CN113962605A - Method and system for evaluating fracturing property of rock stratum and storable medium - Google Patents

Method and system for evaluating fracturing property of rock stratum and storable medium Download PDF

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CN113962605A
CN113962605A CN202111364713.2A CN202111364713A CN113962605A CN 113962605 A CN113962605 A CN 113962605A CN 202111364713 A CN202111364713 A CN 202111364713A CN 113962605 A CN113962605 A CN 113962605A
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杨永明
李霄
鞠杨
李溪雯
李东
高玉洁
熊晟钧
刘红彬
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China University of Mining and Technology Beijing CUMTB
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Abstract

The invention discloses a method and a system for evaluating the fracturing property of a rock stratum and a storable medium, and belongs to the technical field of oil and gas resource reservoirs. Firstly, acquiring sample data of a fracturing evaluation index; secondly, according to the sample data of the fracturing evaluation index, subjective weighting is carried out by utilizing a combined ordered weighted average operator C-OWA to obtain subjective relative weight, and according to the sample data of the fracturing evaluation index, the relevance of the importance degree among indexes is utilized to judge CRITIC objective weighting to obtain objective relative weight; and finally, combining the subjective relative weight and the objective relative weight of each fracability evaluation index to obtain a combined weight of each fracability evaluation, and evaluating the fracability of the rock stratum as the weight of each evaluation index of the fracability evaluation. The invention improves the validity and reliability of the evaluation result by considering the effective information in the subjective and objective weights.

Description

Method and system for evaluating fracturing property of rock stratum and storable medium
Technical Field
The invention relates to the technical field of oil and gas resource reservoirs, in particular to a method and a system for evaluating the fracturing property of a rock stratum and a storable medium.
Background
The rapid development of economy further expands the demand of China on energy, unconventional oil and gas resources such as coal bed gas, shale gas and the like become important guarantees of national energy strategic demands, and the low-permeability hydraulic fracturing technology becomes an important technical means of energy exploitation. Before hydraulic fracturing of a low-permeability complex reservoir, fracturing evaluation of different reservoirs is generally needed, and the judgment of the fracturing of the reservoir has important significance for guiding hydraulic fracturing construction, reducing construction cost and improving the recovery ratio of oil and gas resources.
At present, most fracturing property evaluation methods only determine the weight according to a subjective evaluation method and an objective evaluation method, and perform fracturing property evaluation on a reservoir stratum. The commonly used subjective weighting methods mainly include: delphir's method, analytic hierarchy method, modified analytic hierarchy method, etc. The subjective assignment method directly establishes an importance degree matrix of each evaluation index according to previous research, and the matrix has certain one-sidedness, so that the scientificity of a weight distribution result is poor. The objective weighting method mainly comprises the following steps: entropy method, principal component analysis method, mean square error method, coefficient of variation method, etc. The objective weighting is usually performed according to field measurement data without considering professional knowledge and construction experience.
However, in the field measurement process, a certain deviation of data can occur due to a plurality of uncertain factors, so that the result is not consistent with the reality, the result has an extreme value problem, the weight distribution of the evaluation index is unreasonable, and the fracturing efficiency cannot be improved.
In view of the above, it is an urgent need to solve the problems of the art to provide a method, a system and a storable medium for evaluating the fracability of a rock formation.
Disclosure of Invention
In view of the above, the invention provides a method and a system for evaluating the fracturing property of a rock stratum and a storage medium, wherein the subjective weight of an evaluation index is obtained through C-OWA, and the objective weight of the evaluation index is obtained through CRITIC, so that effective information in the subjective weight and the objective weight is considered, the effectiveness and the reliability of the evaluation result of the fracturing property of the rock are higher, the method and the system have more scientific guiding significance on engineering sites, the cost is effectively saved, and the fracturing efficiency is improved.
