CN111595752B - Method for determining effective porosity of rock - Google Patents
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- CN111595752B CN111595752B CN202010571975.5A CN202010571975A CN111595752B CN 111595752 B CN111595752 B CN 111595752B CN 202010571975 A CN202010571975 A CN 202010571975A CN 111595752 B CN111595752 B CN 111595752B
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- 239000011435 rock Substances 0.000 title claims abstract description 78
- 238000000034 method Methods 0.000 title claims abstract description 23
- 239000011148 porous material Substances 0.000 claims description 28
- 239000000203 mixture Substances 0.000 claims description 16
- 238000009826 distribution Methods 0.000 claims description 8
- 230000005684 electric field Effects 0.000 claims description 7
- 238000005325 percolation Methods 0.000 claims description 6
- 239000012530 fluid Substances 0.000 claims description 4
- 230000000694 effects Effects 0.000 abstract description 2
- 239000002245 particle Substances 0.000 description 4
- 238000011161 development Methods 0.000 description 3
- 238000011160 research Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 2
- 239000000835 fiber Substances 0.000 description 2
- 229910052500 inorganic mineral Inorganic materials 0.000 description 2
- 239000011707 mineral Substances 0.000 description 2
- 230000035699 permeability Effects 0.000 description 2
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 2
- 235000019738 Limestone Nutrition 0.000 description 1
- 238000009792 diffusion process Methods 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- 239000006028 limestone Substances 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 230000000704 physical effect Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000004445 quantitative analysis Methods 0.000 description 1
- 239000004576 sand Substances 0.000 description 1
- 239000003079 shale oil Substances 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 238000003860 storage Methods 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
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- G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
- G01N15/08—Investigating permeability, pore-volume, or surface area of porous materials
- G01N15/088—Investigating volume, surface area, size or distribution of pores; Porosimetry
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- G—PHYSICS
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N27/00—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
- G01N27/02—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance
- G01N27/04—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance by investigating resistance
- G01N27/041—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance by investigating resistance of a solid body
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Abstract
The invention discloses a method for determining the porosity of a rock, which has the problems that most empirical formulas used in the existing method for determining the effective porosity of the rock have limitation or poor accuracy and the like, and a unified standard determination method is not available, so that the actual effective porosity of the rock is difficult to accurately and efficiently measure in actual engineering; the novel empirical formula provided by the invention has the advantages of universality, high efficiency, simplicity, convenience and the like, and can provide better theoretical guidance for actual work. The core of the method is to equalize the seepage phenomenon and the extreme current phenomenon in the rock, and derive the overall effective porosity formula of the rock through the overall electrical properties of the rock. The method for determining the effective porosity of the rock and the empirical formula have obvious effects, can be used for most situations, and has high practicability.
Description
Technical Field
The invention relates to the technical field of engineering exploration, in particular to a method for determining effective porosity of a rock.
Background
In the fields of environmental resource development, engineering exploration and the like, the most encountered objects are various rocks, and various physical and chemical properties of the rocks have great influence on the development of related work, so that various accidents can be caused. The rock is composed of solid matter particles with various shapes, various pore spaces are often formed among the particles, and the existence of the pores greatly influences various physical properties of the rock and has great research value, so that a scholars refer to the volume of all pores in a collected rock sample and the ratio of the volume to the total volume as the total porosity of the rock and conducts intensive research. In practical applications, only those interconnected pores are of practical significance, for example, oil gas and water are mainly stored in the interconnected pores and mutually percolated therein. Therefore, the concept of effective porosity is proposed, wherein effective porosity refers to the ratio of the pore volume which is communicated with each other under the general temperature and pressure condition and allows fluid to flow in the pore volume to the total volume of the rock. Obviously, the effective porosity of the same rock is less than its total porosity.
As is well known, oil and gas reservoir rocks are mainly sandstone and limestone. The sandstone is formed by geological cementing of sand particles with different properties, shapes and sizes, and pores are formed among the particles at positions which are not filled by a cementing material, so that the porosity, permeability and saturation characteristics of reservoir rock are the basis for recognizing the oil storage condition of a reservoir, dividing a main oil reservoir, determining the effective thickness, estimating the reserve and analyzing the production condition of an oil field, and are the most basic rock physical parameters for exploration and development of the oil field.
