Method for calculating horizontal two-direction principal stress difference of shale reservoir

Abstract

The invention relates to a method for calculating a horizontal two-direction principal stress difference of a shale reservoir, and belongs to the technical field of unconventional petroleum and natural gas development. The invention discloses a method for calculating a horizontal two-direction principal stress difference of a shale reservoir. The method comprises the following steps: collecting a data sequence set of change of test fracturing pressure of a target layer of a fractured well along with time; determining a natural fracture approximation angle of the shale reservoir; calculating a time function G according to the data sequence set of the change of the fracturing pressure of the target layer of the fractured well along with time; a p-G, dp / dG-G and G.dp / dG-G relation curve is drawn, and the main fracture ground closing pressure and the natural fracture ground closing pressure are determined; calculating the minimum principal stress of the stratum level and the normal stress acting on the natural fracture surface; and calculating the horizontal two-direction stress difference of the reservoir. According to the method, special coring and mine field testing are not needed, so that the huge investment for carrying out rock core testing is remarkably saved, and the acquisition precision of the horizontal two-direction stress difference is greatly improved. Wide application prospects are realized.

Description

Technical Field

[0001] The invention relates to a method for calculating the horizontal bidirectional principal stress difference of a shale reservoir, and belongs to the technical field of unconventional oil and gas development. Background Art

[0002] In the past 20 years, hydraulic fracturing technology for volume transformation of unconventional reservoirs has made significant progress. The optimization design of segmented multi-cluster completion parameters has become the core technology of volume fracturing transformation. A large number of core experiments and theoretical studies in the industry have proved that unconventional reservoirs are highly heterogeneous and have very developed natural fractures; the horizontal biaxial stress difference is the key parameter that restricts the optimization design of parameters for volume fracturing engineering. The horizontal biaxial principal stress difference is defined as the difference between the maximum horizontal principal stress and the minimum horizontal principal stress. At present, indoor core experiment test methods, logging data interpretation methods based on geostress calculation models, and field micro-fracturing test calculations based on homogeneous isotropic materials can be used. Among them, indoor experimental tests require high costs to drill a limited number of cores, and the experimental results only reflect the stress state near the well wall at the coring location, which is difficult to accurately reflect the principal stress state and horizontal biaxial stress difference of the fracturing well; the progress of the logging data interpretation results significantly depends on the accuracy of the adopted geostress calculation model and the values ​​of each coefficient, so it is also necessary to calibrate with the actual stress field; the conditions of micro-fracturing field tests are very different from those of unconventional reservoir volume fracturing. The industry generally believes that the horizontal minimum principal stress obtained by field tests is more reliable, but the interpreted horizontal maximum principal stress is not accurate. It can be seen that the current method is difficult to obtain a more accurate and reliable horizontal biaxial principal stress difference, which significantly restricts the optimization design of volume fracturing parameters. Summary of the invention

[0003] In order to overcome the defects in the prior art, the present invention aims to provide a method for calculating the horizontal biaxial principal stress difference of a shale reservoir.

[0004] The present invention provides a technical solution to solve the above technical problems: a method for calculating the horizontal biaxial principal stress difference of a shale reservoir, comprising the following steps:

[0005] Step S10, collecting a data series set of changes in the fracturing pressure of the target layer of the fracturing well over time;

[0006] Step S20, determining the natural fracture approach angle of the shale reservoir;

[0007] Step S30, calculating the time function G according to the data series set of the change of the fracturing pressure over time in the target layer of the fracturing well;

[0008] Step S40, calculating the gradient dp / dG of the pressure p versus the G function time according to the time function G, constructing the G.dp / dG function, and drawing the relationship curves of pG, dp / dG-G and G.dp / dG-G;

[0009] Step S50: Determine the main crack ground closure pressure σ according to the dp / dG-G and G.dp / dG-G relationship curves m,s and the natural fracture ground closure pressure σ nf,s ;

[0010] Step S60: According to the main crack ground closing pressure σ m,s and the natural fracture ground closure pressure σ nf,s Calculate the minimum horizontal principal stress σ of the formation h and the normal stress σ acting on the natural fracture surface nf ;

[0011] Step S70: According to the minimum principal stress σ h and the normal stress σ acting on the natural fracture surface nf Calculate the horizontal biaxial stress difference Δσ of the reservoir H .

