CN103670358A - Fracture extension judging method of hydraulic fracturing crack on sand shale thin interbed geological interface - Google Patents

Abstract

The invention provides a fracture extension judging method of a hydraulic fracturing crack on a sand shale thin interbed geological interface. An existing hydraulic crack extension model is revised and improved, and a deviation angle of the hydraulic crack on the geological interface can be accurately determined according to the extension form judgment standard of the hydraulic crack on the thin interbed geological interface. The defects of the existing crack extension model in predicting extension of the hydraulic crack in a thin interbed are overcome.

Description

Hydraulically created fracture is sentenced knowledge method at thin sand-mud interbed geological interface propagation path

Technical field

The invention belongs to hydraulically created fracture control technology field, be specifically related to a kind of hydraulically created fracture and sentence knowledge method at thin sand-mud interbed geological interface propagation path.

Background technology

Crack geometric shape definite is one of key issue of fracturing design, and in the mechanical property of crack geometric shape and of the fracturing fluid character, formation fluid property, formation rock, scope of construction item, seam, the coupled relation of fluid flow characteristics and seepage field and stress field etc. is closely related.Take a broad view of the development of domestic and international fracturing technique, the research of fracture extension Mathematical Modeling has been passed by one from simple to complexity, from the more and more comprehensive process of 2 d-to-3 d, Consideration.

Abroad, before the eighties, the research of most fracture propagation simulations is all the situation of extending based on monolete, generally because not obtaining the accurately extension of simulation fracture of stress distribution.Many different technology that grow up subsequently come predicted stresses along with the rule of change in depth, thereby also make multilayered reservoir well fracturing renovation technique obtain very large development.At present, external 3-dimensional multi-layered pressure break analog synthesis considered fracture height growth, with the factors such as pressure drop, eyelet abrasion, the migration of two-dimentional proppant and heat transmission of time and the fluid rheology of temperature correlation, various filtration mechanism, bridging plug and sand fallout, the nearly limited generation of pit shaft fracture extension.

But for thin sand-mud interbed fracturing, rock composition structure is different between layers, lithology, mechanical property are not identical, and in fracture process, deformation form is not identical yet.Existing model is not considered the impact of geological interface fracture expanded configuration between the difference of rock deformation form and rock stratum, is not suitable for and describes thin sand-mud interbed reservoir fractures expanded configuration.Thin sand-mud interbed oil reservoir is thin, poor properties, non-homogeneity is serious, oiliness heterogeneity, hydraulic fracture expanded configuration in thin sand-mud interbed is complicated, between sand shale geological interface, expand and there will be the complicated phenomenons such as deflection, slippage, the unlatching of secondary crack, effectively support seam short, primary fracture expansion theory and model are difficult to prediction.

For the deficiency existing in current hydraulically created fracture extended model, need to adopt a kind of improvement, perfect thin sand-mud interbed fracturing fracture expanded configuration Forecasting Methodology, to carrying out more accurately and reasonably the prediction of thin sand-mud interbed fracture pattern.

Summary of the invention

Key problem in technology to be solved by this invention is to be to overcome existing model cannot describe crack in the problem of thin sand-mud interbed geological interface place expanded configuration, and the sentence knowledge method of a kind of hydraulically created fracture in thin sand-mud interbed reservoir geology interface expanded configuration is provided.The method is utilized each formation properties of thin sand-mud interbed, determines reservoir geology interfacial stress intensity factor, forms hydraulic fracture at thin sand-mud interbed geological interface expanded configuration decision criteria.By described criterion, can more accurately reflect in thin sand-mud interbed that hydraulic fracture occurs, expansion overall process.Thereby solved original two dimension, intended the full threedimensional model of three peacekeepings and ignore geological interface impact make forecasting inaccuracy when prediction hydraulic fracture expanded configuration, and the problem large with reality cracking situation error.

The present invention provides a kind of hydraulically created fracture to sentence knowledge method at thin sand-mud interbed geological interface propagation path for solveing the technical problem, and adopts following steps:

(1) a selected thin sand-mud interbed is treated fractured well, determines in pressing crack construction process net pressure p in crack, and MPa determines in pressing crack construction process effective shear stress τ in crack _ef, MPa; Well test analysis is measured the individual layer height h of thin sand-mud interbed fractured interval sand layers and shale layer, m; Horizontal major principal stress σ _h, MPa; Horizontal minimum principal stress σ _h, MPa;

(2) measure respectively the Young's modulus of lasticity E of the individual layer of thin sand-mud interbed fractured interval sand layers and shale layer, MPa; Poisson's ratio v, the angle of internal friction of rock stratum

° (degree); The cohesive strength C of rock stratum, MPa;

(3) measure respectively the critical rupture strength factor K of I type of thin sand-mud interbed fractured interval sand layers and shale layer _iC, MPam ^0.5; The critical rupture strength factor K of II type _iIC, MPam ^0.5;

