Analysis of Fracture Initiation Pressure of Tight Sandstone in HangJinQi

Simply increasing the fracture length to enhance the conductivity of the reservoir has limited success in increasing the production rate, thus hampering the pace of production at Hangjinqi. To combat this problem, a mathematical model was developed to determine the onset pressure of tight sandstone in Hangjinqi based on the Mohr-Coulomb criterion. It is shown that the onset angle decreases with increasing trap inclination, thus making it difficult to close the fracture with high horizontal pressure and suction. As for the block, it is one of Sinopec’s major areas for developing tight, low-permeability oil and gas in the Ordos Basin. To address this issue, a mathematical model was developed for the onset pressure of tight sandstone in Hangjinqi, taking into account factors such as vertical principal stress, maximum horizontal principal stress, minimum horizontal principal stress, and fracture inclination.The case of trap HE1 in JPH-416 was solved using a minimal bisection method, showing that the onset angle increases with trap inclination. As the fracture inclination increases, the fracture closure pressure gradually increases, and the effect of the minimum horizontal and vertical principal stresses becomes more pronounced.


Introduction
Hangjinqi block is Sinopec's main replacement area for tight low-permeability oil and gas development in the Ordos Basin.By the end of the 13th Five-Year Plan, it plans to complete the construction task of 3-3.6 billion square meters of production capacity, and the annual output is planned to reach 2-2.5 billion square meters in 2020.However, Hangjinqi block is a large area of gas bearing, low abundance tight sandstone gas reservoir, gas Wells can only be built through reservoir reconstruction.Since 2013, a variety of horizontal well staged fracturing tests have been carried out in Dongsheng Gas field, including multi-stage staged fracturing with pre-positioned pipe packer, continuous tubing driven fracturing, and pumped bridge plug staged fracturing, and certain development effects have been achieved.However, with the gradual increase of development scale and the gradual reduction of favorable reservoir areas, the reservoir quality has gradually deteriorated.To improve the fracture conductivity of the reservoir has not reached the ideal effect of increasing production, which restricts the production pace of Hangjinqi.Therefore, combined with the engineering geological characteristics of the reservoir of Xiashihezi Formation in Hangjinqi block of Dongsheng Gas field, the mixed water volume fracturing technology is studied.While forming the main fracture, the natural fracture is forced to expand continuously, thus forming a more complex fracture network system, improving the fracture conductivity, increasing the fracturing reconstruction volume, improving the fracturing construction and reconstruction effect, and realizing the efficient development of tight sandstone gas reservoir.Provide guarantee for the smooth implementation of production capacity construction and provide technical support for building Sinopec's core engineering technology series for efficient exploration and development of tight and low-pressure gas reservoirs.
Since hydraulic fracturing was first tested in the United States in 1947, more than 1.5 million Wells have been fracked in more than 50 years [1][2].Because hydraulic fracturing technology plays an important role in oil and gas exploitation, a lot of research has been carried out at home and abroad [3][4][5][6][7][8][9][10]. The theory of fracturing, fracturing equipment, materials and process technology have been rapidly developed.However, the success rate of hydraulic fracturing is still very low, according to statistics less than 70%, and it is difficult to make new breakthroughs [11][12][13][14][15][16].
In this paper, the influence of fracturing on fracture initiation pressure, initiation location and fracture extension rule during different phases of fracturing is studied.A mathematical model of the initiation pressure of Hangjinqi tight sandstone is established to explore the way of forming a large flat fracture perpendicular to the minimum horizontal principal stress through fracturing, so as to reduce the fracturing pressure of hydraulic fracturing and improve the success rate and fracturing effect.It provides scientific basis for deep low permeability formation perforation scheme and hydraulic fracturing design.