In order to achieve the above purpose, the invention provides the following technical scheme:
in one aspect, the invention provides a method for evaluating the fracturing property of a rock stratum, which comprises the following steps:
acquiring sample data of a fracturing evaluation index;
according to the sample data of the fracturing evaluation index, subjective weighting is carried out by utilizing a combined ordered weighted average operator C-OWA to obtain subjective relative weight;
according to the sample data of the fracturing evaluation index, the relevance of the importance degree among indexes is utilized to judge the CRITIC objective weighting to obtain objective relative weight;
and combining the subjective relative weight and the objective relative weight of each fracturing evaluation index to obtain a combined weight, and evaluating the fracturing of the rock stratum by using the combined weight.
Preferably, the fracability evaluation index sample data includes: the method comprises the following steps of evaluating index data, data numbers, total number of evaluating indexes, number of stratums to be evaluated and historical measuring data of the evaluating indexes of rock strata.
Preferably, the obtaining of the subjective relative weight by the subjective weighting of the combined ordered weighted average operator C-OWA according to the fracturability evaluation index sample data includes:
establishing an initial matrix for measuring the importance degree of the evaluation index according to the sample data of the evaluation index, and calculating a weighting vector;
and obtaining subjective absolute weight of the evaluation index factors according to the weighting vectors, and obtaining subjective relative weight according to the subjective absolute weight.
Preferably, the calculation formula of the calculation weighting vector is:
Figure BDA0003360188010000021
in the formula (I), the compound is shown in the specification,
Figure BDA0003360188010000022
q is the importance data number of a certain evaluation index, and n is the total number of the evaluation indexes.
Preferably, the calculation formula of the subjective absolute weight of the evaluation index factor obtained according to the weighting vector is as follows:
Figure BDA0003360188010000023
wherein p is each evaluation index number, bpThe matrix corresponding to each evaluation index in the initial matrix;
obtaining subjective relative weight w according to absolute weightpThe calculation formula of (2) is as follows:
Figure BDA0003360188010000031
in the formula (I), the compound is shown in the specification,
Figure BDA0003360188010000032
p is the number of each evaluation index in the table, and n is the total number of the evaluation indexes.
Preferably, the step of judging CRITIC objective weighting according to the sample data of the fracturing evaluation index and the relevance of the importance degrees among the indexes to obtain objective relative weight comprises the following steps:
preprocessing historical measurement data of each rock stratum evaluation index to obtain a dimensionless data set;
and calculating the standard deviation, the index conflict and the information content of each evaluation index through the index variability, and obtaining the objective relative weight of each evaluation index according to the information content.
Preferably, the preprocessing the sample data of the fracturability evaluation index to obtain a dimensionless data set includes:
obtaining an original measurement data matrix of original evaluation indexes according to historical measurement data of each rock stratum evaluation index;
carrying out forward or reverse non-dimensionalization on the evaluation index by adopting a CRITIC method on an original measurement data matrix of the original evaluation index to obtain a non-dimensionalized matrix A, wherein:
forward dimensionless processing formula:
Figure BDA0003360188010000033
a reverse dimensionless processing formula:
Figure BDA0003360188010000034
in the formula, i is the number of the stratum to be evaluated, j is the number of the evaluation index, and xijIs an element of matrix X, aijIs an element of the matrix a.
Preferably, the calculating the standard deviation and the information amount of each evaluation index through the index variability and obtaining the objective relative weight of each evaluation index according to the information amount includes:
calculating the variability of the evaluation index:
Figure BDA0003360188010000035
in the formula, i is the number of the stratum to be evaluated, j is the number of the evaluation index, m is the total number of the stratum to be evaluated, SjIs the standard deviation;
and (3) calculating index conflict:
Figure BDA0003360188010000036
in the formula, rkjIs the correlation coefficient between the evaluation indexes k and j;
calculating the information quantity:
Cj＝Sj×Rj
obtaining objective relative weight w of each evaluation index according to information quantityj：
Figure BDA0003360188010000041
In the formula, j is an evaluation index number, and n is the total number of evaluation indexes.
