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A number of different factors can affect flow performance in perforated completions, such as perforation density, perforation damage, and tunnel geometry. In perforation damage, any compaction at the perforation tunnels will lead to reduced permeability, more significant pressure drop, and lower productivity of the reservoir. The reduced permeability of the crushed zone around the perforation can be formulated as a crushed-zone skin factor. For reservoir flow, earlier research studies show how crushed (compacted) zones cause heightened resistance in radially converging vertical and horizontal flow entering perforations. However, the effects related to crushed zones on the total skin factor are still a moot point, especially for horizontal flows in perforations. Therefore, the present study will look into the varied effects occurring in the crushed zone in relation to the vertical and horizontal flows. The experimental test was carried out using a geotechnical radial flow set-up to measure the differential pressure in the perforation tunnel with a crushed zone. Computational fluid dynamics (CFD) software was used for simulating pressure gradient in a cylindrical perforation tunnel. The single-phase water was radially injected into the core sample with the same flow boundary conditions in the experimental and numerical procedures. In this work, two crushed zone configuration scenarios were applied in conjunction with different perforation parameters, perforation length, crushed zone radius, and crushed zone permeability. In the initial scenario, the crushed zone is assumed to be located at the perforation tunnel’s side only, while in the second scenario, the crushed zone is assumed to be located at a side and the tip of perforation (a tip-crushed zone). The simulated results indicate a good comparison with regard to the two scenarios’ pressure gradients. Furthermore, the simulations’ comparison reveals another pressure drop caused by the tip crushed zone related to the horizontal or plane flow in the perforations. The differences between the two simulations’ results show that currently available models for estimating the skin factor for vertical perforated completions need to be improved based on which of the two cases is closer to reality. This study has presented a better understanding of crushed zone characteristics by employing a different approach to the composition and shape of the crushed zone and permeability reduction levels for the crushed zone in the axial direction of the perforation.

For cased hole completions, the well needs to be perforated in order for communication to be enabled between the formation and wellbore. This is because perforations enhance flow convergence at the near-wellbore region. In comparison with ideal open-hole wells, perforated wells can undergo added pressure gains and losses. Especially when a well has a short length of perforations with lower density, it may lead to a greater drop in pressure at the near-wellbore region, which will lower the overall well productivity. Moreover, when wells are perforated by deep penetrating tunnels, there may be a more expansive communication area between the formation and the perforated wells. When this occurs, the perforations might enhance well productivity due to less pressure drop.

Any added pressure gain or drop that is due to ideal perforation may be formulated as a perforation pseudoskin factor. In this case, this skin factor is related to parameters like wellbore diameter, perforation length, shot density, and phasing angle. Note that during the perforation process, rocks at the perforation tunnels’ sites are crushed. However, the perforation pseudoskin factor measures flow convergence at perforations in ideal perforated wells, neglecting the effect of the crushed (compacted) zone encircling the perforation tunnels. Experimental data indicate that the greatest contribution to total skin is the crushed zone, whereas formation damage skin and perforation pseudoskin make less contribution overall. Furthermore, based on studies (i.e., field and experimental) conducted over the past half-century, a major factor adversely affecting productivity is deficiencies in perforating procedures, perforator design, or both. For example, some studies on perforation damage showed that productivity declined in a gun-perforated hole formation when shots were fired into solid-containing fluid, such as drilling muds. There was also decreased productivity in cases where wellbore pressure exceeded formation pressure. In a typical process of perforation, a low-conductivity hole is created in the damaged formation. Postperforation, the crushed damage expands around the perforation radially from the center of the perforation tunnel. In this evolution, compacted and pulverized rock and other debris from a barrier block the formation’s natural pore spaces. Figure

Schematic diagram of the crushed zone around the perforation.

