CN105507870B - A kind of sandstone reservoir determines method without back-up sand hydraulic fracture flow conductivity - Google Patents
A kind of sandstone reservoir determines method without back-up sand hydraulic fracture flow conductivity Download PDFInfo
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- 239000004576 sand Substances 0.000 title claims abstract description 66
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- 238000010276 construction Methods 0.000 claims description 5
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- 230000035699 permeability Effects 0.000 claims description 5
- 238000003825 pressing Methods 0.000 claims description 5
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- E—FIXED CONSTRUCTIONS
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- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
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Abstract
The present invention specifically provides a kind of sandstone reservoir and determines method without back-up sand hydraulic fracture flow conductivity, based on the correlation theory such as mathematics and rock mechanics, and rock particles particle diameter is considered, closure stress, particle lays the influence of the number of plies and Particle Breakage to hydraulic fracture flow conductivity in the case of particles filled hydraulic fracture, feature is closed by analyzing non-back-up sand hydraulic fracture, establish non-back-up sand hydraulic fracture mathematical modeling, the present invention provides calculation basis for the calculating of non-back-up sand hydraulic fracture flow conductivity, it more can accurately study the hydraulic fracture in the case of not sand fracturing, the flow conductivity of crack or major fracture finger tip partial fracture caused by the induction of effect support is formed without during waterpower sand fracturing, foundation is provided for Oil/gas Well hydraulic fracturing optimization design.
Description
Technical field
The present invention relates to the research field of hydraulic fracturing technology, and in particular to a kind of sandstone reservoir is led without back-up sand hydraulic fracture
Flow capacity judging method.
Background technology
Hydraulic fracturing technology is that Low permeable oil and gas reservoirs develop the most frequently used technology, is to improve having for Low permeable oil and gas reservoirs production capacity
Effect technology, the particularly reservoir in quality preservation difference, hydraulic fracturing technology have become the crucial of this kind of reservoir of exploitation and must
The technology that must be used.
Fracture condudtiviy is one of major parameter that hydraulic fracturing technology is pursued, production capacity after the pressure of Oil/gas Well is played to
Important effect is closed, often fracture condudtiviy size directly determines the height of production capacity after fractured well pressure, therefore studies crack
Flow conductivity has highly important meaning to hydraulic fracturing optimization.Conventional fracture condudtiviy is mainly obtained by experiment method
Taking, only less theoretical calculation model determines sand packed fracture flow conductivity, and for non-back-up sand hydraulic fracture flow conductivity
Theoretical Determination do not have also.The non-back-up sand hydraulic fracture flow conductivity of research, it is impossible to by the back-up sand hydraulic fracture water conservancy diversion of routine
Capability approach is directly applied in non-back-up sand hydraulic fracture, this be non-back-up sand hydraulic fracture flow conductivity research bring it is many not
Just, it is unfavorable for the design optimization of hydraulically fractured wells, is also unfavorable for the hydraulic fracture and not formed to sandstone reservoir not sand fracturing
The effectively research of support hydraulic fracture flow conductivity.
The content of the invention
The purpose of the present invention is to overcome above-mentioned existing issue, therefore, the invention provides a kind of sandstone reservoir without back-up sand water
Power fracture condudtiviy determines method, comprises the following steps：
1) reservoir granularity, reservoir closure stress, hydraulic fracture length and height are obtained；
2) according to assumed condition, distribution of particles model is established, and calculates crack endoparticle quantity, fracture porosity accordingly
And fracture width；
3) derive that sandstone reservoir only considers on permeability and pore structure relation formula according to Gao Caini-Kalman
In the case of wall particles supports without sand packed fracture flow conductivity calculation formula：
In formula：
FCDFor only consider in the case of wall particles supports without sand packed fracture flow conductivity, unit is μm2·cm；
LfFor hydraulic fracture height, unit is m；
HfFor hydraulic fracture length, unit is m；
N is spherical particle projection number total in crack；
R is spherical particle radius, and unit is m；
τ is hole tortuosity；
R is the pore radius of supporting crack, and unit is m.