At present, a plurality of effective porosity calculation formulas under different applicable conditions exist, such as a porous water seepage model formula of Bourbie, a gas fiber tube model formula of Rodriguez, a sandstone model formula of Pape and the like.
Disclosure of Invention
In oil and gas exploration, since oil and gas are mainly present in the pores and fractures of rocks, such as shale gas and shale oil, the effective porosity of rocks becomes an important parameter for indicating the oil and gas reserves in the rocks. However, the rock structure is complex and variable, and the parameter cannot be directly measured, so that a unified and effective quantitative method is not available at present. Some people use total porosity directly instead of effective porosity; some people use fiber tubes and other models to equivalent the pore structure in the rock, indirectly obtain the effective porosity of the rock by measuring the permeability, and others analyze the effective porosity of the rock by back and forth regression of the sound wave time difference and the density. In summary, how to obtain accurate rock effective porosity remains a major concern for the relevant workers.
The technical problem to be solved by the invention is as follows: because most of empirical formulas in the existing determination method of the effective porosity of the rock have the problems of limitation or poor accuracy, the actual effective porosity of the rock is difficult to accurately and efficiently determine in actual engineering, and the novel empirical formula provided by the invention is universal and efficient and can provide better theoretical guidance for actual work.
The technical scheme adopted by the invention is as follows: a method for determining effective porosity of rock is characterized by that the seepage phenomenon and extreme current phenomenon in rock are equalized to obtain the effective porosity of whole rock,
where φ is the total porosity, i.e. the volume percentage of the pore portion, φeffL1 is the spatial orientation factor of the pore section for the effective porosity of the rock as a whole<sin2(m,n)>1L2 is the spatial orientation factor of a rock skeleton part<sin2(m,n)＞2；
Equation (4) is simplified as follows:
which is a function of phieffPart of a hyperbola of sum phi, constant over
And (1,1) two points, and phieffAlways less than phi, and meets the general rules of effective porosity and total porosity.
Wherein the empirical formula is derived from a theoretical calculation formula of the overall conductivity of the mixture, and the conductivity, content and structure of each component of the mixture are related to the overall conductivity as follows:
wherein phiiIs the volume percentage of the ith component, σiIs the conductivity, σ, of the i-th componentmIs the overall conductivity of the mixture, < sin2(m,n)>iAnd<cos2(m,n)>iis the spatial orientation factor of the ith component, the sum of which is1 and is related only to the spatial structure of the mixture, and m and n represent the direction of maximum conductivity change and the direction of the electric field;
the formula uses the concept that the seepage field is consistent with the electric field distribution under extreme conditions, considers each volume infinitesimal in the rock structure, introduces the porosity parameter psi, and simulates the conductivity sigmaiAnd analogizing to obtain the overall effective porosity phi of the rock by using the space orientation factor and formula of the overall conductivity formula of the mixtureeff，
Wherein the porosity parameter ψ satisfies:
where ψ ═ 1 represents that percolation can occur in the element, ψ ═ 0 represents that percolation cannot occur because the fluid flows only in the pores;
therefore, considering the existence of two micro components of pores and a rock skeleton in the rock, the (3) is carried into the (2) to obtain the (4).
Compared with the prior art, the invention has the following advantages:
(1) the empirical formula of the rock effective porosity determination method is universal and has no limitation of use conditions.
(2) The empirical formula of the method for determining the effective porosity of the rock is simple and clear, the used parameters are fewer, and the method is greatly simplified compared with certain empirical formulas.
(3) The method for determining the effective porosity of the rock has the advantages of obvious empirical formula effect, capability of meeting most of conditions and high practicability.
(4) The method for determining the effective porosity of the rock is based on the measurement of the conductivity of a mature rock sample, the actual operation is simple and rapid, the result accuracy is high, and the effective porosity parameters can be obtained by performing simple mathematical processing on later-stage data.
