Flow-Simulation Model Improves Analysis of Perforated-Rock Cleanup and Productivity
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Because of inherent complexities, understanding the characteristics of perforations in downhole environments is a significant challenge. Perforation-flow laboratories have been used to provide insight into cleanup and productivity mechanisms around perforation tunnels. In contrast to previous studies, the model presented in this work uses the perforation-flow laboratory, micro-computed-tomography (CT) and conventional CT imaging, and, most importantly, an advanced simulation approach to provide an accurate assessment of cleanup techniques and productivity. This full-scale 3D flow model accounts for realistic aspects of tunnel geometry, perforation damage, and blockages that impede flow.
In recent years, numerical tools increasingly have been used in conjunction with experiments to provide better insight into the flow characteristics of perforated cores and perforated well-scale formations. Several numerical studies on perforation fluid flow have been conducted for core scale. However, comprehensive details relating to the modeling of perforation-zone damage and thickness, flow directionality, debris mechanisms, and implications for cleanup have not been studied in detail. In addition, most computational fluid dynamics (CFD) studies have used traditional Navier-Stokes-based solvers. In this study, the authors have used a commercially available flow-simulation software based on the lattice Boltzmann method (LBM) to calculate the complex flow and cleanup mechanisms around the perforation tunnel.
Lattice-based methods, an alternative to traditional CFD methods, track the advection and collisions of fluid particles on a computational grid. Because the average number of particles per grid cell far exceeds the computing power required to track them individually, the particles are grouped into an integer number of discrete velocities. LBM has been well validated and is in common use for many flow applications. The flow solver used here includes a turbulence model that is similar conceptually to the large-eddy simulation approach. The flow solver also includes a porous-media model that is used, in this study, to model the rock. The porous-media model invokes a Darcy-type pressure loss by applying a flow resistance determined from the known permeability of the rock. The resistance can include a viscous (linear) and an inertial (quadratic) term with respect to local velocity and can be made to vary spatially to model rock heterogeneity.
Recent flow-laboratory experiments conducted on a heterogeneous analog rock are used as an example for the CFD analysis. The experimental results demonstrate how laboratory testing has provided insight into gun-size selection, underbalance optimization, and cleanup and influence of wellbore fluids. Although the laboratory tests provided valuable information, the nature of the rock led to discrepancies in analyzing the data. Specific concern existed around the compressive strength of the rock, which varied along the length of the core significantly, thereby indicating the presence of a number of bedding planes. The nature of the bedding planes will vary from core to core, thereby increasing the chance of introducing differences in the results. In some test cases, the shaped-charge jet potentially encountered a weak point in a bedding plane, which led to the initiation of fractures/cracks. The comparison of productivity measurements also was inconclusive because of the complex heterogeneity of these different cores. During the testing process, mini- or microfractures may have been created that could impede or enhance flow.
As an alternative solution for addressing these issues, the authors have conducted comprehensive CFD analysis to provide insight into tunnel-flow mechanisms by isolating the heterogeneity and fracture aspects of the test cores.
CFD: Description and Analysis
Traditionally, while performing flow calculations or standard nodal analysis, the perforation geometry has been assumed to be cylindrical. With the advent of CT-scan methods, a smart-CFD approach has been developed that uses the true perforation-tunnel geometry, obtained from CT scans, to predict the flow characteristics around perforations better. In addition, digital techniques are used to characterize the influence of different debris mechanisms on productivity. Commercially available flow-simulation software was used to calculate flow in a perforation tunnel and the surrounding rock matrix. The simulation kernel is an LBM-based approach and is validated for a wide range of industrial applications. The CFD tool was used previously to characterize perforation damage. Here, flow in the rock matrix is modeled with a porous-media model, while the flow in the perforation tunnel is simulated directly.
The primary objectives of the CFD analysis included the following:
- Isolate the effects of core heterogeneity and fractures and quantify the fluid-flow characteristics and productivity around perforations.
- Examine the influence of static underbalance (SUB) on debris and its implications on productivity.
