EP3314547A1 - Procede et dispositif de determination d'une permeabilite au sein d'un reservoir - Google Patents
Procede et dispositif de determination d'une permeabilite au sein d'un reservoirInfo
- Publication number
- EP3314547A1 EP3314547A1 EP16741667.6A EP16741667A EP3314547A1 EP 3314547 A1 EP3314547 A1 EP 3314547A1 EP 16741667 A EP16741667 A EP 16741667A EP 3314547 A1 EP3314547 A1 EP 3314547A1
- Authority
- EP
- European Patent Office
- Prior art keywords
- permeability
- laws
- law
- porosity
- probability
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Withdrawn
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Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N7/00—Computing arrangements based on specific mathematical models
- G06N7/02—Computing arrangements based on specific mathematical models using fuzzy logic
- G06N7/06—Simulation on general purpose computers
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V11/00—Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00
- G01V11/002—Details, e.g. power supply systems for logging instruments, transmitting or recording data, specially adapted for well logging, also if the prospecting method is irrelevant
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N7/00—Computing arrangements based on specific mathematical models
- G06N7/01—Probabilistic graphical models, e.g. probabilistic networks
Definitions
- the invention is in the field of underground reservoir storage of compressible fluids or deposits of hydrocarbons or gases, whether natural deposits or artificial stocks.
- FIG. 1 represents a reservoir 1 containing, for example, hydrocarbons.
- the hydrocarbons are extracted from the reservoir by wells 2.
- These wells 2 correspond to cylinders extending here vertically through the reservoir 1 (non-vertical wells may also exist).
- the rock formation constituting the reservoir 1 is described using the two complementary parameters that are the porosity and the permeability.
- the porosity measures the percentage of pores in the rock that may contain hydrocarbons while the permeability describes the rock's ability to let the fluids flow horizontally (horizontal permeability Kh) or vertically (vertical permeability Kv), this capacity being able to on the other hand, calculated over the entire height of the tank (total horizontal permeability or total vertical permeability).
- the porosity ⁇ and the permeability K along a well 2 can be measured by the analysis of the cores taken from the reservoir rock, for example during the drilling of the well. This gives a set of discrete porosity and permeability measurements for each well 2.
- the ability to perform a measurement on a sample core depends on its consolidation or cementation. In some reservoirs the levels of weak consolidation, corresponding to the highest permeabilities, can not be sampled, which introduces a bias in the representativeness of the measurements.
- the number of wells implemented for a tank is limited.
- the number of porosity and permeability measurements along a well, along its depth is also limited.
- a ⁇ - ⁇ law is determined by a regression implemented from a set of porosity and permeability measurements made for a set of wells.
- the present invention therefore aims, according to a first aspect, a method for determining a plurality of first laws connecting the permeability to porosity within an underground reservoir, for example to estimate the permeability distribution within a underground reservoir, in particular from a set of porosity and permeability measurements carried out within this reservoir.
- This process comprises:
- a step of defining a family of laws connecting the porosity to at least one permeability (laws ⁇ - ⁇ );
- This method can be implemented by a computer system.
- the invention thus proposes to represent the permeability distribution within an underground reservoir by a set of laws ⁇ - ⁇ representing in a simple manner the relation between the permeability and the porosity within the reservoir, the laws of this set being selected for example as the laws for which the result of the enumeration step exceeds a threshold.
- the determination method is based on an analysis of the reproducibility by a family of ⁇ - ⁇ laws of a set of porosity and permeability measurements.
- This set of measurements can be obtained at the scale of the reservoir, a subset of wells in the reservoir or at a single well.
- we obtain a family of laws cp-K for the whole of the reservoir whereas in the last case the family of laws cp-K is only representative of the relation between porosity and permeability on the scale of a single well. For example, it is up to a geologist to segment the reservoir into subsets of wells with the same characteristics in order to calculate different cp-K laws for each of these subsets.
- a measurement is reproduced by a law cp-K when the distance between the point representing this measurement and the curve representing the law cp-K is less than a threshold, this distance being evaluated in space ( cp, K) or in a derived space obtained after a change of variable.
- said selected plurality of laws is chosen from among the laws of the family reproducing at least a minimum number of measurement points of the plurality of measurement points.
- the most representative law by selecting a law corresponding to at least a maximum of the result of the count.
- an enumeration result is weighted to be larger if law-reproduced measurement points are distributed along the neighborhood of the curve representing that law. This makes it possible to favor, for selection, laws that are corroborated by the measurement points over a wider range of values.
- the count result is weighted proportionally to the product of the variances of the components of the plurality of transformed points.
- the laws linking the porosity to the permeability are parameterized by at least two parameters.
- the laws of the family of law are semi-log or log-log laws.
- the logarithm (in base 10) of the permeability is generally correlated with either the porosity ⁇ (semi-log law) or the logarithm (in base 10) of the porosity (law log-log).
- the shape of the laws ⁇ - ⁇ , semi-log or log-log depends on the intrinsic nature of the rock constituting the reservoir and those skilled in the art will be able to choose the adapted form according to this rock.
- the laws of the family of laws are semi-log laws defined by two parameters A and B and the enumeration step comprises:
- the cloud of points (ci, log (Kj)) is represented as an intensity image, the value of each of the points of this image being proportional to the number of data ( ⁇ ,, log (K) observed.
- the selected plurality of laws cp-K is represented by a set of pairs A i ( B, for which this count exceeds a threshold.
