Engineering Approach To Designing Fluid Diverters: Jamming and Plugging
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Fluids introduced into a reservoir for stimulation typically take the path of least resistance and, therefore, frequently go into areas with open flow paths. In many cases, those areas are not the targets of stimulation. To maximize contact between the fluid and intact rock, existing fluid paths must be plugged to divert the fluid. A typical fluid-diversion application can be divided into three steps: placement downhole, downhole plugging/diversion, and corresponding stimulation. The aim of this paper is to review and identify critical parameters controlling the downhole plugging/diversion step.
Jamming and Plugging Efficiency
Successful diversion can be designed and achieved upon full understanding of the jamming and plugging mechanisms that occur at the entrance of existing flow paths. An understanding of the underlying physics of this process allows a system to be modeled that uses the minimal amount of material to create temporary but stable seals that can withstand significant pressure differentials even at flow path openings that are several times larger than the mean particle size. Many complex factors affect diversion efficiency, and they all can be adjusted to minimize flow into existing and highly conductive flow channels. Two major mechanisms control the success of the diversion process: jamming and plugging.
In the first stage of fluid diversion within an opening, a stable and jammed structure should be formed by the larger of the particles, which are progressively deposited from a flowing system. In the jamming stage, an initial stable structure is established around an opening (e.g., a perforation during fracturing, a natural fissure, or wormhole during acidizing). The so-called jammed state refers to a configuration in which relatively large particles provide support for one another, remain immobile, and do not pass through the existing opening. As shown in Fig. 1a above, the passage of sheep through a gate and the possibility of jamming can be used as an analogy. The size, number, shape, and rate of sheep passing through the gate can determine the possibility of jamming for a specific gate size. Although the passing of relatively large particles (the sheep) is restricted in this stage, fluids and smaller particles (small lambs) can still move through the opening (gate) by using the space between the large particles. Therefore, jamming does not necessarily restrict fluid nor, hence, pressure communication.
During plugging, the remaining flow conduits within the jammed structure are filled by smaller particles, which could eventually generate sufficient pressure buildup for designated fluid diversion, as shown in Fig. 1b. To achieve the required pressure buildup, effective plugging should take place along with the stable jammed structure. Smaller particles play an important role in this process; they can form a layered cake between or on top of larger particles and fill any remaining open space. If no stable jammed structure is available, these smaller particles can readily flow through openings instead of filling the open space. Therefore, jamming and plugging are complementary, and both are critical for successful diversion. By effectively combining the two processes, fluid passage is limited and pressure buildup occurs.
Both dynamic fluid flow and pseudostatic particle accumulation are involved in jamming and plugging, and multiple parameters could influence ultimate efficiency. Different parameters affect the stability and success of jamming and plugging differently. Analytical models or coupled computational fluid dynamics (CFD) and discrete element method (DEM) simulations can quantify the effect of the different parameters. Different properties (e.g., particle shape, mechanical properties, frictional properties, size distribution, and flow rate) can be optimized to enhance the probability of jamming.
Once the successful jammed structure is in place, its permeability should be reduced in the plugging step for efficient pressure buildup and fluid diversion.
In addition to particle size, particle shape is a critical factor in the success of a jamming structure. This factor can be investigated with both modeling and experimental techniques detailed in the complete paper. Multiple shapes of available particles should be evaluated and properly selected to enhance the efficiency of fluid diversion. Features embedded in the CFD/DEM numerical simulation can generate particles with any available shape and size to resemble actual particulate diverters. Accordingly, their behavior can be fully investigated by taking into account the particle/particle and particle/fluid mechanical interactions in the dynamic jamming stage. Details of coupled CFD/DEM numerical simulations can be found in the complete paper.
