Geofluids

Volume 2019, Article ID 2167094, 16 pages

https://doi.org/10.1155/2019/2167094

## Research and Application of Radial Borehole Fracturing Based on Numerical Simulation

SINOPEC Petroleum Exploration and Production Research Institute, Beijing 100083, China

Correspondence should be addressed to Xiaolong Li; moc.ceponis@ykys.8102lxil

Received 24 June 2019; Revised 22 August 2019; Accepted 21 October 2019; Published 20 November 2019

Academic Editor: Constantinos Loupasakis

Copyright © 2019 Xiaolong Li and Jiayuan He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The radial borehole fracturing technology has been applied in a certain number of oilfields with good results being achieved. However, the morphology and variation of fracture still require further study. In this paper, the reservoir model based on formation fluid-solid coupling equation is established with the extended finite element method (XFEM) in ABAQUS, and the fracture morphologies in the single-radial borehole, vertical multiradial borehole, and horizontal multiradial borehole are simulated and analyzed with criteria of maximum principal stress and maximum energy release rate as the damage mechanism. Moreover, the accuracy of numerical simulation results is verified with the large-scale true 3D physical simulation experiment. The results show that the induced stress field along the radial borehole during fracturing is the root cause of fracture directional propagation along the radial borehole whose effective guidance distance reaches 40 m. The vertical multiradial borehole can effectively enhance fracture directional propagation and is capable of reducing fracture initiation pressure. In the horizontal multiradial borehole, the major fracture propagating along each radial borehole is formed in the remote-borehole area, and the secondary fracture connecting the neighboring radial boreholes is formed in the near-borehole zone. Coordination of major and secondary fractures can effectively increase the drainage area and reduce the flow resistance in the near-borehole zone. Based on the research on fracture morphology of multiradial borehole fracturing, the scheme of radial borehole arrangement is optimized and verified through numerical simulation of deliverability. The final optimum borehole arrangement scheme is the intersectional angle of 45° between four orthogonal radial boreholes and horizontal maximum principal stress.

#### 1. Introduction

During fracturing in the wells of perforation completion, the dual-wing fracture propagating along the maximum principal stress is always formed, and the fracture network is not likely to occur [1–4]. Moreover, when not being distributed along the maximum principal stress, the remaining oil is not able to be connected by the conventional dual-wing fracture, significantly reducing the effect of stimulation [5].

The radial borehole fracturing technology based on hydraulic jetting technology has been applied experimentally in several oilfields of SINOPEC, with good results being achieved. In this paper, radial borehole fracturing technology means fracturing based on the existing radial boreholes drilling by hydraulic jetting technology. Based on the mature technology of hydraulic jetting [6–9], preliminary conclusions have been obtained in the research on the radial borehole fracturing at a certain level, which indicates that this technology can change the inherent morphology of fracture and effectively improve the effect of reservoir stimulation [10, 11].

Some studies about fracture initiation, fracture propagation, well stability, productivity, and so on have been conducted. The results are shown as follows.

In the fields of fracture propagation and the influence factor, both simulation and experiment were conducted. The fracture propagation path of single radial well was studied based on XFEM, and a two-dimensional model was established. The results show that the diameter of radial well and the azimuth are the major influence factors of failure pressure [12]. Also, the quantitative analysis on different parameters of fracture initiation pressure and fracture starting point was arranged to study local stress accumulation situation. The result shows that initiation pressure and distance between well and fracture starting point increases as the length, diameter, and azimuth of radial well section rise [13]. Another further quantitative analysis was introduced to quantify the guidance of radial borehole row in the vertical multiradial well fracturing. The results show that the directional propagation of fracture is realized through scientifically arranged vertical radial borehole row [14]. By synthesizing the previous studies, the law of influence factors on fracture propagation is preliminarily clarified which is as the radial borehole azimuth increases, the preferential rock tensile fracturing in the axial plane of radial boreholes becomes increasingly difficult. The increase of the radial borehole diameter can enhance the guiding strength [15, 16]. Furthermore, the prediction methods of fracture starting point and fracture morphology were available [17, 18].

In terms of multiwells, experiments with true triaxial fracturing simulation system and numerical simulation were adopted to analyze the influence of different lateral lengths, counts, and azimuths on the fracturing initiation and propagation. The results show that the breakdown pressure will decrease by increasing the lateral length and count; the optimal lateral design for horizontal initiation is four laterals with the phase of 90°, and each lateral is at 45° from the horizontal stress [19].

Regarding well stability, the influence of radial well on well stability was studied according to the criteria of Mises, Tresca, and MAXPS by a finite element method. Mises and Tresca grow with the diameter of radial well, azimuth, and horizontal stress difference rising. Max Principle is negatively correlated with the diameter of radial well and azimuth and positively correlated with the horizontal stress difference [20].

Concerning productivity, a calculation model of distal radial shaft fracture was derived based on the complex potential theory and the mirror image principle. The results show that the flux distribution diagram of radial well is groove shaped, and the flux distribution is large at the heel side and the toe side, while the middle is small and average [21].

Based on the pressure analysis of fracturing initiation of multiple radial holes and the theory of plasticity district, the criteria of multiple radial wells orientating directional fracture propagation in the condition of ground stress are derived in this study. Multiple radial well fracturing will produce a complex stress field, which guarantees to form the fracture interconnecting the radial wells and to form the main crack along the axial direction of the radial wells [22].