In another aspect, the present invention provides a system for evaluating fracability of a rock formation, comprising:
a data acquisition module: the method is used for acquiring sample data of the fracturing evaluation index;
a first calculation module: the data acquisition module is connected with the data acquisition module and used for obtaining subjective relative weight by utilizing the combination ordered weighted average operator C-OWA subjective weighting according to the fracturing evaluation index sample data;
a second calculation module: the CRITIC objective weighting module is connected with the data acquisition module and used for judging CRITIC objective weighting according to the sample data of the fracturing evaluation index and the correlation of the importance degrees among indexes to obtain objective relative weight;
an integration module: and the first calculation module and the second calculation module are connected and used for combining the subjective relative weight and the objective relative weight of each fracability evaluation index to obtain the combined weight of each fracability evaluation index, and the combined weight is used as the weight of each evaluation index of the fracability evaluation to evaluate the fracability of the rock stratum.
In a further aspect, the invention also provides a non-transitory computer readable storage medium storing a computer program, characterized in that the computer program, when executed by a processor, performs the steps of the fracability evaluation method according to claims 1-8.
Compared with the prior art, the rock stratum fracturability evaluation method, the rock stratum fracturability evaluation system and the storage medium have the advantages that effective information in the subjective weight and the objective weight is considered, the problem that errors in a certain range are caused by the fact that the data are easy to separate from field test data when only subjective weighting is conducted is solved, and the problem that the data are deviated to a certain extent due to the fact that a plurality of uncertain factors exist in the field measurement process when only objective weighting is conducted is solved. Therefore, the on-site measurement data is fully utilized, the effective information in the subjective weight and the objective weight is considered, the fracturing performance of the rock stratum is evaluated more scientifically and reasonably, and the effectiveness and the reliability of the evaluation result are higher. The rock stratum fracturability result evaluated by the method has more scientific guiding significance on an engineering site, the cost is effectively saved, and the fracturing efficiency is improved:
(1) the subjective weight of the evaluation index is obtained by utilizing the C-OWA, an importance degree matrix is established by the C-OWA operator on the basis of considering the previous research cognition, the importance degree data are arranged in a descending order and are given to the weight on the basis of the combination number, the problem that the research result has an extreme value can be effectively solved, and the weight distribution of the evaluation index is relatively reasonable;
(2) the objective weight of the evaluation indexes is obtained by using the CRITIC, the difference and the correlation among the evaluation indexes are considered, scientific evaluation is carried out by completely using the objective attributes of the data, and the method carries out weighting according to field measurement data.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method for evaluating the fracability of a formation according to the present invention;
fig. 2 is a schematic structural diagram of the formation fracability evaluation system provided in this embodiment.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to the attached drawing 1, the embodiment of the invention discloses a method for evaluating the fracturing property of a rock stratum, which specifically comprises the following steps:
acquiring sample data of a fracturing evaluation index.
Specifically, the sample data of the fracability evaluation index is historical data of the previous research, and includes: each item of evaluation index data, data number, total number of evaluation indexes, number of stratums to be evaluated and historical measurement data of each rock stratum evaluation index
(II) obtaining subjective weight by C-OWA method
1. According to previous researches, an importance degree matrix of brittleness coefficient, brittleness mineral content, cohesive force and clay mineral content is established, wherein 10 is very important, and 0 is very unimportant. The initial importance data set for each evaluation index was obtained as shown in the following table.
