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This article was submitted to Interdisciplinary Physics, a section of the journal Frontiers in Physics

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In this study, a numerical model of the conglomerate reservoir is established using ABAQUS. Cohesive elements are embedded into the numerical model to simulate the hydraulic fracturing behaviours of the conglomerate reservoir. The cohesive elements split by the high-pressure liquid flow are identified by tracing the crack propagation. A USDFLD (user-defined field variable) subroutine is used to increase the liquid flow’s dynamic viscosity in these cracked cohesive elements. Using this method, ABAQUS successfully simulates the temporary plugging-refracturing processes in the conglomerate reservoir under four

The temporary plugging-refracturing technology achieves the purpose of increasing oil and gas production by injecting high-pressure fluid flow into the oil or gas reservoir to generate tension fractures [

Many numerical methods are used to simulate the hydraulic fracturing problem of rock mass [

Based on previous studies, this paper takes conglomerate reservoirs as the research object and establishes a numerical model using ABAQUS. Then, in this numerical model, the cohesive elements considering seepage-stress coupling behaviors are embedded to simulate the hydraulic fracturing of a conglomerate reservoir. Then, a USDFLD subroutine is coded to simulate the temporary plugging process in the conglomerate reservoir. Finally, the temporary plugging-refracturing processes in conglomerate reservoirs under various

The cohesive element was first applied to the bond crack model in ductile materials such as metals [

The displacement field of the cohesive element can be controlled by the relative displacement of the upper and lower surfaces, and the following expression is established:

Combine the relationship between the displacement field of the solid element and the node displacement. We have

By combining the displacement expression of the solid element and the cohesive element, the following governing equation is established based on the weak solution form of the finite element:

Combined with the stress-strain relationship of solid element and the traction separation law of cohesive element, a complete finite element solution process using the cohesive element can be established as follows:

1) Loop at the

2) Obtain the node code ‘inodes’ of the

3) Obtain the degrees of freedom of the upper and lower surfaces of the

4) Obtain the node displacement of the upper and lower surfaces of the

5) Compute the traction displacement of the

6) Loop each Gaussian integral point by conducting the following procedure.

1) Calculate the traction displacement on the

2) Convert to local coordinate system.

3) Based on the traction-separation constitutive relationship, compute the bond force.

4) Convert the local bond force into the bond force in the global coordinate.

5) Calculate and update the uniform stiffness matrix of the traction-separation criterion.

7) The cohesive element’s node force and stiffness matrix are assembled into the global system to obtain the stiffness matrix and node force.

In ABAQUS, the mechanical behaviours of cohesive element are generally described using a bilinear traction-separation model [

When the nominal traction stress reach the maximum values (peak-strengths)

When the above damage criterion is satisfied, the nominal traction stress decreases linearly, and enters the post-peak linear softening stage. A scalar damage variable

The stress components

For the linear softening, the damage evolution can be expressed as follows:

At the current nominal stress-strain state, the geometry area below the stress-strain curve is the normal and shear fracture energy, which can be denoted using

The water flow in the fractured rock mass is a typical seepage-stress coupling problem (

1) The pore pressure in the fractures affects the strength and deformation of the rock mass, especially the normal deformation of the fracture. The effective stress principle can be expressed as:

2) Joint void

3) Introducing the Darcy seepage formula in the cohesive element can simulate the seepage-stress coupling behaviour of rock mass. The fracture width

The deep conglomerate reservoir is a kind of heterogeneous sedimentary rock. In terms of its geological structure, it is composed of conglomerate particles and filler matrices. When studying its material mechanical and seepage behavior, the heterogeneity of conglomerate reservoir can be simplified as a two-phase material in which conglomerate particles of different sizes are randomly embedded into the filler matrix.

The model size of the core stratum of the conglomerate reservoir is set to a square area of 2000 mm long and 1000 mm wide. Conglomerate aggregates are randomly generated in this area, as shown in

In the geological model of the conglomerate reservoir shown in

The problem concerned in this study is simplified to a plane strain problem to be solved using ABAQUS. The first-order linear plane strain quadrilateral element is used to mesh the geological model. Then, a numerical model is obtained, as shown in

This study uses the cohesive element to simulate the conglomerate reservoir’s discontinuous deformation and failure under hydraulic fracturing loads. We consider that the conglomerate aggregates do not fail and the hydraulic fracturing cracks only occur inside the filler. Therefore, the cohesive elements are only embedded within the plane strain elements of the filler of the conglomerate reservoir.

