CN106567703B - A kind of cloth hole optimization method of more radial hole auxiliary pressure breaks - Google Patents
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- 206010017076 Fracture Diseases 0.000 abstract description 39
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Abstract
本发明公开了一种多径向孔眼辅助压裂的布孔优化方法,包括以下步骤:确定不同径向孔眼条件下的裂缝形态;模拟单一裂缝的波及面积,并用椭圆形进行面积拟合,通过椭圆形同心旋转获取多条主裂缝情况下的总波及面积;计算总波及面积。本发明通过利用单一裂缝在均质储层中的波及面积并叠加模拟多裂缝的波及面积,以多裂缝的最大波及面积综合为评价标准优化径向孔眼的布孔方式,为多裂缝形态提供最优布孔方案的依据。本发明使用椭圆形作为单一裂缝波及面积的替代图形,简化波及面积的求取方法,不同储层、裂缝参数可通过调整椭圆形长短轴的数值达到良好的拟合效果,具备灵活性、普遍性。
The invention discloses a hole layout optimization method for assisted fracturing with multi-radial holes, which comprises the following steps: determining the fracture shape under different radial hole conditions; simulating the swept area of a single fracture, and performing area fitting with an ellipse; The ellipse is rotated concentrically to obtain the total swept area in the case of multiple main fractures; calculate the total swept area. The present invention uses the swept area of a single fracture in a homogeneous reservoir and superimposes the swept area of multiple fractures, and takes the maximum swept area of multiple fractures as the evaluation standard to optimize the radial hole layout method, providing the best solution for the multi-fracture form. Basis for the Ubukon scheme. The present invention uses an ellipse as a substitute figure for a single fracture sweep area, simplifies the calculation method of the sweep area, different reservoirs and fracture parameters can achieve a good fitting effect by adjusting the values of the major and minor axes of the ellipse, and has flexibility and universality .
Description
技术领域technical field
本发明涉及一种多径向孔眼辅助压裂的布孔优化方法,属于径向孔眼辅助压裂技术领域。The invention relates to a hole layout optimization method for multi-radial hole assisted fracturing, and belongs to the technical field of radial hole assisted fracturing.
背景技术Background technique
目前针对常规压裂产生的两翼裂缝多用“裂缝导流能力”指标进行评价,该指标仅适用于评价储层中的单一裂缝,无法评价可产生多裂缝的多径向孔眼辅助压裂。针对体积压裂产生的裂缝多用“储层改造体积”指标进行评价,而体积压裂时会开启大量储层微裂缝、生成大量次级裂缝,依然不适用于微裂缝、次级裂缝较少的多条主裂缝的评价。At present, the "fracture conductivity" index is often used to evaluate the two-wing fractures produced by conventional fracturing. This index is only suitable for evaluating a single fracture in the reservoir, and cannot evaluate the multi-radial hole-assisted fracturing that can produce multiple fractures. For the fractures produced by volume fracturing, the index of "reservoir stimulation volume" is often used to evaluate, but volume fracturing will open a large number of reservoir micro-fractures and generate a large number of secondary fractures, which is still not suitable for micro-fractures and few secondary fractures. Evaluation of multiple primary fractures.
径向孔眼辅助压裂技术中,通过水平同层多孔的布孔方式可构造多条主裂缝沿孔眼方向扩展,极大地提高了储层可动用储量、提高了产能,因此明确多径向孔眼辅助压裂裂缝形态的评价准则及布孔优化方法具有重要意义。In the radial hole-assisted fracturing technology, multiple main fractures can be constructed to expand along the direction of the holes through the horizontal porous hole layout method, which greatly improves the available reserves of the reservoir and improves the production capacity. The evaluation criteria of fracturing fracture shape and the optimization method of hole layout are of great significance.
发明内容Contents of the invention
基于上述技术问题,本发明提供一种多径向孔眼辅助压裂的布孔优化方法。Based on the above technical problems, the present invention provides a hole layout optimization method for assisted fracturing with multi-radial holes.
