Well perforation optimization using an abrasive jet technique to create oriented slotted channels in terrigenous reservoirs

Abstract

Various casing perforation methods are used to ensure a hydrodynamic reservoir-to-well connection. However, perforated wells often do not perform satisfactorily during production. This is largely due to a decrease in the permeability of the near-wellbore formation as a result of casing perforation work. Studies and analysis of existing casing perforation methods have shown the effectiveness of abrasive jet perforation. The paper presents the results of numerical modeling to optimize the layout of slot channels during the abrasive jet perforation (AJP) of terrigenous productive object. Geomechanics analysis of the influence the formation scheme and orientation of the slotted channels in the productive layer during abrasive jet perforation on the permeability of terrigenous reservoirs of the oil fields in the Perm Krai was performed. The disadvantages of widespread methods of exposing perforation are described and the advantages of abrasive jet perforation based on geomechanical modeling are revealed. The calculations carried out on the placement of slotted channels showed that the distance between the systems of slotted channels is not important, since they weakly interact with each other in height with standard schemes. It was established that the best placement scheme for jet slot channels is a system of four slot channels shifted along the length of the well to the height of the slot channel with a phasing of 90°. Comparative calculations of the reservoir permeability of the near-well zone for various perforation methods have been performed.

1. Introduction

The oil and gas industry all over the world has to increase the operation efficiency of previously drilled wells in order to maintain hydrocarbon production volumes and also to develop difficult-to-access deposits and hard-to-recover reserves. Deposits, in turn, require to devise a fundamentally new complex approach to improve the well exploitation efficiency and durability. Moreover there is a need for scientific research that could elaborate technical and technological solutions based on the new knowledge-intensive and successful working methods with production systems at the different stages of wells completion and operation.

The majority of technical and technological solutions in the field of well completion has limited effectiveness as the well's casing is not secured, i.e. it is not leak-proof, and there is no comprehensive approach neither to assess the condition of rocks near the well, nor to analyse geological structure of the deposit.

In addition, there is no systematic final assessment of the technical and economic indicators for the methods used to complete the wells, including casing perforation, and preference is often given to the cheapest and less time-consuming method which could be damaging to the well's casing [1].

The widely applied methods of casing perforation include the following disadvantages [2]:

• −absence of orientation of the formed filtration channels or lack of accuracy in orienting and reference to height. It may lead to entering into water- or gas-saturated areas in thin productive layers that exist, for example, in the Perm Krai and other oil regions of Russia and abroad;
• −absence of a complex assessment of the filtration and geomechanical properties change in the reservoir rocks after casing perforation, hence, lack of related technical and technological solutions for choosing the casing perforation technology in productive layers with a possibility of orienting perforation channels;
• −high requirements to the driving fluid that are impossible to implement without special cleaning means (centrifuges);
• −high pressures appearance (up to 100–300 MPa) and a breach of the well design leakproofness, leading to early water products.

The stages of well completion and their further operation are often considered separately from each other. However, finding a successful solution to the permeability recovery problems of the near wellbore area in the productive layers and obtaining the project flow rates is possible only by preserving the filtration and capacitive properties of reservoir rocks at all working stages.

Beside and before special compositions used during initial opening of reservoir rocks while drilling to reduce the negative impact on their permeability, there are various well completion schemes and methods of flow stimulation during the wells operation. Nevertheless, we should use an opportunity to solve all problems precociously – during the perforation works. Scientists developed effective methods of productive layers perforation in terms of increasing the filtration area of reservoir fluids; considered mechanisms of rocks georethreading (geoloosening) that ensure the casing preservation [[3], [4], [5], [6], [7]], but they have not taken into account the geomechanical assessment of how the different methods of productive layers perforation influence the permeability.

A large number of scientific works describe the technology of abrasive jet perforation for oil and gas wells and mainly consider the advantages of this method in terms of increasing reservoir rocks permeability and the wells productivity [8,9].

Abrasive jet perforation is a gentle method of well perforation, based on the mechanical destruction of the well casing, cement stone and the reservoir rock forming slotted channels from the action of a high-pressure jet [10]. The obvious advantage of abrasive jet perforation is the unloading (reducing the effective stresses) of the near-well zone and ensuring the preservation of its permeability, as well as the possibility of orienting the formed filtration channels, taking into account the direction of the unprocessed hydrocarbon zones and preparing the well for oriented hydraulic fracturing in the future.

In addition, AJP ensures the cement stone safety and the well casing tightness, prevents early watering of well production, and provides reliable communication within the well-formation system.