To this end, three baseline tunnel cases were analyzed using CFD. Three cases, two pertaining to a 2⅞-in. deep-penetrating charge (Tests 7 and 5) and one pertaining to a 3⅛-in. reservoir-driven charge (Test 4), were considered for the analysis. The only difference between Tests 7 and 5 was the hold time before flowing through the perforated core—32 days for Test 7 and 24 hours for Test 5. All three cases exhibited fractures at the tip of the tunnel, which led to challenges in experimentally quantifying tunnel productivity. As part of the CFD analysis, for the purpose of comparisons, simulations were performed for the following scenarios on each tunnel:
- Preshot (no tunnel, no casing)
- Casing only (no tunnel)
- Tunnel only
- Tunnel/damage (3-mm-thick damage zone around the tunnel, reduced to 50% of native permeability)
- Tunnel/damage/debris (debris and damage zone reduced to 50% of native permeability)
- Tunnel/damage/debris (debris and damage zone reduced to 10% of native permeability)
Baseline CFD Analysis
A systematic CFD analysis was conducted to provide insight into the flow characteristics of the tunnels. For the three cases, only the perforation-tunnel geometry and debris were considered. Any fracture- or crack-related geometry or core heterogeneity was ignored.
The productivity ratio (PR) computed through CFD was not quantitatively similar to that of the experiments. This is because, unlike experiments in which significant core heterogeneities exist, CFD simplifies the analysis by assuming homogeneity throughout the core. The key inferences include the following:
- The casing adds significant resistance to flow; PR=0.50 (casing only).
- Adding the tunnel leads to slightly higher productivity compared with preshot productivity; PR=1.02 (tunnel). Damage at 50%/3 mm did not significantly reduce productivity; PR=0.99 (tunnel/damage).
- Debris reduces productivity by a noticeable amount; PR=0.91 (tunnel/damage/debris, 50%/3 mm).
- Reducing permeability of the debris and damage zone to 10% has a significant effect, resulting in PR=0.74 (tunnel/damage/debris, 10%/3 mm).
Productivity results for Test 5 were very similar to those observed in Test 7. Differences were seen in Test 4, where the longer tunnel increased productivity significantly when compared with Tests 5 and 7 (Test 4: PR=1.12; Test 5: PR=1.00; Test 7: PR=1.02). The debris pattern in Test 4 reduces the PR to a range similar to that seen in Tests 5 and 7. For all three tunnels, visualizations of velocity, pressure gradients, and streamlines were visible for further clarification. Such detailed whole-field visualization of flow variables around the perforation tunnel provides insight into the complex dynamics of fluid physics.
Debris Analysis Using CFD
Experimental analysis showed that higher SUB provides reduced debris, indicating better cleanup of the tunnel. To understand the influence that SUB and debris have on productivity, the authors complemented the experimental analysis by conducting a debris-influence study. They considered tests that had similar conditions except for SUB. A unique approach was followed wherein the tunnel geometry remained constant and debris patterns from tests at different SUBs were digitally incorporated into the tunnel. This facilitated a consistent and quantitative analysis of debris and showed the overall effect of SUB on productivity. Fig. 1 shows the three CFD models considered for this debris analysis.
As SUB is decreased, productivity around the tunnel also decreases. This behavior is attributed to the higher debris, and therefore flow resistance, present at low SUB. As expected, a lower permeability in the debris zone (10 vs. 50%) lowers the productivity accordingly.
In-Situ Flow Analysis
In true downhole conditions, flow is driven in both axial and radial directions toward the tunnel. To account for this, the authors also conducted CFD calculations in which flow was driven from both the axial and radial directions (mixed flow). The overall productivity was significantly increased with mixed flow when compared with the results where flow was driven only in the axial directions. Increased productivity was observed in Test 4 when compared with Tests 5 and 7. For reference, additional models were run with a SUB of 8,000 psi using the mixed-flow boundary conditions. As expected, the results showed the increased productivity for 8,000-psi SUB compared with 2,000‑psi SUB.
Upscaling Laboratory CFD to Well-Scale Analysis
This analysis demonstrates how advanced modeling can help address uncertainties from laboratory tests as well as provide insight into strategies for optimized cleanup of perforations and maximized productivity. Computational tools can also enable the upscaling of analysis from laboratory- to field-scale conditions. In this case, the work flow can be expanded to scenarios in which single perforation tunnels (from an in-situ laboratory test) can be upscaled into a system-level model for investigating cleanup mechanisms, tunnel interference, and overall productivity.
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Flow-Simulation Model Improves Analysis of Perforated-Rock Cleanup and Productivity
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