METHOD FOR DETERMINING AN OUTLET CONFIGURATION OF A LINER

Description

TECHNICAL FIELD

The present disclosure generally relates to the field of reservoir stimulation, and more particularly to techniques for designing a liner completion. Certain embodiments may provide for a method for determining an outlet configuration of a liner usable for stimulating a reservoir (e.g., oil, water and/or gas).

BACKGROUND

Long horizontal wells are key to improve the sweep efficiency and hydrocarbon recovery while minimizing resources for field development. Optimum well productivity requires effective stimulation, either hydraulic fracturing or matrix-acid stimulation. Traditionally, a complicating factor in matrix-acid stimulation treatments has been the poor control of the acid placement along the reservoir section. The limited-entry liner (LEL) lower completion addresses the shortcomings of conventional stimulation techniques. It consists of several unevenly spaced outlets (e.g., holes) with the purpose to distribute fluid (e.g., acid) evenly along the reservoir section to be stimulated. Thus, an optimal outlet spacing configuration is necessary to ensure that the fluid is distributed with a user specified coverage (e.g., defined as barrels of acid per feet of the reservoir segment).

In the past, solving the corresponding flow equations in order to determine the outlet spacing configuration was done in an iterative way, mostly by using corresponding optimization techniques.

For example, US patent application US 2009/294122 A1 discloses a method of simulating fluid transport in a system for stimulating a well in a material formation of a resource reservoir. The system comprises a conduit element arranged in said well, the conduit element comprises a conduit wall including one or more openings for discharging a fluid into the material formation surrounding the conduit element and the method comprises establishing and numerically processing a transport model of fluid transport inside the conduit element. The transport model further includes a model of fluid transport in a predetermined space around said conduit element.

However, one main drawback of these approaches is their computational complexity and the required amount of computational resources during executing which are at least in part caused by a large amount of iterations and iterations loops. It is therefore an objective of the present disclosure to provide an improved method of determining an outlet configuration of a liner, thereby overcoming the above-mentioned disadvantages of the prior art at least in part.

SUMMARY OF THE DISCLOSURE

The objective is solved by the subject-matter defined in the independent claims. Advantageous modifications of embodiments of the present disclosure are defined in the dependent claims as well as in the description and the figures.

One aspect of the present disclosure relates to a method for determining an outlet configuration of a liner usable for stimulating a reservoir. The method may comprise a step a. of obtaining a desired fluid outflux distribution along one or more segments of the reservoir, each segment corresponding to a portion of the liner. The method may comprise a step b. of determining, for each portion of the liner, a number of outlets according to: the desired fluid outflux distribution, a predefined outlet size and a difference between an annulus pressure and a liner pressure within the portion. The method may comprise a step c. of evaluating, for each portion, whether an outlet distribution according to the number of outlets of the predefined outlet size satisfies one or more outlet distance constraints within the portion. The method may comprise a step d. of repeating, if the outlet distribution of at least one portion does not satisfy the one or more outlet distance constraints, the steps b. and c. for the at least one portion with an adjusted outlet size as the predefined outlet size.

The outlet configuration determined this way achieves the desired fluid outflux distribution while requiring less computational resources compared to the methods of the prior art. This is mainly due to the fact that the inventors found that by predefining an outlet size and using the desired fluid outflux distribution as well as the difference in pressure between the annulus and liner, the number of outlets required to achieve the corresponding distribution can be determined in a deterministic (i.e., directly solvable without the need of optimization iterations) manner.

Accordingly, throughout the present disclosure the term “determining” with respect to the number of outlets may be defined as a step of determining which does not require an iterative procedure to determine the number of outlets. Instead, “determining” may be defined as a step of determining the number of outlets without performing iterations for obtaining the number of outlets. Accordingly, the step of determining with respect to the number of outlets may differ from other method steps such as “calculating” and/or “deriving” and/or “estimating” as these may require iterations to obtain the corresponding result (e.g., calculating a flow rate using the number of outlets may comprise optimizing an objective function which requires one or more iterations).

Although the present aspects are explained with respect to determining the outlet configuration of a liner usable for stimulating a reservoir (e.g., oil, water and/or gas), the method according to the aspects of the present disclosure is also applicable to determine outlet configurations of liners for stimulating other types of reservoirs such as aquifers or the like, or liners deployed in reservoirs, which do not require stimulation (i.e., the liner may also be usable without stimulating the reservoir).

According to another aspect of the present disclosure, the method may comprise a step of deriving, for each portion of the liner, an annulus portion rate and a liner portion rate based on the desired fluid outflux distribution along the one or more segments of the reservoir. The method may further comprise a step of estimating, based at least in part on the derived liner portion rates, the line pressure and/or estimating, based at least in part on the derived annulus portion rates, the annulus pressure.

The fact that the desired outflux distribution is known allows to derive the corresponding portion rates based on which the corresponding line and/or annulus pressure can be estimated. Accordingly, by using the desired fluid outflux distribution, the portion rates can be efficiently computed without the need of additional optimization iterations.

