Field data suggests that carbonate reservoirs contain abundant natural fractures and cavities. The propagation mechanisms of hydraulic fractures in fracture-cavity reservoirs are different from conventional reservoirs on account of the stress concentration surrounding cavities. In this paper, we develop a fully coupled numerical model using the extended finite element method (XFEM) to investigate the behaviors and propagation mechanisms of hydraulic fractures in fracture-cavity reservoirs. Simulation results show that a higher lateral stress coefficient can enhance the influence of the natural cavity, causing a more curved fracture path. However, lower confining stress or smaller in-situ stress difference can reduce this influence, and thus contributes to the penetration of the hydraulic fracture towards the cavity. Higher fluid viscosity and high fluid pumping rate are both able to attenuate the effect of the cavity. The frictional natural fracture connected to the cavity can significantly change the stress distribution around the cavity, thus dramatically deviates the hydraulic fracture from its original propagation direction. It is also found that the natural cavity existing between two adjacent fracturing stages will significantly influence the stress distribution between fractures and is more likely to result in irregular propagation paths compared to the case without a cavity.

Carbonate reservoirs, which contain naturally-formed fractures and caves, widely exist in the world and have huge potential for exploitation [

During the past decades, based on different numerical approaches like the finite element method (FEM) [

The difference in the propagation mechanisms of hydraulic fractures between fracture-cavity reservoirs and conventional reservoirs is mainly caused by the stress concentration around cavities. As shown in

where

Although some works aiming at explaining the mechanisms of interaction among HF, NF, and cavity have been done by researchers, it still lacks a systematic study and deeper understanding of crucial factors that influence the hydraulic fracturing efficiency in fracture-cavity reservoirs. On the other hand, existing studies mainly focus on simple geometrical configuration, and the study of the influence of cavity on hydraulic fractures in a wellbore is not available in the literature. In this study, the XFEM proposed by Belytschko et al. [

This paper is presented as follows. The description of the numerical model is given in Section 2. Implementation and validation of the proposed numerical model are presented in Section 3. Mechanisms and factors that govern the propagation behavior of hydraulic fractures around natural cavities are systematically studied in Section 4. Major conclusions are summarized in Section 5.

A shown in _{inj}

According to the linear elastic assumption of rock formation, the governing equations for quasi-static deformation can be written as [

where

The fluid flow along the hydraulic fracture can be described by Reynold’s equation [

where _{L}

where _{L}

After introducing the trial function

Besides, by introducing the test function

Spatial and time discretization of

In this paper, we use the XFEM to describe the displacement field around fractures and cavities. By simply introducing additional degrees of freedoms (DOFs), i.e., the enriched DOFs, the remeshing and data mapping between old and new meshes can be avoided [

in which _{I}_{all}_{frac}_{cavity}_{tip}_{junc}_{pen}

where (

which indicates that

Frictional and cemented fractures are two common types of natural fractures in reservoirs [

where

where _{f}_{f}_{f}

In this article, the penalty function method together with the Newton–Raphson method [

and the global conventional DOFs vector

until the following convergence criterion is satisfied

In

In

where _{N}_{T}

The widely adopted maximum hoop-stress criterion [_{I}_{II}

where

If _{e}_{IC}

The proposed numerical model is implemented in an in-house Fortran code called PhiPsi (

The validation of the presented numerical model without considering cavities has been sufficiently conducted in our previous articles [_{1}, _{2}, _{1}, _{2}, and

The simulation of a frictional natural fracture of length 10 m in a plane strain plate under the action of compressive stress will be performed to verify the frictional model presented in Section 2.3. As shown in _{N}_{T}^{4} GPa/m. The applied stress

In this section, interactions between hydraulic fracture and cavity will be studied via a simple model shown in _{inj}^{2}/s, and the fluid leak-off coefficient ^{−5} m/s^{1/2}. The model is discretized into 5,618 quadrilateral elements. The hydraulic fracture propagates by an increment of 0.15 m.