The works of Chacon [11] showed the obvious advantages of sand jet perforation due to improved communication in the well-formation system, which is confirmed by the obtained gas rates. In works of Sharma [12], simulation results are compared with experimental data on the permeability assessment of the obtained perforation slotted channels. All major productivity indicators are increasing for gas and oil wells. In his work Dotson [13] describes the advantages of sandblast perforation. This technology of reservoirs gentle perforating allows to reduce the negative impact on the well of cumulative perforation, which is used in most cases nowadays. Field data confirm the effectiveness of this secondary opening method by increasing the filtration area with less damage of the well casing. Another advantage is that after perforation hydraulic fracturing can be performed as well.

Rastegar and Munawar [14] present the studies results on the damaging effects of cumulative perforation on rocks. The shock wave weakens the reservoir matrix, which increases the risk of sand production. In addition, cumulative perforation forms reduced permeability zones and poor filtration on the perforation channels surface. Cumulative perforation also leads to a decrease in rock permeability in the channel area by 55%, which ultimately results in 60% decrease in well production. Rahman [15] in his works presents the results of evaluating the permeability decrease in the near-wellbore zone of productive formations in case of using explosive methods of well perforation, the permeability compared with an open hole decrease from 30% to 75%, depending on the type of collector and charge model.

Zhang and others [16] denote three main aspects of jet perforation method to enhance the production of oil well, including slotted channels formation, releasing the average effective stress of the well bore immediate vicinity, and penetrating contaminated zone near oil well.

Yu [17] represents the following results: initial permeability and rock strength of the reservoirs vary with average stresses and reservoir pressure. At the elastoplastic stage of deformations, permeability changes already with an increase in load, decrease in load, and constant load. Coalescence of cracks leads to a decrease in permeability. Thus, a decrease in the average effective stress will lead to a restoration of the permeability in the bottom hole formation zone.

In addition, we must not forget about anisotropic permeability. Pan and Ma [18] pointed out that it is an important parameter to measure when analysing fluid flow performance in reservoirs. For example, Sichuan Basin in China has a strong anisotropy of permeability, permeability perpendicular to the bedding represents only about 4% of the permeability along the bedding.

Besides, abrasive jet perforation has proven itself in the wells preparation for hydraulic fracturing, including oriented wells. The combined technology of abrasive jet perforation and subsequent refracturing through an abrasive jet perforating tool carried out by LLC Bashneft-Dobycha has shown its efficiency during repeated fracturing on horizontal multistage wells due to the possibility of using previously uninvolved intervals in the development and launch of the wells with a significant increase in the productivity coefficient [19]. Fryzowicz and Naughton-Rumbo [20] showed that AJP technology allowed to ensure the proppant safety during injection and to prevent its destruction by reducing the resistance at the entrance to the reservoir. Thus, this technology has reduced the time spent on work in accordance with the developed design of hydraulic fracturing. In addition, this technology was improved and successfully tested in field conditions in the works of Solares and Amorocho [21]. The system includes an anchor device, rolling cutting discs, as well as a hydraulic nozzle.

McDaniel and others [22] mention that more and more modern technologies combine the AJP and hydraulic fracturing methods to increase well productivity and the efficiency of oil field development. The application results showed 100% effectiveness of this technology.

At the same time, modern software and the availability of relevant geological and hydrodynamic models of oil deposits allow to increase the efficiency of this technology by using theoretical foundations.

Quattlebaum [23] demonstrates that the modern capabilities of software products for modeling the methods of productive formations perforation using the finite element method make it possible to establish that the hydraulic fracture in a formation with an increase in oil recovery of productive formations would be much more effective if the wells had slotted channels but not holes obtained by cumulative perforation.

El-Domiaty [24] discusses the cutting process consisting of two modes:

• 1.A cutting wear mode, which occurs at the top of the kerf primarily due to particle impact at shallow angles;
• 2.A deformation wear mode, which occurs deeper in the kerf and is associated with large angles of impact.

Permeability increased in the remote zone of the reservoir due to the fact that new cracks formed with a decrease in reservoir pressure during operation. To better understand this change in reservoir pressure around the wells, Wang performed three-dimensional numerical simulations [25], in which the resulting model shows the true distribution of stresses and fracture zones in the reservoir.

Another advantage of the oriented perforation technology is the possibility of forming oriented slot channels. This technology can increase the efficiency by conducting directed controlled hydraulic fracturing in oil producing wells [26]. Oriented slotted channels can also provide stability to poorly cemented reservoirs and prevent sand production. Nakhwa [27] considered the development of an oriented abrasive perforation using coiled tubing, which was applied to eliminate the use of explosives for perforation. It has been designed for reducing debris obstruction and also to enhance safety. Kritsanaphak [28] noticed that in Algerian oil fields, perforation using explosives has become difficult and expensive due to the strict safety requirements associated with the use of explosives. Service companies often experience delays in the explosives supply, which can range from one week to one month, that leads to an increase in time and money.

