comprises:
Thus, with a semi-log model, the change of variable performed by applying the logarithm function to the permeability data makes it possible to obtain a representation space for the measurement points in which the semi-log models are represented by straight lines of equation Y=A·X+B.
In this representation space, the cloud of (φi, log(Ki)) points is represented in the form of an intensity image, the value of each of the points in the image being proportional to the number of observed (φi, log(Ki)) data values.
It should be observed that in this (φi, log(Ki)) space, the number of measurement points in the plurality of measurement points that are reproduced by a semi-log relationship log(K)=A·φ+B is counted merely by counting the number of points lying at a distance from the straight line having the equation Y=A·X+B that is less than a threshold, e.g. as estimated from the resolution of the intensity image.
In the space of the parameters A and B, the selected plurality of φ-K relationships is represented by a set of Ai, Bi pairs for which the count exceeds a threshold.
The count corresponds substantially to integrating this distance for these points along the straight line in question, with each point having the same weight, which operation is intellectually similar to the curvilinear integrals of the Radon transform used in other fields.
In a particular implementation of the invention, the relationships of the family of relationships are log-log relationships defined by two parameters A and B, and the counting step comprises:
the counting comprising counting the number of points in the plurality of transformed points represented in the intensity image that are at a distance that is below a threshold from a straight line having the equation Y=A·X+B.
Thus, for a log-log model, the change of variable performed by applying the logarithm function to the permeability data and to the porosity data makes it possible to obtain a representation space for the measurement points in which log-log models are represented by straight lines of equation Y=A·X+B.
In this representation space, the number of measurement points in the plurality of points that are reproduced by a log-log relationship log(K)=A·log(φ)+B is counted merely by counting the number of points that are at a distance from the straight line having the equation Y=A·X+B that is below a threshold, e.g. as estimated from the resolution of the intensity image.
In a particular implementation of the invention, the method of the invention further comprises a smoothing step of smoothing the intensity image prior to the counting.
Smoothing the intensity image makes it possible to limit excessive disparities between neighboring pixels as generated by the uncertainty on the measurements of porosity data and permeability data.
In a particular implementation of the invention, the porosity data and the first permeability data is obtained by analyzing sample cores from the reservoir or by analyzing logging measurements, and the obtaining step further comprises an addition step for adding additional measurement points to the first plurality of points, the added additional measurement points being selected from the first plurality of measurement points on the basis of analyzing second permeability data obtained from at least one formation test performed within the reservoir.
In the meaning of the invention, an additional measurement point is thus a measurement point that is extracted from the (φi, Ki) data and that is subsequently added to the same (φi, Ki) measurements in order to determine the plurality of first relationships associating porosity with permeability.
The ability to make a measurement on a sample core depends on its consolidation or cementation. In certain reservoirs having low consolidation levels, corresponding to the highest permeabilities, these levels cannot be sampled, thereby leading to bias in the representativity of the measurements.
Thus, and in particularly advantageous manner, the invention makes it possible to correct this bias by improving the representation of the distribution of permeability within an underground reservoir by aggregating permeability data coming from various origins. In particular, when formation tests of the drill stem testing (DST) type are available, the associated measurements integrating permeability over a significant depth of the reservoir are taken into account for determining the φ-K relationships.
It should be observed that formation tests make it possible to obtain horizontal permeability data and vertical permeability data, with vertical permeability data being obtained by tests of the modular dynamic tester (MDT) type or by using measurements of the repeat formation tester (RFT) type.
In a particular implementation of the invention, the addition step further comprises:
Since the permeability measurements obtained on the basis of formation tests are averaged measurements over a significant depth of the reservoir, only a small number of these porosity measurements is generally obtained.
Consequently, the determination method of the invention begins by determining a theoretical histogram for the logarithm of permeability as measured by the formation tests, referred to as the histogram of permeabilities of the tests, and based on the uncertainties relating to interpreting the tests. More precisely, the histogram of the permeabilities of the tests is a discrete distribution obtained by quantifying the distribution of the logarithms of the permeability as measured by the formation tests.
Furthermore, depending on the methods used for measuring permeability, the scale of the description of the characteristics of the reservoir-rock varies in substantial manner.
In order to give precedence to permeability data obtained by formation tests that are corroborated by permeability data obtained by other measurement methods, the determination method determines the probability that a permeability derived from formation tests corresponds to a permeability derived from some other method. The probability corresponds to the product of the theoretical histogram of the test permeabilities multiplied by the histogram of the logarithm of the permeabilities obtained from permeability measurements obtained from analyzing cores or from logging.