TABLE 1 data of degree of importance of each evaluation index
Figure BDA0003360188010000061
The importance degree matrix of the evaluation index is as follows:
Figure BDA0003360188010000062
the data of the importance degree of the brittleness index are arranged as b from large to small1＝[8 8 7 7 6]；
The data of the importance degree of the content of the brittle minerals are arranged in the order b from large to small2＝[6 5 5 4 4]；
The data of the importance degree of the cohesive force are arranged in a descending order as b3＝[3 3 2 2 2](ii) a The data of the importance degree of the clay mineral content are arranged in a sequence b from large to small4＝[2 2 1 1 1]。
2. Weighting vector theta of dataqThe calculation formula is as follows, wherein
Figure BDA0003360188010000063
q is the importance data number of a certain evaluation index, n is the total number of the evaluation indexes, namely:
Figure BDA0003360188010000064
available weighting vectors:
θ＝[0.063 0.250 0.375 0.250 0.063]
3. weighting the decision data to obtain the absolute weight of the evaluation index factors, wherein p is the number of each evaluation index in the table, bpThe matrix corresponding to each evaluation index in the initial matrix is as follows:
Figure BDA0003360188010000071
absolute weight of brittleness index:
Figure BDA0003360188010000072
absolute weight of brittle mineral content:
Figure BDA0003360188010000073
absolute weight of cohesion:
Figure BDA0003360188010000074
absolute weight of clay mineral content:
Figure BDA0003360188010000075
4. calculating relative weight w of each evaluation indexp：
Figure BDA0003360188010000076
A relative weight matrix obtained by each evaluation index through a subjective weighting method:
Wp＝[0.475 0.298 0.145 0.082]T
(III) obtaining objective weight by CRITIC method
1. Assuming that there are seven strata to be evaluated, each stratum has four evaluation indexes, table 2 raw measurement data of each stratum evaluation index
Figure BDA0003360188010000077
The evaluation index original measurement data matrix is as follows:
Figure BDA0003360188010000081
in order to eliminate the order difference of different evaluation indexes, each evaluation index in an X matrix needs to be preprocessed, the CRITIC method is adopted to carry out forward or reverse non-dimensionalization on the evaluation indexes, and a new matrix A ═ a is obtainedij}。
Forward dimensionless processing formula:
Figure BDA0003360188010000082
a reverse dimensionless processing formula:
Figure BDA0003360188010000083
in the formula, i is the number of the stratum to be evaluated, j is the number of the evaluation index, and xijIs an element of matrix X, aijIs an element of the matrix a.
Figure BDA0003360188010000084
2. Evaluation index variability:
Figure BDA0003360188010000085
S1＝0.336,S2＝0.369,S3＝0.349,S4＝0.347,
wherein i is the number of the stratum to be evaluated, j is the number of the evaluation index, m is the total number of the stratum to be evaluated, and S is the standard deviation, and the larger the standard deviation is, the more the information reflected by the evaluation index is, and the larger the evaluation intensity of the evaluation index is.
3. Correlation coefficient between evaluation indexes
Figure BDA0003360188010000086
Index conflict property:
Figure BDA0003360188010000091
wherein r iskjIs a correlation coefficient between the evaluation indexes k and j.
R1＝2.674,R2＝3.027,R3＝3.761,R4＝1.159,
4. Information quantity Cj，CjThe larger the information amount contained in the j-th evaluation index, the more the evaluation index acts on the entire evaluation system, and the more weight is assigned thereto.
Cj＝Sj×Rj
C1＝0.897,C2＝1.118,C3＝1.313,C4＝1.159,
5. Objective relative weight w obtained by objective weighting methodj：
Figure BDA0003360188010000092
The objective relative weight matrix is:
Wj＝[0.200 0.249 0.292 0.258]T
(IV) obtaining the combined weight by the combined weighting method
The combined weight coefficients are:
Figure BDA0003360188010000093
the combined weight matrix is:
Wk＝[0.338 0.274 0.219 0.170]T
TABLE 3 weight coefficient of each evaluation index
Figure BDA0003360188010000094
In conclusion, the combination weight of each fracability evaluation is used as the weight of each evaluation index of the fracability evaluation to evaluate the fracability of the rock stratum.
Specifically, the fracability coefficient matrix of each rock formation is:
Fi＝XWk＝[28.049 17.653 25.119 12.387 24.627 9.083 13.452]T
TABLE 4 fracability coefficients for each formation
Figure BDA0003360188010000101
Namely, the evaluation results were: formation 1 is the most fracturable, followed by formation 3, formation 5, formation 2, formation 7, formation 4, and formation 6.