Besides, field tests of abrasive jet perforation technology at the oil field in the south of Oman have shown its effectiveness compared to the explosive perforation methods due to the fact that the time for perforation and further wells stimulation has been reduced by more than 3 times, work safety has increased, and 10.5 times higher reservoir contact has been achieved [29].

Xu [30] pointed that the deep hydraulic jet perforating technology is also suitable for complex wells that require selective perforation. The greatest depth of the formed channel can be 2 m, depending on the characteristics of the formation. Compared with cumulative perforation, this technology has several advantages:

• −improved connectivity in the well-formation system;
• −increase in fluid filtration area;
• −safety of lining wells.

Above-mentioned technology was successfully applied at the JS Oilfield field for a thin layer with nearby water in order to increase oil production. 10 perforation channels were obtained in the interval of two productive layers with a length of 1.55–2.01 m. The oil production rate doubled.

The technology effectiveness is confirmed by the stand tests results. Huang and others [31,32] designed a new device that can withstand a pressure of 20 MPa to accommodate a casing string and carbonate rock samples in it. The research results showed that mainly the pressure change in the nozzle and the nozzle diameter affect the perforation performance. The hole formation in the casing occurs in less than 1 min. Experiments were also conducted in Kalamayi, China, at the Xinjiang field in October 2004 [31,32]. Two samples of cement cylinders with a diameter of 2.4 m and a height of 1.2 m were made to carry out comparative tests of cumulative perforation and abrasiveness. In comparison with the explosive method, the hole on the casing wall and the slotted channel in the cement were significantly larger.

The simulation experiment in laboratory made by Li and others [33] shows that the casing can be easily cut with the hydraulic sand blasting perforation. The sandstone can be perforated, and a hole with 30 mm in diameter and 780 mm in depth can be made on the sandstone at jetting pressure of 23–24 MPa. The field tests demonstrate the promising potential enhancement of oil production due to this technology. Hydraulic sand blasting perforation improves oil production mainly due to removal of the near-well-bore pollution, looseness of compacted zone, and increase of the formation permeability, which extends the passage-way of oil flow.

Providing conditions to get the initial reservoir permeability will allow to maximise the potential flow rates of oil producing wells and increase the efficiency of a specific reservoir development. It is necessary to assess how and by what amount the permeability of the near wellbore area of productive rocks will change when performing oriented abrasive jet perforation.

The role of stresses arising around the well during its drilling, development, exploitation, and filtration properties formation in the near wellbore area of the well is studied not enough, though in the oil and gas industry during fields exploration and exploitation, especially at large depths, it was found that stress concentrations in the near-a-face zone affect significantly the permeability of layers, filtration processes and, accordingly, the intensity of oil and gas inflow into the well [3,6,7,34].

In addition to the permeability restoration due to the reduction of the reservoir rock stress-strain state (SSS), it is possible to implement the directional unloading method after the slotted channels formation. In-depth research in this area was presented in works [6,7], which are the studies of the mechanisms and proposed technologies of directional unloading, contributing to the improvement of filtration processes in the reservoir. Directional unloading mechanism is possible to implement on the stage of productive layers casing perforation in oil and gas wells after performing a slotted hydro-sandblast perforation (or abrasive jet perforation) (SHSP/AJP) by creating a draw-down on the reservoir.

Special tool and technology of the oriented SHSP, presented by the specialists of Perm national research polytechnic university (PNRPU) [2], reduce the water of well production, increase their productivity and provide qualitative completion of productive layers in the given directions taking into account the stress-strain state of the rocks and direction of the unmined hydrocarbon reserves. As an obvious advantage, conducting an oriented slotted casing perforation of productive layers ensures unloading of the near wellbore area from the applied stresses and provides additional channels for fluid filtration into the well.

The present study conducts geomechanics analysis of the influence of the formation scheme and orientation of the slotted channels in the productive layer during abrasive jet perforation on the permeability of terrigenous reservoirs of the Perm Krai oil fields. Quantitative calculations of permeability are an estimation only and are performed to demonstrate the hole effect during the slotted channels formation.

The rest of the paper is organized as follows. The second section proposes and proves a model of the stress strain state of the formation rocks. The third section presents the simulation results of the average effective stresses before and after perforation, as well as recovery assessment of the formation rocks permeability under different slotted channel placements. The fourth section evaluates the calculation results, gives recommendations on the choice of the slot channels placement, and notes the possibility of well preparing using the AJP technology to conduct a directional hydraulic fracturing in the future. Finally, the paper concludes with a summary.