(4) determine the compound Young's modulus of lasticity E at thin sand-mud interbed reservoir geology interface ^*, MPa, wherein,

$E^{*}=\frac{2E_1{E}_2}{E_1(1+v_2^2)+E_2(1+v_1^2)}$

In formula, E ^*for the compound Young's modulus of elasticity of geological interface, MPa; E is the Young's modulus of elasticity of sand layers and shale layer individual layer, MPa; V is the poisson's ratio of sand layers and shale layer individual layer, and subscript 2 represents crack tip place layer, and extension layer is treated in 1 expression crack;

Note: for the mutual thin interbed of absolute sand shale, thin sand-mud interbed oil reservoir is vertical above distributes in strict accordance with sand layers, shale layer, sand layers, shale layer, this distribution form of sand layers from ground to underground distribution of strata.If crack tip place layer is sand layers, v ₂, E ₂for the Young's modulus of elasticity of sand layers individual layer, v ₁, E ₁young's modulus of elasticity for shale layer individual layer; Otherwise, if crack tip place layer is shale layer, v ₂, E ₂for the Young's modulus of elasticity of shale layer individual layer, v ₁, E ₁young's modulus of elasticity for sand layers individual layer;

(5) determine the different material parameter beta in interface at thin sand-mud interbed reservoir geology interface, wherein,

$\mathrm{\β}=\frac{E_1(1-2v_2)(1+v_2)-E_2(1-2v_1)(1+v_1)}{E_1(2-2v_2)(1+v_2)+E_2(2-2v_1)(1+v_1)}$

In formula, E is the Young's modulus of elasticity of sand layers and shale layer individual layer, MPa; V is the poisson's ratio of sand layers and shale layer individual layer, and subscript 2 represents crack tip place layer, and extension layer is treated in 1 expression crack;

(6) determine the critical rupture strength factor in interface at thin sand-mud interbed reservoir geology interface

with

unit is MPam ^0.5, wherein,

$K_{\mathrm{IC}}^{*}=\frac{K_{\mathrm{IC}1}\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_1+K_{\mathrm{IC}2}\&CenterDot;{\left(h_2\right)}^{3/4}}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_1+h_2}$ $K_{\mathrm{IIC}}^{*}=\frac{K_{\mathrm{IIC}1}\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_1+K_{\mathrm{IIC}2}\&CenterDot;{\left(h_2\right)}^{3/4}}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}$

In formula: K _iC, K _iICbe respectively I type, the critical rupture strength factor of II type of sand layers and shale layer individual layer, MPam ^0.5; H sand layers and shale layer individual layer floor height, m, subscript 2 represents crack tip place layer, extension layer is treated in 1 expression crack.

(7) determine the most advanced and sophisticated composite elastic energy release rate G of thin sand-mud interbed reservoir geology interface fracturing fracture ^*, unit is N/m,

$G^{*}=\frac{1-{\mathrm{\&beta;}}^2}{E^{*}}[{\left(K_I^{*}\right)}^2+{\left(K_{\mathrm{II}}^{*}\right)}^2]$

Wherein: $K_I^{*}=\sqrt{2\mathrm{\&pi;x}}[{\mathrm{\&tau;}}_{\mathrm{ef}}\sin \left(\mathrm{\&epsiv;}\ln x\right)+p\cos \left(\mathrm{\&epsiv;}\ln x\right)],$

$K_{\mathrm{II}}^{*}=\sqrt{2\mathrm{\&pi;x}}[{\mathrm{\&tau;}}_{\mathrm{ef}}\cos \left(\mathrm{\&epsiv;}\ln x\right)+p\sin \left(\mathrm{\&epsiv;}\ln x\right)],$ $\mathrm{\&epsiv;}=\frac{1}{2\mathrm{\&pi;}}\ln \frac{1-\mathrm{\&beta;}}{1+\mathrm{\&beta;}},$

In formula, β is the different material parameter in interface; E ^*for compound Young's modulus of elasticity, MPa;

with

be respectively I type, II type geological interface mixed-mode stress-intensity factor, MPam ^0.5; P is net pressure in crack in pressing crack construction process, MPa; τ _effor effective shear stress in crack in pressing crack construction process, MPa; X is that crack tip is apart from the distance of geological interface, m; σ _h, σ _hbe respectively rock stratum level maximum, minimum principal stress, MPa; for rock stratum angle of internal friction, °; θ is the final cracking azimuth in crack, °; ε is two material medium interface oscillations indexes; C is rock stratum cohesive strength, MPa;

(8) according to the most advanced and sophisticated composite elastic energy release rate G of thin sand-mud interbed reservoir geology interface fracturing fracture ^*size, determine the form in crack.