The earlier studies mentioned above showed the importance of clearing perforating debris away from perforations to optimize the flow capacity. Debris removal, whether of some or most of the damaged material, enables the perforation tunnel to better perform its role as the wellbore’s fluid conduit. One highly efficient way to remove the debris is through underbalanced perforating, although the precise underbalance degree required for generating effective perforations is still a topic of debate. The underbalance is usually calculated by considering the matrix permeability, along with tunnel parameters and fluid, as described by Tariq [

Interactions between formation damage, flow convergence near perforation tunnels, and rock compaction need to be carefully formulated; rock compaction and formation damage can create a higher degree of dynamic interaction between plane flow and flow convergence at the perforations. The effects of rock compaction and formation damage should thus be included in any perforation model that is developed. However, these interactions can be extremely complex in nature, particularly when including parameters such as mechanical skin factor (formation damage), ideal perforation pseudoskin factor, and crushed-zone skin factor. Overall, perforation total skin factor (

A wide range of models (empirical, numerical, experimental, semianalytical, etc.) have been developed over the past several decades for predicting perforated total skin and for determining the effects of the crushed zone. For example, Klotz et al. [

The crushed-zone skin factor is expressed in

Using a finite element simulator, Karakas and Tariq [

In this equation, the initial term indicates flow convergence in the horizontal plane, the second term denotes flow convergence in the vertical plane, and the third term describes the effect of the wellbore geometry. The researchers also employed a formulation somewhat like Equation (

In other related research, Bell et al. [

All the preceding factors have derived several models based on the assumption that a crushed zone is uniform and cylindrical and has a homogeneous permeability and porosity. At the same time, recent studies using modern techniques computerized tomography (CT) and a scanning electron microscope (SEM)) have shown a different perception of the composition and shape of the crushed zone, especially in the axial direction of the perforation tunnel. In recent studies, the researchers have analyzed the results obtained based on the perforation process’s effect. The process of perforation involves shooting a perforation agent into the near-wellbore formation to make holes. However, during this process, the affected rock could experience grain bond breakages in addition to microfractures caused by shock waves [

Schematic of four different zones of crushed change zones in the axial direction of the perforation tunnel.

In addition, Xue et al. [

In addressing this research gap, the present study was conducted experimental and numerical investigations by employing a different approach to the composition and shape of the crushed zone and permeability reduction levels for the crushed zone in the axial direction of the perforation. The two crushed zone configuration scenarios were applied in conjunction with different perforation parameters, perforation length, crushed zone radius, and crushed zone permeability. In the initial scenario, the perforation zone’s tip is assumed to be too far away for the shock wave to reach, leaving the rock matrix intact, so the crushed zone is located at the perforation tunnel’s side. In the second scenario, the force of the shock wave in the perforation zone’s tip is considered to be sufficient to sever every bond between particles, so the crushed area is located at a side and tip of perforation. The two scenarios are applied in conjunction with different perforation parameters, perforation length, crushed zone radius, and a permeability ratio. In additional investigations, the effect of permeability anisotropy in crushed zones on the crushed skin factor has been studied considering these scenarios.

The experimental study was used to validate the numerical model for single-phase flow through the perforation tunnel that includes two different permeability zones. The first region surrounds the perforations and represents the crushed zone with low permeability; the second region exemplifies the formation region with high permeability. Statistical analysis was coupled with numerical simulation to expand the investigation of fluid flow in the near-wellbore region due to the limitations of the experimental setup, especially the small sample size. In the study, two crushed zone configuration scenarios are conducted in conjunction with different perforation parameters, perforation length, crushed zone, and permeability ratio, as shown in Figure

The schematic diagram shows the two scenarios.

In the present study, the experimental set-up initially designed and built by Ahammad et al. [

Schematic diagram of the experiment: water flow meter, inlet and outlet pressure sensors; TS: temperature sensor; and DAQ: data acquisition system.

In the laboratory experiments, a highly permeable synthetic sandstone sample was prepared. The cylindrical sample was made of sand particles measuring 0.18 to 1.18 mm. The synthetic sample has been created from two different sandstone grain sizes. The fine grain size used to create a crushed zone around the perforation and the coarse grain size used to create a formation reservoir zone are demonstrated in Figure

The dimensions of synthetic sandstone sample.

The dimensions and the index properties of the sample.