[0012] A further technical solution is that the specific steps of step S20 are:

[0013] Step S21, obtain the natural fracture trend rose diagram based on the FMI imaging logging interpretation, and determine the natural fracture trend azimuth α nf ;

[0014] Step S22: Determine the horizontal maximum principal stress azimuth α by microseismic monitoring or core test H ;

[0015] Step S23: according to the natural fracture direction azimuth α nf and the horizontal maximum principal stress azimuth α H The natural fracture approach angle β is calculated.

[0016] A further technical solution is that the calculation formula of the natural fracture approach angle β is:

[0017] β=|α nf -α H

[0018] Where: β is the natural fracture approach angle, degrees; α H is the azimuth of the maximum horizontal principal stress, degrees; α nf is the azimuth of the natural fracture, degrees.

[0019] A further technical solution is that the specific steps of step S30 are:

[0020] Step S31: Determine the pump stop time t in the data series of the change of fracturing pressure over time in the target layer of the fracturing well. p ;

[0021] Step S32: Calculate the time function G for each point in the pressure drop-time series after the pump is stopped.

[0022] A further technical solution is that the calculation formula of the time function G is:

[0023]

[0024] g1(Δt D,i )=(1+Δt D,i )sin -1 (1+Δt D,i ) -1 / 2 +Δt D,i 1 / 2

[0025]

[0026] g(Δt D,i )=(g1(Δt D,i )+g2(Δt D,i )) / 2

[0027]

[0028] Where: Δt D,i is the dimensionless voltage drop time of the i-th time series point, dimensionless; t p is the fracturing pump stop time, s; t i is the time elapsed after the start of fracturing at the i-th time series point, s; g(Δt D,i ) is a dimensionless time function; G i is the time function of the i-th time series point.

[0029] A further technical solution is that the specific steps of step S40 are:

[0030] Step S41, calculating the gradient dp / dG of the pressure p versus the G function time for each point in the pressure drop-time series after the pump is stopped;

[0031] Step 42, applying the G function time and the pressure drop G time function gradient to construct G.dp / dG;

[0032] Step 43: Draw the relationship curves of pG, dp / dG-G and G.dp / dG-G in the Cartesian coordinate system.

[0033] A further technical solution is that the calculation formula in step S41 is:

[0034]

[0035] Where: p i is the pressure at the i-th time series point, MPa; p i+1 is the pressure at the i+1th time series point, MPa; G i is the time function of the i-th time series point; G i+1 is the time function of the i+1th time series point; is the gradient of the pressure p at the i-th time series point with respect to the G function time.

[0036] A further technical solution is that in step S50, the data points after the hump appears on the G.dp / dG-G relationship curve are used as the fitting reference line, and the point where the straight line begins to deviate from the hump section is the natural fracture closing point, corresponding to the natural fracture ground closing pressure σ nf,s ; The data points after the hump appears on the G.dp / dG-G relationship curve are used as the fitting reference line, and the points that deviate from the reference line and are close to the horizontal section are used to determine the main crack closing point, which corresponds to the main crack ground closing pressure σ m,s .

[0037] A further technical solution is that the calculation formula in step S60 is:

[0038] σ h =σ m,s +10 -6 ρgH

[0039] σ nf =σ nf,s +10 -6 ρgH

[0040] Where: h is the minimum horizontal principal stress of the formation, MPa; σ nf is the normal stress acting on the natural fracture surface, MPa; ρ is the density of the fracturing fluid, Kg / m 3 ; g is the acceleration due to gravity, 9.8m / s 2 ; H is the middle depth of the target layer, m; σ nf,s is the ground closure pressure of natural fractures, MPa; σ m,s is the ground closure pressure of the main fracture, MPa.

[0041] A further technical solution is that the calculation formula in step S70 is:

[0042] Δσ H =σ H -σ h

[0043]

[0044] Where: β is the natural fracture approach angle, degree; σ h is the minimum horizontal principal stress of the formation, MPa; σ nf is the normal stress acting on the natural fracture surface, MPa; σ H is the maximum horizontal principal stress of the formation, MPa; Δσ H is the horizontal biaxial stress difference of the reservoir, MPa.