4) on the basis of step 3), the fracture guide energy under Laminar Flow is made on coarse fracture faces with reference to Walsh
Power computation model, draw consider in the case of this kind under closure stress without sand packed fracture flow conductivity calculation formula：
In formula：
FCD′For, without sand packed fracture flow conductivity, unit is μm under consideration closure stress2·cm；
WfFor hydraulic fracture width, unit is m；
μ is fracture faces asperities height root mean square, and unit is m；
σ is closure stress, and unit is MPa；
σ0For first closure stress, unit is Mpa
Wσ0For first closure stress σ0Fracture width under effect, unit is m.
5) according to hydraulic fracture wall particle in hydraulic fracturing process it is peeling-off and the characteristics of laid in crack, and
Assuming that seam in peel off particle be uniform-spherical also assume diamond in shape layered arrangement laying, then utilize mathematical knowledge, it can be deduced that consider rock
Stone particle peels off the flow conductivity calculation formula of supporting crack：
In formula：
FCDsTo consider the hydraulic fracture flow conductivity in the case of rock particles peeling rear support hydraulic fracture；
NsFor total spherical particle number in crack in the case of consideration rock particles peeling rear support hydraulic fracture；
N is that the number of plies, convexity layer containing particle are laid in crack；
M is constant, takes 1 or 0.
6) on the basis of the formula in step 5) assume crack in laying rock particles under original closure stress not
Deformation does not crush；Not deformed under high closure stress, it is broken only to occur, and particle uniformly crushes in whole crack, particle
The fragment formed after broken only deforms not filling pore, and unbroken particle still assumes diamond in shape arrangement；Crack wall is convex
The rock particles risen deforms in no instance also not to be crushed, then calculates mould with reference to Harding's Particle Breakage rate
Type, obtain the fracture condudtiviy calculation formula without back-up sand of consideration Particle Breakage in the case of this kind：
In formula
F′CDTo consider the water fracture condudtiviy without back-up sand in the case of Particle Breakage；
Wf0For original fracture width, unit is m；
For fracture porosity, it is expressed as a percentage,
For the fracture porosity under reset condition, it is expressed as a percentage；
δ is Particle Breakage rate, is expressed as a percentage,
W′fTo consider fracture width in the case of crushing, unit is m.
Above-mentioned steps 1) in reservoir granule size using laboratory method obtain, reservoir closure stress size using three-dimensional should
Power experimental result or pressing crack construction analysis calculate, hydraulic fracture length and height can utilize micro-seismic monitoring, well temperature testing or
Post analysis are pressed to obtain.
Above-mentioned steps 2) assumed condition be：According to without back-up sand hydraulic fracture arrangement for closed configuration, it is assumed that rock formation particle is equal
Even, wall particle is raised in hemispherical, and seam endoparticle is arranged as rhombus in spherical, layered arrangement, and in the case of prime stratum
Particle is indeformable, does not crush.
Above-mentioned crack wall particle projection number is considered as being embedded in the granule number of crack wall half for rock particles.
Beneficial effects of the present invention：
(1) this sandstone reservoir of the invention determines that method is based on mathematics and rock power without back-up sand hydraulic fracture flow conductivity
Etc. correlation theory, and considered particle laying in the case of rock particles particle diameter, closure stress, particles filled hydraulic fracture
The influence of the number of plies and Particle Breakage to hydraulic fracture flow conductivity, the characteristics of by analyzing after non-back-up sand hydraulic fracture closure, build
Non- back-up sand hydraulic fracture mathematical modeling has been found, only consideration wall particles supports are established respectively with reference to Gao Caini-Karman formula
Method is determined without back-up sand hydraulic fracture flow conductivity with the sandstone reservoir in the case of rock particles peeling rear support crack, and herein
On the basis of model, using Walsh model and harding model, establish consider that formation closure stress and rock particles are broken respectively
Hydraulic fracture flow conductivity in the case of broken determines method.