Wherein, according to the most advanced and sophisticated composite elastic energy release rate G of thin sand-mud interbed reservoir geology interface fracturing fracture ^*size, determine and be specially the breaking morphology in crack:

1) G ^*while meeting following formula:

$\underset{x\&RightArrow;0}{\lim }{G}^{*}=0$

Determine that crack is when the crack arrest of geological interface place, and the final cracking azimuth angle theta in definite crack, θ=0 °;

2) G ^*while meeting following formula:

$\underset{x\&RightArrow;0}{\lim }{G}^{*}=\&infin;$

Determine that crack directly breaks through geological interface, determine the final cracking azimuth angle theta in crack, θ=0 °;

3) G ^*while meeting following formula:

$\underset{x\&RightArrow;0}{\lim }{G}^{*\&NotEqual;}0,\&infin;$

Determine that crack is in the slippage of geological interface place; And wherein,

When final cracking azimuth angle theta meets following formula,

$\frac{\&PartialD;K_I^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;\mathrm{\&theta;}}=0,$ $\frac{{\&PartialD;}^2{K}_I^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;{\mathrm{\&theta;}}^2}<0,$ $\frac{\left|K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)\right|}{\left|K_I^{*}\left(\mathrm{\&theta;}\right)\right|}\&le;\frac{\left|K_{\mathrm{IIC}}^{*}\right|}{\left|K_{\mathrm{IC}}^{*}\right|},$ And $\frac{\left|K_{I\max }^{*}\left(\mathrm{\&theta;}\right)\right|}{\left|K_{\mathrm{IC}}^{*}\right|}\&GreaterEqual;1$

Or the azimuth angle theta that finally ftractures meets following formula:

$\frac{\&PartialD;K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;\mathrm{\&theta;}}=0,$ $\frac{{\&PartialD;}^2{K}_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;{\mathrm{\&theta;}}^2}<0,$ $\frac{\left|K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)\right|}{\left|K_I^{*}\left(\mathrm{\&theta;}\right)\right|}\&le;\frac{\left|K_{\mathrm{IIC}}^{*}\right|}{\left|K_{\mathrm{IC}}^{*}\right|},$ And $\frac{\left|K_{I\max }^{*}\left(\mathrm{\&theta;}\right)\right|}{\left|K_{\mathrm{IC}}^{*}\right|}\&GreaterEqual;1$

Wherein:

$K_{I\max }^{*}\left(\mathrm{\&theta;}\right)=\max \left\{K_I^{*}\left(\mathrm{\&theta;}\right)\right\},$ $K_{\mathrm{II}\max }^{*}\left(\mathrm{\&theta;}\right)=\max \left\{K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)\right\},$ $K_I^{*}\left(\mathrm{\&theta;}\right)=K_I^{*}{\cos }^3\left(\frac{\mathrm{\&theta;}}{2}\right)+K_{\mathrm{II}}^{*}[-\sin \frac{\mathrm{\&theta;}}{2}{\cos }^2\left(\frac{\mathrm{\&theta;}}{2}\right)],$

$K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)=K_I^{*}\sin \frac{\mathrm{\&theta;}}{2}{\cos }^2\left(\frac{\mathrm{\&theta;}}{2}\right)+K_{\mathrm{II}}^{*}\cos \frac{\mathrm{\&theta;}}{2}[1-3{\sin }^2\left(\frac{\mathrm{\&theta;}}{2}\right)],$ $K_I^{*}=0.79[{\mathrm{\&tau;}}_{\mathrm{ef}}\sin (-2.3\mathrm{\&epsiv;})+p\cos (-2.3\mathrm{\&epsiv;})],$

$K_{\mathrm{II}}^{*}=0.79[{\mathrm{\&tau;}}_{\mathrm{ef}}\cos (-2.3\mathrm{\&epsiv;})-p\sin (-2.3\mathrm{\&epsiv;})],$ $\mathrm{\&epsiv;}=\frac{1}{2\mathrm{\&pi;}}\ln \frac{1-\mathrm{\&beta;}}{1+\mathrm{\&beta;}},$

Determine that crack penetrates geological interface after the slippage of geological interface place;

When final cracking azimuth angle theta meets following formula

$\frac{\&PartialD;K_I^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;\mathrm{\&theta;}}=0,$ $\frac{{\&PartialD;}^2{K}_I^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;{\mathrm{\&theta;}}^2}<0,$ ${\left(\frac{K_{I\max }^{*}\left(\mathrm{\&theta;}\right)}{K_{\mathrm{IC}}^{*}}\right)}^2+{\left(\frac{K_{\mathrm{II}\max }^{*}\left(\mathrm{\&theta;}\right)}{K_{\mathrm{IIC}}^{*}}\right)}^2\&GreaterEqual;1$

Determine crack arrest after the geological interface place slippage of crack.

The present invention has carried out correction, perfect to existing hydraulic fracture extended model, by thin sand-mud interbed hydraulic fracture, in the expanded configuration criterion of thin sand-mud interbed geological interface place, can determine that hydraulic fracture is at the deflection angle at geological interface place.Thereby set up thin sand-mud interbed on-plane surface hydraulic fracture extended model, can accurately reflect that crack, in crack initiation, the expansion overall process at geological interface place, has made up and applied the defect that existing fracture propagation model prediction hydraulic fracture occurs in thin sand-mud interbed expansion.