Thereafter, the determination method selects additional measurement points randomly from the set of existing measurement points (φi, Ki) for which the permeability obtained from the formation tests corresponds to the permeability Ki. By way of example, this random selection is performed by means of a random draw using a uniform probability relationship.
These additional measurement points are then added to the measurement points (φi, Ki), thereby improving the representation of the corresponding permeability distribution.
In a particular implementation of the invention, the first permeability data value and the second permeability data value are horizontal permeabilities.
In another particular implementation of the invention, the first permeability data value and the second permeability data value are vertical permeabilities.
In other words, the determination method of the invention is independent of the anisotropic nature of the permeability of the reservoir.
In the description below, pairs of values defining a φ-K relationship associating porosity with a horizontal permeability are written (Ai, Bi) and pairs of values defining a φ-K relationship associating porosity with a vertical permeability are written (Avi, Bvi).
In a particular implementation of the invention, the family of relationships is determined by a plurality of parameters, the permeability is horizontal permeability, and the method further comprises:
said selection step taking account at least of the analysis of the first intensity signal and of the second intensity signal, said method further comprising determining a plurality of second relationships associating vertical permeability with porosity, said plurality of second relationships being obtained from said plurality of first relationships by shifting the parameters by the translation vector.
In another particular implementation of the invention, the family of relationships is determined by a plurality of parameters and the method further comprises:
said selection step taking account at least of the analysis of the first intensity signal and of the second intensity signal, said method further comprising determining a plurality of second relationships associating horizontal permeability with porosity, the plurality of second relationships being obtained from the plurality of first relationships by shifting the parameters by the vector.
The invention thus makes it possible to take account of all of the horizontal and vertical permeability data in the method of determining φ-K relationships when such data is available.
In this way, it is possible to represent simultaneously the horizontal permeability distribution and the vertical permeability distribution within an underground reservoir by a translation vector and by a single set of φ-K relationships.
Specifically, the inventors have observed that the φ-K relationships that reproduce the greatest number of vertical permeability measurements can be deduced, to a first approximation, merely by shifting the parameters of the φ-K relationships that reproduce the greatest number of horizontal permeability measurements.
Thus, and in particularly advantageous manner, the invention makes it possible to improve the representativity of the φ-K relationships that are selected by taking account of the correlation that exists between the results of the first and second counting steps.
In another particular implementation of the invention, the method further comprises a normalization step for normalizing the first and second intensity signals prior to the estimation step for estimating said translation vector.
In a particular implementation, the various steps of the determination method are determined by computer program instructions.
Consequently, the invention also provides a computer program on a data medium, the program being suitable for being performed in a computer, the program including instructions adapted to performing steps of a determination method as described above.
The program may use any programming language, and be in the form of source codes, object codes, or codes intermediate between source code and object code, such as in a partially compiled form, or in any other desirable form.
The invention also provides a computer-readable data medium including instructions of a computer program as mentioned above.
The data medium may be any entity or device capable of storing the program. For example, the medium may comprise storage means such as a read only memory (ROM), a random access memory (RAM), a programmable read only memory (PROM), an electrically programmable read only memory (EPROM), a compact disk (CD) ROM, or indeed magnetic recording means, e.g. a floppy disk or a hard disk.
Furthermore, the data medium may be a transmissible medium such as an electrical or optical signal that is conveyed by an electrical or optical cable, by radio, or by other means. The program of the invention may in particular be downloaded from an Internet type network.
Alternatively, the data medium may be an integrated circuit in which the program is incorporated, the circuit being adapted to execute or to be used in the execution of the method in question.
The invention also provides a determination device for determining a plurality of first relationships associating permeability with porosity within an underground reservoir, e.g. a device configured to estimate the permeability distribution within an underground reservoir, in particular from a set of measurements of porosity and of permeability taken within the reservoir. The device comprises:
The determination device is configured to perform the determination method as defined above.
In another aspect, the present invention provides a method of estimating at least one mean permeability for a set of wells in an underground reservoir. The method comprises:
The inventors have observed that the experimental distribution of porosity data within a reservoir can be reproduced correctly by a probability relationship. It may be observed that a probability relationship is generally advantageously defined by a small number of parameters, e.g. two parameters for a normal relationship and three parameters for an asymmetric normal relationship.
The invention thus proposes representing a porosity distribution of a set of wells of an underground reservoir by a probability relationship.
When the expression for the probability relationship involves only a limited number of parameters, these parameters enable the porosity distribution of all of the wells to be represented effectively in full.
Furthermore, the permeability distribution in this set of wells is associated with the corresponding porosity distribution by a set of φ-K relationships that have been determined beforehand.