- This enumeration corresponds substantially to an integration of this distance for these points along the line considered, each point having the same weight, operation intellectually similar to the curvilinear integrals of the Radon transform used in other domains.
- the laws of the family of laws are log-log laws defined by two parameters A and B and the enumeration step comprises:
- the method according to the invention further comprises a step of smoothing the intensity image prior to enumeration.
- the smoothing of the intensity image makes it possible to limit the excessive disparities between neighboring pixels that are generated by the uncertainty in the measurements of the porosity and permeability data.
- obtaining the porosity data and the first permeability data comprises an analysis of sample cores from the reservoir or an analysis of logging measurements, and the step of obtaining further comprises a step of adding additional measurement points in the first plurality of points, the additional added measurement points being selected from the first plurality of measurement points from the analysis of the second permeability data obtained. from at least one training test carried out within the tank.
- an additional measurement point is therefore a measurement point extracted from the data ( ⁇ ,, ⁇ ,) and which is then added to these same measurements ( ⁇ ,, ⁇ ,) in order to determine the plurality of first laws connecting porosity to permeability.
- the ability to perform a measurement on a sample core depends on its consolidation or cementation. In some reservoirs the levels of weak consolidation, corresponding to the highest permeabilities, can not be sampled, which introduces a bias in the representativeness of the measurements.
- the invention makes it possible to correct this bias by improving the representation of the permeability distribution within an underground reservoir by aggregating permeability data from various sources.
- DST Drill Stem Testing
- the associated measurements that incorporate the permeability over a significant depth of the reservoir are taken into account to determine the cp-K laws.
- the training tests make it possible to obtain horizontal permeability data and vertical permeability data, the latter being obtained by Modular Dynamic Tester (MDT) type tests or using type RFT (in English “Repeat Training Tester”).
- MDT Modular Dynamic Tester
- RFT in English “Repeat Training Tester”
- the adding step further comprises:
- a step of obtaining a real histogram of the logarithm of the first permeability data (that is to say a discrete distribution obtained by quantization of the distribution of the logarithm of the first porosity data) obtained by core analysis or logging analysis;
- the determination method firstly determines a theoretical histogram of the logarithm of the permeability measured by the formation tests, said histogram of the permeabilities of the tests based on the uncertainties relating to the interpretation of the tests. More precisely, this histogram of the permeabilities of the tests is a discrete distribution obtained by quantization of the distribution of the logarithm of the permeability measured by the formation tests.
- the determination method determines the probability that a permeability resulting from the formation tests corresponds to a permeability resulting from another method. This probability corresponds to the product of the theoretical histogram of the permeabilities of the tests with the histogram of the logarithm of the permeabilities obtained from the permeability measurements obtained by the analysis of cores or logs.
- the determination method randomly selects additional measurement points from the set of existing measurement points ( ⁇ i, Ki) for which the permeability obtained from the formation tests corresponds to the permeability K ,.
- This random selection is implemented by performing for example a draw according to a uniform probability law.
- the first permeability data and the second permeability data are horizontal permeabilities.
- the first permeability data and the second permeability data are vertical permeabilities.
- the determination method according to the invention is independent of the anisotropic nature of the permeability of the reservoir.
- the family of laws is parameterized by a plurality of parameters
- the permeability is a horizontal permeability
- the method furthermore comprises:
- a step of translation of the translation vector of the second intensity signal takes into account at least the analysis of the first intensity signal and the second intensity signal, said method further comprising determining a plurality of second laws connecting the vertical permeability to the porosity, said plurality second laws being obtained from said plurality of first laws by translation of the parameters by the translation vector.
- the family of laws is parameterized by a plurality of parameters and the method furthermore comprises:
- Said selection step takes into account at least the analysis of the first intensity signal and the second intensity signal, said method further comprising the determination of a plurality of second laws connecting the horizontal permeability with the porosity, the plurality of second law being obtained from the plurality of first laws by translation of the parameters by the vector.
- the invention thus makes it possible to take into account all the horizontal and vertical permeability data in the method for determining the laws ⁇ - ⁇ when these data are available.
- the invention makes it possible to improve the representativity of the selected ⁇ - ⁇ laws by taking into account the correlation existing between the results of the first and second enumeration steps.
- the method further comprises a step of normalizing the first and the second intensity signal prior to the step of estimating said translation vector.
- the various steps of the determination method are determined by computer program instructions. Consequently, the invention also relates to a computer program on an information medium, this program being capable of being implemented in a computer, this program comprising instructions adapted to the implementation of the steps of a determination method as described above.
- This program can use any programming language, and be in the form of source codes, object codes, or intermediate codes between source code and object code, such as in a partially compiled form, or in any other desirable shape.
- the invention also relates to a computer-readable information medium, comprising instructions of a computer program as mentioned above.
- the information carrier may be any entity or device capable of storing the program.
- the medium may comprise storage means, such as a ROM, RAM, PROM, EPROM, a CD-ROM or, or a magnetic recording medium, for example a floppy disk or a hard disk. .
- the information medium may be a transmissible medium such as an electrical or optical signal, which may be conveyed via an electrical or optical cable, by radio or by other means.
- the program according to the invention can be downloaded in particular on an Internet type network.
- the information carrier 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 relates to a device for determining a plurality of first laws connecting the permeability to porosity within an underground reservoir, for example a device configured to estimate the permeability distribution within an underground reservoir, in particular from a set of porosity and permeability measurements made within this reservoir.