Dimensions and properties the sample | Values (units) |
---|---|

Sample height ( | 30.48 cm |

Sample radius ( | 7.62 cm |

Perforation tunnel radius ( | 1.27 cm |

Crushed zone radius ( | 5.08 cm |

Perforation length ( | 25.4 cm |

Permeability of crushed zone ( | 6.218 × 10^{-12} m^{2} |

Porosity of skin zone | 26% |

Permeability of formation zone ( | 2.625 ^{-11} m^{2} |

Porosity of formation zone | 21% |

Experiments carried out on perforation methods have primarily relied on rather simplistic assumptions, such as those presented by Rahman et al. [

In the present work, we used Ansys Fluent 18.1 for our computational fluid dynamics (CFD) model. Our aim was to present a single-phase fluid flow simulation for a reservoir described as three-dimensional, vertical, and cylindrically layered. We created a sample that is vertical with a single layer of uniform thickness (

The formation is isotropic and porous, of uniform thickness, and is constantly permeable (i.e., features constant vertical permeability that is nonzero)

The flow through the reservoir can be described as single-phase water and either radial-vertical laminar or Darcy’s flow

The liquid is incompressible with a constant viscosity

Any flux proceeding into the well features uniform distribution across perforated intervals

Thermal effects were ignored

The crushed skin has been considered in the present research. Other skin factors and effects of perforations angle, formation permeability anisotropy, and wellbore radius were neglected

The crushed skin factor is affected by crushed zone parameters and the permeability anisotropy of the crushed zone. In contrast, the perforation skin factor is more affected by perforation angle, formation permeability anisotropy, and the wellbore radius. Therefore, additional CFD investigations analyzed the effect of permeability anisotropy in crushed zones on the crushed skin factor, considering the study’s two mentioned scenarios.

In the numerical work, we injected a measured volume of water into the cylindrical sample. The conservation equations for mass and momentum describing single-phase flow in a porous region could be expressed, respectively, as

The last term in Equation (

For the three coordinate directions (

Uniform mesh and cut mesh methods (Figure

Vertical section shows (a) the outlet and (b) the shape of uniform configuration mesh.

Various methods for examining how different parameters may affect experimental results are applied by using Design of Experiments (DoE) software. The initial step in DoE is identifying independent variables and/or factors that may affect the experimental outcomes. The next step involves identifying the dependent variables and/or factors [

The model is then statistically validated through analysis of variance (ANOVA) [

Two boundary points were then selected, and one midpoint was determined by BBD for the intervals of the parameters, as presented in Table

The range of dimensionless parameters.

Dimensionless parameters and index properties | Values |
---|---|

Penetration ratio ( | 0.125-0.5 |

Ratio of crushed zone radius to perforation radius ( | 2-4 |

The crushed-zone damage permeability ratio ( | 10-100 |

Porosity of skin zone | 20% |

Porosity of formation zone | 25% |

The comparison between the experimental and numerical results of the pressure buildup with the same flow boundary conditions is shown in Figure

Comparison between experimental data and numerical results of the pressure buildup at the same flow boundary conditions (

The validation of numerical results with experimental ones has given full confidence in using the numerical model to conduct huge investigations by creating a crushed zone with different crushed perforation parameters, perforation length, and crushed zone radius. The relative effect of three dimensionless parameters on the crushed skin factor was investigated before conducting statistical analysis. The numerical results showed that the ratio of penetration space to perforation length

The relative effect of three dimensionless parameters on the crushed skin factor.

0.125 | 7.27 | 2 | 10.6 | 10 | 2.2 |

0.3125 | 16.4 | 3 | 16.4 | 55 | 16.4 |

0.5 | 27.8 | 4 | 21.6 | 100 | 30.6 |

Twelve numerical runs were performed and analyzed to obtain a suitable statistical analysis using the ANOVA analysis with the BBD model (Table

Twelve numerical runs.