According to another aspect of the present disclosure, each segment may be associated with a desired segment acid coverage and a segment length. Deriving the annulus portion rate and the liner portion rate for a portion may be based at least in part on the desired segment acid coverage and the segment length of the segment.

Utilizing the desired coverage as well as the corresponding length of the segment allows to accurately calculate the corresponding portion rates.

According to another aspect of the present disclosure, estimating the liner pressure may comprise calculating, for each pair of adjacent portions, a pressure difference between the pair of adjacent portions.

By determining the pressure difference between adjacent portions of the liner, the overall liner pressure can be accurately estimated resulting in an improved manner of determining the number of outlets and thus in an improved outlet configuration of the liner.

According to another aspect of the present disclosure, calculating the pressure difference between a pair of adjacent portions may comprise calculating a friction pressure based at least in part on a friction factor, in particular a Fanning friction factor, a diameter, a pipe length, a velocity and/or a fluid density. The diameter may comprise a diameter of the liner and/or a diameter of an outlet. The pipe length may represent a total pipe length L whereas the pipe may comprise a plurality of segments each having a segment length L_i and wherein the total pipe length L equals the sum of all segment lengths L_i of the plurality of segments.

It was found that the pressure difference between a pair adjacent portion is equal to the friction pressure. Accordingly, calculating the friction pressure is an easily computable way for calculating the pressure difference between adjacent portions.

According to another aspect of the present disclosure, estimating the annulus pressure within each portion may be further based on a pressure within the reservoir, a pipe length L, a viscosity μ, a formation volume factor B, a permeability k, an initial skin factor S and/or a factor depending on boundary conditions of the reservoir, in particular a well type such as a vertical or horizontal well. The pressure within the reservoir may be noted as P_res. The pressure within the reservoir may represent an average reservoir pressure of a drainage area around a well.

It was found that the annulus pressure within each portion can be derived based on an equation/relationship comprising the above-identified factors. As these factors are known prior (e.g., obtained by performing corresponding measurements) the annulus pressure can be estimated without computational expensive operations.

According to another aspect of the present disclosure, the one or more outlet distance constraints may comprise: a distance between adjacent outlets of a portion not exceeding a predefined upper threshold (e.g., 100 ft), a distance between adjacent outlets of a portion exceeding a predefined lower threshold (e.g., 25 ft), an outlet size being within a range of a predefined minimum and maximum value (e.g., 2-8 mm, or 3-4 mm) and/or an outlet spacing distortion not exceeding a predefined value (e.g., 3), wherein the outlet spacing distortion is a ratio between a maximum distance between two outlets within a portion and a minimum distance between two outlets within the portion.

This way, a determined outlet distribution can be efficiently evaluated. Accordingly, it is now possible to verify whether the determined number of outlets is sufficient or not.

According to another aspect of the present disclosure, the adjusted outlet size may comprise a reduced outlet size if the distance between adjacent outlets of the portion exceeds the predefined upper threshold or an increased outlet size if the distance between adjacent outlets of the portion is below the predefined lower threshold.

Adjusting the outlet size results in a value change of the predefined outlet size according to which the number of outlets is determined. While this might result in a re-executing of the determining step of the number of outlets, the inventors found that such a re-execution of the deterministic determining step of the number of outlets can be performed more efficiently compared to optimization algorithms known in the prior art.

According to another aspect of the present disclosure, the method may further comprise calculating, using the number of outlets, a flow rate, a wellhead pressure and/or an acid coverage which satisfies a predetermined set of stimulating constraints. Alternatively, in case the liner is used without stimulation, the method may further comprise calculating, using the number of outlets, a flow rate, a wellhead pressure and/or a coverage which satisfies a predetermined set of constraints.

This way, a configuration of the liner is determined which minimizes the operational time and ensures the best possible jetting effect for wormhole propagation.

According to another aspect of the present disclosure, determining the flow rate, the wellhead pressure and/or the coverage (e.g., acid coverage if the liner is used for stimulation) may be done by optimizing, in particular using an objective function, values of the flow rate, the wellhead pressure and/or the coverage (e.g., acid coverage). The flow rate may be prioritized over the wellhead pressure and/or the coverage (e.g., acid coverage).

According to another aspect of the present disclosure, optimizing may comprise setting an initial value (e.g., 0.25 bbl/min) as the value of the flow rate and/or setting an initial value (e.g., 1000 psia) as the value of the wellhead pressure.

This way, convergence of the objective function is improved resulting in an earlier stoppage of the optimizing.

According to another aspect of the present disclosure, the predetermined set of (stimulating) constraints may comprise an annulus pressure along a predefined section of portions of the one or more portions not exceeding a fracturing pressure along the predefined section of portions, preferably wherein the section is on an annulus side of a lower completion of the liner and/or the wellhead pressure not exceeding a predefined threshold value and/or the flow rate not exceeding a maximum rate capacity of a corresponding pump and/or a jet velocity of fluid entering the reservoir exceeding a predefined wormholing threshold and/or a provided dosage (e.g., acid dosage) exceeding a minimum amount of dosage (e.g., acid dosage) required for wormhole penetration and skin reduction.