[0045] The present invention has the following beneficial effects: the present invention does not require special coring and field testing, which not only significantly saves the huge investment in core testing, but also greatly improves the accuracy of obtaining horizontal biaxial stress differences. It has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is the data chart of the fracturing test seconds of the JY-Test well in Fuling;

[0047] Figure 2 Rose diagram of natural fracture trend interpreted for imaging well logging FMI;

[0048] Figure 3 The horizontal maximum principal stress direction map obtained from the microseismic monitoring data of the Test well test fracturing;

[0049] Figure 4 is the geometric relationship diagram between natural fractures and principal stress directions;

[0050] Figure 5 This is the relationship diagram of the G-time function curve of the fracturing pressure drop in the JY-Test well test. DETAILED DESCRIPTION

[0051] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0052] like Figure 1 As shown, a method for calculating the horizontal biaxial principal stress difference of a shale reservoir of the present invention comprises the following steps:

[0053] Step S10, collecting a data series set of changes in the fracturing pressure of the target layer of the fracturing well over time;

[0054] Step S20, determining the natural fracture approach angle of the shale reservoir;

[0055] Step S21, obtain the natural fracture trend rose diagram based on the FMI imaging logging interpretation, and determine the natural fracture trend azimuth αnf ;

[0056] Step S22: Determine the horizontal maximum principal stress azimuth α by microseismic monitoring or core test H ;

[0057] Step S23: according to the natural fracture direction azimuth α nf and the horizontal maximum principal stress azimuth α H The natural fracture approach angle β is calculated;

[0058] β=|α nf -α H

[0059] Where: β is the natural fracture approach angle, degrees; α H is the azimuth of the maximum horizontal principal stress, degrees; α nf is the azimuth of the natural fracture, degrees;

[0060] Step S30, calculating the time function G according to the data series set of the change of the fracturing pressure over time in the target layer of the fracturing well;

[0061] Step S31: Determine the pump stop time t in the data series of the change of fracturing pressure over time in the target layer of the fracturing well. p ;

[0062] Step S32, calculating the time function G for each point in the pressure drop-time series after the pump is stopped;

[0063]

[0064] g1(Δt D,i )=(1+Δt D,i )sin -1 (1+Δt D,i ) -1 / 2 +Δt D,i 1 / 2

[0065]

[0066] g(Δt D,i )=(g1(Δt D,i )+g2(Δt D,i )) / 2

[0067]

[0068] Where: Δt D,i is the dimensionless voltage drop time of the i-th time series point, dimensionless; t p is the pump stop time for fracturing, s; ti is the time after fracturing starts at the i-th time series point, s; g(ΔtD,i ) is a dimensionless time function; G i is the time function of the i-th time series point;

[0069] Step S40, calculating the gradient dp / dG of the pressure p versus the G function time according to the time function G, constructing the G.dp / dG function, and drawing the relationship curves of pG, dp / dG-G and G.dp / dG-G;

[0070] Step S41, calculating the gradient dp / dG of the pressure p versus the G function time for each point in the pressure drop-time series after the pump is stopped;

[0071]

[0072] Where: p i is the pressure at the i-th time series point, MPa; p i+1 is the pressure at the i+1th time series point, MPa; G i is the time function of the i-th time series point; G i+1 is the time function of the i+1th time series point; is the gradient of the pressure p at the i-th time series point with respect to the G function time;

[0073] Step 42, applying the G function time and the pressure drop G time function gradient to construct G.dp / dG;

[0074] Step 43, draw the relationship curves of pG, dp / dG-G and G.dp / dG-G in the Cartesian coordinate system;

[0075] Step S50: Determine the main crack ground closure pressure σ according to the dp / dG-G and G.dp / dG-G relationship curves m,s and the natural fracture ground closure pressure σ nf,s ;

[0076] The data points after the “hump” appears on the G.dp / dG-G relationship curve are used as the fitting reference line. The point where the straight line begins to deviate from the “hump” section is the natural fracture closing point, corresponding to the ground closing pressure σ of the natural fracture. nf,s ;