- This device comprises:
- a first enumeration module for each law of the family of laws, measurement points of the plurality of points reproduced by the law;
- This determination device is configured for implementing the determination method as defined above.
- the present invention also aims, in another aspect, a method of estimating at least a mean permeability for a set of wells of an underground reservoir. This process comprises:
- a probability law is generally advantageously defined by a reduced number of parameters, for example two parameters for a normal distribution and three parameters for an asymmetric normal distribution.
- the invention therefore proposes to represent a porosity distribution of a set of wells of an underground reservoir by a law of probability.
- the permeability distribution at this set of wells is related to the corresponding porosity distribution by a set of laws ⁇ - ⁇ having been previously determined.
- the rock formation constituting the reservoir is described at the level of a set of wells by a distribution of porosity modeled by a law of probability and by a distribution of permeability modeled by a set of laws ⁇ -K.
- the invention also makes it possible to model a porosity distribution at a set of wells or a single well as a function of the desired analysis scale.
- the step of obtaining a probability law is performed by minimizing an objective function taking into account at least one of the following three terms:
- a first term favoring the laws of probability that best approximate the distribution of porosity data
- a third term favoring the probability laws which minimize for each selected law of the first plurality of laws the sum of the differences between the value of the average permeability calculated after application of the selected law to the distribution of porosity data and the value of the average permeability calculated after application of the selected law to the law of probability.
- the porosity distribution is represented by a probability law that best reproduces at the same time the porosity distribution and the average of the porosity and permeability distributions.
- the objective function is a linear combination E t + (1 - ⁇ ) [(1 - ⁇ ) ⁇ 3 + ⁇ 2 ], where a and ⁇ are two positive coefficients and less than one and where:
- the second term E2 is equal to ( ⁇ ⁇ - LP (S 1 ( S g )) 2 ;
- the third term E3 is equal to ⁇
- N is the cardinal of said determined region of the space defined by the parameters
- n is the number of intervals of the porosity data distribution
- F j is the frequency of occurrence associated with each of the porosity intervals ⁇
- Said at least one average permeability is a mean horizontal permeability K ⁇ 1 ⁇ 2 given by the formula:
- the objective function is a linear combination ⁇ + (1 - ⁇ ) [(1 - ⁇ ) ⁇ 3 + ⁇ 2 ], where ⁇ and ⁇ are two positive coefficients and less than one and where:
- the second term E2 is equal to ( ⁇ ⁇ - ⁇ ⁇ , ..., S g )) 2 ;
- N is the cardinal of the determined region of the space defined by the parameters
- n is the number of intervals of the porosity data distribution
- F is the frequency of occurrence associated with each of the porosity intervals ⁇ ,
- ⁇ is the value associated with said porosity intervals
- said at least one average permeability is a vertical mean permeability K ⁇ 3 ⁇ 4 given by the formula:
- the method further comprises a step of obtaining a plurality of third laws connecting the porosity to the vertical permeability based on at least the result of the second count and wherein:
- the plurality of first laws connects the porosity to the horizontal permeability
- the step of obtaining a normal probability distribution is performed by minimizing an objective function taking into account at least one of the following three terms:
- a first term favoring the laws of probability that best approximate the distribution of porosity data
- a third term favoring the probability laws that minimize for each selected law of the first plurality of laws and for each selected law of the third plurality of laws the sum of the differences between the value of the total horizontal mean permeability calculated after application of the laws; selected for the distribution of porosity data and the value of the total horizontal mean permeability calculated after application of the selected laws to the law of probability;
- Said at least one average permeability is a total horizontal average permeability.
- the estimation method also makes it possible to estimate the horizontal total average permeability by adequately defining the objective function to be minimized for obtaining the probability law representing the porosity distribution.
- the plurality of first laws is defined by the relation log (Kh) - (A j, f (cp) + Bj) where Kh is a horizontal permeability, A, and B, are two real parameters belonging to a determined region of the space defined by the parameters A, B and where f is the identity function or the log function;
- the objective function is a linear combination OCE-L + (1 - ⁇ ) [(1 - ⁇ ) ⁇ 3 + ⁇ 2 ], where a and ⁇ are two positive coefficients and less than one and where:
- the second term E2 is equal to ( ⁇ - ⁇ ⁇ , S g )) 2 ; and
- the third term E3 is equal to
- Kht (A 1, B 1, Av m , B v m ) C h . (A ,, B,) + (1 - C h ). K ⁇ (Av m , Bv m ),
- C h is a positive coefficient between 0 and 1
- N is the cardinal of the determined region of the space defined by the parameters A, B,
- M is the cardinal of the determined region of the space defined by the parameters Av, Bv,
- n is the number of intervals of the porosity data distribution
- F j is the frequency of occurrence associated with each of the porosity intervals
- Said at least one average permeability is a total horizontal mean permeability given by one of the formulas:
- the method further comprises a step of obtaining a plurality of third laws connecting the porosity to the vertical permeability on the basis of at least the result of the second count and in which :
- the plurality of first laws relates the porosity to the horizontal permeability, and the step of obtaining a normal law of probability is performed by minimizing an objective function taking into account at least one of the following three terms:
- a third term favoring the probability laws that minimize for each selected law of the first plurality of laws and for each selected law of the plurality of third laws the sum of the differences between the value of the total vertical mean permeability calculated after application of the laws; selected for the distribution of porosity data and the value of the total vertical mean permeability calculated after application of the selected laws to the law of probability;
- Said at least one average permeability is a total vertical mean permeability.