This way, a configuration of the liner is determined which minimizes the operational time and ensures the best possible jetting effect for wormhole propagation.

According to another aspect of the present disclosure, the method may further comprise performing a feasibility check of the construction of the liner comprising the provided outlet distribution for each of the one or more portions based on a set of construction constraints.

This way, it can be determined whether construction of the liner according to the provided outlet distribution is feasible given the actual hardware conditions at the reservoir (e.g., number of pipe joints on the rig etc.).

According to another aspect of the present disclosure, the method may further comprise determining that the feasibility check of the construction is negative and repeating, for at least one portion of the one or more portions step b. and/or c. with an adjusted outlet size as the predefined outlet size.

This way, a trade off for the liner construction between the optimal outlet configuration and implementing the manufactured liner for production or injection within the reservoir.

According to another aspect of the present disclosure, the method may comprise a step of providing the outlet distribution for each portion that satisfies the one or more outlet distance constraints. Providing may comprise causing a display of one or more visualizations associated with the construction of the liner comprising the one or more portions.

This way, the outlet distribution for each portion which satisfies the constraints can be for example be stored and thus used for determining the overall outlet configuration once the outlet distribution for each portion has been determined. Corresponding visualizations may allow a user (e.g., a petroleum engineer) to monitor the process in a transparent manner.

According to another aspect of the present disclosure, the method may further comprise issuing a notification, in particular a flag displayed on a display, whenever a constraint is not satisfied.

This way, a user is able to evaluate the notifications and assess whether not satisfying the constraint is acceptable for the present task at hand or simply monitor the process of determining the overall outlet configuration for the liner.

According to another aspect of the present disclosure, the method may further comprise segmenting the reservoir along the liner by applying one or more packers, in particular swellable packers, to obtain the one or more segments of the reservoir.

This way zonal isolation of the reservoir along the liner can be achieved.

According to another aspect of the present disclosure, the liner may be a limited-entry liner.

According to another aspect of the present disclosure, the method may further comprise constructing and/or manufacturing the liner for stimulating the reservoir.

According to another aspect of the present disclosure, stimulating the reservoir may comprise distributing a fluid, in particular acid, along one or more sections of the reservoir.

According to another aspect of the present disclosure, determining the outlet configuration of the liner may comprise determining an optimum outlet spacing. The optimum outlet spacing may comprise a number of outlets along the liner, a size of the outlets along the liner and/or a positioning of the outlets along the liner. The outlets of the outlet may be unequally or equally spaced.

According to another aspect of the present disclosure, an outlet may be an opening such as a hole.

According to another aspect of the present disclosure, the step of repeating may be performed until the outlet distribution of each portion satisfies the one or more outlet distance constraints.

Another aspect of the present disclosure relates to a data-processing apparatus comprising means for performing the method of any one of the aspects described herein.

Another aspect of the present disclosure relates to a computer program or a computer-readable medium comprising a computer program, wherein the computer program comprises instructions, which when executed by a computer, cause the computer to perform the method of any one of the aspects described herein.

Another aspect of the present disclosure relates to a method for manufacturing a liner usable for stimulating a reservoir. The method may comprise a step of determining an outlet configuration of a liner according to any one of the aspects described herein. The method may comprise a step of arranging the outlets of the liner according to the determined outlet configuration.

By arranging the outlets according to the determined outlet configuration using the method according to the aspects of the present disclosure, a desired outflux distribution is achieved which results in an improved stimulation of the reservoir when using the line for stimulating the reservoir.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure may be better understood by reference to the following drawings:

FIG. 1 A schematic overview of a liner in accordance with embodiments of the present disclosure.

FIG. 2 A flowchart of a method for determining an outlet configuration of a liner in accordance with embodiments of the present disclosure.

FIG. 3 A schematic overview of a liner completion in accordance with embodiments of the present disclosure.

FIGS. 4-6 Visualizations associated with the construction of a liner in accordance with embodiments of the present disclosure.

DETAILED DESCRIPTION

In the following, representative embodiments illustrated in the accompanying drawings will be explained. It should be understood that the illustrated embodiments and the following descriptions refer to examples which are not intended to limit the embodiments to one preferred embodiment.