Accompanying drawing explanation

Fig. 1 is fracturing fracture schematic diagram in thin sand-mud interbed oil reservoir.

Fig. 2 be in thin sand-mud interbed oil reservoir fracturing fracture at geological interface place crack arrest schematic diagram.

Fig. 3 is that in thin sand-mud interbed oil reservoir, fracturing fracture is vertically broken through geological interface schematic diagram.

Fig. 4 is that in thin sand-mud interbed oil reservoir, fracturing fracture penetrates interface schematic diagram after the slippage of geological interface place.

Fig. 5 is pressure break crack arrest schematic diagram after the slippage of geological interface place in crack in thin sand-mud interbed oil reservoir.

In figure:

1 treats extension layer for thin sand-mud interbed fracturing fracture; 2 is thin sand-mud interbed fracturing fracture place layer; 3 for being adjacent to the geological interface of interlayer; 4 is hydraulically created fracture;

Specific implementation method

Below in conjunction with accompanying drawing, content of the present invention is elaborated:

For thin sand-mud interbed oil reservoir, because its deposition is that reservoir (sandstone) alternately occurs mutually with non-reservoir (mud stone, shale) in the vertical, reservoir rock composition is different, and sand shale deformation form difference is large and thickness is all less, makes them obviously different from the form of thick oil pay fracturing fracture.Particularly at geological interface place, because nature of subterranean reservoirs on geological interface is different, the ability that stratum deforms is also different, geological interface different in kind, this has just determined that hydraulically created fracture is complicated and changeable in the expanded configuration of longitudinal geology interface, according to investigation, find, (see figure 1) when hydraulically created fracture expands to geological interface, at geological interface place, may there is directly to penetrate interface (Fig. 3) in hydraulic fracture, crack arrest (Fig. 2), crack arrest after slippage (Fig. 5), or after slippage, penetrate again interface (Fig. 4), therefore need to consider the form of geological interface place fracture propagation, and hydraulic fracture extended model in the past can not meet the needs of thin sand-mud interbed oil reservoir pressure break.Consider thin sand-mud interbed oil reservoir on-plane surface character, set up hydraulic fracture at the expanded configuration model of thin sand-mud interbed oil reservoir interface.Concrete steps are as follows:

(1) a selected thin sand-mud interbed is treated fractured well, determines in pressing crack construction process net pressure p in crack, and MPa determines in pressing crack construction process effective shear stress τ in crack _ef, MPa; Well test analysis is measured the individual layer height h of thin sand-mud interbed fractured interval sand layers and shale layer, m; Horizontal major principal stress σ _h, MPa; Horizontal minimum principal stress σ _h, MPa.

(2) measure respectively the Young's modulus of lasticity E of the individual layer of thin sand-mud interbed fractured interval sand layers and shale layer, MPa; Poisson's ratio v, the angle of internal friction of rock stratum

° (degree); The cohesive strength C of rock stratum, MPa; Preferably can learn experiment by rock core three-axis force and measure, can certainly measure by other known method of this area.

(3) measure respectively the critical rupture strength factor K of I type (opening mode) of thin sand-mud interbed fractured interval sand layers and shale layer _iC, MPam ^0.5; The critical rupture strength factor K of II type (shearing-type) _iIC, MPam ^0.5; Preferably can measure by endurance testing machine Experiments of Machanics, can certainly measure by other known method of this area.

(4) determine the compound Young's modulus of lasticity E at thin sand-mud interbed reservoir geology interface ^*, MPa;

According to the upper and lower stratum of geological interface (being stratum to be expanded with crack, stratum, current place, crack) mechanics parameter, calculate the compound Young's modulus of lasticity E at thin sand-mud interbed reservoir geology interface ^*, the present invention calculates in accordance with the following methods,

$E^{*}=\frac{2E_1{E}_2}{E_1(1+{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">v</figure-callout>}}_2^2)+E_2(1+{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">v</figure-callout>}}_1^2)}$

In formula, E ^*for the compound Young's modulus of elasticity of geological interface, MPa; E is the Young's modulus of elasticity of sand layers and shale layer individual layer, MPa; V is the poisson's ratio of sand layers and shale layer individual layer, and subscript 2 represents crack tip place layer, and extension layer is treated in 1 expression crack.

(5) determine the different material parameter beta in interface at thin sand-mud interbed reservoir geology interface;

Calculate the different material parameter beta in thin sand-mud interbed reservoir geology interface, the present invention specifically in accordance with the following methods:

$\mathrm{\&beta;}=\frac{E_1(1-2v_2)(1+v_2)-E_2(1-2v_1)(1+v_1)}{E_1(2-2v_2)(1+v_2)+E_2(2-2v_1)(1+v_1)}$

In formula, E is the Young's modulus of elasticity of sand layers and shale layer individual layer, MPa; V is the poisson's ratio of sand layers and shale layer individual layer, and subscript 2 represents crack tip place layer, and extension layer is treated in 1 expression crack.

