Geofluids

Volume 2018, Article ID 4763414, 12 pages

https://doi.org/10.1155/2018/4763414

## Well Performance Simulation and Parametric Study for Different Refracturing Scenarios in Shale Reservoir

^{1}State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, China^{2}School of Petroleum and Natural Gas Engineering, Chongqing University of Science and Technology, Chongqing 401331, China^{3}Shu’nan Gas-Mine Field, PetroChina Southwest Oil and Gas Field Company, Luzhou, Sichuan 646000, China

Correspondence should be addressed to Jing Huang; moc.361@ipws_gnijgnauh and Jinzhou Zhao; nc.ude.upws@zjoahz

Received 8 May 2018; Revised 6 July 2018; Accepted 17 July 2018; Published 23 August 2018

Academic Editor: Mandadige S. A. Perera

Copyright © 2018 Jing Huang et al. 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

Refracturing is an encouraging way to uplift gas flow rate and ultimate gas recovery from shale gas wells. A numerical model, considering the stimulated reservoir volume and multiscale gas transport, is applied to simulate the gas production from a refractured shale gas well. The model is verified against field data from a shale gas reservoir in Sichuan Basin. Two refracturing scenarios: refracturing through existing perforation clusters and refracturing through new perforation zones, are included in the simulation work. Three years after production is determined to be the optimum time for refracturing based on the evolution analysis of reservoir pressure, effective stress, fracture permeability, and gas recovery. The role that the hydraulic fracture conductivity and hydraulic fracture half-length play in gas production for different refracturing cases is explored. Pumping parameters of the refracturing job in Sichuan Basin are discussed combining with sensitivity analysis, and suggestions for pumping parameters optimization are proposed.

#### 1. Introduction

The gas flow rate of shale wells declines significantly in the very first years after the initial hydraulic stimulation, and the large volume of gas still remains in a shale reservoir [1]. Some wells might not achieve an economical gas flow rate when the initial stimulation is inadequate: small treatment size, low proppant concentration, poor proppant distribution, poor fracturing fluid selection, insufficient perforations, and operational problems with completion [2–7]. Refracturing is an encouraging way to uplift shale reservoir gas production and ultimate gas recovery by enlarging fracture geometry, creating new fractures, improving pay coverage, reinflating natural fractures, increasing proppant conductivity, and restoring fracture conductivity [8–11]. Compared to drilling and completing of infill wells, refracturing is an economical alternative to promote well productivity when the right candidate is selected [12–16]. The refracturing process has been developed and applied to Barnett, Haynesville, Bakken, Fayetteville, Eagle Ford, and Woodford shale reservoirs in recent years [6, 15].

Gas flow from an ultralow permeability shale reservoir through a complex fracture network, stress, and pressure field change must be modeled so that restimulation designs and completion strategies can be properly evaluated. It is difficult to predict gas production and improvement in hydrocarbon recovery post refracturing treatment. Several previous works developed numerical simulation approaches to model fluid flow, complex fracture networks, and initial hydraulic fractures of refracturing treatment. Tavassoli et al. perform a sensitivity study on the effect of different reservoir and hydraulic fracture parameters on refracturing performance based on a dual permeability model [11]. Rodvelt et al. use an analytical production simulator to forecast the productivity index and EUR of Marcellus shale wells [8]. Haddad et al. use commercial software program to simulate the gas production of a refractured shale reservoir [16]. Urban et al. use a dual permeability simulator that takes into account free gas in matrix and fractures and adsorbed gas to simulate refracturing in the Eagle Ford shale [17]. Huang et al. use a finite element method to evaluate the well performance under different refracturing designs [18]. However, these models are still not applicable to describe the complex gas flow transport mechanism in shale gas reservoirs due to the different sorption behavior and flow regimes between kerogen pockets and the inorganic solid medium.

In this paper, a numerical model, considering the stimulated reservoir volume and multiscale gas transport, is applied to simulate the gas production from a refractured shale gas well. The model is verified against field data of a refractured shale horizontal well in Sichuan Basin, Southwest of China. The evolution of effective stress, reservoir pressure, fracture permeability, and gas recovery is analyzed to determine the optimum time for refracturing. Two refracturing scenarios: refracturing through existing perforation clusters and refracturing through new perforation zones, are included in the simulation work. The role that the hydraulic fracture conductivity and hydraulic fracture half-length play in gas production for different refracturing cases is explored. In addition, the pumping parameters of the refracturing job are discussed combined with sensitivity analysis.