[0077] The data points after the “hump” appears on the G.dp / dG-G relationship curve are used as the fitting reference line. The points that deviate from the reference line and are close to the horizontal section are used to determine the main crack closing point, corresponding to the ground closing pressure σ of the main crack. m,s ;

[0078] Step S60: According to the main crack ground closing pressure σ m,s and the natural fracture ground closure pressure σ nf,s Calculate the minimum horizontal principal stress σ of the formation hand the normal stress σ acting on the natural fracture surface nf ;

[0079] σ h =σ m,s +10 -6 ρgH

[0080] σ nf =σ nf,s +10 -6 ρgH

[0081] Where: h is the minimum horizontal principal stress of the formation, MPa; σ nf is the normal stress acting on the natural fracture surface, MPa; ρ is the density of the fracturing fluid, Kg / m 3 ; g is the acceleration due to gravity, 9.8m / s 2 ; H is the middle depth of the target layer, m; σ nf,s is the ground closure pressure of natural fractures, MPa; σ m,s is the ground closure pressure of the main fracture, MPa;

[0082] Step S70: According to the minimum principal stress σ h and the normal stress σ acting on the natural fracture surface nf Calculate the horizontal biaxial stress difference Δσ of the reservoir H ;

[0083] Δσ H =σ H -σ h

[0084]

[0085] Where: β is the natural fracture approach angle, degree; σ h is the minimum horizontal principal stress of the formation, MPa; σ nf is the normal stress acting on the natural fracture surface, MPa; σ H is the maximum horizontal principal stress of the formation, MPa; Δσ H is the horizontal biaxial stress difference of the reservoir, MP.

[0086] Example

[0087] The vertical depth of the target layer of a shale gas well in Fuling, Chongqing, China is 2800m. The well is subjected to FMI imaging logging, field test fracturing and microseismic monitoring. The method of the present invention is now used to calculate the horizontal biaxial principal stress difference. The steps are as follows:

[0088] A. Collect the data series of the changes of fracturing pressure over time in the target formation of the fracturing well;

[0089] The test fracturing second data (4460 seconds in total) is as shown in the attached Figure 1 As shown. The fracturing pump injection time is 2290s, and the pressure drop time after stopping the pump is 2170s.

[0090] B. Determine the approach angle of natural fractures;

[0091] (1) Using FMI imaging logging interpretation to obtain the natural fracture trend rose diagram as shown in the attached figure Figure 2 shown.

[0092] The dominant orientation of natural fractures is: α nf =NE5°;

[0093] (2) Determine the orientation of the horizontal principal stress using microseismic monitoring or core experimental testing;

[0094] Based on the attached Figure 3 The microseismic event point is determined by least squares regression to determine the maximum horizontal principal stress orientation: α H =NE50°;

[0095] (3) The approach angle of natural fractures is calculated according to the following formula.

[0096] β=|α nf -α H |=|NE50-NE5|=45°

[0097] The geometric relationship between the horizontal maximum principal stress orientation and the natural fracture direction determined in step B can be represented as follows: Figure 4 .

[0098] C. Calculate the time function G using the collected data of pressure change over time after the hydraulic fracturing pump is stopped;

[0099] (1) Determine the pump stop time (the time corresponding to when the injection displacement is zero) in the fracturing monitoring pressure data.

[0100] t p =2290s

[0101] (2) For each point in the pressure drop-time series after the pump is stopped, calculate the time function G according to the following formula;

[0102]

[0103] g1(Δt D,i )=(1+Δt D,i )sin -1 (1+Δt D,i ) -1 / 2 +Δt D,i 1 / 2

[0104]

[0105] g(Δt D,i )=(g1(Δt D,i )+g2(Δt D,i )) / 2

[0106]

[0107] Where: Δt D,i is the dimensionless voltage drop time of the i-th time series point, dimensionless; t p is the fracturing pump stop time, s; t i is the time elapsed after the start of fracturing at the i-th time series point, s; g(Δt D,i ) is a dimensionless time function; G i is the time function of the i-th time series point;

[0108] D. Calculate dp / dG by programming and construct G.dp / dG function; draw the relationship curves of pG, dp / dG-G and G.dp / dG-G;

[0109] (1) For each point in the pressure drop-time series after the pump is stopped, the gradient dp / dG of the pressure p versus the G function time is calculated by programming;

[0110]

[0111] (2) Apply the G function time and pressure drop G time function gradient to construct G.dp / dG;

[0112] (3) Draw the relationship curves of pG, dp / dG-G and G.dp / dG-G in the Cartesian coordinate system, as shown in the attached figure. Figure 5 shown.