本发明所采用的技术解决方案是:The technical solution adopted in the present invention is:
一种多径向孔眼辅助压裂的布孔优化方法,包括以下步骤:A hole layout optimization method for multi-radial hole assisted fracturing, comprising the following steps:
a确定不同径向孔眼条件下的裂缝形态;a Determine the fracture shape under different radial hole conditions;
b模拟单一裂缝的波及面积,并用椭圆形进行面积拟合,通过椭圆形同心旋转获取多条主裂缝情况下的总波及面积;b Simulate the swept area of a single fracture, and use the ellipse to fit the area, and obtain the total swept area in the case of multiple main fractures through the concentric rotation of the ellipse;
c计算总波及面积c Calculate the total affected area
c1孔眼相位角为时两椭圆存在交点A(xA,yA)、B(xB,yB)、C(xC,yC)、D(xD,yD),两椭圆重叠区域内与X轴的交点E(xE,0)、F(xF,0),而两椭圆存在中心旋转对应关系,则通过椭圆方程可得到如下方程组:c1 aperture phase angle is When the two ellipses have intersections A(x A ,y A ), B(x B ,y B ), C(x C ,y C ), D(x D ,y D ), the intersection of the two ellipses with the X axis The intersection points E(x E ,0), F(x F ,0), and the two ellipses have a corresponding relationship of center rotation, then the following equations can be obtained through the ellipse equation:
式(1)中,a、b分别为椭圆的长、短轴数值,联立上式即可求得两椭圆形的四个交点A、B、C、D的具体坐标;In the formula (1), a and b are respectively the major and minor axis values of the ellipse, and the above formula can be used to obtain the specific coordinates of the four intersection points A, B, C and D of the two ellipses;
c2根据椭圆型面积公式S=πab可知,均质储层中各孔眼裂缝的波及面积相同,总波及面积为各孔眼裂缝的波及面积之和减重叠面积,即c2 According to the elliptical area formula S=πab, it can be known that the swept area of each hole and fracture in a homogeneous reservoir is the same, and the total swept area is the sum of the swept area of each hole and fracture minus the overlapping area, that is
Se=nS-(n-1)Sr (2)S e =nS-(n-1)S r (2)
式(2)中,n为孔眼个数,n≥2;In formula (2), n is the number of holes, n≥2;
Sr可通过积分求解:S r can be solved by integration:
c3联立式(1)、式(2)及式(3)即可求得最大总波及面积Semax,此时对应的孔眼相位角即是优化后的布孔方位角,多孔条件下为最优化布孔方式。c3 Simultaneous formula (1), formula (2) and formula (3) can get the maximum total swept area S emax , at this time the corresponding aperture phase angle That is, the optimized azimuth angle of hole distribution, under porous conditions In order to optimize the layout of holes.
优选的,步骤a中:所述裂缝形态是指单一主裂缝或多条主裂缝。Preferably, in step a: the fracture shape refers to a single main fracture or multiple main fractures.
优选的,步骤b中:采用长方形替代椭圆形进行面积拟合。Preferably, in step b: using a rectangle instead of an ellipse for area fitting.
本发明的有益技术效果是:The beneficial technical effect of the present invention is:
1、本发明通过利用单一裂缝在均质储层中的波及面积并叠加模拟多裂缝的波及面积,以多裂缝的最大波及面积综合为评价标准优化径向孔眼的布孔方式,为多裂缝形态提供最优布孔方案的依据。1. The present invention uses the swept area of a single fracture in a homogeneous reservoir and superimposes the swept area of multiple fractures, and takes the maximum swept area of multiple fractures as the evaluation standard to optimize the radial hole layout method, which is a multi-fracture form Provide the basis for the optimal hole layout scheme.
2、本发明使用椭圆形作为单一裂缝波及面积的替代图形,简化波及面积的求取方法,不同储层、裂缝参数可通过调整椭圆形长短轴的数值达到良好的拟合效果,具备灵活性、普遍性。2. The present invention uses an ellipse as a substitute figure for the affected area of a single fracture, and simplifies the calculation method of the affected area. The parameters of different reservoirs and fractures can achieve a good fitting effect by adjusting the values of the major and minor axes of the ellipse, which has flexibility, universality.
附图说明Description of drawings
图1为单裂缝形态图;Figure 1 is a single fracture morphology diagram;
图2为多裂缝形态图;Figure 2 is a multi-crack morphology diagram;
图3为多裂缝使用椭圆形作为裂缝波及面积进行面积拟合的示意图。Fig. 3 is a schematic diagram of area fitting of multiple fractures using an ellipse as the fracture sweep area.