2. Materials and methods

2.1. Modeling of rock stress and permeability during AJP

The need of a geomechanics analysis in the process of slotted perforations using abrasive jet is related to the fact that the creation of channels. Can cause noticeable changes in the stress-strain state in the borehole area of the layer. It is known that the permeability of terrigenous reservoirs depends on the stress state: as effective stresses increase, the permeability of the rock decreases and vice versa [2,4,5,7]. In addition to increase of the infiltration area of the well, reducing the effective stresses of rocks in the near-wellbore zone can be an additional positive effect from slotted perforation. Therefore, a proposed mathematical model considers the development of unloading zones (deconsolidation) in the rock; the interaction of perforations, also their stability, i.e. the possibility of rock failure in the stress concentration zones. The calculations were done by the finite-element technique for conditions typical for terrigenous oil reservoirs in the Perm Region of Russia.

During oil and gas production change in reservoir pressure can strongly influence the mechanical state of the rock formation. In some cases (for example, in thermal methods of extractionor high-pressure water injection), high-temperature and pressure can also affect the stress-strain state of rocks. In a general case in saturated porous media, it is necessary to consider adjoint problems, i.e. perform a joint solution of the differential equations of deformation of solids and fluid filtration. The equations of the Biot's theory [35,36], including the equilibrium equations, which in this problem reflect the relationship between stresses and gravitational loads, as well as the relationship of total and effective stresses (1)–(3):

$$\nabla \bullet \mathrm{\sigma }+{\mathrm{\gamma }}_{\mathrm{b}}{\mathbf{g}}_{\mathrm{\nu }}=0$$ (1)

$$\nabla \left({\mathrm{\sigma }}^{″}-\mathrm{\alpha }\text{pI}\right){\mathrm{\gamma }}_{\mathrm{b}}\bullet {\mathbf{g}}_{\mathrm{\nu }}=0$$ (2)

$$\mathrm{\alpha }\bullet {\mathrm{\epsilon }}_{\mathrm{\nu }}+\frac{1}{{\mathrm{K}}_{\mathrm{m}}}\bullet \mathrm{p}+\nabla \bullet \mathbf{q}=\mathbf{s}$$ (3)

where $\nabla$ — divergence operator, σ — total stress tensor, ${\gamma }_b$ — bulk density, N/m³, ${\mathbf{g}}_{\mathrm{\nu }}$— direction of gravity load, ${\mathrm{\sigma }}^{″}$— effective stress tensor, $\alpha$ — Biot's coefficient, $p$ — reservoir pressure, Pa, $I$ — unit matrix, ${\epsilon }_v$ — cubic strain of the hard frame, Pa, ${\mathrm{K}}_{\mathrm{m}}$— Biot's modulus, q — flow vector, s — source vector.

Biot's coefficient $\alpha$ (4) is related to the modulus of rock volumetric compression С_b, Pa, and modulus of rock frame volumetric compression C_s, Pa:

$$\alpha =1-\frac{C_b}{C_s}$$ (4)

Total bulk density γ_b (5) is calculated via porousness $n$, fr. unit, bulk density of the rock solid matrix ${\gamma }_s$, N/m³, and bulk density of the fluid ${\gamma }_f$, N/m³:

$${\gamma }_b=\left(1-n\right){\gamma }_s+n{\gamma }_f$$ (5)

During isothermal straining of elastic porous media co-relation between effective stress and strain is calculated with the help of Hook's law relation (6) (physical relations):

$${\mathrm{\sigma }}^{″}=\mathbf{D}\bullet \bullet {\mathrm{\epsilon }}^{\mathbf{e}}$$ (6)

where ${\mathrm{\epsilon }}^{\mathbf{e}}$—elastic deformation tensor, D—elastic constant fourth-rank tensor (is shown via two independent parameters – coefficient of elasticity E, Pa, Poisson's number $\nu$, fr. unit, modulus of cubic compressibility C_b, Pa, or rigidity modulus $G$).

Deformation tensor $\mathrm{\epsilon }$ (7) is shown via displacement $\mathbf{u}$ by the following (Cauchy relation):

$$\mathrm{\epsilon }=\frac{1}{2}\left(\nabla \mathit{u}+{\left(\nabla \mathit{u}\right)}^T\right)\text{.}$$ (7)

Apart from that, the following condition of compatibility of strain must be exercised (8):

$$\nabla \times \left(\nabla \times \mathrm{\epsilon }\right)=0$$ (8)

To give complete characteristic of the elastic porous media, the equation system must be supplemented by the equation of filtration of the fluid in the pores. The relationship between the flow vector q and reservoir pressure p is given through Darcy's law (9) [35,36]:

$$\mathbf{q}=\frac{\mathbf{K}}{{\mathrm{\gamma }}_{\mathrm{f}}}\bullet \left(-\nabla \mathrm{p}+{\mathrm{\gamma }}_{\mathrm{f}}{\mathbf{g}}_{\mathrm{\nu }}\right)$$ (9)

where K — permeability second-order tensor permeability.