Consequently, the rock formation constituting the reservoir is described for a set of wells by a porosity distribution modeled by a probability relationship and by a permeability distribution modeled by a set of φ-K relationships.
Naturally, the invention also makes it possible to model a porosity distribution for a set of wells or for only one well, depending on the scale desired for analysis.
In a particular implementation of the invention, the obtaining step for obtaining a probability relationship is performed by minimizing a target function taking account of at least one term from among the following three terms:
Thus, the porosity distribution is represented by a probability relationship that best reproduces simultaneously the porosity distribution and the mean of the porosity and permeability distributions.
More particularly, and in a particular implementation of the invention, said plurality of first relationships is defined by the relationship log(Kh)=(Ai·f(ϕ)+Bi) where Kh is a horizontal permeability, Ai and Bi are two real parameters belonging to a determined region of space defined by the parameters A, B and where f is the identity function or the log function; and
(
where LPS is the probability relationship minimizing the target function.
In another particular implementation of the invention, said plurality of first relationships is defined by the relationship log(Kv)=(Avi.f(ϕ)+Bvi) where Kv is a vertical permeability, Avi and Bvi are two real parameters belonging to a determined region of space defined by the parameters Av, By and where f is the identity function or the log function; and
(
where LPS is the probability relationship minimizing the target function.
In a particular implementation of the invention, the method further comprises an obtaining step for obtaining a plurality of third relationships associating porosity to vertical permeability on the basis of at least the result of the second counting step, and in which:
Thus, the estimation method also makes it possible to estimate the horizontal total mean permeability by appropriately defining the target function that is to be minimized in order to obtain the probability relationship representing the porosity distribution.
In a particular implementation of the invention, the plurality of first relationships is defined by the relationship log(Kh)=(Ai·f(ϕ)+Bi) where Kh is a horizontal permeability, Ai and Bi are two real parameters belonging to a determined region of space defined by the parameters A, B and where f is the identity function or the log function;
(
where LPS is the probability relationship minimizing the target function.
In a particular implementation of the invention, the method further comprises an obtaining step for obtaining a plurality of third relationships associating porosity with vertical permeability on the basis of at least the result of the second counting step, and wherein:
(
where LPS is the probability relationship minimizing the target function.
In a particular implementation of the invention, the obtaining step for obtaining a probability relationship is performed on the basis of at least said plurality of second relationships, the method further comprising an estimation step for estimating at least one total vertical mean permeability on the basis of at least the probability relationship and of said plurality of second relationships.
In other words, in this particular implementation of the invention, the estimation method makes it possible simultaneously to estimate the horizontal total mean permeability and the vertical total mean permeability.
This joint estimation of the horizontal total mean permeability and of the vertical total mean permeability makes it necessary to define appropriately the target function that is to be minimized in order to obtain the probability relationship that represents the porosity distribution.
Thus, in a particular implementation of the invention, the obtaining step for obtaining a probability relationship is performed by minimizing a target function taking account of at least one term from among the following three terms:
In a particular implementation of the invention, the plurality of first relationships is defined by the relationship log(KH)=(Ai·f(ϕ)+Bi) where Kh is a horizontal permeability, Ai and Bi are two real parameters belonging to a determined region of space defined by the parameters A, B and where f is the identity function or the log function;
(
where LPS is the probability relationship minimizing the target function; and
In a particular implementation of the invention, the probability relationship is a normal relationship or a linear combination of normal relationships.
In another particular implementation of the invention, the probability distribution is an asymmetric normal relationship.
It should be recalled that an asymmetric normal relationship LNA(φ) is defined from its mode m, its standard deviation S1, and its asymmetry coefficient S1/S2 by means of the equation:
m, Si, and S2 being three real coefficients.
In a particular implementation of the invention, the coefficient Ch is greater than 0.75 and less than 1.
In a particular implementation of the invention, the coefficient Cv is greater than 0 and less than 0.25.
In a particular implementation, the various steps of the estimation method are determined by computer program instructions.
Consequently, the invention also provides a computer program on a data medium, the program being suitable for being performed in a computer, the program including instructions adapted to performing steps of a estimation method as described above.
The program may use any programming language, and be in the form of source codes, object codes, or codes intermediate between source code and object code, such as in a partially compiled form, or in any other desirable form.
The invention also provides a computer-readable data medium including instructions of a computer program as mentioned above.
The data medium may be any entity or device capable of storing the program. For example, the medium may comprise storage means such as a ROM, a RAM, a PROM, an EPROM, a CD ROM, or indeed magnetic recording means, e.g. a floppy disk or a hard disk.