Model Building
The rock is subjected to the principal stress σ1 in the vertical direction of the far field and σ3 in the horizontal direction.For closed fractures, it is usually assumed that the fracture is linear or sharp, and the fracture half-length is a.
The tensile stress is specified as normal stress here, and it is also specified as normal stress in all subsequent studies of fracture initiation and propagation.Let λ1 be the coefficient of side pressure (0<λ1<1), and the two principal stresses satisfy the relation σ1=σ, σ3=λσ1, MPa.σn and σT are the normal stress and tangential stress on the fracture surface, MPa, τn are the shear stress on the fracture surface, MPa, p is the fluid pressure in the fracture, MPa, β are the fracture inclination, °.The value meets the following expression: σ1= -73.5MPa, σ3=-69.2MPa.According to the theory of fracture mechanics and considering the non-singular stress term of the fracture tip, Williams expansion is carried out in polar coordinates with the fracture tip as the origin: where, σr, σθ and τrθ are the radial, forward and tangential stresses at the fracture tip respectively, MPa; KI and KII are type I and type II stress intensity factors of fracture tip, respectively.θ is the fracture initiation Angle, °; Both T and N are the components of the non-singular stress term (T stress) parallel to and perpendicular to the fracture plane, MPa.Generally, the T stress can be ignored for pure type I fracturing, but when the fracture is I-II or pure type II fracturing, the influence of T stress can be ignored, which may cause significant errors in the calculation results.
The Moore-Coulomb yield quasi-expression is: where, the component can be expressed as: The equation is deformed: (5) where: c is the cohesion of the rock, MPa; φ is the internal friction Angle of the rock, °.Considering that the contact between the upper and lower surfaces of the closed fracture is bound to produce friction, the relative sliding of the fracture surface is inhibited.
It is necessary to modify the shear stress on the fracture surface to the effective shear stress (τeff, MPa), that is, τeff and τn satisfy the following relation: (6) where: μ is the friction coefficient of the fracture surface and has no dimensionality.The type II stress intensity factor KII=τeff (πa)0.5 on the fracture surface.Since the fracture surface of the closed fracture is always under pressure in the normal direction, and the corresponding two points on the fracture surface do not have relative motion in the Y-axis direction, the type I stress intensity factor KI=0 is constant.
Since the onset Angle of type II fracturing in closed fractures is 0°, according to the normal stress and shear stress on the fracture surface, it can be simplified as follows: (7) The initiation criterion of shear fracturing of closed fractures can be obtained:   (8) where r is the critical size of the fracture tip, m.

Model Solving
The maximum circumferential stress criterion for tensile failure is assumed as follows: , where: σt is the tensile strength of the rock, (σθ)max is the maximum value of the circumferential stress at the fracture tip, and the corresponding fracture initiation Angle is θ=θ1. ( The value of theta 1 can be obtained by solving the equation.By bringing it into the equation, the maximum circumferential stress (σθ)max can be obtained, and it can be determined whether the fracture has tensile fracturing.The Moore-Coulomb criterion is still used for shear fracturing of open fractures.At the same time, it is assumed that: (1) the positive and negative values of shear stress only represent the difference in stress direction, and the shear fracture will expand along the direction of the maximum absolute value of the effective shear stress, and the corresponding initiation Angle is θ=θ2; (2) When the absolute value of the effective shear stress meets the Moore-Coulomb criterion, that is, the equation fractures occur shear fracturing, which is specifically expressed as follows: , When the effective shear stress is the maximum, the initiation Angle should satisfy the equation: The value of θ2 can be obtained by solving the equation, and the maximum value of the absolute value of the effective shear stress can be obtained by bringing it into the equation, and the shear initiation of fractures can be determined according to the Moore-Coulomb criterion.
The equation is solved by dichotomous method.By dividing the interval where the zero point of the function f(x) is located in two parts, the two endpoints of the interval gradually approach the zero point.