The Biot's modulus $K_m$ is calculated by the following (10):

$$\frac{1}{K_m}=\frac{\alpha -n}{C_s}+\frac{n}{C_f}$$ (10)

where $n$—porosity, fr. unit, C_s—volumetric compression module of the solid matrix, Pa, C_f—volumetric compression modulus of the fluid, Pa.

An exact analytical solution of the presented equations is known only for a limited range of elementary problems, therefore, numerical methods are used more often [4,35,36]. In this work, the finite element software complex ‘ANSYS’ version 18.0 was used. This version has a specialized set of models 'Geomechanics’, which contains, among other things, the conjugate model of the pore media considered above. There is a possibility to solve both – elastic and plastic – problems. Different strength criteria are used to calculate the plastic deformations (Mises, Mohr-Coulomb, ‘truncated’ model, etc.). This work solves elastic problems, and the possibility of rock destruction was estimated basing on the presence of zones of inelastic deformations [35], for this the criteria of Mohr-Coulomb destruction was calculated (11):

$${\sigma }_1-p=UCS+\left({\sigma }_3-р\right)\frac{1+\sin \phi }{1-\sin \phi }\text{,}$$ (11)

where σ₁, σ₃ – the principal stresses, Pa; UCS – unconfined compressive strength, Pa; φ – internal friction angle, deg; р – reservoir pressure, Pa.

If plastic areas are not large, then this approach is applicable for an overall borehole stability assessment and slotted perforation.

2.2. Getting initial data for calculating the stress-strain state of a wellbore area with slotted perforations

For the analysis of the SSS of a well with slotted perforations, data about the initial stressed state of the rock mass, physico-mechanical and filtration-capacitive properties of rocks are needed (Table 1). The sources for obtaining these parameters are well logging suite, fracturing results (or LOT, FIT tests), as well as laboratory tests of core material for determining static elastic and strength properties of rocks.

Table 1.

Initial data for calculation the well SSS with the slotted perforation.

№	Parameters	Value
Parameters of the stress pattern of the rock
1	σV – vertical rock pressure, MPa	40.0
2	σH – maximum horizontal pressure, MPa	34.0
3	σh – minimum horizontal pressure, MPa	34.0
4	ασ – bearing action σH, deg.	130
5	р – reservoir pressure, MPa	15.0
Physical and mechanical properties of the rocks
6	Е – static modulus of elasticity, MPa	20,000
7	ν – Poisson's static coefficient, fr. unit	0.17
8	α – Biot's coefficient, fr. unit	0.85
9	γ – average bulk density of overlying, МN/m3	0.025
10	UCS – unconfined compressive strength, MPa	24.0
11	φ – internal friction angle, deg.	28.0
Reservoir properties
12	n – porosity, fr. unit	0.15
13	kav – average reservoir permeability, mD	100.0
14	η – fluid viscosity, mPa-sec	2.0
15	Кf – modulus of the fluid dilatation, MPa	1000
16	γf – bulk density of the fluid, MN/m3	0.0078

To determine the basic physical and mechanical properties of the considered productive object, the logging results from 24 wells of the Shershnevsky oilfield were used (Fig. 1) and taking Tulskiy reservoir as a case study. The characteristics of the reservoir are the following: reservoir type – terrigenous; vertical depth 1577 m; effective oil-saturated thickness – 3.6 m; porosity – 0.15; initial formation pressure – 15.0 MPa. Graphic drill materials (gamma-ray logging, acoustic and density logging, VAK-D) were used to determine the elastic and strength properties, as well as the correlation dependencies obtained in the PNRPU during core material testing [37].

Fig. 1.

Physico-mechanical properties of the rocks of the Tulskiy reservoir.

The vertical rock stress was calculated basing on the density logging data and was equal to σ_V = 40 MPa. The minimum component of the lateral rock pressure was determined according to the available data of the mini-fracturing treatment on the object: σ_h = 40.0 MPa. An isotropic field of horizontal stresses (σ_Н = σ_h) was accepted, as according to acoustic broadband VAC-D logging, the acoustic anisotropy of the array is very small, and there is no other data for a reliable assessment of σ_Н.

Fig. 1 shows the values of the static elastic and strength properties of rocks, calculated from the available correlation dependencies.

Further calculations were done for average values of physico-mechanical properties in the target interval (Table 1).

