Method for calculating mineral content of stratum
阅读说明：本技术 一种计算地层矿物含量的方法 (Method for calculating mineral content of stratum ) 是由 廖东良 曾义金 王志战 刘江涛 张元春 于 2018-08-22 设计创作，主要内容包括：本发明公开了一种计算地层矿物含量的方法,构造线性规划数学模型,利用线性规划方法计算地层矿物含量,包括：利用X射线荧光录井/测试数据作为约束条件；以地层矿物类型作为决策变量；针对地层矿物含量构造目标函数。本发明利用X射线荧光录井/测试数据,通过构建适当的目标函数,利用元素响应方程的不等式约束和等式约束,应用线性规划方法快速、准确地反演地层体积含量,节省了费用和时间,为加快国内页岩地层勘探、开发起积极作用。(The invention discloses a method for calculating the mineral content of a stratum, which constructs a linear programming mathematical model and calculates the mineral content of the stratum by using a linear programming method, and comprises the following steps: using X-ray fluorescence logging/test data as constraint conditions; taking the type of the formation mineral as a decision variable; an objective function is constructed for the formation mineral content. The invention utilizes X-ray fluorescence logging/test data, constructs a proper target function, utilizes inequality constraint and equality constraint of an element response equation, applies a linear programming method to quickly and accurately invert the volume content of the stratum, saves cost and time, and plays a positive role in accelerating the exploration and development of the shale stratum in China.)
1. A method for calculating the mineral content of a stratum is characterized in that a linear programming mathematical model is constructed, and the mineral content of the stratum is calculated by using a linear programming method, and the method comprises the following steps:
using X-ray fluorescence logging/test data as constraint conditions;
taking the type of the formation mineral as a decision variable;
an objective function is constructed for the formation mineral content.
2. The method according to claim 1, characterized in that X-ray fluorescence logging/test data is used as constraints, wherein X-ray fluorescence data of downhole, surface logging and/or laboratory measurements are acquired.
3. The method according to claim 1 or 2, characterized in that X-ray fluorescence logging/test data is used as constraints, wherein X-ray fluorescence logging/test data is used to establish conventional response inequality/equality equations under a formation mineral model as constraints.
4. The method of claim 3, wherein the linear programming mathematical model is constructed by converting a general linear programming problem of shale formation mineral content problems to a standard form of a linear programming problem.
5. The method of claim 3 or 4, wherein the X-ray fluorescence data response equation is characterized by a formation mineral model:
wherein:
Yjis an elemental measurement result;
Vithe content of the mineral in the stratum is,
MCijis a value coefficient.
6. The method of claim 5, wherein the linear programming problem is of the standard form:
Vi≥0(i＝1,Λ,n)
7. the method of any one of claims 1-6, further comprising:
and determining the value coefficient of the objective function according to the relation between the contents of the formation minerals and the elements.
8. The method according to any one of claims 1 to 7, wherein the shale formation mineral content is calculated by a simplex method in a linear programming method.
9. The method of claim 8, wherein the shale formation mineral content is calculated using a simplex method of a linear programming method, wherein:
judging whether the calculation result is an optimal solution or not, wherein the calculation result is compared with the actual mineral result of the stratum, and if the difference between the calculation result and the actual mineral content is less than 3%, the optimal solution is obtained;
if not, the objective function is modified and solved again.
10. The method of any one of claims 1-9, further comprising:
the stratum minerals are classified into argillaceous, siliceous, calcareous and ferruginous minerals, wherein:
the argillaceous minerals comprise illite, chlorite, montmorillonite, and kaolinite;
the siliceous mineral comprises quartz and feldspar;
calcareous materials include dolomite and calcite;
the iron mineral comprises pyrite and hematite.
Technical Field
The invention relates to the field of geological exploration, in particular to a method for calculating the content of stratum minerals.
Background
The types and the contents of minerals in the stratum have very important meanings in the aspects of stratum identification, lithology division, determination of the content and the type of stratum clay, calculation of framework parameters, research of deposition environment and the like.