On the other hand, referring to fig. 2, an embodiment of the present invention discloses a system for evaluating the fracability of a rock formation, including:
a data acquisition module: the method is used for acquiring sample data of the fracturing evaluation index;
a first calculation module: the data acquisition module is connected with the data acquisition module and is used for obtaining subjective relative weight by utilizing C-OWA subjective weighting according to the fracturing evaluation index sample data;
a second calculation module: the CRITIC objective weighting module is connected with the data acquisition module and used for obtaining objective relative weight by utilizing CRITIC objective weighting according to sample data of the fracturing evaluation index;
an integration module: and the first calculation module and the second calculation module are connected and used for combining the subjective relative weight and the objective relative weight of each fracability evaluation index to obtain the combined weight of each fracability evaluation index, and the combined weight is used as the weight of each evaluation index of the fracability evaluation to evaluate the fracability of the rock stratum.
In yet another aspect, a non-transitory computer readable storage medium stores a computer program which, when executed, performs steps comprising the above-described method embodiments; and the aforementioned storage medium includes: a mobile storage device, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
Alternatively, the integrated module of the present invention may be stored in a computer-readable storage medium if it is implemented in the form of a software functional module and sold or used as a separate product. Based on such understanding, the technical solutions of the embodiments of the present invention may be essentially implemented or a part contributing to the prior art may be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the methods described in the embodiments of the present invention. And the aforementioned storage medium includes: a removable storage device, a ROM, a RAM, a magnetic or optical disk, or various other media that can store program code.
Compared with the prior art, the rock stratum fracturability evaluation method, the rock stratum fracturability evaluation system and the storage medium have the advantages that effective information in the subjective weight and the objective weight is considered, the problem that errors in a certain range are caused by the fact that the data are easy to separate from field test data when only subjective weighting is conducted is solved, and the problem that the data are deviated to a certain extent due to the fact that a plurality of uncertain factors exist in the field measurement process when only objective weighting is conducted is solved. Therefore, the on-site measurement data is fully utilized, the effective information in the subjective weight and the objective weight is considered, the fracturing performance of the rock stratum is evaluated more scientifically and reasonably, and the effectiveness and the reliability of the evaluation result are higher. The rock stratum fracturability result evaluated by the method has more scientific guiding significance on an engineering site, the cost is effectively saved, and the fracturing efficiency is improved:
(1) the subjective weight of the evaluation index is obtained by utilizing the C-OWA, an importance degree matrix is established by the C-OWA operator on the basis of considering the previous research cognition, the importance degree data are arranged in a descending order and are given to the weight on the basis of the combination number, the problem that the research result has an extreme value can be effectively solved, and the weight distribution of the evaluation index is relatively reasonable;
(2) the objective weight of the evaluation indexes is obtained by using the CRITIC, the difference and the correlation among the evaluation indexes are considered, scientific evaluation is carried out by completely using the objective attributes of the data, and the method carries out weighting according to field measurement data.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (10)

1. A method for evaluating the fracability of a rock formation, comprising the steps of:
acquiring sample data of a fracturing evaluation index;
according to the sample data of the fracturing evaluation index, subjective weighting is carried out by utilizing a combined ordered weighted average operator C-OWA to obtain subjective relative weight;
according to the sample data of the fracturing evaluation index, the relevance of the importance degree among indexes is utilized to judge the CRITIC objective weighting to obtain objective relative weight;
and combining the subjective relative weight and the objective relative weight of each fracturing evaluation index to obtain a combined weight, and evaluating the fracturing of the rock stratum by using the combined weight.
2. The method of claim 1, wherein the fracability evaluation index sample data comprises: the method comprises the following steps of evaluating index data, data numbers, total number of evaluating indexes, number of stratums to be evaluated and historical measuring data of the evaluating indexes of rock strata.
3. The method according to claim 2, wherein the subjective weighting of the combination order weighted average operator C-OWA according to the fracability evaluation index sample data to obtain the subjective relative weight comprises:
establishing an initial matrix for measuring the importance degree of the evaluation index according to sample data of the fracturing evaluation index, and calculating a weighting vector;
and obtaining subjective absolute weight of the evaluation index factors according to the weighting vectors, and obtaining subjective relative weight according to the subjective absolute weight.
