Integrated Approach Improves Modeling of Rejuvenation in Unconventional Plays

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An integrated understanding of geomechanical effects, fracture propagation, and reservoir dynamics is critical in the efficient and cost-effective application of rejuvenation technologies for unconventional plays. While various reservoir models depicting the hydraulic-fracturing process are available in the industry, many tend to be simplified or do not capture the numerous parameters that affect both the initial and restimulation processes. This work takes a further step toward building a more-realistic picture of fracturing in unconventional plays.


A common assumption in reservoir simulation is that the proppant-fluid mixture is present in the hydraulic fracture before flowback and production. The quantity of water assumed to be present in the hydraulic fractures is a conjecture and is calibrated generally with production-logging tools. These assumptions may skew the results of hydrocarbon recovery.

A method of incorporating geomechanical aspects of fracturing into the model involves the concept of pressure-dependent permeability variation in natural fractures that results in formation of pressure-dependent stimulated reservoir volume (SRV). Hysteretic permeability models employed in numerical modeling can offer a description of the SRV and also can be used in addressing longer-term geomechanical effects in a practical manner. While this concept has matured in the context of modeling hydraulic fracturing in reservoir simulation, it is being newly applied in modeling refracturing treatments.

Because the importance of capillary effect in low-permeability formations is recognized, the authors also incorporate capillary pressure in their model. In addition to pressure-dependent permeability variation, results explain how capillarity is significant in understanding fluid migration, the trapping of fluid in the matrix, and, consequently, restimulation.


The main challenge in selecting good candidate wells for this study was in finding wells that targeted the same formation, used varying refracturing technologies, and had sufficient data to build a reservoir-simulation model with input for the reservoir properties.

After studying a large number of wells, the authors focused on two horizontal gas wells producing from the Barnett Shale. One well was identified to be refractured with a selective zone-­treatment method, while the other used a method of fluid diversion. The wells are located approximately 3 miles from each other and approximately 1,600 ft from neighboring wells. These wells have differing production signatures, but this is not indicative of a difference in the performance of two technologies. Understanding the difference in performance may be key to planning a successful refracturing operation.

Model Setup

A commercial simulator is used to build a single-well, dual-permeability/dual-­porosity box model. Typical half-lengths were approximately 700 ft. This fracture half-length acts as the entire half-length that is formed upon fracturing, including both the propped and unpropped lengths of the fracture.

Important Input Parameters. During fracturing, while the proppant-fluid mixture is injected into the formation, growth of the SRV is governed by the enhancement or stimulation of the natural fractures. These changes in natural fractures are input into the reservoir model by means of dilation and compaction tables.

Fig. 1 shows an example of permeability multiplier vs. pressure curve, showing the elastic, dilation, unloading, and reloading segments of the curve. In the reservoir simulator, pressure refers to the pore pressure of the grid cell, while permeability refers to permeability of the natural fractures.

Fig. 1—Dilation-compaction curves used as input for the reservoir model.


At initial pressure, the reservoir lies on the elastic segment of the curve. During injection, as the pressure increases in the reservoir, the reservoir permeability undergoes a slight increase as it follows this curve. When the critical pressure or shear dilation onset pressure is reached at Point A, the natural fractures begin to slip. If a sufficient number of natural fractures slip at this pressure, there is an abrupt change in permeability of the natural fractures.

During flowback or production, grid cells that do not reach the critical pressure will return to their original permeability state along the elastic part of the curve. There is no permeability retention, and natural fractures return to their original state. Grid cells that experience a pressure surge higher than the critical pressure will now follow unloading Curve BC (Fig. 1). The original permeability is altered while Curve BC is followed, accounting for permeability hysteresis.

During the refracturing process, the natural fractures will experience yet another increase in pressure because of fluid injection. If the grid cells did not originally retain any permeability, they will, once again, follow Curve AB until they reach the critical pressure. If the grid cells previously retained permeability, they will now follow reloading Curve CD as pressure increases during reinjection of the proppant-fluid mixture. Therefore, a pressure-dependent SRV is formed, which influences natural fracture enhancement and, subsequently, hydrocarbon recovery. Matrix permeability remains unchanged with increase in pressure.

Apart from pressure-dependent SRV, another important parameter in understanding how the fluid mixture imbibes into the formation is capillary pressure. In this work, it is seen that capillary pressure is an important parameter that is influential in the amount of fluid that remains trapped in the matrix.