- the objective function is a linear combination CCE-L + (1 -) [(1 - ⁇ ) ⁇ 3 + ⁇ 2 ], where a and ⁇ are two positive coefficients and less than one and where:
- the second term E2 is equal to ( ⁇ ⁇ - LP (S 1 ( S g )) 2 ;
- the third term E3 is equal to
- K ⁇ t (A i , B i , Av m , Bv m ) Cv. KHCA ⁇ Bi) + (1 - C v ).
- Cv is a positive coefficient between 0 and 1
- N is the cardinal of said determined region of the space defined by the parameters A, B
- M is the cardinal of said determined region of the space defined by the parameters Av, Bv,
- n is the number of intervals of said porosity data distribution
- F j is the frequency of occurrence associated with each of the porosity intervals
- ⁇ is the value associated with said porosity intervals
- Said at least one average permeability is a total vertical mean permeability given by one of the formulas:
- the step of obtaining a probability law is carried out on the basis of at least said plurality of second laws
- the method further comprises a step of estimating at least one total vertical average permeability based on at least the probability law and said plurality of second laws.
- the estimation method makes it possible to simultaneously estimate the total mean horizontal permeability and the total vertical mean permeability.
- the step of obtaining a probability law is performed by minimizing an objective function taking into account at least one of the following three terms:
- a first term favoring the laws of probability that best approximate the distribution of porosity data
- a third term favoring the probability laws that minimize for each selected law of said first plurality of laws o the sum of the differences between the value of the total horizontal mean permeability calculated after application of the selected law to the distribution of porosity data and the value of the total horizontal mean permeability calculated after applying the selected law to the probability law, as well as
- K v ((Ai + dA) f (cp) + B j + dB.)
- Kv is a vertical permeability and dA and dB are two real parameters
- the objective function is a linear combination o Ei + (1 - ⁇ ) [(1 - ⁇ ) ⁇ 3 + ⁇ 2 ], where a and ⁇ are two positive coefficients and less than one and where:
- the second term E2 is equal to (cp; LP (S 1 ( ..., S g )) 2 ;
- Kvt (Al, Bi) C v . Kh (A j , Bi) + (1 - C v ). K (Al, Bi),
- C h and C v are positive coefficients between 0 and 1
- N is the cardinal of the determined region of the space defined by the parameters
- n is the number of intervals of said porosity data distribution
- F j is the frequency of occurrence associated with each of the porosity intervals ⁇ ⁇ , is the value associated with said porosity intervals, and
- og (Kv) ((A j + dA).
- Said at least one average permeability is a total horizontal mean permeability given by one of the formulas:
- Said at least one total vertical mean permeability is given by one of the formulas:
- the probability law is a normal law or a linear combination of normal laws.
- the probability law is an asymmetric normal law.
- the coefficient Q is greater than 0.75 and less than 1.
- the coefficient Q is greater than 0 and less than 0.25.
- the various steps of the estimation method are determined by instructions of computer programs.
- the invention also relates to a computer program on an information medium, this program being capable of being implemented in a computer, this program comprising instructions adapted to the implementation of the steps of an estimation method as described above.
- This program can use any programming language, and be in the form of source codes, object codes, or intermediate codes between source code and object code, such as in a partially compiled form, or in any other desirable shape.
- the invention also relates to a computer-readable information medium, comprising instructions of a computer program as mentioned above.
- the information carrier may be any entity or device capable of storing the program.
- the medium may comprise storage means, such as a ROM, RAM, PROM, EPROM, a CD-ROM or, or a magnetic recording medium, for example a floppy disk or a hard disk. .
- the information medium may be a transmissible medium such as an electrical or optical signal, which may be conveyed via an electrical or optical cable, by radio or by other means.
- the program according to the invention can be downloaded in particular on an Internet type network.
- the information carrier 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 relates to a device for estimating at least one average permeability for a set of wells of an underground reservoir, this device comprising: a module for obtaining a distribution of porosity data for the whole wells;
- a probability law obtaining module approximating the distribution of porosity data on the basis of said plurality of first laws
- This estimation device is configured for implementing the estimation method as defined above.
- the present invention also aims, in yet another aspect, a method of calculating a mean permeability at a location of an underground reservoir. This process comprises:
- the invention thus makes it possible to estimate the permeability distribution at any point of a reservoir from a plurality of ⁇ - ⁇ laws and modeling in the form of probability distributions of the porosity distributions at a given level. plurality of wells of an underground reservoir.
- the calculation method further comprises a step of calculating an average porosity in the location starting from at least the probability law in the location.
- the various steps of the method of calculating a mean permeability are determined by instructions of computer programs.
- the invention also relates to a computer program on an information medium, this program being capable of being implemented in a computer, this program comprising instructions adapted to the implementation of the steps of a method for calculating a mean permeability as described above.
- This program can use any programming language, and be in the form of source codes, object codes, or intermediate codes between source code and object code, such as in a partially compiled form, or in any other desirable shape.
- the invention also relates to a computer-readable information medium, comprising instructions of a computer program as mentioned above.
- the information carrier may be any entity or device capable of storing the program.
- the medium may comprise storage means, such as a ROM, RAM, PROM, EPROM, a CD-ROM or, or a magnetic recording medium, for example a floppy disk or a hard disk.