FIG. 1 illustrates a schematic overview 100 of a liner 104 in accordance with an exemplary embodiment. The liner 104 is placed within an annulus 106 within a reservoir 102. The reservoir 102 may comprise one or more segments 110a-b, which may be obtained may placing one or more packers 108. Each segment 110a-b of the reservoir 102 may thus be associated with a corresponding portion 112a-b of the liner 104. A portion 112a-b of the liner 104 corresponds to the corresponding segment 110a-b of the reservoir due to the segmentation achieved by the packers 108. Segmenting using the packers 108 may allow to isolate segments 110a-b of the reservoir 102 with different reservoir pressure and/or permeability and the completion design can accommodate that. For example, the portion 112a of the liner 104 may correspond to the segment 110a of the reservoir 102 and the portion 112b of the liner 104 may correspond to the segment 110b of the reservoir 102. Accordingly, each portion 112a-b may provide a corresponding outflux distribution within the corresponding segment 110a-b by means of a corresponding outlet configuration. In the illustrated example, an outlet refers to a hole. The outlet configuration may be determined using the method according to aspects of the present disclosure. As can be seen, executing said method may determine a corresponding outlet configuration. For example. three holes with a corresponding positioning, size and spacing for the portion 112a of the liner 104 and six holes with corresponding positioning, size and spacing for the portion 112b of the liner 104. By applying said optimal outlet configuration, a desired fluid outflux distribution is achieved while satisfying corresponding constraints.

By utilizing the liner 104 with the corresponding outlet configuration, fluid (e.g., acid) is bull-headed from the surface through the production tubing and without the need of a coiled tubing and enters the liner 104 from the left. When the fluid reaches the first hole of the portion 112a, a pressure drop across the hole is so large that only a small percentage of the fluid exits the liner through this hole. The remaining fluid continues along the liner 104 until it reaches the next hole where the same process is repeated. An optimal outlet configuration as determined using the method according to aspects of the present disclosure makes it possible to ensure that fluid is distributed according to the desired fluid outflux distribution (e.g., a user-specified acid coverage, defined as barrels of acid per feet of reservoir section). As a result, constructing or manufacturing the liner 104 using the method according to aspects of the present disclosure and using the liner 104 for stimulating the reservoir 102 will result in the fluid being distributed according to the desired fluid outflux distribution.

FIG. 2 illustrates a flowchart of a method 200 for determining an outlet configuration of a liner 104 usable for stimulating an oil, water and/or gas reservoir 102 in accordance with an exemplary embodiment. The method 200 may comprise a step of obtaining 202 a desired fluid outflux distribution along one or more segments 110a-b of the reservoir 102, each segment 110a-b corresponding to a portion 112a-b of the liner 104. The method 200 may comprise a step of determining 204, for each portion 112a-b of the liner 104, a number of outlets according to: the desired fluid outflux distribution, a predefined outlet size and a difference between an annulus pressure and a liner pressure within the portion 112a-b. The method 200 may comprise a step of evaluating 206, for each portion 112a-b, whether an outlet distribution according to the number of outlets of the predefined outlet size satisfies one or more outlet distance constraints within the portion 112a-b. The method 200 may comprise a step of repeating 208, if the outlet distribution of at least one portion 112a-b does not satisfy the one or more outlet distance constraints, the steps 204 and 206 for the at least one portion 112a-b with an adjusted outlet size as the predefined outlet size.

The method 200 may comprise a step of deriving, for each portion 112a-b of the liner 104, an annulus portion rate and a liner portion rate based on the desired fluid outflux distribution along the one or more segments 110a-b of the reservoir 102. The method 200 may further comprise a step of estimating, based at least in part on the derived liner portion rates, the line pressure and/or estimating, based at least in part on the derived annulus portion rates, the annulus pressure.

The rates may be calculated according to the following equation:

Q i = Q ⁢ Cov i × L i ∑ i Cov i × L i ,

wherein Q is the total fluid outflux, Q_i is the fluid outflux for a segment i (e.g., a desired segment acid coverage in bbl/ft) and L_i is the length of segment i. Accordingly, the proposed invention takes advantage of the fact that the desired fluid outflux distribution is known. This means that the rate at any point inside the liner 104 is known. A user may specify a certain desired fluid outflux distribution, which thereby fixes the individual annulus segment rates and hence also the rates inside the liner 104.

Each segment 110a-b may be associated with a desired segment acid coverage and a segment length. Deriving the annulus portion rate and the liner portion rate for a portion may be based at least in part on the desired segment acid coverage and the segment length of the segment 110a-b.

Estimating the liner pressure may comprise calculating, for each pair of adjacent portions 112a-b, a pressure difference between the pair of adjacent portions 1120a-b.

Calculating the pressure difference between a pair of adjacent portions 112a-b may comprise calculating a friction pressure based at least in part on a friction factor, in particular a Fanning friction factor, a diameter, a pipe length, a velocity and/or a fluid density.

This may be done according to the following equation:

Δ ⁢ P fr ⁢ ic = - 4 ⁢ f D ⁢ pv 2 2 ⁢ L ,

wherein f is the Fanning friction factor, D the diameter, L the pipe length, v the velocity and p the fluid density. The diameter may comprise a diameter of the liner and/or a diameter of an outlet. The pipe length may represent a total pipe length L whereas the pipe may comprise a plurality of segments each having a segment length L_i and wherein the total pipe length L substantially equals the sum of all segment lengths L_i of the plurality of segments.