In the prior art, formation mineral content is typically calculated based on well log data. Logging, also called geophysical logging or petroleum logging, short for logging, is a method for measuring geophysical parameters by using the geophysical characteristics of rock stratum, such as electrochemical characteristics, electric conduction characteristics, acoustic characteristics, radioactivity and the like. Generally, well logging is performed by lowering a special logging instrument to the bottom of a well and pulling the logging instrument up, and logging data are collected during pulling up. The method is limited by drilling site conditions, the cost of logging instruments and the like, and a large amount of manpower and material resources cost is consumed for obtaining detailed logging data. The degree of detail of the logging data directly influences the accuracy and precision of the calculation of the mineral content of the stratum. Therefore, in the prior art, calculating the mineral content of the formation requires consuming a significant portion of the resources involved in the acquisition of the well log data.
Disclosure of Invention
The invention provides a method for calculating the mineral content of a stratum, which constructs a linear programming mathematical model and calculates the mineral content of the stratum by using a linear programming method, and comprises the following steps:
using X-ray fluorescence logging/test data as constraint conditions;
taking the type of the formation mineral as a decision variable;
an objective function is constructed for the formation mineral content.
In an embodiment, X-ray fluorescence logging/test data is utilized as a constraint, wherein X-ray fluorescence data of downhole, surface logging and/or laboratory measurements is acquired.
In one embodiment, the constraint is the use of X-ray fluorescence logging/test data, which is used to establish the conventional response inequality/equality equation under the formation mineral model.
In one embodiment, the linear programming mathematical model is constructed by converting a general linear programming problem to a standard form of a linear programming problem for shale formation mineral content problems.
In one embodiment, the X-ray fluorescence data response equation is characterized by a formation mineral model:
wherein:
Yjis an elemental measurement result;
Vithe content of the mineral in the stratum is,
MCijis a value coefficient.
In one embodiment, the standard form of the linear programming problem is:
in one embodiment, the method further comprises:
and determining the value coefficient of the objective function according to the relation between the contents of the formation minerals and the elements.
In one embodiment, the shale formation mineral content is calculated using a simplex method of a linear programming method.
In one embodiment, the shale formation mineral content is calculated using a simplex method in a linear programming method, wherein:
judging whether the calculation result is an optimal solution or not, wherein the calculation result is compared with the actual mineral result of the stratum, and if the difference between the calculation result and the actual mineral content is less than 3%, the optimal solution is obtained;
if not, the objective function is modified and solved again.
In one embodiment, the method further comprises:
the stratum minerals are classified into argillaceous, siliceous, calcareous and ferruginous minerals, wherein:
the argillaceous minerals comprise illite, chlorite, montmorillonite, and kaolinite;
the siliceous mineral comprises quartz and feldspar;
calcareous materials include dolomite and calcite;
the iron mineral comprises pyrite and hematite.
The invention utilizes X-ray fluorescence logging data, constructs a proper target function, utilizes inequality constraint and equality constraint of an element response equation, applies a linear programming method to quickly and accurately invert the volume content of the stratum, saves cost and time, and plays a positive role in accelerating the exploration and development of the shale stratum in China.
Additional features and advantages of the invention will be set forth in the description which follows. Also, some of the features and advantages of the invention will be apparent from the description, or may be learned by practice of the invention. The objectives and some of the advantages of the invention may be realized and attained by the process particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 and 2 are flowcharts of methods according to embodiments of the invention.
Detailed Description
The following detailed description will be provided for the embodiments of the present invention with reference to the accompanying drawings and examples, so that the practitioner of the present invention can fully understand how to apply the technical means to solve the technical problems, achieve the technical effects, and implement the present invention according to the implementation procedures. It should be noted that, as long as there is no conflict, the embodiments and the features of the embodiments of the present invention may be combined with each other, and the technical solutions formed are within the scope of the present invention.
The types and the contents of minerals in the stratum have very important meanings in the aspects of stratum identification, lithology division, determination of the content and the type of stratum clay, calculation of framework parameters, research of deposition environment and the like.
In the prior art, formation mineral content is typically calculated based on well log data. Logging, also called geophysical logging or petroleum logging, short for logging, is a method for measuring geophysical parameters by using the geophysical characteristics of rock stratum, such as electrochemical characteristics, electric conduction characteristics, acoustic characteristics, radioactivity and the like. Generally, well logging is performed by lowering a special logging instrument to the bottom of a well and pulling the logging instrument up, and logging data are collected during pulling up. The method is limited by drilling site conditions, the cost of logging instruments and the like, and a large amount of manpower and material resources cost is consumed for obtaining detailed logging data. The degree of detail of the logging data directly influences the accuracy and precision of the calculation of the mineral content of the stratum. Therefore, in the prior art, calculating the mineral content of the formation requires consuming a significant portion of the resources involved in the acquisition of the well log data.