具体实施方式Detailed ways
本发明通过利用单一裂缝在均质储层中的波及面积并叠加模拟多裂缝的波及面积,以多裂缝的最大波及面积综合为评价标准优化径向孔眼的布孔方式。下面结合附图与具体实施方式对本发明作进一步说明:In the present invention, the swept area of a single fracture in a homogeneous reservoir is superimposed to simulate the swept area of multiple fractures, and the maximum swept area of multiple fractures is used as an evaluation standard to optimize the radial hole layout method. Below in conjunction with accompanying drawing and specific embodiment the present invention will be further described:
一种多径向孔眼辅助压裂的布孔优化方法,包括以下步骤:A hole layout optimization method for multi-radial hole assisted fracturing, comprising the following steps:
a应用数值模拟软件确定不同径向孔眼条件下的裂缝形态(单一主裂缝或多条主裂缝),如图1、图2所示。a The numerical simulation software is used to determine the fracture shape (single main fracture or multiple main fractures) under different radial hole conditions, as shown in Fig. 1 and Fig. 2.
b应用数值模拟软件模拟单一裂缝的波及面积,并用椭圆形进行面积拟合,通过椭圆形同心旋转获取多条主裂缝情况下的总波及面积。如图3所示,图3左为数值模拟软件的模拟结果,在平面俯视图中将含油饱和度变化的面积定义为波及面积,通过椭圆形进行拟合;通过椭圆形同心旋转即可获取多条主裂缝情况下的总波及面积,如图3右。b Apply numerical simulation software to simulate the swept area of a single fracture, and use an ellipse to fit the area, and obtain the total swept area in the case of multiple main fractures through the concentric rotation of the ellipse. As shown in Fig. 3, the left side of Fig. 3 is the simulation result of the numerical simulation software. In the top view, the area of oil saturation change is defined as the swept area, which is fitted by an ellipse; multiple concentric rotations of the ellipse can be obtained The total swept area in the case of main fractures is shown in Fig. 3 right.
c计算总波及面积c Calculate the total affected area
在均质地层中相位角条件下进行多孔眼辅助压裂改造中,总体波及面积为各孔眼单独压裂时波及面积的叠加,则在确定其他参数的条件下唯一影响总体波及面积的变量为孔眼相位角 Phase angle in homogeneous formations In multi-hole assisted fracturing stimulation under the same conditions, the overall swept area is the superposition of the swept area when each hole is individually fractured, and the only variable that affects the overall swept area under the condition of determining other parameters is the phase angle of the hole
c1孔眼相位角为时两椭圆存在交点A(xA,yA)、B(xB,yB)、C(xC,yC)、D(xD,yD),两椭圆重叠区域内与X轴的交点E(xE,0)、F(xF,0),而两椭圆存在中心旋转对应关系,则通过椭圆方程可得到如下方程组:c1 aperture phase angle is When the two ellipses have intersections A(x A ,y A ), B(x B ,y B ), C(x C ,y C ), D(x D ,y D ), the intersection of the two ellipses with the X axis The intersection points E(x E ,0), F(x F ,0), and the two ellipses have a corresponding relationship of center rotation, then the following equations can be obtained through the ellipse equation:
式(1)中,a、b分别为椭圆的长、短轴数值,为椭圆方程,x1、y1、x2、y2分别指代1、2两个椭圆的坐标),联立上式即可求得两椭圆形的四个交点A、B、C、D的具体坐标。In formula (1), a and b are the major and minor axis values of the ellipse respectively, is an ellipse equation, x 1 , y 1 , x 2 , and y 2 refer to the coordinates of the two ellipses 1 and 2 respectively), and the four intersection points A, B, C, and D of the two ellipses can be obtained by combining the above formulas specific coordinates.
c2根据椭圆型面积公式S=πab可知,均质储层中各孔眼裂缝的波及面积相同,总波及面积为各孔眼裂缝的波及面积之和减重叠面积,即c2 According to the elliptical area formula S=πab, it can be known that the swept area of each hole and fracture in a homogeneous reservoir is the same, and the total swept area is the sum of the swept area of each hole and fracture minus the overlapping area, that is
Se=nS-(n-1)Sr (2)S e =nS-(n-1)S r (2)
式(2)中,n为孔眼个数,n≥2;以同层两孔为例,Se=S1+S2-Sr=2S-Sr;Sr可通过积分求解:In formula (2), n is the number of holes, n≥2; taking two holes in the same layer as an example, S e =S 1 +S 2 -S r =2S-S r ; S r can be solved by integral:
式中因椭圆重叠区为中心对称图形,故通过对称性可只求取Y轴正半轴部分面积,加倍后即为整体重叠区面积。In the formula, since the overlapping area of the ellipse is a centrally symmetrical figure, only the area of the positive semi-axis of the Y axis can be obtained through symmetry, and the area of the overall overlapping area can be obtained after doubling.