Furthermore, the data medium may be a transmissible medium such as an electrical or optical signal that is conveyed by an electrical or optical cable, by radio, or by other means. The program of the invention may in particular be downloaded from an Internet type network.
Alternatively, the data medium may be an integrated circuit in which the program is incorporated, the circuit being adapted to execute or to be used in the execution of the method in question.
The invention also provides an estimation device for estimating at least a mean permeability for a set of wells of an underground reservoir, the device comprising:
The estimation device is configured to perform the estimation method as defined above.
In yet another aspect, the present invention also provides a calculation method for calculating a mean permeability at a location of an underground reservoir. The method comprises:
The invention thus makes it possible to estimate the permeability distribution at any point in a reservoir from a plurality of φ-K relationships and using a model in the form of probability relationships for porosity distributions at a plurality of wells in an underground reservoir.
In a particular implementation, the calculation method further comprises a calculation step for calculating a mean porosity at the location from at least the probability relationship at the location.
In a particular implementation, the various steps of the method of calculating a mean permeability are determined by computer program instructions.
Consequently, the invention also provides a computer program on a data medium, the program being suitable for being performed in a computer, the program including instructions adapted to performing steps of a method of calculating a mean permeability as described above.
The program may use any programming language, and be in the form of source codes, object codes, or codes intermediate between source code and object code, such as in a partially compiled form, or in any other desirable form.
The invention also provides a computer-readable data medium including instructions of a computer program as mentioned above.
The data medium may be any entity or device capable of storing the program. For example, the medium may comprise storage means such as a ROM, a RAM, a PROM, an EPROM, a CD ROM, or indeed magnetic recording means, e.g. a floppy disk or a hard disk.
Furthermore, the data medium may be a transmissible medium such as an electrical or optical signal that is conveyed by an electrical or optical cable, by radio, or by other means. The program of the invention may in particular be downloaded from an Internet type network.
Alternatively, the data medium may be an integrated circuit in which the program is incorporated, the circuit being adapted to execute or to be used in the execution of the method in question.
The invention also provides a device for calculating a mean permeability at a location of an underground reservoir. The device comprises:
Particular characteristics and advantages of the present invention appear from the detailed description given below with reference to the accompanying figures, in which:
In the following examples, the wells that are described are vertical wells. As an alternative, it is equally possible to implement the invention in the context of wells that are not vertical.
Thus, the determination device 3 comprises in particular a processor 3A, a ROM 3B, a RAM 3C, a non-volatile memory 3D, and communication means 3E.
The ROM 3B of the determination device constitutes a data medium readable by the processor 3A and storing a computer program in accordance with the invention including instructions for executing steps of a determination method of the invention for determining a plurality of first relationships associating permeability with porosity within an underground reservoir, the steps of the determination method being described below with reference to
In equivalent manner, the computer program defines functional modules of the determination device, such as in particular an obtaining module 3B1 for obtaining a plurality of measurement points comprising a porosity data value and a first permeability data value, a definition module 3B2 for defining a family of relationships associating porosity with at least one permeability, a first counter module 3B3 for each relationship of the family of relationships, for counting measurement points of the plurality of points that are reproduced by the relationship so as to obtain a first intensity of points associated with each relationship, and a selector module 3B4 for selecting a plurality of first relationships from the family of relationships on the basis of at least the result of the counting performed by the first counter module. The obtaining module 3B1 for obtaining a plurality of measurement points makes use in particular of the communication means 3E.
There follows a description with reference to
It is assumed that during a step E100, the determination device 3 acquires a set of measurements of permeability (specifically of a “first” permeability in the meaning of the invention) and of porosity within the reservoir 1.
By way of example, the porosity as acquired in this way may comprise measurements of useful porosity obtained by applying a cutoff. In other words, the measurements of useful porosity are measurements of porosity lying within a range of porosity values defined by a low threshold.
With reference to
In a variant, the measurements φi may be obtained by analyzing results of logging performed within the reservoir 1.
In the presently-described example, the set of measurements φi, Ki is obtained at the scale of the reservoir 1.
In a variant, the set of measurements φi, Ki is obtained at the scale of a subset of the wells of the reservoir 1.
In
In the presently-described example, the permeability measurements Ki are horizontal permeability measurements.
In a variant, the permeability measurements Ki could be vertical permeability measurements.
In the presently-described implementation, additional measurement points φi, K′i are added to the measurement point during a step E150. In the description below, the added measurement points φi, K′i are also written φi. Ki.
A detailed implementation of the step E150 is shown in non-limiting manner in
During a step E200 of the method, a semi-log or log-log model is selected as a function of the intrinsic nature of the rock constituting the reservoir 1. In the presently-described example, the model selected during this step and corresponding best to the properties of the rock constituting the reservoir is a log-log model.