Drawings
FIG. 1 is a graph of actual data relating effective porosity to total porosity for koponen;
fig. 2 is a fitting result of the determination method of effective porosity of rock of the present invention, wherein fig. 2(a) is a schematic diagram of a fitting result of actual data to Koponen, and fig. 2(b) is a schematic diagram of a fitting result of actual data to Berg.
Detailed Description
At present, relevant scholars propose a large number of empirical formulas of effective porosity determination methods based on different medium structures and rock types, but certain limitations and disadvantages exist, and no acknowledged empirical formula of a general effective determination method exists, but the invention proposes an empirical formula of a determination method for describing the relationship between effective porosity and total porosity more generally, and can be effectively applied to relevant research and work.
Effective porosity phi of rockeffThe relationship with total porosity phi has long been studied. koponen found from the extensive experimental data in fig. 1 that the effective porosity versus total porosity curve had a typical cross-sectional distance of 0.3, which resulted in the earlier empirical formula:
φeff＝φ-0.3 (1)
later, related scholars propose other empirical formulas with different medium structures and rock types, but the empirical formulas have certain limitations or limited application range, only use certain special models or use too many parameters, and are very complex, so that the need of obtaining a simpler general empirical formula is very high.
In order to obtain a more general formula, the pore seepage system and the current diffusion system of the rock are consistent under certain conditions, which is represented by the following steps: the distribution of current in the electric field is related to the conductivity distribution, the current density is large at the place with large conductivity, the current density is small at the place with small conductivity, and the conductivity distribution is related to the structural factors such as the skeleton and pore distribution of the rock; the same is true for the pore seepage phenomenon in the rock, and considering the impermeability of the rock skeleton, the seepage phenomenon exists only in the area where the pores exist, and the seepage does not exist in the place where the pores do not exist, and the two share the same set of space structure influence factors. Therefore, the seepage phenomenon of the pores in the rock can be equivalently regarded as the extreme current field distribution condition with the conductivity of the rock skeleton being 0.
The Lijianhao scholars put forward a theoretical calculation formula for determining the overall conductivity of the mixture in 2005, and the conductivity, content and structure of each component of the mixture are related to the overall conductivity as follows:
wherein phiiIs the volume percentage of the ith component, σiIs the conductivity, σ, of the i-th componentmIs the overall conductivity of the mixture, < sin2(m,n)〉iAnd < cos2(m,n)>iIs the spatial orientation factor of the i-th component, the sum of which is 1, and is related only to the spatial structure of the mixture, and m and n represent the direction of maximum conductivity change and the direction of the electric field.
By using the concept that the seepage field is consistent with the electric field distribution under extreme conditions, each volume infinitesimal in the rock structure is considered, the porosity parameter psi is introduced to simulate the conductivity sigmaiAnd analogizing to obtain the overall effective porosity phi of the rock by using the space orientation factor and formula of the overall conductivity formula of the mixtureeff。
Wherein the porosity parameter ψ satisfies:
where ψ -1 represents that percolation can occur in the element, ψ -0 represents that percolation cannot occur because the fluid flows only in the pores.
Therefore, considering the existence of two micro components of pores and a rock skeleton in the rock, the method carries out the following steps of (3) into (2):
where φ is the total porosity, i.e. the volume percentage of the pore portion, φeffBeing integral with the rockL1 is the spatial orientation factor of the pore portion<sin2(m,n)>1L2 is the spatial orientation factor sin of a rock skeleton part2(m,n)>2This is the general formula of rock effective porosity to total porosity.
Equation (4) is simplified as follows:
this is a function of phieffPart of a hyperbola of sum phi, constant over
And (1,1) two points, and phieffAlways less than phi, and meets the general rules of effective porosity and total porosity.
The present invention uses two sets of spatial orientation factors L1 and L2 fitted to prior (bulk and component conductivity actual) data, substituted into the formula, to fit to actual measured effective and total porosity data, the results of which are shown in fig. 2.