3. Results

A well schematics and general view of the finite element model are shown in Fig. 2. The internal radius of the model R_w is 0.108 m, the outer radius of the model is R = 50⋅R_w (Fig. 2). The height of the model varied depending on the situation being under consideration, i.e. from the number and mutual arrangement of the slots.

Fig. 2.

Well schematics and general view of the finite element model.

Elements of the casing and cement column were not reproduced in the model as they do not have a significant effect on the results of calculations. In such situation, the stress state of the well in the absence of slotted perforation can be calculated analytically [5]. To verify the correctness of the finite element model, the case without slotted channels is considered. Fig. 3 shows a comparison of the numerical (full lines) and analytical calculations for the operation of a well with a draw-down of 5 MPa in steady state (the remaining parameters are listed in Table 1). Obtained results show the correctness of the work of the constructed model.

Fig. 3.

Comparison of analytical (points) and numerical (full lines) well SSS.

The internal radius of the model is 0.108 m, the outer radius is 5.4 m. The model's height was 2.75 m in design options № 1,2; 3.25 m in option № 3 and 3.5 m in option № 4. Contiguous finite elements of the type CPT216 (reservoir pressure) were used, their total number amounted to 178,900 in the design options № 1,2; 288,000 in № 3 and 310,500 in № 4.

Static load was applied. The lateral rock pressure and the initial reservoir pressure were set at the external boundary of the model, and the bottomhole pressure was set at the well and the slots boundary. The absence of fluid flow and movement along the normal to the upper and lower faces of the model was also set.

Four main options of forming (placement) slot channels were considered taking into account the design of modern perforating devices for slotted well perforation.

The considered schemes of slot channels formation were selected taking into account the different number of slots, phasing angles and shifts in height to determine the best option for unloading productive rocks and remain permeability:

• −two slots on the angle of 180° (Fig. 4a);
• −four slots on the angle of 90° (Fig. 4b);
• −two slot systems on the angle of 180°, spread vertically on the height of 0.25 m (Fig. 4c);
• −four slots with a shift in height by the size of the slot and phasing around the circumference by 90° (Fig. 6).

Fig. 4.

Options 1, 2 and 3 of forming slot channels.

Fig. 6.

The layout of the slots with a shift in height by the size of the slot and phasing around the circumference by 90° and perforator.

Using options of forming slot № 1–3 was investigated the unloading effect of the slots on the bottomhole zone (Fig. 5a–c). The change in permeability of the rock was considered, as well as the stability of the slots, i.e. development of fracture zones during well operation with a draw-down of 5 MPa. In all cases, the length of the slots was 0.4 m, height – 0.25 m and width – 0.04 m. The unloading effect of the slots on the bottomhole zone, change in permeability of the rock, also the stability of the slots, i.e. development of fracture zones during the well operation with a draw-down of 5 MPa. The unloading of the rock was estimated basing on the change of the average effective stress Δσ (12). The unloading zones were limited to a value of Δσ in 20% of the initial stress level. It was assumed that if the change in the average effective stress is less than this value, then its effect on the permeability of the rock will be negligible:

$$\Delta \sigma =\frac{\left({\sigma }_1^{\left(1\right)}+{\sigma }_2^{\left(1\right)}+{\sigma }_3^{\left(1\right)}\right)-\left({\sigma }_1^{\left(0\right)}+{\sigma }_2^{\left(0\right)}+{\sigma }_3^{\left(0\right)}\right)}{3}\text{,}$$ (12)

where Δσ – change of the average effective stress, Pa; σ₁, σ₂, σ₃ – main effective stress, Pa.

Fig. 5.

Decreasing of effective stresses area of the rock for (a) the option № 1. (b) The option № 2. (c) The option № 3. (Shaded areas – unloading areas).

Index (0) corresponds to the stress state before the formation of the slots, index (1) corresponds to the stressed state after the formation of the slots. The unloading areas of the rock correspond to areas with negative Δσ. The unloading zones were limited to a value of Δσ in 20% of the initial stress level. It was assumed that if the change in the average effective stress is less than this value, then its effect on the permeability of the rock will be negligible.

One more case performed for the slot placement option shown in Fig. 6. Such placement of the slotted channels is necessary to prevent the erosion of the perforator body during perforation works on the well and possibly in the case of using the well tool which was developed at PNRPU and its design is specified in work [2].

For the final justification of the number and system of slot placement, functional dependences of the collector permeability on the stress state of the rock are required. To establish such dependencies appropriate experimental studies of the core samples from particular deposits are necessary. In order to demonstrate the unloading effect of the slots, estimation calculations were made to assess their effect on permeability using permeability dependency versus the all-round effective stress (Fig. 7) given in Ref. [4]. Thus, in a sample with an initial permeability of 100 mD, with an increase of the effective stress up to 30 MPa, the permeability decreases to 80 mD (p. A in Fig. 7), and with a pressure increase of up to 33 MPa, down to 52 mD (p. B in Fig. 7).