(6) determine the critical rupture strength factor in interface at thin sand-mud interbed reservoir geology interface

with

unit is MPam ^0.5, the present invention specifically in accordance with the following methods:

$K_{\mathrm{IC}}^{*}=\frac{{\mathrm{<figure-callout\; id="1"\; label="K\; IC"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">K</figure-callout>}}_{\mathrm{IC}}\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="K\; IC"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">K</figure-callout>}}_{\mathrm{IC}}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^{3/4}}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_2},$ $K_{\mathrm{IIC}}^{*}=\frac{{\mathrm{<figure-callout\; id="1"\; label="K\; IIC"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">K</figure-callout>}}_{\mathrm{IIC}}\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="K\; IIC"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">K</figure-callout>}}_{\mathrm{IIC}}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^{3/4}}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA0000421379900000011.png,HDA0000421379900000012.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}$

In formula: K _iC, K _iICbe respectively I type, the critical rupture strength factor of II type of sand layers and shale layer individual layer, MPam ^0.5; H sand layers and shale layer individual layer floor height, m, subscript 2 represents crack tip place layer, extension layer is treated in 1 expression crack.

(7) determine the most advanced and sophisticated composite elastic energy release rate G of thin sand-mud interbed reservoir geology interface fracturing fracture ^*, unit is N/m, the present invention specifically in accordance with the following methods:

$G^{*}=\frac{1-{\mathrm{\&beta;}}^2}{E^{*}}[{\left(K_I^{*}\right)}^2+{\left(K_{\mathrm{II}}^{*}\right)}^2]$

Wherein: $K_I^{*}=\sqrt{2\mathrm{\&pi;x}}[{\mathrm{\&tau;}}_{\mathrm{ef}}\sin \left(\mathrm{\&epsiv;}\ln x\right)+p\cos \left(\mathrm{\&epsiv;}\ln x\right)],$

$K_{\mathrm{II}}^{*}=\sqrt{2\mathrm{\&pi;x}}[{\mathrm{\&tau;}}_{\mathrm{ef}}\cos \left(\mathrm{\&epsiv;}\ln x\right)+p\sin \left(\mathrm{\&epsiv;}\ln x\right)],$ $\mathrm{\&epsiv;}=\frac{1}{2\mathrm{\&pi;}}\ln \frac{1-\mathrm{\&beta;}}{1+\mathrm{\&beta;}},$

In formula, β is the different material parameter in interface; E ^*for compound Young's modulus of elasticity, MPa;

with

be respectively I type, II type geological interface mixed-mode stress-intensity factor, MPam ^0.5; P is net pressure in crack in pressing crack construction process, MPa; τ _effor effective shear stress in crack in pressing crack construction process, MPa; X is that crack tip is apart from the distance of geological interface, m; σ _h, σ _hbe respectively rock stratum level maximum, minimum principal stress, MPa;

for rock stratum angle of internal friction, °; θ is the final cracking azimuth in crack, °; ε is two material medium interface oscillations indexes; C is rock stratum cohesive strength, MPa.

(8) according to the most advanced and sophisticated composite elastic energy release rate G of thin sand-mud interbed reservoir geology interface fracturing fracture ^*size, determine the breaking morphology in crack.

1) the most advanced and sophisticated composite elastic energy release rate G of described sand mud ground matter interface fracturing fracture ^*meet hydraulic fracture (see figure 2) when the crack arrest of geological interface place, G ^*meet following formula:

$\underset{x\&RightArrow;0}{\lim }{G}^{*}=0$

Determine the final cracking azimuth angle theta in crack, θ=0 °.

2) the most advanced and sophisticated composite elastic energy release rate G of described sand mud ground matter interface fracturing fracture ^*(see figure 3) when meeting hydraulic fracture and directly breaking through geological interface, G ^*meet following formula:

$\underset{x\&RightArrow;0}{\lim }{G}^{*}=\&infin;$

Determine the final cracking azimuth angle theta in crack, θ=0 °.