The strongly deflected fracture propagation path and the stress distribution in

The level of in-situ stress increases with the increase of the reservoir depth. On the other hand, as discussed in the introduction section, the stress field surrounding the cavity is strongly affected by the lateral stress coefficient

Parameters | Base case | Case 1 | Case 2 | Case 3 |
---|---|---|---|---|

40 | 90 | 10 | 1 | |

50 | 100 | 50 | 5 | |

10 | 10 | 40 | 4 | |

0.8 | 0.9 | 0.2 | 0.2 |

Fluid viscosity is an important factor in hydraulic fracturing treatments. In this section, a fluid of higher viscosity, 0.1

In this section, we investigate the effect of another key factor, the fluid pumping rate. Different from the base simulation case, a higher pumping rate, 0.01 m^{2}/s, is applied. The simulated propagation path is also shown in

Cavities with greatly different scales are widely distributed in fracture-cavity carbonate reservoirs [

Natural cavities are of quite irregular shapes in fracture-cavity reservoirs [

As shown in _{N}_{T}^{4} GPa/m. In

This section is aimed to study the influence of cavity on hydraulic fracturing in a wellbore. As illustrated in _{IC}_{inj}^{2}/s, respectively. The fluid leak-off coefficient ^{−5} m/s^{1/2}. The proppant volume concentration of the injected fluid [_{p}_{o}

The propagation paths of Stages 1 and 2 fractures for both cases without and with cavity are illustrated in

In this paper, we established a fully-coupled numerical model to investigate the mechanisms of hydraulic fractures in fracture-cavity reservoirs using the XFEM. The Heaviside, cavity, fracture tip, T-shaped junction, and penetration enrichment functions are proposed to describe the displacement jump across the fracture surface, displacement discontinuity over the cavity boundary, singular displacement field near the fracture tip, intersection between the hydro-fracture and the natural fracture, and penetration of a fracture into the cavity, respectively. Hence, tedious remeshing can be avoided. The fluid flow within fractures is described by Reynold’s equation which is discretized using the FEM. Afterwards, the fully-coupled governing equations are solved iteratively using the Newton–Raphson method. After the validation of the proposed model in Section 3, several cases are simulated to investigate the effects of factors such as in-situ stress, fluid viscosity, fluid pumping rate, cavity size and shape, and natural fractures in Section 4.1. Besides, the effects of a cavity on the sequential hydraulic fracturing in a wellbore are studied in Section 4.2. According to the cases studied in this paper, the major conclusions can be reached as follows:

Both the lateral stress coefficient and the level of confining stress (or in-situ stress difference) have a strong influence on propagation paths of hydraulic fractures near cavities. A higher lateral stress coefficient can enhance the influence of the natural cavity, causing a more curved fracture path. However, lower confining stress or smaller in-situ stress difference can reduce this influence, and thus contributes to the penetration of the hydraulic fracture towards the cavity.

The fluid viscosity and fluid pumping rate are two dominant factors on the propagation path in hydraulic fracturing treatments when natural cavities are considered. Higher fluid viscosity and high fluid pumping rate are both able to attenuate the effect of the cavity, and thus benefit the propagation of the hydraulic fracture along its original direction.

The influence of a cavity depends not only on its size but also on its shape. Cavities of irregular shape (ellipse, for example) have a stronger influence on the propagation path of hydraulic fracture than regular circle cavity.

The frictional natural fracture disconnected from the cavity, even with a very small distance between the fracture tip and the cavity, has limited influence on the stress field around the cavity. Nevertheless, a frictional natural fracture connected to the cavity can significantly change the stress distribution around the cavity, thus dramatically deviates the hydraulic fracture from its original propagation direction.

Natural cavity existing between two adjacent fracturing stages will significantly influence the stress distribution between fractures and is more likely to result in irregular propagation paths compared to the case without cavity.