4. A method for evaluating the fracability of a rock formation according to claim 3, wherein the calculation formula of the weighting vector is:
Figure FDA0003360188000000011
in the formula (I), the compound is shown in the specification,
Figure FDA0003360188000000012
q is the importance data number of a certain evaluation index, and n is the total number of the evaluation indexes.
5. The method according to claim 2, wherein the calculation formula of the subjective absolute weight of the evaluation index factor obtained from the weighting vector is:
Figure FDA0003360188000000013
wherein p is each evaluation index number, bpThe matrix corresponding to each evaluation index in the initial matrix;
obtaining subjective relative weight w according to absolute weightpThe calculation formula of (2) is as follows:
Figure FDA0003360188000000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003360188000000022
p is the number of each evaluation index in the table, and n is the total number of the evaluation indexes.
6. The method for evaluating the fracturing capability of the rock stratum according to claim 2, wherein the step of judging the CRITIC objective weighting according to the sample data of the fracturing capability evaluation index and the relevance of the importance degrees among the indexes to obtain the objective relative weight comprises the following steps:
preprocessing historical measurement data of each rock stratum evaluation index to obtain a dimensionless data set;
and calculating the standard deviation, the index conflict and the information content of each evaluation index through the index variability, and obtaining the objective relative weight of each evaluation index according to the information content.
7. The method according to claim 6, wherein the preprocessing of the fracability evaluation index sample data to obtain a dimensionless data set comprises:
obtaining an original measurement data matrix of original evaluation indexes according to historical measurement data of each rock stratum evaluation index;
adopting the correlation of importance degree among indexes to judge CRITIC method to carry out forward or reverse non-dimensionalization on the evaluation indexes to obtain a non-dimensionalized matrix A for the original measurement data matrix of the original evaluation indexes, wherein:
forward dimensionless processing formula:
Figure FDA0003360188000000023
a reverse dimensionless processing formula:
Figure FDA0003360188000000024
in the formula, i is the number of the stratum to be evaluated, j is the number of the evaluation index, and xijIs an element of matrix X, aijIs an element of the matrix a.
8. The method of claim 6, wherein the calculating the standard deviation and the information content of each evaluation index through the index variability and obtaining the objective relative weight of each evaluation index according to the information content comprises:
calculating the variability of the evaluation index:
Figure FDA0003360188000000025
in the formula, i is the number of the stratum to be evaluated, j is the number of the evaluation index, m is the total number of the stratum to be evaluated, SjIs the standard deviation;
and (3) calculating index conflict:
Figure FDA0003360188000000031
in the formula, rkjIs the correlation coefficient between the evaluation indexes k and j;
calculating the information quantity:
Cj＝Sj×Rj
obtaining objective relative weight w of each evaluation index according to information quantityj：
Figure FDA0003360188000000032
In the formula, j is an evaluation index number, and n is the total number of evaluation indexes.
9. A system for evaluating the fracability of a rock formation, comprising:
a data acquisition module: the method is used for acquiring sample data of the fracturing evaluation index;
a first calculation module: the data acquisition module is connected with the data acquisition module and used for obtaining subjective relative weight by utilizing the combination ordered weighted average operator C-OWA subjective weighting according to the fracturing evaluation index sample data;
a second calculation module: the CRITIC objective weighting module is connected with the data acquisition module and used for judging CRITIC objective weighting according to the sample data of the fracturing evaluation index and the correlation of the importance degrees among indexes to obtain objective relative weight;
an integration module: and the first calculation module and the second calculation module are connected and used for combining the subjective relative weight and the objective relative weight of each fracability evaluation index to obtain the combined weight of each fracability evaluation index, and the combined weight is used as the weight of each evaluation index of the fracability evaluation to evaluate the fracability of the rock stratum.
10. A non-transitory computer readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the fracability evaluation method of claims 1-8.
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