In order to solve the problems, the invention provides a method for calculating the mineral content of the stratum.
Logging is the operation of recording and logging various relevant information during the drilling process. The logging technology is the most basic technology in oil and gas exploration and development activities, is the most timely and direct means for finding and evaluating oil and gas reservoirs, and has the characteristics of timely and various underground information acquisition and quick analysis and interpretation. In general, the cost and difficulty of performing logging operations are relatively low compared to logging operations.
In the invention, the content of the formation minerals is calculated based on the logging data, so that the cost and difficulty of obtaining the original and real content are greatly reduced.
In particular, logging includes X-ray fluorescence (XRF) logging. In the prior art, a lithologic identification function of element logging in a Bohai sea oil field is established by locking noble and Tan pit loyalty and the like (an element logging lithologic identification technology and application thereof in the Bohai sea oil field, Chinese offshore oil gas, 2016, 28(4)30-34), firstly, quantitative analysis is carried out on X-ray fluorescence (XRF) logging element combination parameters of typical clastic rock, carbonate rock and magma rock by utilizing a statistical method, and an element variable combination which is sensitive to various lithologies is screened out; then inputting the variable of the sensitive element into software for training, solving the coefficient of the variable parameter of different elements and establishing a lithological discrimination function; and finally substituting the element sequence value corresponding to a certain depth point into the Fisher judgment criterion, wherein the real lithology corresponding to the depth point is the one with the maximum lithology judgment function value.
The lithology while drilling discrimination method is researched by utilizing the content, spectrogram and logging information of elements in micro rock debris measured by X-ray fluorescence (XRF) by virtue of Lechunshan, Chenyiyiyi and Sunwei (a lithology while drilling discrimination method utilizing the logging information of the elements, 2011, 35(6), 66-70).
Based on the analysis of the prior art, the correlation between the X-ray fluorescence logging data and the formation mineral content is high, so in the method, the formation mineral content is calculated based on the X-ray fluorescence logging data.
Further, in the prior art, Linear Programming (LP) is one of the important branches of operations research, and is widely applied in practice, and the method thereof is mature, and is a mathematical method for assisting people in scientific management. Solving a problem by using a linear programming method, wherein an objective function is a linear function of a plurality of decision variables, and solving the maximum value or the minimum value of the objective function; the constraint to solve the problem is a set of linear inequalities or equations for a number of decision variables. These problems are consistent with the problems encountered in determining the mineral content of the formation. Therefore, in the method of the invention, a linear programming method is applied to solve the volume content of the formation minerals.
Specifically, establishing a mathematical model is a key step of linear programming. The mathematical model of Linear Programming (mathematical model of Linear Programming) is composed of three elements, Decision variables (decisions), objective functions (objective functions) and Constraints (Constraints). The general assumption is that there are m constraints and n decision variables x in the linear programming mathematical modeljJ is 1, 2, …, n, and the variable coefficient of the objective function is cjIs represented by cjReferred to as the figure of merit. Variable coefficient of constraint condition is aijIs shown as aijReferred to as the process coefficient. Constant on right end of constraint condition biIs represented by biReferred to as resource coefficients. The general expression for the linear programming mathematical model can be written as: is composed of
xj≥0(j＝1,2,K,n) (3)
Wherein:
c＝(c1,c2,...,cnvalance variable);
x＝(x1,x2,...,xnand) are decision variables.
In the invention, a linear programming mathematical model is constructed by using X-ray fluorescence logging/test data as constraint conditions, using stratum mineral types as decision variables and constructing an objective function aiming at the stratum mineral content, and the shale stratum mineral content is calculated by using a linear programming method.
The invention utilizes X-ray fluorescence logging/test data, constructs a proper target function, utilizes inequality constraint and equality constraint of an element response equation, applies a linear programming method to quickly and accurately invert the volume content of the stratum, saves cost and time, and plays a positive role in accelerating the exploration and development of the shale stratum in China.