3) the most advanced and sophisticated composite elastic energy release rate G of described sand mud ground matter interface fracturing fracture ^*, meet hydraulic fracture when the slippage of geological interface place, G ^*meet following formula:

$\underset{x\&RightArrow;0}{\lim }{G}^{*\&NotEqual;}0,\&infin;$

(see figure 4) when 1. determining hydraulic fracture final cracking azimuth angle theta meeting hydraulic fracture penetrate geological interface after the slippage of geological interface place at geological interface place, θ meets following formula:

$\frac{\&PartialD;K_I^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;\mathrm{\&theta;}}=0,$ $\frac{{\&PartialD;}^2{K}_I^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;{\mathrm{\&theta;}}^2}<0,$ $\frac{\left|K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)\right|}{\left|K_I^{*}\left(\mathrm{\&theta;}\right)\right|}\&le;\frac{\left|K_{\mathrm{IIC}}^{*}\right|}{\left|K_{\mathrm{IC}}^{*}\right|},$ And $\frac{\left|K_{I\max }^{*}\left(\mathrm{\&theta;}\right)\right|}{\left|K_{\mathrm{IC}}^{*}\right|}\&GreaterEqual;1$

Or θ meets following formula:

$\frac{\&PartialD;K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;\mathrm{\&theta;}}=0,$ $\frac{{\&PartialD;}^2{K}_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;{\mathrm{\&theta;}}^2}<0,$ $\frac{\left|K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)\right|}{\left|K_I^{*}\left(\mathrm{\&theta;}\right)\right|}\&le;\frac{\left|K_{\mathrm{IIC}}^{*}\right|}{\left|K_{\mathrm{IC}}^{*}\right|},$ And $\frac{\left|K_{I\max }^{*}\left(\mathrm{\&theta;}\right)\right|}{\left|K_{\mathrm{IC}}^{*}\right|}\&GreaterEqual;1$

Wherein:

$K_{I\max }^{*}\left(\mathrm{\&theta;}\right)=\max \left\{K_I^{*}\left(\mathrm{\&theta;}\right)\right\},$ $K_{\mathrm{II}\max }^{*}\left(\mathrm{\&theta;}\right)=\max \left\{K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)\right\},$ $K_I^{*}\left(\mathrm{\&theta;}\right)=K_I^{*}{\cos }^3\left(\frac{\mathrm{\&theta;}}{2}\right)+K_{\mathrm{II}}^{*}[-\sin \frac{\mathrm{\&theta;}}{2}{\cos }^2\left(\frac{\mathrm{\&theta;}}{2}\right)],$

$K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)=K_I^{*}\sin \frac{\mathrm{\&theta;}}{2}{\cos }^2\left(\frac{\mathrm{\&theta;}}{2}\right)+K_{\mathrm{II}}^{*}\cos \frac{\mathrm{\&theta;}}{2}[1-3{\sin }^2\left(\frac{\mathrm{\&theta;}}{2}\right)],$ $K_I^{*}=0.79[{\mathrm{\&tau;}}_{\mathrm{ef}}\sin (-2.3\mathrm{\&epsiv;})+p\cos (-2.3\mathrm{\&epsiv;})],$

$K_{\mathrm{II}}^{*}=0.79[{\mathrm{\&tau;}}_{\mathrm{ef}}\cos (-2.3\mathrm{\&epsiv;})-p\sin (-2.3\mathrm{\&epsiv;})],$ $\mathrm{\&epsiv;}=\frac{1}{2\mathrm{\&pi;}}\ln \frac{1-\mathrm{\&beta;}}{1+\mathrm{\&beta;}},$

2. determine that final cracking azimuth angle theta meets hydraulic fracture (see figure 5) during crack arrest after the slippage of geological interface place to hydraulic fracture at geological interface place, θ meets following formula:

$\frac{\&PartialD;K_I^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;\mathrm{\&theta;}}=0,$ $\frac{{\&PartialD;}^2{K}_I^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;{\mathrm{\&theta;}}^2}<0,$ ${\left(\frac{K_{I\max }^{*}\left(\mathrm{\&theta;}\right)}{K_{\mathrm{IC}}^{*}}\right)}^2+{\left(\frac{K_{\mathrm{II}\max }^{*}\left(\mathrm{\&theta;}\right)}{K_{\mathrm{IIC}}^{*}}\right)}^2\&GreaterEqual;1$

By above-mentioned analysis, just can judge crack in the expanded configuration at thin sand-mud interbed geological interface place.

With respect to existing hydraulic fracture extended model, do not consider ground interlayer mechanics parameter, the analog case of the greatest differences of deformability and the factors such as stress state of geological interface, the present invention revises it, perfect, by thin sand-mud interbed hydraulic fracture in the expanded configuration criterion of thin sand-mud interbed geological interface place, can determine that hydraulic fracture is at the deflection angle at geological interface place, more accurately reflect that crack is in the crack initiation at geological interface place, expansion overall process, made up and applied the defect that existing fracture propagation model prediction hydraulic fracture occurs in thin sand-mud interbed expansion.