(2) this sandstone reservoir of the invention determines that method is primarily adapted for use in Oil/gas Well without back-up sand hydraulic fracture flow conductivity
Hydraulic fracturing calculates without back-up sand hydraulic fracture or the fracture condudtiviy being not added with the case of sand hydraulic fracturing.But the present invention's
Computational methods can calculate the flow conductivity of intrinsic fracture after carrying out appropriate deformation, and be produced after can apply to hydraulic fracturing pressure
It can simulate in calculating, have great importance to hydraulic fracturing design optimization.
(3) this sandstone reservoir of the invention determines that method considers rock particles grain without back-up sand hydraulic fracture flow conductivity
Particle lays the number of plies and Particle Breakage to hydraulic fracture flow conductivity in the case of footpath, closure stress, particles filled hydraulic fracture
Influence, the characteristics of by analyzing after non-back-up sand hydraulic fracture closure, using mathematics and mechanical knowledge, establish non-back-up sand waterpower and split
Flow conductivity computation model is stitched, providing accurately research to the hydraulic fracture flow conductivity research in the case of non-back-up sand thinks
Road.
(4) this sandstone reservoir of the invention determines method by using laboratory method without back-up sand hydraulic fracture flow conductivity
Reservoir granule size is obtained, reservoir closure stress size is calculated by three-dimensional stress experimental result or pressing crack construction analysis, passed through
Micro-seismic monitoring, well temperature testing or pressure post analysis obtain hydraulic fracture height and length, further ensure the standard of result of calculation
True property.
The present invention is described in further details below with reference to accompanying drawing.
Brief description of the drawings
Fig. 1 sandstone reservoirs of the present invention determine method flow diagram without back-up sand hydraulic fracture flow conductivity；
Fig. 2 is only to consider the hydraulic fracture profile under wall rock particles raised support；
Fig. 3 is that hydraulic fracture endoparticle lays schematic diagram.
Embodiment
Embodiment 1：
Present embodiments provide a kind of sandstone reservoir as shown in Figure 1 and determine method without back-up sand hydraulic fracture flow conductivity,
It is characterized in that：Comprise the following steps：
1) reservoir granularity, reservoir closure stress, hydraulic fracture length and height are obtained；
2) according to assumed condition, distribution of particles model is established, and calculates crack endoparticle quantity, fracture porosity accordingly
And fracture width；
3) derive that sandstone reservoir only considers on permeability and pore structure relation formula according to Gao Caini-Kalman
In the case of wall particles supports without sand packed fracture flow conductivity calculation formula：
In formula：
FCDFor only consider in the case of wall particles supports without sand packed fracture flow conductivity, unit is μm2·cm；
LfFor hydraulic fracture height, unit is m；
HfFor hydraulic fracture length, unit is m；
N is spherical particle projection number total in crack；
R is spherical particle radius, and unit is m；
τ is hole tortuosity；
R is the pore radius of supporting crack, and unit is m.
4) on the basis of step 3), the fracture guide energy under Laminar Flow is made on coarse fracture faces with reference to Walsh
Power computation model, draw consider in the case of this kind under closure stress without sand packed fracture flow conductivity calculation formula：
In formula：
FCD′For, without sand packed fracture flow conductivity, unit is μm under consideration closure stress2·cm；
WfFor hydraulic fracture width, unit is m；
μ is fracture faces asperities height root mean square, and unit is m；
σ is closure stress, and unit is MPa；
σ0For first closure stress, unit is Mpa
Wσ0For first closure stress σ0Fracture width under effect, unit is m.