According to the available research results, the technology of radial borehole fracturing shows several advantages as follows: (i)The diameter of the radial borehole is small, so it is suitable for the development of thin interbed(ii)The radial borehole is capable of guiding the directional fracture initiation and reducing fracture initiation pressure, and the fractures can propagate directionally under some conditions(iii)The multiradial borehole fracturing creates major fractures, significantly increasing the drainage area and improving the reservoir production(iv)Compared with the horizontal well, the radial borehole has less requirements in terms of the treatment scale, time and cost, small treatment scale, short time, and low cost and hence causes small damage to the reservoir

The fracture morphology and propagation rule during radial borehole fracturing are still not clearly defined, and there is no systematic theoretical support, especially for multiradial boreholes. Based on the actual reservoir parameters from the target well in Shengli Oil Field and considering the fluid-solid coupling effect, the 3D geological model is established with the extended finite element method (XFEM) in ABAQUS, and the fracture morphologies in the multiradial boreholes are defined. The simulation is verified by triaxial rock mechanics test experiment. Based on this, the scheme of radial bore arrangement hole is optimized, providing theoretical basis for radial borehole fracturing and showing practical importance. Also, the accuracy of arrangement optimization is verified by productivity simulation from CMG. At last, the morphology of fracture and the mechanism of fracture propagation are revealed; the radial bore arrangement hole is optimized. The technical system of radial borehole fracturing is established preliminary.

#### 2. Fracture Morphology and Arrangement of Radial Borehole Fracturing Based on XFEM

##### 2.1. Establishment of a Radial Borehole Fracturing Model

###### 2.1.1. The Mechanism of a Model Based on XFEM

The core concept of extended finite element method (XFEM) is to introduce the additional function to improve the displacement space of a unit, e.g., using asymptotic function and discontinuous function to characterize the fracture tip, which ensures good simulation of fracture tip morphology and enhances the computational accuracy of grid.

In this paper, ABAQUS XFEM platform adopts the linear elastic traction-separation model and the compound fracture propagation morphology. In the model, the process of material damage is simulated with initiation and evolution stages. When the material meets the damage initiation criteria, the fracture will propagate according to the evolution rule. In this paper, the maximum principal stress (MAXPS) is applied as the criterion of judging the material damage initiation and implying that the damage occurs when the maximum principal stress of material exceeds a certain critical value. MAXPS is expressed as which indicates that the compressive stress will not cause the damage.

After damage initiation, the material damage evolution is based on the criterion of maximum energy release rate, with an assumption of the fracture with a length occurring in a slab of infinite unit thickness. The formula of fracture strain energy is expressed as where is the surface energy of fracture.

Fracture propagation distance should meet the condition as follows: where is the surface energy of unit area.

Formula (3) means that if the driving force of fracture propagation equals to the resistance of fracture propagation, the critical value of driving force can be derived with Formula (3), and the surface energy is replaced with the critical strain energy release rate in the lithological material.

ABAQUS provides three methods of calculating the maximum energy release rate, including the BK law, Power law, and Reeder law, among which the BK law is used in this paper to calculate the maximum energy release rate and is expressed as where is the critical fracturing energy release rate, N/mm, and when the energy release rate in the fracture tip exceeds this value, the fracture tip cracks and the fracture propagates. and represent the fracturing toughness in the normal and first tangential direction, N/mm; , , and represent the fracture energy release rate in the normal, first tangential, and second tangential direction, N/mm; is the work of each stress in the corresponding displacement.

Here, the criteria of fracture initiation (maximum principal stress) and propagation (maximum energy release rate) are established, and the damage mechanism of the model is defined [23].

The variation of effective stress in the formation porous media will change the permeability and porosity; hence, the coupling relationship between formation stress field and porous flow field should be considered. According to the virtual work principle, the stress equilibrium equation is expressed as
where is the virtual velocity, m/s; is the virtual strain rate, s^{-1}; is the body force of unit volume, N/m^{3}; is the surface external force of unit area, N/m^{2}; and represents the total stress of porous medium, Pa.

According to the principle of mass conservation, the continuity equation of a fluid medium is expressed as
where is the variation rate of pore volume; is the ratio of formation liquid volume to total pore formation volume; is the liquid density in the pore, kg/m^{3}; is the direction vector of fluid flow in the pore, m; and is the liquid flow velocity in the pore, m/s.

The relationship between liquid velocity of seepage flow and the gradient pressure in a porous medium could be expressed by Darcy’s formula: where is the hydraulic conductivity tensor and is the gravity acceleration vector.

The conditions of a porous medium are defined with the simultaneous equations of Formulas (5) and (6). By integrating the equation set and the boundary conditions, the equilibrium and the continuity equations can be approximately expressed as the finite element equation set with interpolation function introduced in the finite element discretization. The stress-flow coupling equation matrix is eventually established and is resolved with the Newton method in ABAQUS.

Here, a model considering multiple factors such as geostress and rock mechanics properties is established by combining XFEM in ABAQUS with fluid-solid coupling, in which the criterion of maximum principal stress is applied to determine the position of rock fracture (fracture initiation), the criterion of maximum energy release rate is applied to judge the fracture damage evolution (fracture propagation morphology), and the fracture propagation in the radial borehole fracturing is studied [24]. The simulation provides a real and visual result, with the reference and guidance value.

###### 2.1.2. Establishment and Validation of a Model

The model assumes that the direction of axis is consistent with that of the horizontal maximum principal stress with 0° azimuth, and the azimuth increases in the anticlockwise direction with borehole as the center; the intersection angle between radial borehole and horizontal maximum principal stress is defined as the radial borehole azimuth (the radial borehole with minimum is considered as the reference well in case of multiradial borehole). axis is defined as the direction of vertical stress. The unit of stress is kPa, and the tensile stress is positive in the model.

The basic models of single radial borehole, horizontal multiradial borehole, and vertical multiradial borehole (Figure 1) are established, and the fracture propagation is simulated with XFEM to obtain the fracture morphology under different parameters. The intersection angle between two radial boreholes in the same layer is defined as the phase angle . About 10,000 elements are generated in the model, and the type of element is structured.