One of the main mechanical parameters that controls jamming is the mechanical stability of the structure and macroscopic contacting forces between particles. The maximum jammable opening size for a specific particle size and shape increases with the friction factor. The dependence is more dominant in the low-friction range. Under higher friction factors, tangential forces aid in creating more mechanical stability for the jammed structure. In this condition, the probability of jamming increases for the cases with higher particle-friction coefficient. To investigate this mechanical effect, DEM simulation has been performed for a constant particle size with a spherical shape and different friction coefficients. Higher friction factors enhance the jamming probability and can effectively create the mechanical structure even on openings up to four times larger than the median particle diameter. In contrast, and for the low friction factor, no successful jammed structure was observed for openings larger than two-and-a-half times the median particle diameter. Comparing the two cases reveals that higher friction factors could boost the success of jamming, especially for the case with larger openings. Higher friction factors could stabilize the mechanical structures required to withstand higher differential pressures during diversion.
In combination with the intrinsic properties of particles (e.g., size, shape, and friction factor), the external geometry of an opening, which is one of the key operational parameters, could influence the engineering design of the diversion operations significantly. Directionally, both the length and cross-sectional area of an opening could change the probability of jamming in different ways, and, hence, different empirical correlations could be obtained.
Understanding the jamming and plugging process and designing the related operational parameters is critical. For example, in a particulate diverter application, selecting proper particle size and concentration is important for creating a stable jamming structure on top of an existing opening as soon as possible during the diversion operation. The complete paper introduces an analytical model for optimizing the desired jamming structure by using sufficient particle concentration.
In this study, coupled CFD/DEM simulations were performed to check the accuracy of the proposed analytical model in predicting the minimum required particle concentration.
Plugging and Pressure Buildup
Once an initial stable structure has formed on top of an opening, a low-permeability pack should form to mitigate fluid flow and divert it. This is the plugging step, which is the second stage of the diversion process. By the end of the plugging step, the low-permeability pack is expected to result in an additional pressure drop required for successful fluid diversion. The complete paper investigates a mathematical formulation to quantify the effect of the associated pressure drop on the formation of a low-permeability pack.
Pressure drop upon successful plugging is a complex function of particle size, particle ratio, fluid viscosity, and flow rate. These parameters could separately and cumulatively influence the success of the plugging stage and should be considered and assessed in an engineering design. The established correlations between the pressure drop and the operational parameters should be implemented into fracturing models to simulate the dynamic process of fluid diversion.
Large particles mainly control the jamming stage and the stability of the structure under applied differential pressure. Both small and large particles affect the permeability of the formed particle pack and the corresponding pressure drop required to divert the fluid. Accordingly, having sufficient mass of particles of each size is critical for both a stable jammed structure and plugging.
Accordingly, the particle ratio of a diverter system involving multiple types of particles is one of the key parameters affecting diversion efficiency. Actually, the particle ratio plays a significant role in both the jamming and plugging. However, its effects on these steps cannot be completely isolated from each other. Therefore, the particle ratio and the corresponding concentration should be selected properly by considering the two major mechanisms to ensure ultimate efficiency.
Solid particulate materials are capable of degrading over time from a solid polymer state to a clear, nondamaging liquid monomer solution, which eliminates the need for mechanical removal after intervention. This is a key criterion for creating the next generation of fluid diverters. Although the entire degradation could take several hours, the stability of the jammed structure and the efficiency of the plugging could reduce in the first few hours. Using the engineering approach explained in the complete paper, this process can be optimized to ensure efficient diversion throughout the entire operation.
This study thoroughly investigates the physics and mechanisms behind a typical and complex fluid-diversion process by using biodegradable solid-particulate diverters. Two major processes—jamming and plugging—are identified. They dictate the overall success of a planned diversion. Separately, multiple parameters could influence the two processes differently. By understanding the associated mechanisms, building a comprehensive engine and integrated work flow is feasible.
The complete paper reviews multiple experiments to quantify the effect of different factors in the fluid-diversion process and provides necessary calibrations for proposed analytical and numerical models. By using the proposed methodologies, field engineers can optimize the engineering design and minimize the risk of failure and the cost of fluid-diversion operations.
Engineering Approach To Designing Fluid Diverters: Jamming and Plugging
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12 June 2018