5) according to hydraulic fracture wall particle in hydraulic fracturing process it is peeling-off and the characteristics of laid in crack, and
Assuming that seam in peel off particle be uniform-spherical also assume diamond in shape layered arrangement laying, then utilize mathematical knowledge, it can be deduced that consider rock
Stone particle peels off the flow conductivity calculation formula of supporting crack：
In formula：
FCDsTo consider the hydraulic fracture flow conductivity in the case of rock particles peeling rear support hydraulic fracture；
NsFor total spherical particle number in crack in the case of consideration rock particles peeling rear support hydraulic fracture；
N is that the number of plies, convexity layer containing particle are laid in crack；
M is constant, takes 1 or 0.
6) on the basis of the formula in step 5) assume crack in laying rock particles under original closure stress not
Deformation does not crush；Not deformed under high closure stress, it is broken only to occur, and particle uniformly crushes in whole crack, particle
The fragment formed after broken only deforms not filling pore, and unbroken particle still assumes diamond in shape arrangement；Crack wall is convex
The rock particles risen deforms in no instance also not to be crushed.Then combine harding model percentage of damage and calculate mould
Type, obtain considering the fracture condudtiviy calculation formula without back-up sand under Particle Breakage in the case of this kind：
In formula
F′CDTo consider the water fracture condudtiviy without back-up sand in the case of Particle Breakage；
Wf0For original fracture width, unit is m；
For fracture porosity, it is expressed as a percentage,
For the fracture porosity under reset condition, it is expressed as a percentage；
δ is Particle Breakage rate, is expressed as a percentage,
W′fTo consider fracture width in the case of crushing, unit is m.
This sandstone reservoir of the invention without back-up sand hydraulic fracture flow conductivity determine method consider rock particles particle diameter,
Particle lays the shadow of the number of plies and Particle Breakage to hydraulic fracture flow conductivity in the case of closure stress, particles filled hydraulic fracture
Ring, the characteristics of by analyzing after non-back-up sand hydraulic fracture closure, using mathematics and mechanical knowledge, establish non-back-up sand hydraulic fracture
Flow conductivity computation model, accurately research is provided to the hydraulic fracture flow conductivity research in the case of non-back-up sand and thought
Road.
Embodiment 2：
In order to ensure the accuracy of result of calculation, on the basis of embodiment 1, one kind is present embodiments provided such as Fig. 1 institutes
The sandstone reservoir shown determines method without back-up sand hydraulic fracture flow conductivity, and reservoir granule size utilizes laboratory in the step 1)
Method is obtained, and reservoir closure stress size is calculated using three-dimensional stress experimental result or pressing crack construction analysis, hydraulic fracture length
Obtained with height using micro-seismic monitoring, well temperature testing or pressure post analysis.
Embodiment 3：
Present embodiments provide a kind of sandstone reservoir as shown in Figure 1 and determine method without back-up sand hydraulic fracture flow conductivity,
Reservoir granule size is obtained using laboratory particle size method；Reservoir is calculated using three-dimensional stress experimental result or pressing crack construction analysis
Closure stress size；Hydraulic fracture length and height are obtained using micro-seismic monitoring, well temperature testing or pressure post analysis.
1st, the hydraulic fracture flow conductivity computation model only considered under wall roughness is established
Assuming that stratum is homogeneous reservoir, rock particles is uniform and is in spherical, and particle is indeformable in the case of prime stratum, does not break
It is broken；Crack wall is raised in hemispherical, and diamond array (Fig. 2).Wall particle projection number, which can then be obtained, is：
According to the concept, assumed condition and geometric knowledge of porosity, can obtain：
Gao Caini-Kalman is substituted the above on permeability and the relational expression of pore structure, according to fracture guide energy
Power defines, and can obtain the hydraulic fracture flow conductivity calculation formula only considered under wall roughness：
2nd, the hydraulic fracture flow conductivity computation model considered under clossing pressure is established
It will only consider that the hydraulic fracture flow conductivity calculation formula under wall roughness brings Walsh on coarse crack
Surface is made in the fracture condudtiviy computation model under Laminar Flow, can must consider being led without sand packed fracture in the case of closure stress
Flow capacity calculation formula：
3rd, the hydraulic fracture flow conductivity computation model established in the case of consideration wall roughness and particle stripping filling
In addition to above-mentioned hypothesis, it is assumed that the particle in hydraulic fracture is not embedded in stratum, and under reset condition in crack
Grain is not broken, indeformable；Crack endoparticle is in spherical, and by diamond array, and stratiform is superimposed (Fig. 3).