Claims (2)

1. hydraulically created fracture is sentenced a knowledge method at thin sand-mud interbed geological interface propagation path, it is characterized in that, concrete steps are as follows:

Step 1: a selected thin sand-mud interbed is treated fractured well, determines in pressing crack construction process net pressure p in crack, and MPa determines in pressing crack construction process effective shear stress τ in crack _ef, MPa; Well test analysis is measured the individual layer height h of thin sand-mud interbed fractured interval sand layers and shale layer, m; Horizontal major principal stress σ _h, MPa; Horizontal minimum principal stress σ _h, MPa;

Step 2: measure respectively the Young's modulus of lasticity E of the individual layer of thin sand-mud interbed fractured interval sand layers and shale layer, MPa; Poisson's ratio v, the angle of internal friction of rock stratum

°; The cohesive strength C of rock stratum, MPa;

Step 3: the critical rupture strength factor K of I type of measuring respectively thin sand-mud interbed fractured interval sand layers and shale layer _iC, MPam ^0.5; The critical rupture strength factor K of II type _iIC, MPam ^0.5;

Step 4: the compound Young's modulus of lasticity E of determining thin sand-mud interbed reservoir geology interface by following formula (1) ^*,

$E^{*}=\frac{2E_1{E}_2}{E_1(1+v_2^2)+E_2(1+v_1^2)}---\left(1\right)$

Wherein, in formula, E ^*for the compound Young's modulus of elasticity of geological interface, MPa; E is the Young's modulus of elasticity of sand layers and shale layer individual layer, MPa; V is the poisson's ratio of sand layers and shale layer individual layer, and subscript 2 represents crack tip place layer, and extension layer is treated in 1 expression crack;

Step 5: through type (2) is determined the different material parameter beta in the interface at thin sand-mud interbed reservoir geology interface,

$\mathrm{\&beta;}=\frac{E_1(1-2v_2)(1+v_2)-E_2(1-2v_1)(1+v_1)}{E_1(2-2v_2)(1+v_2)+E_2(2-2v_1)(1+v_1)}---\left(2\right)$

Wherein, in formula, E is the Young's modulus of elasticity of sand layers and shale layer individual layer, MPa; V is the poisson's ratio of sand layers and shale layer individual layer, and subscript 2 represents crack tip place layer, and extension layer is treated in 1 expression crack;

Step 6: the critical rupture strength factor in interface at thin sand-mud interbed reservoir geology interface is determined in through type (3) and (4)

with

unit is MPam ^0.5,

$K_{\mathrm{IC}}^{*}=\frac{K_{\mathrm{IC}1}\&CenterDot;h_1+K_{\mathrm{IC}2}\&CenterDot;{\left(h_2\right)}^{3/4}}{h_1+h_2}---\left(3\right),$

$K_{\mathrm{IIC}}^{*}=\frac{K_{\mathrm{IIC}1}\&CenterDot;h_1+K_{\mathrm{IIC}2}\&CenterDot;{\left(h_2\right)}^{3/4}}{h_1+h_2}---\left(4\right)$

Wherein, in formula: K _iC, K _iICbe respectively I type, the critical rupture strength factor of II type of sand layers and shale layer individual layer, MPam ^0.5; H sand layers and shale layer individual layer floor height, m, subscript 2 represents crack tip place layer, extension layer is treated in 1 expression crack.

Step 7: determine the most advanced and sophisticated composite elastic energy release rate G of thin sand-mud interbed reservoir geology interface fracturing fracture according to (5) ^*, unit is N/m,

$G^{*}=\frac{1-{\mathrm{\&beta;}}^2}{E^{*}}[{\left(K_I^{*}\right)}^2+{\left(K_{\mathrm{II}}^{*}\right)}^2]---\left(5\right),$

Wherein: $K_I^{*}=\sqrt{2\mathrm{\&pi;x}}[{\mathrm{\&tau;}}_{\mathrm{ef}}\sin \left(\mathrm{\&epsiv;}\ln x\right)+p\cos \left(\mathrm{\&epsiv;}\ln x\right)],$

$K_{\mathrm{II}}^{*}=\sqrt{2\mathrm{\&pi;x}}[{\mathrm{\&tau;}}_{\mathrm{ef}}\cos \left(\mathrm{\&epsiv;}\ln x\right)+p\sin \left(\mathrm{\&epsiv;}\ln x\right)],$ $\mathrm{\&epsiv;}=\frac{1}{2\mathrm{\&pi;}}\ln \frac{1-\mathrm{\&beta;}}{1+\mathrm{\&beta;}},$

In formula, β is the different material parameter in interface; E ^*for compound Young's modulus of elasticity, MPa;

with

be respectively I type, II type geological interface mixed-mode stress-intensity factor, MPam ^0.5; P is net pressure in crack in pressing crack construction process, MPa; τ _effor effective shear stress in crack in pressing crack construction process, MPa; X is that crack tip is apart from the distance of geological interface, m; σ _h, σ _hbe respectively rock stratum level maximum, minimum principal stress, MPa;

for rock stratum angle of internal friction, °; θ is the final cracking azimuth in crack, °; ε is two material medium interface oscillations indexes; C is rock stratum cohesive strength, MPa;

Step 8: according to the most advanced and sophisticated composite elastic energy release rate G of thin sand-mud interbed reservoir geology interface fracturing fracture ^*size, determine the form in crack.