- the information medium may be a transmissible medium such as an electrical or optical signal, which may be conveyed via an electrical or optical cable, by radio or by other means.
- the program according to the invention can be downloaded in particular on an Internet type network.
- the information carrier 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 relates to a device for calculating a mean permeability at a location of an underground reservoir.
- This device comprises:
- FIG. 1 already described, illustrates an underground hydrocarbon reservoir
- FIG. 2 illustrates an exemplary hardware architecture of a device for determining a plurality of first laws connecting the permeability to porosity within an underground reservoir according to the invention
- FIG. 3 represents, in the form of a flow chart, the main steps of a method for determining a plurality of first laws connecting the permeability to porosity within an underground reservoir, the method being in accordance with the invention in a first implementation variant;
- FIG. 4 graphically illustrates the various steps of a method for determining a plurality of first laws connecting the permeability to porosity within an underground reservoir in a first implementation variant;
- FIG. 5 represents, in the form of a flow chart, the main steps of a method of adding additional measurement points
- FIG. 6 graphically illustrates a global theoretical distribution associated with permeability measurements obtained from formation tests and a distribution associated with permeability measurements obtained from analysis of sample cores;
- FIG. 7 represents, in the form of a flow chart, the main steps of a method for determining a plurality of first laws connecting the permeability to porosity within an underground reservoir, the method being in accordance with the invention in a second implementation variant;
- FIG. 8 graphically illustrates certain steps of a method for determining a plurality of first laws connecting the horizontal and vertical permeabilities to the porosity within an underground reservoir in a second implementation variant
- FIG. 9 illustrates an example of a hardware architecture of a device for estimating a mean permeability along a portion of a well of an underground reservoir according to the invention
- FIG. 10 represents, in the form of a flow chart, the main steps of a method for estimating a mean permeability along a portion of a well of an underground reservoir, the method being in accordance with FIG. invention in a first implementation variant;
- FIG. 11 illustrates an underground hydrocarbon reservoir and a distribution of porosity data associated with a well
- FIG. 12 represents, in the form of a flow chart, the main steps of a method for estimating a total horizontal mean permeability along a portion of a well of an underground reservoir, the method being in accordance with FIG. the invention in a second implementation variant;
- FIG. 13 illustrates an example of a hardware architecture of a device for calculating a mean permeability at a point of an underground reservoir according to the invention.
- FIG. 14 represents, in the form of a flow chart, the main steps of a method for calculating a mean permeability at a point in an underground reservoir, the method being in accordance with the invention in a first implementation variant.
- the described wells are vertical wells.
- FIG. 2 represents a device 3 for determining a plurality of first laws connecting the permeability to porosity within an underground reservoir according to the invention in a particular embodiment.
- This determination device 3 has the hardware architecture of a computer.
- the determination device 3 comprises in particular a processor 3A, a read-only memory 3B, a random access memory 3C, a non-volatile memory 3D and communication means 3E.
- the read-only memory 3B of the determination device constitutes a recording medium readable by the processor 3A and on which is recorded a computer program according to the invention, comprising instructions for performing the steps of a determination method.
- This computer program equivalently defines functional modules of the determination device, such as, in particular, a obtaining module 3B1 of a first plurality of measurement points comprising a porosity data item and a first permeability data item; 3B2 definition of a family of laws connecting the porosity to at least one permeability, a first counting module 3B3, for each law of the family of laws, measuring points of the plurality of points reproduced by this law so as to obtain a first intensity of points depending on each law, and a selection module 3B4 of a plurality of first laws in the family of laws on the basis of at least the result of the enumeration performed by the first enumeration module.
- the obtaining module 3B1 of a first plurality of measurement points notably uses the communication means 3E.
- FIG. 3 can be read taking into account FIGS. 4a) to 4d), which graphically illustrate the various steps of the method of FIG. 3.
- the determination device 3 acquires during a step E100 a set of permeability measurements (a first permeability in the sense of the invention) and porosity within the tank 1.
- the porosity measurements thus acquired may, for example, be useful porosity measurements obtained by application of a "cutoff".
- the useful porosity measurements are the porosity measurements belonging to an interval of porosity values defined by a low threshold.
- this set of measurements of porosity cp j and permeability K j is constituted for example by the set of discrete measurements ⁇
- j is an index corresponding to a well
- I is an index corresponding to a vertical position along this well.
- the pair ⁇ ⁇ , ⁇ ⁇ is measured in a portion of the cylinder of the well.
- the measurements ⁇ ⁇ can be obtained from the analysis of results of logs made within the tank 1.
- the set of measurements ⁇ ⁇ ( K j is obtained at the scale of the tank 1.
- the set of measurements ( j , K) is obtained at the scale of a subset of wells of the tank 1.
- FIG. 4a there is shown a cloud of measurement points each corresponding to a pair ⁇ ⁇ ( K j having been previously measured.
- the permeability measurements K j are horizontal permeability measurements.
- the permeability measurements K j are vertical permeability measurements.
- additional measurement points (p u K1 are added to the measurement points ( j , k j during a step E150)
- the added measurement points ⁇ ⁇ ; K [are also denoted ⁇ ⁇ ; K j .
- step E150 A detailed example of implementation of step E150 is illustrated in a nonlimiting manner in FIG. 5, described later.
- a semi-log or log-log model is selected according to the intrinsic nature of the rock constituting the reservoir 1.