#### 2. Governing Equations

A shale reservoir is a triple-continuum formation which consists of organic matter, inorganic matrix, and natural fractures [19]. During the production process, the gas release follows the mechanism: kerogen system-inorganic matrix system-fracture system [20]. The effective stress increases while the reservoir pressure depletes, in which, in turn, the porosity and permeability of shale reservoir change due to rock matrix deformation. The stress sensitivity will further reduce the flow capacity of the fracture system in the stimulated area [21], which is a critical factor for production prediction and optimal designation of restimulation. The existing complex fracture network is properly characterized in this numerical model; in addition, the solid deformation effect and complex gas flow behavior are taken into consideration. Sang et al. presented the model assumptions [22].

##### 2.1. Deformation of Fractured Porous Shale

###### 2.1.1. Constitutive Equation

Considering the kerogen matrix, inorganic matrix, and fractured solid system as linearly elastic media, the constitutive equation for fractured porous shale can be generally expressed as

###### 2.1.2. Initial and Boundary Conditions

Assuming that the well is not disturbed under the original geological state, therefore, the displacement of shale rock is zero and the initial condition can be presented as

The boundary conditions can be presented as

##### 2.2. Stress-Dependent Porosity and Permeability

The effective pressure of triple-continuum formation can be presented as [23]

Stress-dependent correlations are used to consider porosity and permeability reduction. Based on experimental and numerical simulation results [24], power law correlations are used to calculate these stress-dependent properties as follows:

##### 2.3. Gas Flow

###### 2.3.1. Continuity Equation of Kerogen System

The transport mechanisms in the kerogen system include viscous flow, Knudsen diffusion, and surface diffusion. Regardless of the space transmission of the gas in kerogen, the continuity equation of the kerogen system can be present as where is the adsorbed gas volume per unit volume kerogen and defined as where is the apparent kerogen permeability and defined as where is Knudsen diffusivity of the kerogen system and defined as

###### 2.3.2. Continuity Equation of Inorganic Matrix System

The free gas transport in an inorganic matrix involves two transfer terms. On the one hand, the adsorbed gas diffuses from the kerogen system to the inorganic matrix system. On the other hand, the inorganic matrix system supplies gas for the fracture system. Considering the slippage effect, Knudsen diffusion, and viscous flow, the gas continuity equation of the inorganic matrix system can be presented as where is the apparent inorganic matrix permeability and defined as where is the slippage factor and defined as where is the Knudsen diffusivity of the inorganic matrix system and can be defined as where is the transfer term between the inorganic matrix system and fractures. It can be presented based on the Warren-Root transfer model: where is the pseudosteady state shape factor, which can be defined as [25]

###### 2.3.3. Continuity Equation of Fracture System

The pore diameters in the fracture system are equal to the millimeter scale, the Knudsen diffusion in the fracture system is notably small, and only viscous flow is taken into account. Therefore, according to the conservation of mass, the continuity equation of the fracture system can be present as where is the production rate of the fracture system and can be defined based on the Peaceman model [26]:

###### 2.3.4. Initial and Boundary Conditions

Assuming that the initial pressures of the kerogen system, inorganic matrix system, and fracture system are identical, then the initial condition can be presented as

The shale formation is considered a closed unit. The bottom hole flow pressure is applied as the inner boundary condition:

The no-flow outer boundary condition is applied: where represents the inner boundary of the production well and represents the outer boundary.

##### 2.4. Simulation Procedure

The finite difference method is used to solve the highly nonlinear mathematical model. The simulation procedure is as follows:

*Step 1. *The stimulated area and hydraulic fractures are meshed by the nonuniform rectangular grid system.

*Step 2. *The pressure in the kerogen system, inorganic system, and fracture system is calculated, respectively.

*Step 3. *The pressure calculated in Step 2 is used to calculate the volume strain of grid points; after further calculating the average effective stress, the reservoir parameters are renewed and transferred to the gas flow model. The calculation pauses at the time for refracturing.

*Step 4. *Hydraulic fracture and reservoir parameters are updated at the time node of refracturing; the iterative computation will stop at the end of simulation time.

The simulation procedure detail is shown in Figure 1.