2. method according to claim 1, is characterized in that, in described step 8 according to the most advanced and sophisticated composite elastic energy release rate G of thin sand-mud interbed reservoir geology interface fracturing fracture ^*size, determine and be specially the breaking morphology in crack:

Work as G ^*while meeting following formula:

$\underset{x\&RightArrow;0}{\lim }{G}^{*}=0$

Determine that crack is when the crack arrest of geological interface place, and the final cracking azimuth angle theta in definite crack, θ=0 °;

Work as G ^*while meeting following formula:

$\underset{x\&RightArrow;0}{\lim }{G}^{*}=\&infin;$

Determine that crack directly breaks through geological interface, determine the final cracking azimuth angle theta in crack, θ=0 °;

3) G ^*while meeting following formula:

$\underset{x\&RightArrow;0}{\lim }{G}^{*\&NotEqual;}0,\&infin;$

Determine that crack is in the slippage of geological interface place; And wherein,

1. when final cracking azimuth angle theta meets following formula,

$\frac{\&PartialD;K_I^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;\mathrm{\&theta;}}=0,$ $\frac{{\&PartialD;}^2{K}_I^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;{\mathrm{\&theta;}}^2}<0,$ $\frac{\left|K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)\right|}{\left|K_I^{*}\left(\mathrm{\&theta;}\right)\right|}\&le;\frac{\left|K_{\mathrm{IIC}}^{*}\right|}{\left|K_{\mathrm{IC}}^{*}\right|},$ And $\frac{\left|K_{I\max }^{*}\left(\mathrm{\&theta;}\right)\right|}{\left|K_{\mathrm{IC}}^{*}\right|}\&GreaterEqual;1$

Or the azimuth angle theta that finally ftractures meets following formula:

$\frac{\&PartialD;K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;\mathrm{\&theta;}}=0,$ $\frac{{\&PartialD;}^2{K}_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;{\mathrm{\&theta;}}^2}<0,$ $\frac{\left|K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)\right|}{\left|K_I^{*}\left(\mathrm{\&theta;}\right)\right|}\&le;\frac{\left|K_{\mathrm{IIC}}^{*}\right|}{\left|K_{\mathrm{IC}}^{*}\right|},$ And $\frac{\left|K_{I\max }^{*}\left(\mathrm{\&theta;}\right)\right|}{\left|K_{\mathrm{IC}}^{*}\right|}\&GreaterEqual;1$

Wherein:

$K_{I\max }^{*}\left(\mathrm{\&theta;}\right)=\max \left\{K_I^{*}\left(\mathrm{\&theta;}\right)\right\},$ $K_{\mathrm{II}\max }^{*}\left(\mathrm{\&theta;}\right)=\max \left\{K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)\right\},$ $K_I^{*}\left(\mathrm{\&theta;}\right)=K_I^{*}{\cos }^3\left(\frac{\mathrm{\&theta;}}{2}\right)+K_{\mathrm{II}}^{*}[-\sin \frac{\mathrm{\&theta;}}{2}{\cos }^2\left(\frac{\mathrm{\&theta;}}{2}\right)],$

$K_{\mathrm{II}}^{*}\left(\mathrm{\&theta;}\right)=K_I^{*}\sin \frac{\mathrm{\&theta;}}{2}{\cos }^2\left(\frac{\mathrm{\&theta;}}{2}\right)+K_{\mathrm{II}}^{*}\cos \frac{\mathrm{\&theta;}}{2}[1-3{\sin }^2\left(\frac{\mathrm{\&theta;}}{2}\right)],$ $K_I^{*}=0.79[{\mathrm{\&tau;}}_{\mathrm{ef}}\sin (-2.3\mathrm{\&epsiv;})+p\cos (-2.3\mathrm{\&epsiv;})],$

$K_{\mathrm{II}}^{*}=0.79[{\mathrm{\&tau;}}_{\mathrm{ef}}\cos (-2.3\mathrm{\&epsiv;})-p\sin (-2.3\mathrm{\&epsiv;})],$ $\mathrm{\&epsiv;}=\frac{1}{2\mathrm{\&pi;}}\ln \frac{1-\mathrm{\&beta;}}{1+\mathrm{\&beta;}},$

Determine that crack penetrates geological interface after the slippage of geological interface place;

2. when final cracking azimuth angle theta meets following formula

$\frac{\&PartialD;K_I^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;\mathrm{\&theta;}}=0,$ $\frac{{\&PartialD;}^2{K}_I^{*}\left(\mathrm{\&theta;}\right)}{\&PartialD;{\mathrm{\&theta;}}^2}<0,$ ${\left(\frac{K_{I\max }^{*}\left(\mathrm{\&theta;}\right)}{K_{\mathrm{IC}}^{*}}\right)}^2+{\left(\frac{K_{\mathrm{II}\max }^{*}\left(\mathrm{\&theta;}\right)}{K_{\mathrm{IIC}}^{*}}\right)}^2\&GreaterEqual;1$ Determine crack arrest after the geological interface place slippage of crack.

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