- the model selected during this step and best suited to the properties of the rock constituting the reservoir is a log-log model.
- a new cloud of points log (pi), log (K,) is obtained (step E300) as illustrated in FIG. 4b).
- FIG. 4b represents the cloud of points log (cpi), log (Ki) in the form of an intensity image, the value of each of the points of this image being proportional to the number of data log (cpj), log (Kj) observed.
- This image may be optionally smoothed during an E350 step, for example by performing a Gaussian filtering, so as to be more easily exploitable.
- step E400 lower and upper bounds for the coefficients
- a and B are chosen. This choice can be made according to the usual values of the parameters of the laws cp-K.
- A is between -14 and 0 and B is between 0 and 14.
- the inventors have observed that the choice of these lower and upper bounds for the coefficients A and B is satisfactory as well.
- the permeability measurements K are vertical permeability measurements only in the case where the permeability measurements Kj are horizontal permeability measurements.
- the result of the count can be, optionally but advantageously, multiplied by the product of the variance ( ⁇ ( ⁇ ⁇ )), evaluated on the whole point cloud. , distances to the model of each of the points along the log (cp) axis, and the variance a (log tfi)), evaluated over the whole cloud of points, distances to the curve representing the law ⁇ - ⁇ of each point along the log axis (K).
- the value obtained for each pair A, B is representative of the adequation of the ⁇ -K law to the cloud of points, and, in the implementation in which the result is weighted by the product of the variances mentioned above, the value obtained is increased if the scatter plot is distributed along the line representing the law cp-K in the representation space log (cp), log (K).
- step E600 for each pair A, B, within the limits defined by the minimum and maximum limits of these variables in step E400, the result of counting, possibly weighted as mentioned above, in the form of an intensity associated with the corresponding point in the space of the values A, B.
- FIG. 4 d) represents, in the form of a grayscale image and called Radon, the intensities obtained in the space of the values A, B.
- Radon the intensities obtained in the space of the values A, B.
- a color code or a luminous intensity for represent the intensity obtained. It may be noted that this image is not strictly speaking an image of Radon, that being so, this formulation is used by analogy.
- the sum of the intensities of the space of the values A, B shown in Fig. 4d) is normalized to one.
- each of the intensities of the space of the values A, B considered ie in this example, A is between -14 and 0 and B is between 0 and 14
- the selection of a region of the space (A, B) is performed by selecting all the points corresponding to a cumulative probability threshold, for example 10 %, this threshold may for example be determined according to the nature of the reservoir.
- the estimation method according to the invention makes it possible to obtain a probabilistic set of laws ⁇ - ⁇ that is more representative. of the distribution of porosity and permeability measurements.
- step F100 a series of permeability data K [> ST (second permeability data in the sense of the invention) associated with an uncertainty ⁇ 357 " are obtained from the interpretation of measurements made from training tests carried out in the tank 1.
- a theoretical unit distribution of the logarithm of the permeability is calculated (step F200) by convoluting this point data with a Gaussian of average logCAT- 057- ), standard deviation log (a sr ) and whose amplitude is calculated in such a way that the integral on R of this Gaussian is equal to 1.
- the determination device also calculates during a step F400 the distribution of the logarithm of the data K, existing measurement points which is then quantized to obtain a real histogram Dist2.
- the quantization is a uniform scalar quantization, the quantization step and the decision levels being for example chosen by a reservoir engineer or a geologist.
- the quantization used is non-uniform scalar quantization.
- the overall theoretical distribution is quantized to obtain an overall theoretical histogram Distl, this discretization being performed using the same quantization step and the same decision levels as for the quantization of the distribution of the logarithm of the data. ,.
- the classes (i.e. intervals) of the Distl histogram are equal to the classes of the histogram Dist2.
- the determining device 3 calculates (step F500) the product normalized in probability (i.e. the integral on R of this product is normalized to 1) of the two histograms Distl and Dist2 in order to identify their intersection.
- the determination device 3 acquires a total number N t of additional measurement points to be added to the existing measurement points ( ⁇ , ⁇ ).
- the determination device 3 determines a number of additional measurement points (step F550) and selects randomly additional measurement points (step F600) out of the set of existing measurement points (cpj, Kj) for which log (K w ) is equal to the quantized value of log (Kj).
- the number N ' is determined as being the product of the product value of the two distributions Distl and Dist2 evaluated on the interval w by the total number N t of additional measurement points to be added to the existing measurement points ( ⁇ . ⁇ ,).
- the previously selected additional measurement points are then added to the measurement points (cpj, Kj) during a step F700.
- this set of porosity measurements c j of a horizontal permeability K Hi and vertical permeability K vi is constituted for example of the set of discrete steps ⁇ pj K J HI K J V1 conducted by analyzing the cores taken from the reservoir rock 1 for a set of wells 2.
- j is an index corresponding to a well
- I is an index corresponding to a vertical position along this well.
- ⁇ is measured in a portion of the cylinder of the well.
- additional measurement points are added to the measurement points (Pi, K Hi in step G150) and additional measurement points are added to the measurement points ( ⁇ ⁇ , K vi ) in step G160.
- Step G150 and step G160 are implemented in a manner similar to step E150 illustrated in a nonlimiting manner in FIG. 5 previously described.
- a model for example semi-log or log-log, is selected according to the intrinsic nature of the rock constituting the reservoir 1.