Thus, the family of φ-K relationships is defined by the equation log(K)=B·log(q))+A, depending on two parameters A and B.
Thereafter, a new cloud of points log(φi), log(Ki) is obtained in step E300, as shown in
This image may optionally be smoothed during a step E350, e.g. by performing Gaussian filtering, so as to be easier to use.
During a step E400, low and high bounds are selected for the coefficients A and B. This selection may be carried out as a function of the usual values for the parameters of φ-K relationships.
In the example of
For each pair of coefficients A and B, in the context of these bounds, the straight line of equation y=A·x+B is determined in the space of the log(φ), log(K) representation of
In order to take account of the distribution of points along the straight line in question, the result of the count may optionally, but advantageously, be multiplied by the product of the variance σ(log(φi)) as evaluated on all of the cloud of points of the distances to the model of each of the points along the log(φ) axis, multiplied by the variance σ(log(Ki)) as evaluated for all of the cloud of points for the distances to the curve representing the φ-K relationship for each of the points along the log(K) axis.
The value obtained for each pair A, B is representative of the match between the φ-K relationship and the cloud of points, and in the implementation in which the result is weighted by the above-mentioned product of variances, the value obtained increases if the cloud of points is distributed along the line representing the φ-K relationship in the log(φ), log(K) representation space.
During a step E600, for each pair A, B within the limits defined by the minimum and maximum bounds for these variables in step E400, the result of the counting, possibly weighted as mentioned above, is converted into the form of an intensity associated with the corresponding points in the space of the values A, B.
Thereafter, during a step E700, a region in the (A, B) space is selected that corresponds to a set of relationships describing the relationship between log(q) and log(K) and corresponding to acceptable φ-K relationships. By way of example, this selection is performed by selecting all of the intensities that exceed a threshold, e.g. as set by the user.
In a variant, the sum of intensities in the space of the values A, B as shown in
Unlike the prior art, in which a regression is performed in order to provide a single φ-K relationship, the estimation method of the invention makes it possible to obtain a probabilistic set of φ-K relationships that is more representative of the distribution of the measurements of porosity and permeability.
It should be observed that the calculation of (A, B) φ-K relationships described above for a log-log model is equally applicable to a semi-log model or to any other model that may be selected by the person skilled in the art by replacing the log(φ), log(K) representation space of
With reference to
During the step F100, a permeability data series KiDST (constituting second permeability values in the meaning of the invention) associated with an uncertainty σiDST is obtained by interpreting measurements taken from formation tests carried out within the reservoir 1.
For each of these values, a unitary theoretical distribution of the logarithm of the permeability is calculated (step F200) by convolution of the data points with a Gaussian distribution of mean (log(KiDST), having a standard deviation log(σiDST) and of amplitude that is calculated in such a manner that the integral over R of the Gaussian distribution is equal to 1.
The unitary theoretical distributions associated with each of the permeability values KiDST are then added in a step F300 in order to form a global theoretical distribution.
During a step F400, the determination device also calculates the distribution of the logarithm of the values Ki of the existing measurement points, which distribution is then quantified in order to obtain a real histogram Dist2.
In the presently-described implementation, the quantification is uniform scalar quantification, with the quantification stepsize and the decision levels being selected by a reservoir engineer or by a geologist, for example.
In another implementation, the quantification used is non-uniform scalar quantification.
During a step F450, the global theoretical distribution is quantified in order to obtain a global theoretical histogram Dist1, with this discretization being performed using the same quantification stepsize and the same decision levels as for quantification of the distribution of the logarithm of the values Ki. In other words, the classes (i.e. the intervals) of the histogram Dist1 are equal to the classes of the histogram Dist2.
Thereafter (step F500), the determination device 3 calculates the probability-normalized product (i.e. the integral over R of the product is normalized relative to 1) of the two histograms Distl and Dist2 in order to identify their intersection.
The intersection of the two histograms Dist1 and Dist2 serves to identify permeability measurements coming from the analysis of sample cores that corroborate permeability measurements coming from analyzing formation tests.
During a step F550, the determination device 3 acquires a total number Nt of additional measurement points to be added to the existing measurement points (φi, Ki).
For each of the intervals w associated with a log(Kw) value for which there is a non-zero intersection of the two distributions Dist1 and Dist2, the determination device 3 determines a number N′ of additional measurement points (step 550) and randomly selects N′ additional measurement points (step F600) from the set of existing measurement points (φi, Ki) for which log (Kw) is equal to the quantified value of log(Ki).