Modeling the Fracturing Process. The fracturing process—both the initial and restimulation phases—is modeled using four main periods: injection, flowback, shut-in, and production.

During the injection period, the fluid, along with the proppant, is injected into the formation at high flow rates. With the increase in pressure in the reservoir, natural fractures are enhanced and form an SRV around each fracture. This methodology is a proxy for modeling the fracture propagation.

During the flowback process, the injected fracturing fluid will first flow back, leaving some proppant behind that helps keep the fracture open. The well is then shut in for a period of time, allowing for water trapped in the matrix to imbibe further into the formation and into fractures. During production, the enhanced natural fractures, as part of the SRV, contribute significantly to hydrocarbon flow.


Selective Zone Treatment. Shearing of natural fractures, and transmissibility between the fracture and the matrix, causes entry of water into the natural fractures, consequently enhancing the natural fractures. This results in the formation of the SRV.

Water-saturation plots show that a significant amount of water is trapped in the matrix, even after flowback and production. This is enabled by capillary-pressure effects in the reservoir, especially during the soaking period or shut-in time of the well, demonstrating that not much water is remaining in the natural fractures.

In selective zone treatment, ­original fractures are isolated or plugged off. When refracturing or restimulating between the original fractures, the treatment fluid encounters reservoir areas that were previously depleted because of the initial stimulation. The low-pressure, depleted area enables easy imbibition of fluid into the matrix. Consequently, the corresponding natural fractures are not well-stimulated and the SRV formation is hindered. In contrast, when the treatment is pumped into areas that have not been previously depleted, it is difficult for treatment fluid to be imbibed into the low-permeability matrix. Thus, the natural fractures are well-stimulated and the SRV is well-formed.

Fluid-Diversion Treatment. The initial stimulation process is similar to that used in the case of selective zone treatment. Only the rejuvenation treatment is focused upon in this paper. This model divides the treatment into two main parts:

  • The treatment fluid is injected along with the diverting agent.
  • The remaining treatment is then pumped into the wellbore in hopes that the remaining fractures will be restimulated.

Sensitivities are measured for the fractures that are restimulated to assess the range of recoverable volumes and to provide a methodology to understand the potential of fluid diversion as a successful restimulation technology.

In the complete paper, the cases of three successful initial stimulations and three restimulations are presented for visualization.

In the second stage of the restimulation treatment for this well, while the initial fractures are plugged by the diverting agent, the remaining treatment fluid goes into untouched parts of the reservoir where perforations already exist and where treatment fluid failed to reach during the initial treatment. It is difficult for this fluid to access the matrix because of its low permeability, but the corresponding natural fractures are stimulated. Additionally, formation of the SRV because of natural fractures during restimulation may be hindered by the presence of a depleted zone nearby. These depleted areas were created during the initial stimulation treatment. Depending on the amount of treatment pumped during this second stage of the restimulation treatment, the depleted zone may attract treatment fluid into the low-pressure region. As a result, a percentage of fluid is lost to this depleted region, and the resulting fracture half-length created during restimulation is shorter.


This study presents a comprehensive modeling approach based on the presented restimulation technology and recognizes the importance of various reservoir parameters. Two important variables that affect the growth of the SRV and, consequently, hydrocarbon recovery, are capillary pressure and pressure-dependent permeability variation.

The two restimulation technologies that are modeled at a high level on the basis of their reservoir response include

  • Selective zone treatment. The location of the restimulation treatment must be planned carefully. For new fractures planned in previously depleted areas, low-pressure matrix zones may imbibe large volumes of treatment fluid, preventing the enhancement of natural fractures and, thus, formation of the SRV.
  • Fluid-diversion technology. Sensitivity studies performed on the basis of cluster efficiency provide a range on recoverable reserves, helping to understand uncertainty in the prospects of a successful treatment and its economic feasibility.
This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 191457, “Coupling Geomechanical Effects and Reservoir Dynamics for Modeling Rejuvenation in Unconventional Plays,” by R. Dutta, SPE, Drilling Info; R. Pinto, Sciences Po University; and J.C. Flores, S.M. Stolyarov, SPE, and J. Yang, Baker Hughes, a GE Company, prepared for the 2018 SPE International Hydraulic Fracturing Technology Conference and Exhibition, Muscat, Oman, 16–18 October. The paper has not been peer reviewed.

Integrated Approach Improves Modeling of Rejuvenation in Unconventional Plays

01 July 2019

Volume: 71 | Issue: 7