The friction pressure may be estimated solving the following implicit equation iteratively:

1 f = 4 ⁢ log 1 ⁢ 0 ( R ⁢ e ⁢ f ) - 0 . 4 = - 4 ⁢ log 1 ⁢ 0 [ 1 . 2 ⁢ 6 R ⁢ e ⁢ f + ε 3 . 7 ⁢ D ] ,

wherein Re is the Reynolds number defines as

R ⁢ e = ρ ⁢ uD μ .

Estimating the annulus pressure within each portion 112a-b may be further based on a pressure within the reservoir 102, a pipe length L, a viscosity μ, a formation volume factor B, a permeability k, an initial skin factor S and/or a factor depending on boundary conditions of the reservoir, in particular a well type such as a vertical or horizontal well. The pressure within the reservoir may be noted as P_res. The pressure within the reservoir may represent an average reservoir pressure of a drainage area around a well.

Estimating the annulus pressure may be done using the following equation:

p annulus = p res + Q ⁢ μ ⁢ B kL ⁢ ( p D + S ) ,

wherein the pD function can take various form depending on boundary conditions of the reservoir. For example, for vertical wells pD may be given as p_d=0.5(ln t_D+0.80907) with

t d = kt φμ ⁢ c t ⁢ r we 2 .

For example, for horizontal wells, pD may be given as

p a = π 4 × k k y × ∫ 0 t d A × B τ × d ⁢ τ ,

wherein

A = ( erf [ k ky + x D 2 ⁢ t ] + erf [ k ky - x D 2 ⁢ t ] ) × e y D 2 4 ⁢ τ ⁢ and B = 1 + 2 × ∑ n = 1 ∞ ⁢ exp [ - τ ⁡ ( n ⁢ π ⁢ L D ) 2 ] × cos [ n ⁢ π ⁢ z D ] × cos [ n ⁢ π ⁢ z wD ] ⁢ and ⁢ t a = 0.001055 kt φμ ⁢ c t ⁢ L 2 .

Accordingly, the difference between the annulus pressure and the liner pressure may equal the pressure across the outlets (e.g., orifice holes) and may be notated as:

Δ ⁢ P hole = P liner - P annulus = 0 . 2 ⁢ 3 ⁢ 6 ⁢ 9 ⁢ ρ ⁢ Q hole 2 [ nC d ⁢ D hole 2 ] 2 ,

with C_D being a discharge coefficient.

Accordingly, the only unknowns are the number of outlets and the size of the outlets. Thus, by fixing a predefined outlet size, the number of outlets (n) in each portion 110a-b can be determined using for example the following equation:

n = 0.2369 ρ ⁢ Q hole 2 ( P liner - P annulus ) [ C d ⁢ D hole 2 ] 2 .

This number n may then be converted to an integer value, which may then inherently satisfy the desired fluid outfiux distribution. Hence the step of determining 204, for each portion 112a-b of the liner 104 does not require any iteration resulting in an improved/reduced complexity and thus less consumption of computational resources.

The one or more outlet distance constraints may comprise: a distance between adjacent outlets of a portion 112a-b not exceeding a predefined upper threshold (e.g., 100 ft), a distance between adjacent outlets of a portion 112a-b exceeding a predefined lower threshold (e.g., 25 ft), an outlet size being within a range of a predefined minimum and maximum value (e.g., 2-8 mm, or 3-4 mm) and/or an outlet spacing distortion not exceeding a predefined value (e.g., 3), wherein the outlet spacing distortion is a ratio between a maximum distance between two outlets within a portion and a minimum distance between two outlets within the portion.

The adjusted outlet size may comprise a reduced outlet size if the distance between adjacent outlets of the portion 112a-b exceeds the predefined upper threshold or an increased outlet size if the distance between adjacent outlets of the portion 112a-b is below the predefined lower threshold.

The method 200 may further comprise calculating, using the number of outlets, a flow rate, a wellhead pressure and/or an acid coverage which satisfies a predetermined set of stimulating constraints.

Calculating the flow rate, the wellhead pressure and/or the acid coverage may be done by optimizing, in particular using an objective function, values of the flow rate, the wellhead pressure and/or the acid coverage. The flow rate may be prioritized over the wellhead pressure and/or the acid coverage. Optimizing may comprise setting an initial value (e.g., 0.25 bbl/min) as the value of the flow rate and/or setting an initial value (e.g., 1000 psia) as the value of the wellhead pressure. The flow rate may be prioritized because it minimizes operational time and ensures the best possible jetting effect for wormhole propagation. In a situation in which the liner pressure is not larger than the annulus pressure, the flowrate across the corresponding outlet may be reversed and thus become negative. This way, convergence of the optimizing is ensured. An evaluation of the optimizing has shown that fully convergence typically requires less than 15 seconds.