Case Analysis
Taking JPH-416 well box 1 as an example, according to DST test data of vertical well in this area, the average pressure coefficient of box 1 section is 0.92, and the average temperature gradient is 2.97℃/100m.The vertical depth of the horizontal section is 3242.36m,and the formation pressure of II tan 2    Figure 3 shows the well initiation Angle prediction chart of JPH-416 well box 1. Horizontal fractures and fractures with high strike Angle have high closure stress, high closure degree of fractures, poor seepage capacity, and high initiation pressure because the formation is difficult to absorb liquid during fracturing reconstruction.The change of initiation pressure is not obvious with the increase of well inclination Angle.However, with the increase of horizontal ground stress ratio, the initiation pressure tends to decrease as a whole.With the increase of phase Angle, the initiation pressure showed a trend of overall decrease.Figure 4 shows the effect of minimum horizontal principal stress on fracture closure pressure in tight sandstone.As the minimum horizontal principal stress decreases, the closing pressure decreases.The minimum horizontal principal stress has a greater influence on the closing stress of small fracture inclination Angle.With the increase of fracture inclination Angle, the effect of minimum horizontal principal stress on closure pressure becomes weaker.Compared with σ3=59.2MPa, the minimum horizontal principal stress σ1=29.2MPadecreases by 30MPa and the closing pressure increases by 31.51MPa.Figure 5 shows the effect of vertical principal stress on fracture closure pressure in tight sandstone.With the increase of the vertical principal stress, the closing pressure presents an increasing trend.The increasing trend of the closing pressure is more obvious in the interval of fracture inclination from 0° to 60°, while the changing trend of the closing pressure is not obvious in the interval of fracture inclination greater than 60°.Compared with σ1=93.5MPa, the vertical principal stress σ1=63.5MPaincreases by 30MPa and the closing pressure increases by 16.81MPa.The vertical principal stress has a great influence on the closing stress of small fracture inclination Angle.

Conclusion
By calculating and solving a mathematical model of fracture pressure in the Hangjinqi compact sandstone, the following conclusions can be drawn: (1) Horizontal fractures and fractures with a high strike angle exhibit high closing high fracture closure degree, poor seepage capacity, and a poor ability to absorb liquid during fracturing reconstruction, resulting in high fracturing pressure.The effect of trap inclination on onset pressure is less pronounced.
(2) The onset pressure generally decreases as the ratio of horizontal ground stress increases.In addition, the onset pressure decreases with increasing phase angle.
(3) The closing pressure increases with the increase of the maximum principal stress, Poisson's ratio, and elastic modulus, whereas it decreases with the increase of the minimum horizontal principal stress.Moreover, as the inclination angle increases, the fracture closure stress gradually increases, and the effect of the minimum horizontal and vertical principal stresses becomes more pronounced.It is important to consider the impact of fracture orientation, ground stress ratio, and principal stress on the fracturing pressure in the Hangjinqi sandstone, which could aid in optimizing the fracturing process.

Figure 2
Figure 2 shows the well initiation Angle prediction chart of JPH-416 well box 1.After the fracture is determined to be an open fracture, according to the criterion of the maximum circumferential stress of the open fracture, the corresponding parameters are brought into the equation to obtain the fracture initiation Angle corresponding to the maximum circumferential stress under different well inclination angles.Then the initiation Angle is brought into the equation of circumferential stress to calculate the maximum circumferential stress under different fracture inclination angles.With the increase of well inclination Angle of JPH-416 well box 1, the fracture initiation Angle shows a decreasing trend.As the order of the three-way ground stress is, the closing stress of the fracture surface gradually approaches the vertical stress with the increase of the inclination Angle.With the increase of strike Angle, the fracture surface closing stress increases from minimum to maximum horizontal principal stress.

Figure 4 .
Figure 4. Effect of minimum horizontal principal stress on fracture closure pressure in tight sandstone.

7 Figure 5 .
Figure 5.Effect of vertical principal stress on fracture closure pressure in tight sandstone.

Table 1 .
Technical index of water-based fracturing fluid.