It should be observed that the number N′ is determined as being the product of the value of the products of the two distributions Dist1 and Dist2 evaluated over the interval w multiplied by the total number Nt of additional measurement points to be added to the existing measurement points (φi, Ki).
The previously selected additional measurement points are then added to the measurement points (φi, Ki) during a step F700.
With reference to
It is assumed that during a step G100, the determination device 3 acquires a set of measurements of porosity, of horizontal permeability (of “first” permeability data in the meaning of the invention), and of vertical permeability (of “third” permeability data in the meaning of the invention) within the reservoir 1. With reference to
In the presently-described implementation, additional measurement points are added to the measurement points φi, KHi during the step G150. Likewise, additional measurement points are added to the measurement points (φi, KVi) during the step G160.
In a variant, no additional measurement point is added to the measurement points (φi, KHi).
In another variant, no additional measurement point is added to the measurement points (φi, KVi).
It should be observed that formation tests make it possible to obtain horizontal permeability values K′Hi and vertical permeability values K′Vi, which values are obtained by tests of the modular dynamic tester (MDT) type or by using measurements of the repeat formation tester (RFT) type.
The step G150 and the step G160 are performed in similar manner to the step E150 as illustrated in non-limiting manner in above-described
During a step G200 of the method, a model, e.g. a semi-log or a log-log model, is selected as a function of the intrinsic nature of the rock constituting the reservoir 1. In the presently-described example, the model selected during this step and corresponding best to the properties of the rock constituting the reservoir is a semi-log model.
Thus, the family of φ-K relationships is defined by the equation log(K)=A·φ+B that depends on the two parameters A and B.
During a step G300, low and high bounds are selected for the coefficients A and B. This selection may be made as a function of the parameters of usual φ-K relationships. In the presently-described example, A lies in the range −14 to 0, and B lies in the range 0 to 14.
Thereafter, during a step G400, the determination device 3 calculates the horizontal Radon image, written RadonH, for the data pairs φi, KHi. More precisely, during this step G400, the cloud of φi, log(KHi) points is represented in the form of an optionally filtered intensity image. For each pair of values A and B, the points φi, log(KHi) at a distance from the straight line of equation y=A·x+B in the space of the (p, log(K) representation is below a threshold, e.g. estimated from the resolution of the intensity image, are counted and the possibly-weighted result of the counting is represented in the form of an intensity associated with the corresponding point in the Radon space of the values A, B.
Likewise, during a step G500, the determination device 3 calculates the vertical Radon image, written RadonV, of the data pairs φi, KVi by counting the points log(Kvi) at a distance from the straight line having the equation y=A·x+B in the space of the φ, log(K) representation that is below a threshold, e.g. as estimated from the resolution of the intensity image.
Thereafter, during a step G600, the determination device 3 calculates the intercorrelation between the RadonH and RadonV images and identifies a maximum in this intercorrelation signal. This intercorrelation is shown in
Thereafter, in a step G700, the determination device 3 shifts the RadonV image along a translation vector (dA, dB) prior to calculating the RadonHV image corresponding to the product of the RadonH image multiplied by the shifted RadonV image (step G800). A RadonHV image is shown in
Thereafter, during a step G900, a region of the (A, B) space is selected that corresponds to the set of relationships between φ and log(KH) that correspond to acceptable φ-K relationships. By way of example, this selection may be performed by selecting all intensities exceeding a threshold, which threshold may be set previously by the user, or a probability if the image has been normalized (the sum of the pixels of the image being equal to 1).
All φ-K relationships that acceptably describe the relationship between φ and log(KV) correspond to using a translation vector (dA, dB) to shift the parameters A and B corresponding to the region previously.
In the presently-described example, the same low and high bounds are selected for the coefficients A and B when determining the images RadonH and RadonV.
In a variant, different bounds could be used when determining the images RadonH and RadonV, providing the RadonV image is interpolated over the coordinates of the RadonH image prior to calculating the intercorrelation between the two images.
With reference to
In this example, mean permeability along the well is obtained by using an asymmetric normal relationship. That said, other probability relationships could be used.
The estimator device 4 has the hardware architecture of a computer. Thus, the estimator device 4 comprises in particular a processor 4A, a ROM 4B, a RAM 4C, a non-volatile memory 4D, and communication means 4E.