The predetermined set of stimulating constraints may comprises an annulus pressure along a predefined section of portions 112a-b of the one or more portions 112a-b not exceeding a fracturing pressure along the predefined section of portions 112a-b, preferably wherein the section is on an annulus side 106 of a lower completion of the liner 104 and/or the wellhead pressure not exceeding a predefined threshold value and/or the flow rate not exceeding a maximum rate capacity of a corresponding pump and/or a jet velocity of fluid entering the reservoir 102 exceeding a predefined wormholing threshold and/or a provided acid dosage exceeding a minimum amount of acid dosage required for wormhole penetration and skin reduction. With respect to the jet velocity, typically 15 m/s are considered as reasonable for a minimum jet velocity.

Alternatively, in case a liner is used for no stimulation (e.g., instead the line may serve to distribute oil and/or gas (for production wells), or inject water (for injection wells)), the predetermined set of constraints may comprises an annulus pressure along a predefined section of portions 112a-b of the one or more portions 112a-b not exceeding a fracturing pressure along the predefined section of portions 112a-b, preferably wherein the section is on an annulus side 106 of a lower completion of the liner 104 and/or the wellhead pressure not exceeding a predefined threshold value and/or the flow rate not exceeding a maximum rate capacity of a corresponding pump and/or a jet velocity of fluid entering the reservoir 102 exceeding a predefined wormholing threshold.

The method 200 may further comprise performing a feasibility check of the construction of the liner 104 comprising the provided outlet distribution for each of the one or more portions 112a-b based on a set of construction constraints. The feasibility check may concern that the outlet configuration and/or the overall liner completion satisfies the pipe joints available on the right such as the total number of joints including blank joints (i.e., joints without any outlets) as well as joints with outlets (e.g., 1-4 holes) with a particular outlet size/diameter. If joints with different outlet sizes are involved, then the outlet size of some portions of the liner may be changed to satisfy the available joints.

The method 200 may further comprise determining that the feasibility check of the construction is negative and repeating, for at least one portion 112a-b of the one or more portions 112a-b step 204 and/or 206 with an adjusted outlet size as the predefined outlet size.

The method 200 may comprise a step of providing the outlet distribution for each portion 112a-b that satisfies the one or more outlet distance constraints. Providing may comprise causing a display of one or more visualizations associated with the construction of the liner 104 comprising the one or more portions 112a-b.

The method 200 may further comprise issuing a notification, in particular a flag displayed on a display, whenever a constraint is not satisfied.

The method 200 may further comprise segmenting the reservoir 102 along the liner 104 by applying one or more packers 108, in particular swellable packers, to obtain the sone or segments 110a-b of the reservoir 102. The liner may be a limited-entry liner. The method may 200 further comprise constructing and/or manufacturing the liner 104 for stimulating the reservoir 102. Stimulating the reservoir 102 may comprise distributing a fluid, in particular acid, along one or more sections 110a-b of the reservoir 102.

Determining the outlet configuration of the liner 104 may comprise determining an optimum outlet spacing. The optimum outlet spacing may comprises a number of outlets along the liner 104, a size of the outlets along the liner 104 and/or a positioning of the outlets along the liner 104. The outlets of the outlet may be unequally or equally spaced. An outlet may be an opening such as a hole or valve.

The step of repeating may be performed until the outlet distribution of each portion 112a-b satisfies the one or more outlet distance constraints.

FIG. 3 illustrates a schematic overview 300 of a liner 104 completion in accordance with embodiments of the present disclosure. In the upper part 302 the liner 104 completion is illustrated as discretized into cell elements. As one can see, the liner 104 is discretized into cell elements (indicated by the squares). The same applies to the surrounding annulus 106 and the reservoir 102. The reservoir 102 is segmented into two segments using a swellable packer as indicated by the greyed square. Accordingly, the line 104 also is divided into two corresponding portions wherein each portion comprises one outlet (e.g., an orifice hole).

In the lower part 303 the liner 104 completion is illustrated as discretized into segments. As one can see, a desired fluid outflux distribution Q is distributed over 4 segments Q1-4 of the reservoir 102. For this purpose, 3 corresponding packers (illustrated by the grey squares) are placed. Each corresponding portion of the liner 104 is thus arranged with a corresponding outlet configuration. In this simplified example, each portion of the liner 104 comprises one outlet (e.g., an orifice hole).

FIG. 4 illustrates visualizations 402-412 associated with the construction of a liner 102 in accordance with embodiments of the present disclosure.

Visualization 402 illustrates a distribution of outlet sizes (e.g., hole diameters) along the segments of the reservoir 102 as determined using the method 200. As one can see, the reservoir 102 in this example comprises 15 segments, wherein the first 7 segments have a hole diameter of 3 mm whereas the remaining 8 segments have a hole diameter of 4 mm.

Visualization 404 illustrates an acid coverage along the segments of the reservoir 102 resulting from executing the method 200. As one can see, the reservoir 102 in this example comprises 15 segments, wherein an equal coverage of 1 bbl/ft is achieved along each segment due to the outlet configuration determined using the method 200.