1 | 0.3125 | 2 | 100 | 20.01 | 9.52 | 2032 | 1082 | 211 |

2 | 0.125 | 3 | 10 | 1.23 | 1.14 | 217 | 208 | 104 |

3 | 0.125 | 2 | 55 | 4.68 | 3.64 | 532 | 437 | 104 |

4 | 0.5 | 2 | 55 | 18.08 | 8.78 | 1929 | 1079 | 276 |

5 | 0.5 | 4 | 55 | 34.13 | 11.86 | 3351 | 1361 | 276 |

6 | 0.5 | 3 | 100 | 51.31 | 13.28 | 4968 | 1491 | 276 |

7 | 0.125 | 4 | 55 | 9.045 | 6.06 | 931 | 658 | 104 |

8 | 0.5 | 3 | 10 | 4.63 | 3.62 | 799.6 | 607 | 276 |

9 | 0.3125 | 4 | 10 | 3.77 | 2.18 | 550 | 395 | 221 |

10 | 0.3125 | 2 | 10 | 1.74 | 1.68 | 370 | 365 | 211 |

11 | 0.125 | 3 | 100 | 13.33 | 7.7 | 1323 | 808 | 104 |

12 | 0.3125 | 4 | 100 | 40.77 | 9.4 | 3938 | 1071 | 211 |

Therefore, crushed perforation parameters are analyzed by using statistical analysis coupled with the numerical simulation model. This study provided two correlations from the statistical analysis, based on the numerical results. These correlations were used to determine the relative impact of each factor for the two scenarios on the crushed skin factor.

The results clearly indicate the crushed perforation parameters effects on both the crushed skin factor and pressure gradient values. The results show that crushed skin increases the pressure drop and thus contributes to a reduction in the productivity index. As illustrated in Figure

The dimensionless parameters’ (

The dimensionless parameters’ ^{2}, ^{2},

Moreover, the numerical results show a clear view of pressure distribution for the perforation with a crushed tip, without a crushed tip, and ideal perforations cases. For example, the pressure gradient for the three cases at dimensions’ parameters values (

The distribution of the pressure gradient for three cases: (a) perforations with crushed tip, (b) perforations without crushed tip, and (c) ideal perforations without crushed zone at boundary conditions of ^{2}, ^{2},

In order to compare and discuss the accuracy of the common models, one model by Karakas and Tariq [

The crushed skin factor results of the first correlation with a tip-crushed zone

The comparison between the crushed skin factor results of two scenario correlations and the model of [

Also, the present study looks at the effect of permeability anisotropy in crushed zones on the skin factor with regard to the study’s two scenarios. In the CFD simulations, the interaction effect between permeability anisotropy

CFD results of crushed skin factor under the effect of permeability-anisotropy

CFD results of crushed skin factor under the effect of permeability-anisotropy

The study was conducted in order to further investigate the accuracy of Karakas and Tariq’s [

The experimental data showed good agreement with the numerical model results used in this work to conduct more investigations

The study showed a clear view of the effect of the three dimensionless parameters (

The comparison of the simulations reveals that there is a significant difference between each of the two tip-crushed zone scenarios

The numerical model gave almost identical results as for Karakas and Tariq’s model, if the length of the perforations was assumed to be shorter than their real length by a thickness of crushed zone

The differences between the two simulations’ results show that the currently available model [

The study presented two novel correlations that give more than one option to calculate the crushed skin factor

The outcomes of this study underscore the need to include the crushed zone anisotropy effect through the improvement of available models for determining the crushed skin factor

Body force

Inertial resistance factor

Formation thickness

Permeability of crushed zone

Horizontal permeability of crushed zone

Vertical permeability of crushed zone

Permeability of damaged zone

Formation permeability

Permeability ratio

Perforation length

Number of perforations (number of shots per foot)

Pressure

Penetration ratio

Flow rate

Radius of crushed zone around perforation

Reservoir radius

Perforation radius

Ratio of crushed zone to perforation radius

Wellbore radius

Skin due to rock crushed around perforations

Skin due to formation damage

Skin due to horizontal flow effect

Skin due to ideal perforations

Total perforation skin factor

Skin due to vertical converging effect

Skin due to wellbore effect

Skin due to crushed zone without tip

Skin due to crushed zone with tip

Time

Velocity

Velocity components for

Porosity

Porosity of formation zone

Porosity of crushed zone

Perforation angle

Fluid density

Stress tensor related to viscous flow

Fluid viscosity

Medium thickness

Pressure drop due to total skin factor

Pressure drop (ideal perforations without crushed zone)

Pressure drop due to crushed zone without tip

Pressure drop due to crushed zone with tip

Analysis of variance

Box-Behnken design

Computational fluid dynamics

Data acquisition

Design of experiments

Radial flow cell

Response surface methodology.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors certify that this work is original, has not been published, and will not be submitted elsewhere for publication. Statements made herein are solely the responsibility of the authors.

The authors certify that they have no known competing financial interests that could have influenced the work reported in this manuscript.

This publication was also made possible by the grant NPRP10-0101-170091 from Qatar National Research Fund (a member of the Qatar Foundation).