The ROM 4B of the estimator device constitutes a data medium that is readable by the processor 4A and storing a computer program in accordance with the invention including instructions for executing steps of an estimation method for estimating a mean permeability within an underground reservoir in accordance with the invention, the steps of this estimation method being described below with reference to
In equivalent manner, the computer program defines functional modules of the estimator device, such as in particular an obtaining module 4B1 for obtaining a porosity data distribution for the portion of the well, a determination device 4B2 for determining a plurality of first relationships associating porosity with permeability for the portion of the well in accordance with the invention, an obtaining module 4B3 for obtaining an asymmetric normal relationship approximating the porosity data distribution on the basis of at least said plurality of first relationships, and an estimator module 4B4 for estimating the mean permeability along the portion of the well from at least the asymmetric normal relationship and said plurality of first relationships. The obtaining module 4B1 for obtaining a porosity data distribution for the portion of the well and the determination device make use in particular of the communication means 4E.
With reference to
With reference also to
In a variant, porosity φ′(z) along the portion S of the well 2 may be measured by analyzing sample cores, providing the corresponding porosity measurements are representative, i.e. regular and not spaced too far apart along the axis z.
During a step H200, a porosity data histogram φ′(z) is obtained. In other words, the porosity data φ′(z) obtained in step H100 is quantified, e.g. by a uniform scalar quantifier. The experimental histogram Dist3 of this discretized data, an example of which is shown in
is satisfied.
In the presently-described example, the estimator device acts during step H300 to calculate a set of φ-K relationships associating porosity with horizontal permeability for the section S of the well by applying a determination method in accordance with the invention for determining such a set of relationships. The φ-K relationships obtained in this way are expressed in the form log(Kh)=(Ai·f(ϕ′)+Bi) where Kh is a horizontal permeability, Ai and Bi are two real parameters belonging to a determined region of cardinal number N of the space defined by the parameters A, B, and where f is the function f(φ′)=φ′ or the function f(φ′)=log(φ′) or any other mathematical function.
Thereafter, during a step H400, the estimator device determines the parameters of the asymmetric normal relationship LNAS (φ′; mS, S1,s, S1,s/S2,s) that minimizes a target function E=αE1+(1−α)[(1−β)E3+βE2], where α and β are two positive coefficients that are less than one, and where:
favors asymmetric normal relationships that best approximate the experimental porosity distribution;
E
2=(
favors asymmetric normal relationships LNA(m, S1, S1/S2) of mean value
favors asymmetric normal relationships for which the values of the horizontal mean permeability as defined by the equation
calculated by applying the relationship
log(Khj(Ai,Bi,ϕj′))=(Ai·f(φ′j)+Bi)
to the experimental porosity data φi′ are close to the horizontal mean permeability values
The target function E is minimized, e.g. by using the method of conjugate gradients using as the initial point (m, S1, Si/S2)=(
During step H500, at least one horizontal mean permeability
In other words, the horizontal mean permeability
In the above-described embodiment, the estimator device estimates a horizontal mean permeability.
In another embodiment, the estimator device estimates a vertical mean permeability by:
and then during step H500, calculating at least one vertical mean permeability from the equations:
In another embodiment, the estimator device estimates a total horizontal mean permeability by:
and where 0.75<Ch<1 (the low bound of this coefficient being determined for example by the user as a function of the nature of the reservoir) and, during the step H500, calculating at least one total horizontal mean permeability from the equations:
In another embodiment, the estimator device estimates a total vertical mean permeability by:
and where 0<Cv<0.25 (the high bound of this coefficient being determined for example by the user as a function of the nature of the reservoir) and during the step H500, calculating at least one total vertical mean permeability from the equations:
With reference to
During a step M100, the estimator device 4 acquires a measurement of the porosity φ′(z) along the portion S of the well 2.
During a step M200, the porosity data φ′(z) obtained in step M100 is made discrete occupying n values and the experimental distribution Dist3 of the discrete data ϕi′ is calculated. This experimental distribution Dist3 is characterized by the frequencies Fi at which each of the values for ϕi′ occurs. It should be observed that by definition the following relationship is true:
In the presently-described example, the estimator device 4 acts during the step M300 to calculate a first set of φ-K relationships associating porosity with horizontal permeability for the section S of the well 2 by applying a method in accordance with the invention for determining such a set of relationships. The first set of φ-K relationships as obtained in this way is expressed in the form log(Kh)=(Ai·f(ϕ′)+Bi), where Kh is a horizontal permeability, Ai and Bi are two real parameters belonging to a determined region of cardinal number N of the space defined by the parameters A, B, and f is the function f(φ′)=φ′ or the function f(φ′)=log(φ′).
During step M300, while performing the determination method, the estimator device 4 also determines a second set of φ-K relationships associating porosity with vertical permeability for the section S of the well 2. This second set of φ-K relationships is expressed in the form log(Kv)=((Ai+dA)·f(ϕ′)+Bi+dB), where Kv is a vertical permeability and dA and dB are two real parameters.