The detailed flow of a method according to an embodiment of the invention is described in detail below based on the accompanying drawings, the steps shown in the flow chart of which can be executed in a computer system containing instructions such as a set of computer executable instructions. Although a logical order of steps is illustrated in the flowcharts, in some cases, the steps illustrated or described may be performed in an order different than presented herein.
Specifically, as shown in fig. 1, the method includes:
s110, constructing a linear programming mathematical model, wherein an objective function is constructed aiming at the content of the formation minerals (S113) by using X-ray fluorescence logging/test data as constraint conditions (S111) and using the type of the formation minerals as decision variables (S112);
and S120, calculating the mineral content of the shale formation by using a linear programming method.
Specifically, in one embodiment, X-ray fluorographic data is collected from downhole, surface, and/or laboratory measurements.
Further, in one embodiment, the conventional response inequality/equality equation under the formation mineral model is established as a constraint using the X-ray fluorescence logging/test data in the process of using the X-ray fluorescence logging data as a constraint.
Further, in one embodiment, the cost factor of the objective function is determined based on the relationship between the formation minerals and the element content.
Specifically, in one embodiment, the cost factor of the objective function is determined according to Table 1 (a table of the specific gravity of the elements contained in the formation minerals).
Mineral substance
Al
Ca
Fe
K
Mg
Na
S
Si
Quartz crystal
0
0
0
0
0
0
0
0.467
Anorthite
0.194
0.144
0
0
0
0
0
0.202
Calcite
0
0.4
0
0
0
0
0
0
Dolomite
0
0.217
0
0
0.132
0
0
0
Kaolinite
0.204
0.001
0.008
0.001
0.001
0.001
0
0.21
Illite stone
0.132
0.005
0.048
0.045
0.012
0.004
0
0.249
Montmorillonite (montmorillonite)
0.07
0.007
0.015
0.006
0.015
0.008
0
0.205
Pyrite
0
0
0.466
0
0
0
0.535
0
TABLE 1
Specifically, in one embodiment, the X-ray fluorescence logging data response equation is characterized by a formation mineral model:
wherein:
Yjis an elemental measurement result;
Vithe content of the mineral in the stratum is,
MCijis the cost coefficient of the objective function.
Specifically, in one embodiment, MCijAre the corresponding figure of merit in table 1.
Further, in one embodiment, the linear programming mathematical model is constructed by converting a general linear programming problem to a standard form of a linear programming problem for shale formation mineral content problems.
Specifically, in one embodiment, the standard form of the linear programming problem is:
further, in one embodiment, the shale formation mineral content is calculated using a simplex method of a linear programming method.
Specifically, in one embodiment, the shale formation mineral content is calculated based on the constructed linear programming mathematical model, whether the calculation result is the optimal solution or not is judged, and if not, the objective function is modified and solved again.
Specifically, in an embodiment, the method for determining whether the solution is the optimal solution includes: comparing the calculation result with the actual mineral result of the stratum, and if the difference between the calculation result and the actual mineral content is less than 3%, determining that the calculation result is an optimal solution; otherwise, the objective function is modified again.
Specifically, as shown in fig. 2, in an embodiment, the method includes the following steps:
s211, collecting XRF data comprising one of downhole, surface or laboratory measurements;
s212, acquiring the type of the stratum minerals, and setting decision variables of a linear programming mathematical model;
s213, determining the content relation of the formation minerals and the elements;
s214, determining a value coefficient in the objective function according to the relation between the contents of the formation minerals and the elements;
s220, applying constraint conditions to the decision variables by using XRF data response, establishing an inequality equation, obtaining the inequality constraint conditions of the linear programming mathematical model, constructing an extreme value objective function of the solved variables, and establishing the linear programming mathematical model;
s230, calculating the content of the formation minerals by using a linear programming method;
s240, judging whether the unique optimal solution exists in the solution obtained in the step S230, if the unique optimal solution does not exist, modifying the objective function (returning to the step S220) and recalculating (S230) until the optimal solution is obtained;
and S250, if the optimal solution is obtained, outputting a calculation result of the mineral content of the stratum.
Further, in consideration of the variety of the formation minerals, in order to simplify the calculation process and clarify the calculation results on the premise of satisfying the research and analysis requirements, in one embodiment, the formation minerals are classified into several categories according to the research and analysis requirements, so that the final output calculation result is the content of each category of minerals in the formation.