According to assumed condition, then the total spherical particle number in crack is：
According to geometric knowledge, fracture width can obtain；Regard the particle for facing crack wall as " insertion " stratum half, can
Calculate embedded volume.Similar to the hydraulic fracture flow conductivity computation model processing side only considered under wall rock particles projection
Method, then：
4th, the hydraulic fracture flow conductivity computation model considered under high closure stress in the case of Particle Breakage is established：
Do not crushed assuming that the rock particles laid in crack is indeformable under original closure stress；Under high closure stress not
Deformation is only broken, and particle uniformly crushes in whole crack, and the fragment formed after Particle Breakage, which only deforms, not to be filled out
Fill hole, unbroken particle still assumes diamond in shape arrangement；Wall raised rock particles in crack becomes in no instance
Shape does not also crush.
According to space conservation law, then the average width in crack is changed into：
Total porosity can be caused to diminish because intermediate particle layer is broken, then consider that fracture porosity is changed into the case of crushing：
According to Gao Caini-Kalman's permeability and porosity structural relation formula, then the water conservancy diversion energy in crack in that case
Power is：
In summary, the present invention is based on the correlation theory such as mathematics and rock mechanics, and considered rock particles particle diameter,
Particle lays the shadow of the number of plies and Particle Breakage to hydraulic fracture flow conductivity in the case of closure stress, particles filled hydraulic fracture
Ring, the characteristics of by analyzing after non-back-up sand hydraulic fracture closure, establish non-back-up sand hydraulic fracture mathematical modeling, with reference to it is high
Buddhist nun-Karman formula establishes the sandstone only considered in the case of wall particles supports and rock particles peeling rear support crack respectively
Reservoir determines method without back-up sand hydraulic fracture flow conductivity, and on the basis of this model, utilizes Walsh model and Harding's mould
Type, establish respectively consider formation closure stress and rock particles it is broken in the case of hydraulic fracture flow conductivity determine method.
The present invention can provide calculation basis to the calculating of non-back-up sand hydraulic fracture flow conductivity, also more can accurately study water
The induction generation crack that effect support is formed without during splitting or major fracture finger ends split flow ability are forced, is Oil/gas Well waterpower
Optimized fracturing design provides foundation.
It is exemplified as above be only to the present invention for example, do not form the limitation to protection scope of the present invention, it is all
It is to be belonged to the same or analogous design of the present invention within protection scope of the present invention.