- the model selected during this step which corresponds best to the properties of the rock constituting the reservoir, is a semi-log model.
- a step G300 lower and upper bounds for the coefficients A and B are chosen. This choice can be made according to the parameters of the usual ⁇ - ⁇ laws. In the example described here, A is between -14 and 0 and B is between 0 and 14.
- a threshold for example estimated for example from the resolution of the intensity image
- FIG. 8 (a) represents the RadonH image associated with the data couples ci, K H i whereas FIG. 8 (b) represents the RadonV image associated with the data pairs (j, K Vi .
- the determination device 3 then proceeds, during a step G600, to calculate the cross-correlation between the RadonH and RadonV images and to identify a maximum of this intercorrelation signal. This intercorrelation is shown in Figure 8 (c) and the location (dA, dB) of its maximum value. Then, the determination device 3 translates the RadonV image of a translation vector (dA, dB) during a step G700 before calculating the RadonHV image corresponding to the product of the RadonH image with the RadonV translated image. (step G800). A RadonHV image is shown in Figure 8 (d).
- (A, B) corresponding to a set of laws describing the relation between ⁇ and log (K H ) and corresponding to acceptable cp-K laws. This selection is made for example by selecting all the intensities exceeding a threshold which may for example have been previously set by the user or a probability if the image is normalized (the sum of the pixels of the image is equal to 1).
- the set of laws cp-K describing in an acceptable way the relation between ⁇ and log (Kv) correspond to the translation of a translation vector (dA, dB) of the parameters A and B corresponding to the region previously.
- the same lower and upper bounds for the coefficients A and B are chosen during the determination of the RadonH and RadonV images.
- different bounds may be used in the determination of the RadonH and RadonV images provided that the RadonV image is interpolated on the coordinates of the RadonH image before calculating the intercorrelation between these two images.
- an estimation device 4 of average permeability along the portion S of a well 2 according to the invention in a particular embodiment.
- the average permeability along the well is obtained using an asymmetric normal law.
- probability laws can be used.
- the estimation device 4 has the hardware architecture of a computer.
- the estimation device 4 comprises in particular a processor 4A, a read-only memory 4B, a random access memory 4C, a non-volatile memory 4D and communication means 4E.
- the read-only memory 4B of the estimation device constitutes a recording medium readable by the processor 4A and on which is recorded a computer program according to the invention, comprising instructions for the execution of the steps of a method of estimation of a mean permeability within an underground reservoir according to the invention, the steps of this estimation method being described later with reference to FIG. 9, in a particular embodiment.
- This computer program equivalently defines functional modules of the estimation device, such as, in particular, a module 4B1 for obtaining a distribution of porosity data for the portion of the well, a determination device 4B2 of a plurality first laws connecting the porosity to the permeability for the portion of the well according to the invention, a module 4B3 obtaining an asymmetric normal law approximating the distribution of porosity data on the basis of at least said plurality of first laws and an estimation module 4B4 of the average permeability along the portion of the well from at least the asymmetric normal law and said plurality of first laws.
- the obtaining module 4B1 of a porosity data distribution for the portion of the well and the determination device notably uses the communication means 4E.
- the estimation device acquires, during a step H100, a measurement of the porosity ⁇ '(z) along the portion S of the well 2, for example at from a set of logs in the well 2.
- the logs measure physical parameters connected by laws of physics to the porosity of the reservoir. From these parameters, mathematical optimization or inversion methods are used to find the continuous function ⁇ '(z) representing the porosity as a function of the depth and best explaining the logging measurements.
- the porosity measurement ⁇ '(z) along the portion S of the well 2 can be obtained from the analysis of sample cores, provided that the corresponding porosity measurements are representative, i; e . regular and slightly spaced along the z axis.
- a histogram of the porosity data ⁇ '(z) is obtained.
- the porosity data ⁇ '(z) obtained in step H100 are quantized, for example by a uniform scalar quantizer.
- the estimation device calculates in step H300 a set of laws cp-K connecting the porosity to the horizontal permeability for the section S of the well by applying a method for determining such a set of laws according to the invention.
- E 2 ( ⁇ , '- LNA (m, S 1 ( S X / S 2 )) 2 favors the asymmetric normal laws LNA (m, Si, Si / S 2 ) whose mean value LNA (m, S ⁇ SL /
- step H500 at least one horizontal mean permeability Kh s is estimated for the portion S of the well 2 from the optimal asymmetric normal law determined during step H400 and the set of laws ⁇ - ⁇ connecting porosity at horizontal permeability for the S section of the well.
- Kh s (A i ( B g ⁇ ( ⁇ ( . F ( ⁇ p ',) + ⁇ ,).
- the estimation device estimates a mean horizontal permeability.
- the estimation device estimates a vertical mean permeability in:
- the estimation device estimates a total horizontal mean permeability in:
- the estimation device estimates a total vertical mean permeability of: LNA S ( ⁇ , ', m, S)
- K ⁇ t (A i , B i , Av m , Bv m ) C v . Kh (Al, Bj) + (1 - C v ). K ⁇ (Av m , Bv m ),
- the estimation device 4 acquires, during a step M100, a measurement of the porosity ⁇ '(z) along the portion S of the well 2.
- a step M200 the porosity data ⁇ '(z) obtained in the step M 100 are discretized in n data and the experimental distribution Dist3 of these discretized data ⁇ [is calculated.