Specifically, in one embodiment, the formation minerals are classified as argillaceous, siliceous, calcareous and ferrous minerals, wherein:
the argillaceous minerals comprise illite, chlorite, montmorillonite, and kaolinite;
the siliceous mineral comprises quartz and feldspar;
calcareous materials include dolomite and calcite;
the iron mineral comprises pyrite and hematite.
Specifically, according to the method of an embodiment of the present invention, in a specific application scenario, a certain stratum includes kaolinite, illite, sandstone, feldspar, calcite, dolomite, and pyrite, that is, 7 unknowns of basic solution variables in linear programming are used as decision variables, 8 element measurement results are used as inequality constraint conditions and 1 equality constraint equation, a value coefficient in an objective function is obtained according to table 1, the shale stratum is solved for 7 mineral contents, and finally, siliceous, calcareous, argillaceous, and pyrite are summarized.
Table 2 is that the linear programming is utilized to solve the mineral content of the stratum in a certain stratum, and 3680-3697.5 m is used for calculating that the stratum mainly comprises sandstone and mudstone and contains a small amount of pyrite; 3713-3715 m, the calculation is mainly carried out on gray matter, sandstone and mudstone, and the product contains a small amount of pyrite.
Depth of field
Mg
Al
Si
P
S
K
Ca
Fe
Siliceous material
Calcareous material
Argillaceous material
Pyrite
3680
0.082873
0.133949
0.424894
0.001302
0.008674
0.037432
0.13047
0.036466
0.851976
0
0.131811
0.016213
36805
0063735
0139095
0459276
0001573
0014661
0042302
006634
0043456
098346
0
0
001654
3681
0.073063
0.166997
0.420682
0.00062
0.012131
0.060872
0.059654
0.044409
0.823214
0
0.176786
0
3681.5
0.058857
0.140451
0.503445
0.00148
0.012512
0.037206
0.100109
0.033616
1
0
0
0
3682
0.07585
0.140995
0.43087
0.001426
0.008794
0.042531
0.122801
0.031696
0.859416
0
0.140584
0
3682.5
0.079048
0.133827
0.448973
0.001564
0.01202
0.037478
0.130846
0.033723
0.948774
0
0.028759
0.022467
3683
0.073013
0.118301
0.432835
0.001565
0.010985
0.036964
0.134277
0.032643
0.885665
0
0.093802
0.020533
3683.5
0.074757
0.111573
0.425426
0.001577
0.00976
0.036485
0.158921
0.030821
0.838233
0
0.161767
0
3684
0.073157
0.124994
0.427751
0.001183
0.009795
0.037362
0.142651
0.031119
0.84728
0
0.15272
0
3684.5
0.08113
0.115903
0.444318
0.00159
0.010472
0.03515
0.134481
0.033177
0.928743
0
0.051683
0.019574
3685
0.072892
0.08657
0.415521
0.000481
0.008812
0.031234
0.128989
0.031598
0.816403
0
0.167126
0.016471
3685.5
0.078546
0.119508
0.440602
0.001514
0.010131
0.03629
0.13406
0.034115
0.914061
0
0.067003
0.018936
3686
0.082786
0.085733
0.404656
0.001314
0.010365
0.035422
0.172691
0.030455
0.757416
0
0.242584
0
3686.5
0.077608
0.103558
0.500916
0.00146
0.014541
0.035312
0.116982
0.044704
1
0
0
0
3687
0.076005
0.108875
0.440732
0.001515
0.009628
0.036279
0.13814
0.031575
0.89779
0
0.10221
0
3687.5
0.058053
0.116073
0.526393
0.000526
0.006485
0.035366
0.105513
0.027601
1
0
0
0
3688
0.066947
0.069536
0.430818
0.001366
0.007807
0.03155
0.166809
0.026357
0.859214
0
0.140786
0
3688.5
0.077049
0.096345
0.439121
0.001267
0.011425
0.034418
0.155268
0.031697
0.910301
0
0.068344
0.021355
3689
0.076417
0.119103
0.500484
0.001497
0.011698
0.036357
0.111805
0.037939
1
0
0
0
3689.5
0.078921
0.100324
0.431851
0.001324
0.009606
0.035844
0.146392
0.03057
0.863233
0
0.136767
0
3690
0.093507
0.07375
0.404108
0.001365
0.00844
0.032771
0.180709
0.030096
0.755284
0
0.244716
0
3690.5
0.089138
0.052439
0.377263
0.001356
0.008693
0.031834
0.194178
0.029414
0.596026
0
0.397265
0.006709
3691
0.075083
0.132378