Visualization 406 illustrates the permeability (mD) along the segments of the reservoir 102 resulting from executing the method 200. As one can see, the reservoir 102 in this example comprises 15 segments with an equal permeability of 0.9 mD along each segment.

Visualization 408 illustrates a fracture pressure margin (psia) along the segments of the reservoir 102 as determined using the method 200. As one can see, the reservoir 102 in this example comprises 15 segments with an equal fracture pressure margin of 900 psia along each segment. The margin may be defined as fracture pressure minus annulus injection pressure.

Visualization 410 illustrates the number of outlets (e.g., number of holes) for each segment of the reservoir 102 resulting from executing the method 200. As one can see, the reservoir 102 in this example comprises 15 segments. The portion of the liner 104 corresponding to the first segment comprises 10 holes. The portion of the liner 104 corresponding to the second segment comprises 11 holes. The portion of the liner 104 corresponding to the third segment comprises 12 holes. The portions of the liner 104 corresponding to the fourth and fifth segments comprise 14 holes each. The portion of the liner 104 corresponding to the sixth segment comprises 16 holes. The portion of the liner 104 corresponding to the seventh segment comprises 17 holes. The portion of the liner 104 corresponding to the eighth segment comprises 11 holes. The portion of the liner 104 corresponding to the ninth segment comprises 12 holes. The portions of the liner 104 corresponding to the tenth and eleventh segments comprise 13 holes each. The portion of the liner 104 corresponding to the twelfth segment comprises 14 holes. The portions of the liner 104 corresponding to the thirteenth, fourteenth and fifteenth segments comprise 15 holes each.

Visualization 412 illustrates the thickness (ft) along the segments of the reservoir 102 resulting from executing the method 200. As one can see, the reservoir 102 in this example comprises 15 segments with an equal thickness of 50 ft along each segment.

FIG. 5 illustrates visualizations 502-508 associated with the construction of a liner 102 in accordance with embodiments of the present disclosure.

Visualization 502 illustrates a distribution of the reservoir pressure (psia) along the segments of the reservoir 102 as determined using the method 200. As one can see, the reservoir 102 in this example comprises 15 segments, wherein in each segment a Pres of 4000 psia is present. The Pwf in each segment is 5000 psia. The Liner pressure in the first 5 segments is larger than 5000 psia but decreases slowly towards 5000 psia at the last 5 segments.

Visualization 504 illustrates the liner rates (bpm) along the segments of the reservoir 102 resulting from executing the method 200. As one can see, the liner rate starts at 16 bpm at the first segment and linearly decreases to 1 bpm at the final fifteenth segment.

Visualization 506 illustrates the initial skin along the segments of the reservoir 102 as determined using the method 200. As one can see, the reservoir 102 in this example comprises 15 segments with initial skin of zero along each segment.

Visualization 508 illustrates the retention time (min) along the segments of the reservoir 102 resulting from executing the method 200. As one can see, the retention time starts at slightly over 0 min at the first segment and increases to roughly 42.5 min at the final fifteenth segment.

FIG. 6 illustrates visualizations 602-608 associated with the construction of a liner 102 in accordance with embodiments of the present disclosure.

Visualization 602 illustrates a distribution of the outlet distances (e.g., hole distances in ft) along the segments of the reservoir 102 as determined using the method 200. As one can see, the reservoir 102 in this example comprises 15 segments.

The portion of the liner 104 corresponding to the first segment comprises a hole distance of 85 ft. The portion of the liner 104 corresponding to the second segment comprises a hole distance of 75 ft. The portion of the liner 104 corresponding to the third segment comprises a hole distance of 70 ft. The portions of the liner 104 corresponding to the fourth and fifth segments comprise a hole distance of 62 and 60 ft. The portion of the liner 104 corresponding to the sixth segment comprises a hole distance of 52 ft. The portion of the liner 104 corresponding to the seventh segment comprises a hole distance of 49 ft. The portion of the liner 104 corresponding to the eighth segment comprises a hole distance of 75 ft. The portion of the liner 104 corresponding to the ninth segment comprises a hole distance of 72 ft. The portions of the liner 104 corresponding to the tenth and eleventh segments comprise a hole distance of 65 ft each. The portion of the liner 104 corresponding to the twelfth segment comprises a hole distance of 60 ft. The portions of the liner 104 corresponding to the thirteenth, fourteenth and fifteenth segments comprise a hole distance of 58 ft and 55 ft each.

Visualization 604 illustrates the jet velocity (m/s) along the segments of the reservoir 102 resulting from executing the method 200. As one can see, the jet velocity starts at 40 m/s at the first segment and decreases to 15 m/s at the final fifteenth segment.

Visualization 606 illustrates the pressure drop (dP) for the outlets (psia) along the segments of the reservoir 102 resulting from executing the method 200. As one can see, the dP starts at roughly 200 psia at the first segment and decreases in a cubic manner to 25 psia at the final fifteenth segment.