- the estimation device 4 calculates in the step M300 a first set of laws ⁇ - ⁇ connecting the porosity to the horizontal permeability for the section S of the well 2 by applying a method of determining such a set of laws according to the invention.
- the estimation device 4 also determines a second set of laws ⁇ - ⁇ connecting the porosity to the vertical permeability for the section S of the well 2.
- At least one total horizontal mean permeability Kht s is estimated for the portion S of the well 2 from the optimal asymmetric normal law determined during the step M400 and the first and second sets of laws ⁇ - ⁇ connecting the porosity to horizontal permeability and vertical permeability for the S section of the well.
- the total horizontal mean permeability Kht s is determined for at least one pair (A i ( B,) from the equation
- step M600 the estimation device determines the total vertical mean permeability Kvt s for at least one pair ( ⁇ ,, B,) from the equation:
- This computing device 5 has the hardware architecture of a computer.
- the computing device 5 comprises in particular a processor 5A, a read-only memory 5B, a random access memory 5C, a non-volatile memory 5D and communication means 5E.
- the read-only memory 5B of the computing device constitutes a recording medium readable by the processor 5A and on which is recorded a computer program according to the invention, comprising instructions for the execution of the steps of a calculation method.
- a mean permeability according to the invention the steps of this method of calculation being described later with reference to Figure 14, in a particular embodiment.
- This computer program equivalently defines functional modules of the computing device, such as, in particular, a selection module 5B1 of a set of wells of a reservoir, a device for determining a plurality of first laws 5B2, a obtaining module 5B3 of a porosity data distribution, a probability obtaining module 5B4, a calculation module 5B5 of a probability law, a calculation module 5B6 of the average permeability.
- the computing device 5 selects (step J100) a set of wells from the tank 1.
- the set of wells contains a plurality of wells 2.
- the computing device 5 determines a plurality of first laws cp-K connecting the permeability to the porosity for the set of selected wells. To carry out this determination, the computing device 5 uses the determination device 5B2.
- the computing device 5 obtains a porosity data distribution for the well and an asymmetric normal law approximating this distribution of porosity data on the basis of plurality.
- first laws ⁇ - ⁇ step J300.
- Obtaining an asymmetric normal law is performed for example according to the H200, H300 and H400 steps previously described. It is further assumed that the uniform scalar quantizer used in step H200 is the same for each of the wells of the set of selected wells.
- step J400 the computing device 5 calculates an asymmetric normal law LNA 3 ⁇ 4y at the location (x, y) from the asymmetrical normal laws obtained for each of the wells during the step J300.
- the parameters m, Si and S 2 of the asymmetric normal law in the location (x, y) are obtained by interpolation (for example linear) of the parameters m, Si and S 2 of the asymmetric normal laws obtained for each of the well during step J400.
- the computing device 5 then calculates during the step J500 a mean permeability at the location (x, y) by using the asymmetric normal law at the point (x, y), a law ⁇ - ⁇ among the plurality of first laws. ⁇ - ⁇
- B are the coefficients that define the chosen law among the plurality of laws ⁇ - ⁇ , ⁇
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FR1555885A FR3038091B1 (fr) | 2015-06-25 | 2015-06-25 | Procede et dispositif de determination d'une permeabilite au sein d'un reservoir |
PCT/FR2016/051557 WO2016207567A1 (fr) | 2015-06-25 | 2016-06-24 | Procede et dispositif de determination d'une permeabilite au sein d'un reservoir |
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EP16741667.6A Withdrawn EP3314547A1 (fr) | 2015-06-25 | 2016-06-24 | Procede et dispositif de determination d'une permeabilite au sein d'un reservoir |
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US (1) | US20180172879A1 (fr) |
EP (1) | EP3314547A1 (fr) |
FR (1) | FR3038091B1 (fr) |
WO (1) | WO2016207567A1 (fr) |
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US11028648B1 (en) | 2020-11-05 | 2021-06-08 | Quaise, Inc. | Basement rock hybrid drilling |
US20230153843A1 (en) * | 2021-11-12 | 2023-05-18 | Oracle International Corporation | System to combine intelligence from multiple sources that use disparate data sets |
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US7486589B2 (en) * | 2006-02-09 | 2009-02-03 | Schlumberger Technology Corporation | Methods and apparatus for predicting the hydrocarbon production of a well location |
FR2918777B1 (fr) * | 2007-07-09 | 2009-09-25 | Total Sa | Procede, programme et systeme informatique de consiliation de donnees de modele de reservoir d'hydrocarbure. |
US8078403B2 (en) * | 2007-11-21 | 2011-12-13 | Schlumberger Technology Corporation | Determining permeability using formation testing data |
EP2348337B1 (fr) * | 2010-01-14 | 2014-04-16 | Services Pétroliers Schlumberger | Mesures corrigées de porosité de formations souterraines |
US8649980B2 (en) * | 2010-03-05 | 2014-02-11 | Vialogy Llc | Active noise injection computations for improved predictability in oil and gas reservoir characterization and microseismic event analysis |
US20140052377A1 (en) * | 2012-08-17 | 2014-02-20 | Schlumberger Technology Corporation | System and method for performing reservoir stimulation operations |
US10329903B2 (en) * | 2013-03-15 | 2019-06-25 | Schlumberger Technology Corporation | Methods of characterizing earth formations using physiochemical model |
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WO2016207567A1 (fr) | 2016-12-29 |
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