Thereafter, during a step M400, the estimator device determines the parameters of the asymmetric normal relationship LNAS(φ′; mS, S1,s, S1,s/S2,s) that minimizes a target function E=αE1+(1−α)[(1−β)E3+βE2], where α and β are two positive coefficients that are less than one, and where:
favors asymmetric normal relationships that best approximate the experimental porosity distribution;
E
2=(
favors asymmetric normal relationships LNA(m, S1, S1/S2) of mean value
favors asymmetric normal relationships for which:
and 0.75<Ch<1) as calculated after applying the relationships:
log(Khj(Ai,Bi))=(Ai·f(ϕ′j)+Bi)
and
log(Kvj(Ai,Bi))=((Ai+dA)·f(ϕ′j)+Bi+dB)
to the experimental porosity data φi′ are close to the values of the total horizontal mean permeability
and
0<Cv<0.25) calculated after applying the relationships:
log(Khj(Ai,Bi))=(Ai·f(ϕ′j)+Bi)
and
log(Kvj(Ai,Bi))=((Ai+dA)·f(ϕ′j)+Bi+dB)
to the experimental porosity data φi′ are close to the values of the total vertical mean permeability
The target function E is minimized, e.g. by using the conjugate gradient method with as the initial point (m, S1, S1/S2)=(
During the step M500, at least one total horizontal mean permeability
In other words, the total horizontal mean permeability
where LNAS is the asymmetric normal relationship minimizing the target function E.
During the step M600, the estimator device determines the total vertical mean permeability
With reference to
Thus, the calculation device 5 comprises in particular a processor 5A, a ROM 5B, a RAM 5C, a non-volatile memory 5D, and communication means 5E.
The ROM 5B of the calculation device constitutes a data medium that is readable by the processor aA and that stores a computer program in accordance with the invention comprising instructions for executing steps of a calculation method for calculating a mean permeability in accordance with the invention, the steps of the calculation method being described below with reference to
In equivalent manner, the computer program defines functional modules of the calculation device, such as in particular a selection module 5B1 for selecting a set of wells of a reservoir, a determination device 5B2 for determining a plurality of first relationships, an obtaining module 5B3 for obtaining a porosity data distribution, an obtaining module 5B4 for obtaining a probability relationship, a calculation module 5B5 for calculating a probability relationship, and a calculation module 5B6 for calculating the mean permeability.
With reference to
In a step J100, the calculation device 5 selects a set of wells of the reservoir 1. In the presently-described example, the set of wells contains a plurality of wells 2.
In a step J200, the calculation device 5 determines a plurality of first φ-K relationships associating permeability with porosity for the set of selected wells. In order to perform this determination, the calculation device 5 makes use of the determination device 5B2.
For each of the wells of the set of wells selected in step J100, the calculation device 5 obtains a porosity data distribution for the well and an asymmetric normal relationship approximating this porosity data distribution on the basis of the plurality of first φ-K relationships (step J300). By way of example, the asymmetric normal relationship is obtained in compliance with above-described steps H200, H300, and H400. It is also assumed that the uniform scalar quantifier used during step H200 is the same for each of the wells of the set of selected wells.
During step J400, the calculation device 5 calculates an asymmetric normal relationship LNAx,y at the location (x, y) from the asymmetric normal relationships obtained for each of the wells during the step J300.
More precisely, the parameters m, S1, and S2 of the asymmetric normal relationship at the location (x, y) are obtained by interpolation (e.g. linear interpolation) of the parameters m, S1, and S2 of the asymmetric normal relationships obtained for each of the wells during the step J400.
It should be observed that this asymmetric normal relationship LNAx,y represents the porosity distribution at the location (x, y).
Thereafter, during the step J500, the calculation device 5 calculates a mean permeability at the location (x, y) by using the asymmetric normal relationship at the point (x, y), and one of the φ-K relationships from the plurality of first φ-K relationships.
For example, when the permeability is a horizontal permeability, the mean of the horizontal permeability
where Ai and Bi are coefficients that define the relationship selected from the plurality of φ-K relationships.
In a variant, when the permeability is a vertical permeability, the mean
1/
where Ai and Bi are coefficients that define the relationship selected from the plurality of φ-K relationships, ϕj′ representing the quantified values associated with a porosity value interval.
It should be observed that the asymmetric normal relationship LNAx,y also serves in step J600 to calculate the mean porosity at the point (x, y) of the reservoir. This mean porosity at the point (x, y) is given by the formula:
Number | Date | Country | Kind |
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1555885 | Jun 2015 | FR | national |
Filing Document | Filing Date | Country | Kind |
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PCT/FR16/51557 | 6/24/2016 | WO | 00 |