Fig. 7.

Permeability reduction as a function of effective stress for core samples from the Shershnevskiy oilfield (the initial average permeability of the cores is of 100 mD (figure from the monograph (Kashnikov and Ashikhmin, 2007 [4])).

For terrigenous reservoirs of the Shershnevskiy field, it was established [4] that in case of a prolonged action of the effective stress, exceeding the natural one, their permeability decreases significantly. The degree of decrease in permeability is higher for samples with a higher initial permeability. Thus, for a sample with an initial permeability of 100 mD with increase of effective stress permeability decreases to 52 mD (Fig. 7). The dependency of permeability on stress can be described by a linear dependence (13) and the results of this dependence are presented in Table 2:

К = К₀ – λ⋅Δσ, (13)

where К₀ – initial permeability, D; К – current permeability, D; Δσ – change of an average effective stress; λ – coefficient of the permeability reduction.

Table 2.

The dependence of the values of the maximum effective stress and the restoration of the permeability of the near-well zone of the productive reservoir on the formation scheme of slot channels.

Slot channels (№ of option)	Location	Maximum eff. stress, MPa	Permeability, mD	Max permeability reduction, %
1	slots walls	14.3	100	0
	around the slots	38.4–51.1	50–62	38–50
	between slots around the wellbore	37.2–51.1	50–64	36–50
2	slots walls	14.3	100	0
	around the slots	38.4–51.1	50–62	38–50
	between slots around the wellbore	21.7–51.1	50–73	27–50
3	slots walls	14,3	100	0
	around the slots	38.4–51.1	50– – 62	38–50
	between slots along the wellbore	21.7–51.1	50–73	27–50
4	slots walls	14.3	100	0
	around the slots	38.4–51.1	50–62	38–50
	between slots along the wellbore	14.3–21.7	73–100	0–27

The error due to the absence of a casing column and cement ring was estimated preliminarily in a simplified 2D case (plane deformation). We considered stress-strain state around the slot in two cases: 1 – cased borehole; 2 – uncased. Cased borehole parameters are as follows: modulus of steel elasticity E = 200 GPa, Poisson's coefficient ν = 0.3; modulus of cement elasticity Е = 5 GPa, Poisson's coefficient ν = 0.2; column diameter was 0.147 m. For cased and uncased boreholes SSS of the near-hole zone was calculated for a well working with a draw-down of 5 MPa, and a change in the average effective stress Δσ relatively to the initial state of the rock was calculated according to formula 12. The calculation error δ (14) of the value of Δσ due to the neglect of the casing and cement column was defined as follows:

$$\delta =\frac{\Delta {\sigma }_2-\Delta {\sigma }_1}{\Delta {\sigma }_1}\text{,}$$ (14)

where δ – error; Δσ₁, Δσ₂ – change of an average effective stress calculated on the models of cased and open well correspondingly, Pa. The results of calculations of distribution of tangential stresses and distribution of average stress are presented at Fig. 8a and b.

Fig. 8.

(a) Distribution of average stress (σ_r + σ_Θ + σ_z)/3 (MPa) in the vicinity of slots. (b) Graph of average stress distribution (σ_r + σ_Θ + σ_z)/3 (MPa) in the vicinity of slots.

Fig. 9a shows the calculation of permeability reduction for a well without slotted perforation working with a draw-down (depression) of 5 MPa. There is a natural decrease of permeability around the well, which in the bottom-hole zone reduces down to 77 mD. In the case of slotted perforation (4 slots with phasing 90°), the picture is quite different. The distribution of reservoir pressure is not axissymmetric (Fig. 9b), and there are areas where the permeability decreases to the critical level – up to 52 mD (Fig. 9c).

Fig. 9.

(a) Distribution of permeability (mD) around the area of an open well before perforation at a draw-down of 5 MPa. (b) Reservoir pressure around the well with a slotted perforation (draw-down 5 MPa). (c) Distribution of permeability (mD) at a draw-down of 5 MPa around the well with a slotted perforation.

The results of the permeability calculation for the case of placement of slot channels presented in Fig. 6 are shown in Fig. 10a and b.

Fig. 10.

(a) Distribution of permeability (mD) at a draw-down of 5 MPa around the well with a slotted perforation shown at Fig. 6. (b) Graph of permeability (mD) distribution at a draw-down of 5 MPa around the well with a slotted perforation shown at Fig. 6.