[0113] E. Determine the ground closure pressure of the main artificial fracture of hydraulic fracturing and the ground closure pressure of the natural fracture

[0114] (1) Attachment Figure 5 The data points after the "hump" appears on the G.dp / dG-G relationship curve are used as fitting reference lines. The points where the straight line begins to deviate from the "hump" segment (black dots in the figure) are the closing points of the natural fractures, corresponding to the ground closing pressure σ of the natural fractures. nf,s =35.97MPa;

[0115] (2) Attachment Figure 5 The data points after the "hump" appears on the G.dp / dG-G relationship curve are used as fitting reference lines. The points that deviate from the reference line and are close to the horizontal segment (green dots in the figure) are used to determine the main crack closing point, corresponding to the ground closing pressure σ of the main crack. m,s =30.12MPa;

[0116] F. Calculate the minimum horizontal principal stress σ of the formation h and the normal stress σ acting on the natural fracture surface nf .

[0117] After the pump is stopped, there is no fluid flow in the fracturing string. The minimum principal stress σ of the formation is calculated based on the pressure balance principle. h and the normal stress σ acting on the natural fracture surface nf .

[0118] σ h =σ m,s +10 -6 ρgH=30.12+10 -6 ×1000×9.8×2800=57.56MPa

[0119] σ nf =σ nf,s +10 -6 ρgH=35.97+10 -6 ×1000×9.8×2800=63.41MPa

[0120] G. Calculate the horizontal biaxial stress difference of the reservoir.

[0121] (1) According to the attached Figure 4 The geometric relationship between the horizontal maximum principal stress orientation and the natural fracture direction is shown. According to the material mechanics theory, the horizontal maximum principal stress can be obtained. The calculation formula is as follows:

[0122]

[0123] (2) Calculation of the horizontal biaxial principal stress difference Δσ H =σ H -σ h =69.26-57.56=11.7MPa.

[0124] The above description is not intended to limit the present invention in any form. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are within the scope of the technical solution of the present invention.

Claims

1. A method for calculating the horizontal biaxial principal stress difference of a shale reservoir, characterized in that: The following steps are involved: Step S10, collecting a data series set of changes in the fracturing pressure of the target layer of the fracturing well over time; Step S20, determining the natural fracture approach angle of the shale reservoir; Step S30, calculating the time function G according to the data series set of the change of the fracturing pressure over time in the target layer of the fracturing well; Step S40, calculating the gradient dp / dG of the pressure p versus the G function time according to the time function G, constructing the G.dp / dG function, and drawing the relationship curves of pG, dp / dG-G and G.dp / dG-G; Step S50: Determine the main crack ground closure pressure σ according to the dp / dG-G and G.dp / dG-G relationship curves m,s and the natural fracture ground closure pressure σ nf,s ; Step S60: According to the main crack ground closing pressure σ m,s and the natural fracture ground closure pressure σ nf,s Calculate the minimum horizontal principal stress σ of the formation h and the normal stress σ acting on the natural fracture surface nf ; Step S70: According to the minimum principal stress σ h and the normal stress σ acting on the natural fracture surface nf Calculate the horizontal biaxial stress difference Δσ of the reservoir H .

2. The method for calculating the horizontal biaxial principal stress difference of a shale reservoir according to claim 1, characterized in that: The specific steps of step S20 are: Step S21, obtain the natural fracture trend rose diagram based on the FMI imaging logging interpretation, and determine the natural fracture trend azimuth α nf ; Step S22: Determine the horizontal maximum principal stress azimuth α by microseismic monitoring or core test H ; Step S23: according to the natural fracture direction azimuth α nf and the horizontal maximum principal stress azimuth α H The natural fracture approach angle β is calculated.