0.514334
0.001288
0.014294
0.036606
0.089172
0.044718
1
0
0
0
3691.5
0.09179
0.037042
0.3866
0.001136
0.007377
0.029038
0.216335
0.024611
0.678213
0.027377
0.280621
0.013789
3692
0.079611
0.059829
0.444842
0.001528
0.015441
0.028857
0.133904
0.042353
0.913782
0
0.086218
0
3692.5
0.077099
0.112482
0.517004
0.001259
0.012905
0.0358
0.097883
0.037547
1
0
0
0
3693
0.095718
0.085883
0.40872
0.001447
0.009053
0.034844
0.170416
0.030821
0.790797
0
0.192281
0.016921
3693.5
0.081095
0.081598
0.434858
0.001409
0.013994
0.032857
0.1508
0.038717
0.897787
0
0.076056
0.026157
3694
0.069988
0.123106
0.529364
0.000644
0.012925
0.035193
0.050511
0.043694
1
0
0
0
3694.5
0.069045
0.155958
0.426511
0.000529
0.022333
0.052583
0.034264
0.038582
0.845462
0
0.154538
0
3695
0.072771
0.141219
0.440926
0.001591
0.016146
0.041523
0.090373
0.043462
0.924095
0
0.045726
0.030179
3695.5
0.097519
0.087575
0.397091
0.001377
0.00978
0.035268
0.159547
0.032154
0.747475
0
0.234245
0.01828
3696
0.074432
0.118412
0.424225
0.001104
0.014762
0.037281
0.101324
0.044144
0.858326
0
0.114081
0.027593
3696.5
0.076338
0.127421
0.444334
0.001308
0.016679
0.037518
0.095873
0.040266
0.937882
0
0.030943
0.031176
3697
0.076045
0.141322
0.455127
0.001285
0.017658
0.040082
0.084754
0.034881
0.954683
0
0.045317
0
3697.5
0.076024
0.127881
0.440186
0.000558
0.015921
0.035768
0.095105
0.044119
0.920941
0
0.0493
0.029759
3713
0.038943
0.048395
0.266117
0.005392
0.003844
0.026639
0.304412
0.016994
0.377778
0.260573
0.361649
0
3713.5
0.016641
0.036849
0.170764
0.007209
0.005084
0.021533
0.348297
0.013478
0.216817
0.503856
0.279159
0.000168
3714
0.045156
0.050372
0.275636
0.003808
0.022491
0.035889
0.210265
0.048632
0.386758
0.189596
0.381606
0.042039
3714.5
0.034268
0.028625
0.111108
0.007871
0.005492
0.020189
0.356363
0.011981
0.122293
0.657478
0.216856
0.003373
3715
0036473
003274
0107284
0005071
0002405
0023449
0348871
0008709
0115563
0662751
0221686
0
TABLE 2
The method utilizes XRF data, constructs an element response equation under a stratum mineral model and utilizes a linear programming method to calculate the stratum mineral content. By constructing a proper objective function, utilizing inequality constraints and equality constraints of a logging response equation and applying a linear programming method, the method is favorable for quickly and accurately inverting the volume content of the stratum, reduces expensive logging projects such as logging by using elements, saves cost and time, and plays a positive role in accelerating exploration and development of the shale stratum in China.
It is to be understood that the disclosed embodiments of the invention are not limited to the particular structures, process steps, or materials disclosed herein but are extended to equivalents thereof as would be understood by those ordinarily skilled in the relevant arts. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting.
Reference in the specification to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Thus, appearances of the phrase "an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment.
Although the embodiments of the present invention have been described above, the above description is only for the convenience of understanding the present invention, and is not intended to limit the present invention. There are various other embodiments of the method of the present invention. Various corresponding changes or modifications may be made by those skilled in the art without departing from the spirit of the invention, and these corresponding changes or modifications are intended to fall within the scope of the appended claims.
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