Claims (4)
1. a kind of sandstone reservoir determines method without back-up sand hydraulic fracture flow conductivity, it is characterised in that：Comprise the following steps：
1) reservoir granularity, reservoir closure stress, hydraulic fracture length and height are obtained；
2) according to assumed condition, distribution of particles model is established, and calculates crack endoparticle quantity, fracture porosity accordingly and splits
Slit width degree；
3) derive that sandstone reservoir only considers wall on permeability and pore structure relation formula according to Gao Caini-Kalman
In the case of particles supports without sand packed fracture flow conductivity calculation formula：
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FCDFor only consider in the case of wall particles supports without sand packed fracture flow conductivity, unit is μm2·cm；
LfFor hydraulic fracture height, unit is m；
HfFor hydraulic fracture length, unit is m；
N is spherical particle projection number total in crack；
R is spherical particle radius, and unit is m；
τ is hole tortuosity；
R is the pore radius of supporting crack, and unit is m；
4) on the basis of step 3), the fracture condudtiviy meter under Laminar Flow is made on coarse fracture faces with reference to Walsh
Calculate model, draw consider in the case of this kind under closure stress without sand packed fracture flow conductivity calculation formula：
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In formula：
FCD’For, without sand packed fracture flow conductivity, unit is μm under consideration closure stress2·cm；
WfFor hydraulic fracture width, unit is m；
μ is fracture faces asperities height root mean square, and unit is m；
σ is closure stress, and unit is MPa；
σ0For first closure stress, unit is Mpa；
Wσ0For first closure stress σ0Fracture width under effect, unit is m；
5) according to hydraulic fracture wall particle in hydraulic fracturing process it is peeling-off and the characteristics of laid in crack, and assume
Seam in peel off particle be uniform-spherical also assume diamond in shape layered arrangement laying, then utilize mathematical knowledge, it can be deduced that consider rock
Grain peels off the flow conductivity calculation formula of supporting crack：
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<mi>R</mi>
<msqrt>
<mn>6</mn>
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<mn>3</mn>
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<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<msub>
<mi>&pi;N</mi>
<mi>s</mi>
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<mn>14</mn>
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<mi>&tau;</mi>
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<msub>
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In formula：
<mrow>
<msub>
<mi>N</mi>
<mi>s</mi>
</msub>
<mo>=</mo>
<mo>{</mo>
<mi>n</mi>
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</mrow>
<mi>int</mi>
</msub>
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FCDsTo consider the hydraulic fracture flow conductivity in the case of rock particles peeling rear support hydraulic fracture；
NsFor total spherical particle number in crack in the case of consideration rock particles peeling rear support hydraulic fracture；
N is that the number of plies, convexity layer containing particle are laid in crack；
M is constant, takes 1 or 0；
6) assume that the rock particles of laying in crack is indeformable under original closure stress on the basis of the formula in step 5)
Do not crush；Not deformed under high closure stress, it is broken only to occur, and particle uniformly crushes in whole crack, Particle Breakage
The fragment formed afterwards only deforms not filling pore, and unbroken particle still assumes diamond in shape arrangement；Crack wall projection
Rock particles deforms also do not crush in no instance, then with reference to Harding's Particle Breakage rate computation model, obtains
The fracture condudtiviy calculation formula without back-up sand of Particle Breakage is considered in the case of to this kind：
In formula
F′CDTo consider the water fracture condudtiviy without back-up sand in the case of Particle Breakage；
Wf0For original fracture width, unit is m；
For fracture porosity, it is expressed as a percentage,
For the fracture porosity under reset condition, it is expressed as a percentage；
δ is Particle Breakage rate, is expressed as a percentage,
W′fTo consider fracture width in the case of crushing, unit is m.
2. a kind of sandstone reservoir as claimed in claim 1 determines method without back-up sand hydraulic fracture flow conductivity, it is characterised in that：
Reservoir granule size is obtained using laboratory method in the step 1), and reservoir closure stress size utilizes three-dimensional stress experiment knot
Fruit or pressing crack construction analysis calculate acquisition, after hydraulic fracture length and height can utilize micro-seismic monitoring, well temperature testing or pressure
The method of analysis obtains.
3. a kind of sandstone reservoir as claimed in claim 1 determines method without back-up sand hydraulic fracture flow conductivity, it is characterised in that：
The assumed condition of the step 2) is：According to without back-up sand hydraulic fracture arrangement for closed configuration, it is assumed that rock formation particle is uniform, wall
Grain projection is in hemispherical, is arranged as rhombus, layered arrangement, and particle is indeformable in the case of prime stratum, does not crush.
4. a kind of sandstone reservoir as claimed in claim 1 determines method without back-up sand hydraulic fracture flow conductivity, it is characterised in that：
The crack wall particle projection number is considered as the granule number of crack wall particle insertion stratum half.
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