3. The method for calculating the horizontal biaxial principal stress difference of a shale reservoir according to claim 1, characterized in that: The calculation formula of the natural fracture approach angle β is: β＝|α nf -α H | Where: β is the natural fracture approach angle, degrees; α H is the azimuth of the maximum horizontal principal stress, degrees; α nf is the azimuth of the natural fracture, degrees.

4. The method for calculating the horizontal biaxial principal stress difference of a shale reservoir according to claim 1, characterized in that: The specific steps of step S30 are: Step S31: Determine the pump stop time t in the data series of the change of fracturing pressure over time in the target layer of the fracturing well. p ; Step S32: Calculate the time function G for each point in the pressure drop-time series after the pump is stopped.

5. The method for calculating the horizontal biaxial principal stress difference of a shale reservoir according to claim 1, characterized in that: The calculation formula of the time function G is: g1(Δt D,i )=(1+Δt D,i )sin -1 (1+Δt D,i ) -1 / 2 +Δt D,i 1 / 2 g(Δt D,i )=(g1(Δt D,i )+g2(Δt D,i )) / 2 Where: Δt D,i is the dimensionless voltage drop time of the i-th time series point, dimensionless; t p is the pump stop time for fracturing, s; ti is the time after fracturing starts at the i-th time series point, s; g(Δt D,i ) is a dimensionless time function; G i is the time function of the i-th time series point.

6. The method for calculating the horizontal biaxial principal stress difference of a shale reservoir according to claim 1, characterized in that: The specific steps of step S40 are: Step S41, calculating the gradient dp / dG of the pressure p versus the G function time for each point in the pressure drop-time series after the pump is stopped; Step 42, applying the G function time and the pressure drop G time function gradient to construct G.dp / dG; Step 43: Draw the relationship curves of pG, dp / dG-G and G.dp / dG-G in the Cartesian coordinate system.

7. A method for calculating the horizontal biaxial principal stress difference of a shale reservoir according to claim 6, characterized in that: The calculation formula in step S41 is: Where: p i is the pressure at the i-th time series point, MPa; p i+1 is the pressure at the i+1th time series point, MPa; G i is the time function of the i-th time series point; G i+1 is the time function of the i+1th time series point; is the gradient of the pressure p at the i-th time series point with respect to the G function time.

8. The method for calculating the horizontal biaxial principal stress difference of a shale reservoir according to claim 1, characterized in that: In step S50, the data points after the hump appears on the G.dp / dG-G relationship curve are used as the fitting reference line, and the point where the straight line begins to deviate from the hump section is the natural fracture closing point, corresponding to the natural fracture ground closing pressure σ nf,s ; The data point after the hump appears on the G.dp / dG-G relationship curve is used as the fitting reference line. The point that deviates from the reference line and approaches the horizontal section is the main crack closing point, which corresponds to the main crack ground closing pressure σ m,s .

9. The method for calculating the horizontal biaxial principal stress difference of a shale reservoir according to claim 1, characterized in that: The calculation formula in step S60 is: s h =s m,s +10 -6 ρgH s nf =s nf,s +10 -6 ρgH Where: h is the minimum horizontal principal stress of the formation, MPa; σ nf is the normal stress acting on the natural fracture surface, MPa; ρ is the density of the fracturing fluid, Kg / m 3 ; g is the acceleration due to gravity, 9.8m / s 2 ; H is the middle depth of the target layer, m; σ nf,s is the ground closure pressure of natural fractures, MPa; σ m,s is the ground closure pressure of the main fracture, MPa.

10. The method for calculating the horizontal biaxial principal stress difference of a shale reservoir according to claim 1, characterized in that: The calculation formula in step S70 is: Board H =s H -s h Where: β is the natural fracture approach angle, degree; σ h is the minimum horizontal principal stress of the formation, MPa; σ nf is the normal stress acting on the natural fracture surface, MPa; σ H is the maximum horizontal principal stress of the formation, MPa; Δσ H is the horizontal biaxial stress difference of the reservoir, MPa.

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