The model’s left side is the symmetrical plane, which is an impervious boundary. The midpoint of the initial fracture on the left side is the fluid injection point (

All of the nodes in the model are set as constant pore pressure conditions. The initial pore pressure of these nodes is set to 0 MPa, and the initial void ratio is set as

As shown in

In this numerical model, four types of geomaterials are involved: surrounding rocks, conglomerate aggregates, fillers, and cohesive interfaces around the aggregates. The material parameters used in the numerical simulations are given in

Mechanical parameters of the geomaterials used in the numerical simulations.

Geomaterial | Elastic modulus (MPa) | Poisson’s ratio | Permeability coefficient (mm/s) | Fracture strength (MPa) | Fracture energy (N/mm) |
---|---|---|---|---|---|

Conglomerate aggregate | 60,000 | 0.3 | — | — | — |

Filler | 45,000 | 0.3 | 1e-6 | 15 | 0.0045 |

Surrounding rock | 50,000 | 0.3 | 1e-6 | — | — |

Cohesive interfaces | 45,000 | — | — | 10 | 0.002 |

The numerical modeling of the temporary plugging treatment in the rock mass is difficult in FEM simulations. In order to realize this modeling in ABAQUS, an available method is by reading the crack propagation data of the cohesive elements and increasing the fluid’s dynamic viscosity in these positions.

In actual execution, the coordinates of the crack tips in the cohesive elements at the temporary plugging moment can be recorded. Then, a USDFLD subroutine (user-defined field variable) is called by ABAQUS to increase the liquid flow’s dynamic viscosity in these cohesive elements in the subsequent calculations. Thereby, an increase in the fluid’s resistance passing through these cohesive elements would force the initiation and propagation of new branch fractures in other locations with lower resistance.

The calculation time lasts to 21 s, divided into two stages. 1) During the period of

When the

It is observed from

When time exceeds 6 s, the pore pressures at the fluid injection point enter relatively flat plateaus under the four

When time = 8 s, the cracks produced by the first hydraulic fracturing are temporarily blocked. After the temporary plugging treatment, for the case of

In the case of

For the case of

In this study, ABAQUS is used to numerically simulate the temporary plugging-refracturing process in the conglomerate reservoir under four

1) In FEM analysis, the cohesive element can effectively simulate the discontinuous deformation and failure of the rock mass. Furthermore, the cohesive element containing the constitutive relationship of Darcy seepage is capable of simulating the seepage-stress coupling behaviour of the fractured rock mass.

2) In this study, by reading the data of crack propagation, the cracked cohesive elements are identified. A USDFLD subroutine is used to increase the dynamic viscosity of the liquid flow in these cracked cohesive elements. The numerical simulation of plugging treatment is successfully realized.

3) While under higher horizontal

4) During temporary plugging-refracturing process, pore pressure distribution and fracture propagation can be observed. By analyzing the pore pressure-time history curve of the fluid injection point, the hydraulic fracturing events in the conglomerate reservoir can be judged.

5) The numerical simulation results obtained in this study are relatively intuitive, but the model of the conglomerate reservoir is somewhat different from the actual geological condition. When the actual engineering geological conditions are clear and there are accurate calculation parameters, the work carried out in this research can provide effective and reasonable suggestions for the actual petroleum engineering.

The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.

Numerical simulations were contributed by JC and JZ. Programming the USDFLD subroutine was mainly contributed by QZ. Drafting the manuscript was contributed by JC and JZ.

This research was financially supported by the Open Research Fund of Key Laboratory of Construction and Safety of Water Engineering of the Ministry of Water Resources, China Institute of Water Resources and Hydropower Research (Grant No. 202101) and by National Natural Science Foundation of China (Grant No. 12062026).

JC is employed by Sany Heavy Industry Co. Ltd.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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