Visualization 608 illustrates the outlet area (e.g., holes) in mm² along the segments of the reservoir 102 resulting from executing the method 200. As one can see, the hole area starts at 70 mm² at the first segment and linearly increases to 190 mm² at the thirteenth segment before slightly decreasing and saturating at 180 mm² at the fourteenth and fifteenth segment.

As used herein the term “and/or” includes any and all combinations of one or more of the associated listed items and may be abbreviated as “/”.

Although some aspects have been described in the context of an apparatus, it is clear that these aspects also represent a description of the corresponding method, where a block or device corresponds to a method step or a feature of a method step. Analogously, aspects described in the context of a method step also represent a description of a corresponding block or item or feature of a corresponding apparatus.

Embodiments of the present disclosure may be implemented on a computer system. The computer system may be a local computer device (e.g., personal computer, laptop, tablet computer or mobile phone) with one or more processors and one or more storage devices or may be a distributed computer system (e.g., a cloud computing system with one or more processors and one or more storage devices distributed at various locations, for example, at a local client and/or one or more remote server farms and/or data centers). The computer system may comprise any circuit or combination of circuits. In one embodiment, the computer system may include one or more processors which can be of any type. As used herein, processor may mean any type of computational circuit, such as but not limited to a microprocessor, a microcontroller, a complex instruction set computing (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, a graphics processor, a digital signal processor (DSP), multiple core processor, a field programmable gate array (FPGA), or any other type of processor or processing circuit. Other types of circuits that may be included in the computer system may be a custom circuit, an application-specific integrated circuit (ASIC), or the like, such as, for example, one or more circuits (such as a communication circuit) for use in wireless devices like mobile telephones, tablet computers, laptop computers, two-way radios, and similar electronic systems. The computer system may include one or more storage devices, which may include one or more memory elements suitable to the particular application, such as a main memory in the form of random-access memory (RAM), one or more hard drives, and/or one or more drives that handle removable media such as compact disks (CD), flash memory cards, digital video disk (DVD), and the like. The computer system may also include a display device, one or more speakers, and a keyboard and/or controller, which can include a mouse, trackball, touch screen, voice-recognition device, or any other device that permits a system user to input information into and receive information from the computer system.

Some or all of the method steps may be executed by (or using) a hardware apparatus, like for example, a processor, a microprocessor, a programmable computer or an electronic circuit. In some embodiments, some one or more of the most important method steps may be executed by such an apparatus.

Depending on certain implementation requirements, embodiments of the present disclosure can be implemented in hardware or in software. The implementation can be performed using a non-transitory storage medium such as a digital storage medium, for example a floppy disc, a DVD, a Blu-Ray, a CD, a ROM, a PROM, and EPROM, an EEPROM or a FLASH memory, having electronically readable control signals stored thereon, which cooperate (or are capable of cooperating) with a programmable computer system such that the respective method is performed. Therefore, the digital storage medium may be computer readable.

Some embodiments according to the present disclosure comprise a data carrier having electronically readable control signals, which are capable of cooperating with a programmable computer system, such that one of the methods described herein is performed.

Generally, embodiments of the present disclosure can be implemented as a computer program product with a program code, the program code being operative for performing one of the methods when the computer program product runs on a computer. The program code may, for example, be stored on a machine-readable carrier.

Other embodiments comprise the computer program for performing one of the methods described herein, stored on a machine-readable carrier.

In other words, an embodiment of the present disclosure is, therefore, a computer program having a program code for performing one of the methods described herein, when the computer program runs on a computer.

A further embodiment of the present disclosure is, therefore, a storage medium (or a data carrier, or a computer-readable medium) comprising, stored thereon, the computer program for performing one of the methods described herein when it is performed by a processor. The data carrier, the digital storage medium or the recorded medium are typically tangible and/or non-transitory. A further embodiment of the present disclosure is an apparatus as described herein comprising a processor and the storage medium.

A further embodiment of the present disclosure is, therefore, a data stream or a sequence of signals representing the computer program for performing one of the methods described herein. The data stream or the sequence of signals may, for example, be configured to be transferred via a data communication connection, for example, via the internet.

A further embodiment comprises a processing means, for example, a computer or a programmable logic device, configured to, or adapted to, perform one of the methods described herein.

A further embodiment comprises a computer having installed thereon the computer program for performing one of the methods described herein.

A further embodiment according to the present disclosure comprises an apparatus or a system configured to transfer (for example, electronically or optically) a computer program for performing one of the methods described herein to a receiver. The receiver may, for example, be a computer, a mobile device, a memory device or the like. The apparatus or system may, for example, comprise a file server for transferring the computer program to the receiver.

In some embodiments, a programmable logic device (for example, a field programmable gate array) may be used to perform some or all of the functionalities of the methods described herein. In some embodiments, a field programmable gate array may cooperate with a microprocessor in order to perform one of the methods described herein. Generally, the methods are preferably performed by any hardware apparatus.