It has been found that the fit is good and it is believed that the present invention has found a more general empirical formula describing the relationship between effective porosity and total porosity.
In the practical engineering implementation, in order to obtain the effective porosity, the overall conductivity of the collected rock sample is measured, data fitting is carried out on the conductivity of standard mineral rocks, space orientation factors L1 and L2 of the structure of the rock sample are obtained, the total porosity phi of the rock sample is obtained by calculating the volume and the mass of the rock sample and the density of the mineral composition, the theoretical effective porosity of the rock sample can be obtained by substituting the three data into the empirical formula provided by the invention, and the result can further guide the practical engineering implementation.
Claims (2)
1. A method for determining effective porosity of rock, characterized by: the method is equivalent to the seepage phenomenon and the extreme current phenomenon in the rock, and the formula for obtaining the effective porosity of the whole rock is as follows,
where φ is the total porosity, i.e. the volume percentage of the pore portion, φeffL1 is the spatial orientation factor of the pore section for the effective porosity of the rock as a whole<sin2(m,n)>1L2 is the spatial orientation factor of a rock skeleton part<sin2(m,n)>2；
Equation (4) is simplified as follows:
which is a function of phieffPart of a hyperbola of sum phi, constant over
And (1,1) two points, and phieffAlways less than phi, and meets the general rules of effective porosity and total porosity.
2. A method of determining the effective porosity of a rock according to claim 1, wherein: the above formula (5) for effective porosity of rock is based on a theoretical calculation formula for the overall conductivity of the mixture, and the formula (5) relates the conductivity, content and structure of each component of the mixture to the overall conductivity, as follows:
wherein phiiIs the volume percentage of the ith component, σiIs the conductivity, σ, of the i-th componentmAs regards the overall electrical conductivity of the mixture,<sin2(m,n)>iand<cos2(m,n)>iis the spatial orientation factor of the ith component, the sum of the two is 1, and is only related to the spatial structure of the mixture, and m and n represent the maximum direction of conductivity change and the direction of an electric field;
the formula (5) introduces a porosity parameter psi by using the concept that the seepage field is consistent with the electric field distribution under extreme conditions, considering each volume infinitesimal in the rock structure, so as to simulate the electrical conductivity sigmaiAnd analogizing to obtain the overall effective porosity phi of the rock by using the space orientation factor and formula of the overall conductivity formula of the mixtureeff，
Wherein the porosity parameter ψ satisfies:
where ψ ═ 1 represents that percolation can occur in the element, ψ ═ 0 represents that percolation cannot occur because the fluid flows only in the pores;
therefore, considering the existence of two micro components of pores and a rock skeleton in the rock, the (3) is carried into the (2) to obtain the (4).
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103543474A (en) * | 2012-07-16 | 2014-01-29 | 中国石油化工股份有限公司 | Hydrocarbon saturation evaluation method based on non-conductive pore model |
| CN109374497A (en) * | 2018-10-29 | 2019-02-22 | 河海大学 | A kind of rock micropore structure test method |
| CN110716235A (en) * | 2018-07-13 | 2020-01-21 | 中国石油化工股份有限公司 | Sand shale well logging pore structure inversion method |
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| CN104101905B (en) * | 2013-04-11 | 2017-02-08 | 中国石油天然气集团公司 | Reservoir classification method based on rock electricity parameters |
| CN106321087B (en) * | 2015-07-06 | 2019-05-07 | 中国石油化工股份有限公司 | A method of obtaining lithostratigraphy factor |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103543474A (en) * | 2012-07-16 | 2014-01-29 | 中国石油化工股份有限公司 | Hydrocarbon saturation evaluation method based on non-conductive pore model |
| CN110716235A (en) * | 2018-07-13 | 2020-01-21 | 中国石油化工股份有限公司 | Sand shale well logging pore structure inversion method |
| CN109374497A (en) * | 2018-10-29 | 2019-02-22 | 河海大学 | A kind of rock micropore structure test method |
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| 混合物整体电导率的研究;李剑浩;《地球物理学报》;20051117;第48卷(第6期);1408 * |
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