4. Discussions

Analysing the unloading areas obtained for options of forming slot № 1, 2, 3 and 4 (Fig. 4, Fig. 5), the following conclusions can be done. In the case of two slots with phasing 180° (Fig. 4c), the unloading zone is limited by the surface of the slot itself and the near-well zone. For four slots with phasing 90° (Fig. 4b), the unloading zone is much larger, i.e. the slots interacts and this option is more preferable. The calculations also showed that the slots interact very weakly heightwise: the discharge zones in cases № 1 and № 3 are almost the same, although the slot systems are spaced only 0.25 m in height (i.e. the size of the slot itself).

Thus, a more preferable option of slotted perforation is the creation of four slots with a shift in height by the size of the slot and phasing around the circumference by 90° (Fig. 6). The distance between the slot systems in height does not play an important role, as the slots interact weakly in this direction.

In local areas the error δ can reach 100–150%, but in general the error is relatively small in the calculated region. The area in which the error exceeds 20% adjoins directly to the slot and its extent is not more than the radius of the well. The thickness of this zone is comparable to the thickness of the slot (Fig. 8). Thus, estimated calculations of the permeability change can be done with a simplified model of an open well. Results of the corresponding calculations are shown in Fig. 9, Fig. 10.

The areas of permeability decrease are concentrated in zones of high stress concentration along the perimeter of the slots. The main part of the rock between the slots is in the unloading zone, where the permeability remains on the initial level (Fig. 9c).

The sufficient degree of stability of the slots as the conditional zones of inelastic deformations are relatively small (Fig. 11). The main zones of destruction are concentrated in the bottomhole zone and are due to a simplified statement of the problem, i.e. lack of casing and cement column in the model. The presence of these structural elements should ensure the safety of slots and wells at specified values of the strength properties of the rock.

Fig. 11.

Stability of the slots as the conditional zones of inelastic deformations around the slotted perforation.

Thus, in addition to the improved “well-reservoir” communication an additional effect of slotted perforation is the unloading of the rocks from the operating stresses which has a positive effect on the permeability of the reservoir. Also, a positive effect of the proposed technology is the possibility of orienting the slot channels which will allow to prepare the well for the oriented hydraulic fracturing, to direct the slotted channels taking into account the anisotropy and azimuths of the minimum and maximum principal horizontal stresses, and also taking into account the direction of occurrence of the unprocessed hydrocarbon reserves.

5. Conclusion

• 1.The presented calculations were performed by the finite element method for conditions characteristic of terrigenous reservoirs. The preferred option for optimizing slot perforation is to create four slotted channels with a height shift by the size of the slot and a phasing of 90°. The total number of contiguous finite elements in model in this option of slotted channel placement was 310,500. Casing and cement stone were not taken into account in the model, as they do not significantly affect the results of calculations. The lateral rock pressure and initial reservoir pressure were set at the external boundary of the model, and bottom-hole pressure was set at the well and the slotted channels boundary. Also the absence of fluid flow and movement along the normal to the upper and lower faces of the model was set.
• 2.The results of numerical and analytical modeling have shown the correctness of the developed model. Using the dependence of the permeability terrigenous rocks pore-type reservoirs on the magnitude of effective stresses obtained during testing of core samples, comparative calculations of the permeability of the near-well zone for various perforation methods were performed. The use of this technology makes it possible to restore the permeability of the near-well zone the formation to the initial values due to the unloading of reservoir rocks from the operating average effective stresses.
• 3.The oriented abrasive jet perforation as a method of perforation works of oil-reservoirs represented by terrigenous pore-type rocks allows:

• to unload the productive rocks and to remain their permeability on the initial level;

• to increase the filtration area of fluid up to 6 times compared with the explosive (shaped-charge) perforation method and thereby increase the flow rate of the well;

• to ensure the recovery of the permeability of the near-wellbore area to the initial values (an increase in permeability up to 2 times compared with the explosive perforation method) and to obtain a potential the flow rate of well;

• create conditions for the directional hydraulic fracturing of reservoirs in future when the effect of the oriented abrasive jet perforation finished.

It is planned to evaluate the effectiveness of this method of dissection using a geological and hydrodynamic model for developing of the reservoir, as well as to develop a method for selecting wells-candidates for implementing this perforation technology.

Data availability statement

Data will be made available on request.

CRediT authorship contribution statement

Sergey E. Chernyshov: Conceptualization, Data curation, Project administration, Writing – original draft. Sergey G. Ashikhmin: Conceptualization, Data curation, Formal analysis, Methodology, Software, Supervision. Yury A. Kashnikov: Conceptualization, Data curation, Methodology, Software, Supervision, Validation, Visualization. Shaoran Ren: Data curation, Methodology, Project administration, Validation. Vadim V. Derendyaev: Resources, Visualization, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements