## Computational Model Predicts Breakdown Pressures in Unconventional Plays

Unconventional shale reservoirs are characterized by extreme low permeability and high in-situ stress. Multistage hydraulic fracturing plays a key role in developing such reservoirs. However, depending on the in-situ stress magnitude or regime, breakdown pressures can be too extreme to achieve, given available surface horsepower and downhole completion capabilities. This paper presents a newly developed model to predict the breakdown pressures in cased and perforated wells.

## Introduction

In unconventional shale reservoirs, multi­stage hydraulic fracturing often is applied to stimulate a number of clusters across the target zone. Once the clusters are perforated and hydraulic fracturing is applied, these clusters initiate transverse fractures, creating a fracture network that is required for reservoir depletion. At each cluster, the pressure delivered from the surface pumping units is exerted on the rock until the breakdown pressure is achieved. If the breakdown pressure is not achieved at a given cluster, there will be no induced fractures and, consequently, no production.

The main objective of the author’s study is to investigate the physics behind fracture initiation of cased and perforated wells in extremely tight reservoirs. This involves building a computational model to calculate the breakdown pressure for an inclined well at given azimuth and inclination angles. The developed model considers the in-situ stress magnitudes and faulting stress regimes to analyze local stresses around the perforations to predict the fracture-initiation pressure and orientation. Fracture propagation is outside of the scope of study.

## Development of the Proposed Model

Stress Distribution Around the Wellbore. The stresses acting on the rock deposited at a given depth include the vertical (overburden) stress, the maximum horizontal stress (SH), and the minimum horizontal stress (Sh). These are called in-situ stresses, or far-field stresses, and, depending on their magnitudes, they define the faulting stress regimes. When a wellbore is drilled into the rock and a mud pressure is exerted, the wellbore becomes a free surface and stresses are perturbed near the wellbore wall. Assuming the rock is elastic and isotropic, the local stresses converge near the wellbore wall at the azimuth of the minimum horizontal stress magnitude, creating a high compressive area that is prone to drilling breakouts. The stresses diverge in the azimuth of the maximum horizontal stress orientation, creating a low compressive area that is prone to drilling tensile failure. Therefore, these local stresses need to be deduced from the in-situ stresses to analyze the near-wellbore area. To take the effective stress into account in the calculation, the pore pressure needs to be subtracted from the in-situ stress. Previous formulas from the literature are modified to take the effective stress concept into account. A new coordinate system is introduced in the complete paper. Stresses at the wellbore wall (transformation of Cartesian stresses to cylindrical stresses) also are analyzed.

Stress Distribution Around Perforations. To analyze the stress distribution around perforations, the following assumptions are made:

• Rock is elastic and isotropic.
• Good cement bonding exists between the hole and the casing.
• Perforations are cylindrical in shape.

The same transformation from Cartesian to cylindrical coordinate systems previously applied to the wellbore is applied here.

## Results and Discussion

Rock properties and wellbore trajectories for the following determinations are provided in the complete paper.

Normal Faulting Stress Regime. The in-situ stress coordinate system can be transformed to the Cartesian coordinate system, and the cylindrical coordinate system can be calculated. For a horizontal well oriented toward Sh and the value of r taken from the wellbore radius (2.25 in.) to a typical perforation penetration depth (18 in.), local stresses converge to the far-field in-situ stresses at the depth of penetration. Stresses exerted on the rock by the cement are ignored in this model. However, future work will consider the stresses exerted by a combination of the fully hydrated cement and the respective stress-relaxation rate on the rock face. For this model, the radius of investigation will be at the tip of the perforation tunnel because the induced stress from the cement will not influence the local stresses at the tip owing to the long penetration depth.

Fig. 1 shows the breakdown pressure distribution at different wellbore azimuth angles (0° corresponding to SH orientation) and perforation angles (0° corresponding to a perforation on top of the wellbore). There are two extreme cases:

• Minimum breakdown for a well oriented toward Sh (90°) and side perforations (90° perforation-phasing angle)
• Maximum breakdown for a well oriented toward SH (0°) and 52° perforation-phasing angle

Strike/Slip Faulting Stress Regime. Fig. 2 shows the breakdown pressure distribution for different wellbore azimuth angles and perforation-phasing angles. There are two extreme cases:

• Minimum breakdown for a well with top perforations (0° perforation-phasing angle)
• Maximum breakdown for a well with side perforations (90° perforation-phasing angle) at 40° wellbore azimuth angle

Reverse Faulting Stress Regime. Fig. 3 shows the breakdown pressure distribution for different wellbore azimuth angles and perforation-phasing angles. There are two extreme cases:

• Minimum breakdown for a well with side perforations (90° perforation-phasing angle) and SH wellbore orientation (0° azimuth angle)
• Maximum breakdown for a well with 45° perforation-phasing angle for a wellbore oriented toward Sh (90° wellbore azimuth angle)

## Conclusion

Depending on the in-situ stress magnitudes and the faulting stress regime, shale reservoirs require significant surface-pumping horsepower to break down the formation, but often breakdown cannot be achieved. Therefore, an accurate calculation of breakdown pressure is required to select the optimal surface and downhole completion design to achieve breakdown. Several models were developed to calculate the breakdown pressure. The complete paper reviews these models and adopts some concepts to build a new model.

The results from the developed model recommend deep penetration depths to expose the perforation tunnels to far-field in-situ stresses. Also, different faulting stress regimes are considered. For normal faulting stress regimes, the results from the model predict the lowest breakdown pressure for a wellbore aligned with minimum horizontal stress, a typical wellbore orientation for shale reservoirs. Therefore, steering the drilling bit as close as possible to minimum horizontal stress azimuth is recommended, as is orienting perforations on the sides of the wellbore to achieve the lowest breakdown pressures. For wellbores oriented toward the maximum horizontal stress, perforating on the top and bottom of the wellbore is recommended. For a strike/slip faulting stress regime, perforating on top and bottom of the wellbore for any wellbore azimuth angles is recommended, whereas perforating on the sides of the wellbore for reverse faulting stress regimes is recommended.

Oil and gas operators use a phased perforation technique because the local stresses around the perforations generally are unknown. This study recommends using oriented perforations to minimize the formation breakdown pressures. This could result in avoiding excessive surface pumping horsepower and downhole completions, saving well completion and stimulation costs.

For a limited time, the complete paper SPE 194038 STU is free to SPE members.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 194038 STU, “A New Computational Model To Predict Breakdown Pressures in Cased and Perforated Wells in Unconventional Reservoirs,” by Mohammed Kurdi, University of New South Wales, prepared for the 2018 SPE Annual Technical Conference and Exhibition, Dallas, 24–26 September. The paper has not been peer reviewed.

Computational Model Predicts Breakdown Pressures in Unconventional Plays

01 June 2019

Volume: 71 | Issue: 6

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