c3联立式(1)、式(2)及式(3)即可求得最大总波及面积Semax,此时对应的孔眼相位角即是优化后的布孔方位角,也即同层多孔条件下的布孔方式,多孔条件下为最优化布孔方式,n为孔眼个数。如四孔条件下为最优化布孔方式。c3 Simultaneous formula (1), formula (2) and formula (3) can get the maximum total swept area S emax , at this time the corresponding aperture phase angle That is, the optimized hole layout azimuth, that is, the hole layout method under the porous condition of the same layer, and the hole layout method under the porous condition In order to optimize the way of hole layout, n is the number of holes. For example, under the condition of four holes In order to optimize the layout of holes.
上述步骤中:也可采用长方形替代椭圆形进行面积拟合,求解思路相同。In the above steps: a rectangle can also be used instead of an ellipse for area fitting, and the solution idea is the same.
上述方式中未述及的部分采取或借鉴已有技术即可实现。Parts not mentioned in the above methods can be realized by adopting or referring to existing technologies.
需要说明的是,在本说明书的教导下,本领域技术人员所做出的任何等同替代方式,或明显变型方式,均应在本发明的保护范围之内。It should be noted that under the teaching of this specification, any equivalent replacement or obvious modification made by those skilled in the art shall fall within the protection scope of the present invention.
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Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5960371A (en) * | 1997-09-04 | 1999-09-28 | Schlumberger Technology Corporation | Method of determining dips and azimuths of fractures from borehole images |
CN105178952A (en) * | 2015-09-09 | 2015-12-23 | 中国石油天然气股份有限公司 | Method and device for determining spacing of artificial fractures of horizontal well |
CN105354639A (en) * | 2015-11-10 | 2016-02-24 | 中国石油天然气股份有限公司 | Full-cycle capacity prediction method and device for dense oil multi-medium coupling seepage |
CN105370268A (en) * | 2015-10-23 | 2016-03-02 | 中国石油天然气集团公司 | Method and device of optimizing staged fracturing parameters of horizontal well |
CN105625990A (en) * | 2014-10-30 | 2016-06-01 | 中国石油化工股份有限公司 | Method for mining shale oil by virtue of horizontal well through performing volume fracturing on reservoirs |
Family Cites Families (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
SA109300196B1 (en) * | 2008-03-27 | 2013-12-10 | بردريل ستريسيس ا | Prospect Stress Prediction |
FR2967200A1 (en) * | 2010-11-10 | 2012-05-11 | IFP Energies Nouvelles | METHOD FOR CHARACTERIZING FRACTURE FRACTURE NETWORK AND METHOD FOR OPERATING IT |
US8967262B2 (en) * | 2011-09-14 | 2015-03-03 | Baker Hughes Incorporated | Method for determining fracture spacing and well fracturing using the method |
-
2016
- 2016-10-08 CN CN201610875279.7A patent/CN106567703B/en not_active Expired - Fee Related
Patent Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5960371A (en) * | 1997-09-04 | 1999-09-28 | Schlumberger Technology Corporation | Method of determining dips and azimuths of fractures from borehole images |
CN105625990A (en) * | 2014-10-30 | 2016-06-01 | 中国石油化工股份有限公司 | Method for mining shale oil by virtue of horizontal well through performing volume fracturing on reservoirs |
CN105178952A (en) * | 2015-09-09 | 2015-12-23 | 中国石油天然气股份有限公司 | Method and device for determining spacing of artificial fractures of horizontal well |
CN105370268A (en) * | 2015-10-23 | 2016-03-02 | 中国石油天然气集团公司 | Method and device of optimizing staged fracturing parameters of horizontal well |
CN105354639A (en) * | 2015-11-10 | 2016-02-24 | 中国石油天然气股份有限公司 | Full-cycle capacity prediction method and device for dense oil multi-medium coupling seepage |
Non-Patent Citations (2)
Title |
---|
压裂水平井数值模拟理论与方法研究;单娴;《中国博士学位论文全文数据库,工程科技Ⅰ辑》;20150615(第6期);全文 * |
压裂水平井裂缝与井筒成任意角度时的产能预测模型;王立军 等;《油气地质与采收率》;20081130;第15卷(第6期);全文 * |
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