RU2590265C2 - Systems and methods for assessment of moments of penetration of fluid in locations of production wells - Google Patents

Abstract

FIELD: mining.

SUBSTANCE: invention relates to estimation of moments of penetration of fluid in location of producer. More specifically present invention relates to estimation of moments of penetration of fluid in location of producer based on simulation of distribution of fluid. Method includes identification of tracking data current line; calculation of average time of current lines run in each cell network based on tracking data current line; identification of shortest or fastest current line for production well using average time of current lines run in each cell network; calculation of average time of flight for shortest or fastest line current through each traverse cell network using processor computer; evaluation of fluid invasion point in producer, using data modelling distribution of fluid and mean time span for shortest or fastest current line.

EFFECT: technical result consists in increase of accuracy of estimating moments of penetration of fluid in location of producer based on simulation of distribution of fluid.

20 cl, 2 tbl, 13 dwg

Description

CROSS REFERENCE TO RELATED APPLICATIONS

No.

STATEMENT REGARDING THE STUDY FINANCED FROM THE FEDERAL BUDGET

Not applicable.

FIELD OF THE INVENTION

The present invention generally relates to estimating fluid breakthroughs at a production well location. More specifically, the present invention relates to estimating fluid breakthroughs at a production well location based on fluid distribution modeling.

BACKGROUND OF THE INVENTION

Various systems and methods are known for estimating the moment of fluid breakthrough at the location of a producing well, including model adaptation (HM). Model Adaptation (HM) is a systematic procedure for changing the reservoir simulation model to reproduce the dynamic response of the field. In HM applications and adapting a field model to production data, the main tasks are: a) integration of production data in the field model; b) flexibility, cost-effectiveness and computational efficiency; and c) full load of dynamic data.

In the last decade, HM technology has been rapidly developed and has received significant recognition and expansion from the traditional (i.e., manual, deterministic) approach, mainly based on stratigraphic methods, to new developments like probabilistic modeling, HM based on the sensitivity tube method based on current / gradient and experimental model.

The HM workflow largely considers minimizing the mismatch between the measured and simulated dynamic response of the fluid (e.g., oil or water) in a separate production well as one of the inverse main goals. In studies of enhanced oil recovery (EOR) through water injection, for example, the response mismatch is a differential or integrated water cut curve with two main characteristics: 1) the moment of fluid breakthrough and 2) the direction and shape of the response. While both characteristics are important variables in minimizing discrepancies, the moment of fluid breakthrough is what reveals the greatest impact on productivity economies. Moreover, the interval (that is, the time frame) of the fluid breakthrough is always burdened with uncertainty, which makes the assessment effort with the highest possible confidence even more significant. In fact, it is advisable to consider the moment of breakthrough as a first-order effect in HM dynamic well data, and fluctuations in the directional / shape curve as a second-order effect, since they mainly affect the operating conditions.

Despite advances in HM technology, this is still undoubtedly the most time-consuming aspect of model building / simulation, and the HM flowchart faces many challenges that include:

i) non-linear results between production response and reservoir characteristics;

ii) ambiguous decisions that require a definition of some kind of ″ uniqueness ″;

iii) the relative effects of key parameters may not be apparent;

iv) conditions are not limited, and uncertainties in variables are rarely known; and

v) production data may be erroneously and initially distorted.

SUMMARY OF THE INVENTION

The present invention thus meets the above needs and overcomes one or more of the drawbacks of the prior art by providing systems and methods for estimating fluid breakthroughs at a production well location based on fluid distribution modeling.

In one embodiment, the present invention includes a method for estimating a fluid breakthrough in a production well based on fluid distribution simulation data, comprising: i) identifying flow line tracking data; ii) calculating the average travel time in each cell of the network based on streamline tracking data; iii) the identification of the shortest or fastest streamline for a given production well, using the average travel time of the streamline in each cell of the network; iv) calculating the average transit time for the shortest or fastest flow line through each cell passed through the network using a computer processor, and v) estimate the moment of fluid breakthrough in the production well using fluid propagation simulation data and the average transit time for the shortest or fastest flow line.

In another embodiment, the present invention includes a non-volatile program storage device materially carrying computer-executable instructions for estimating a breakthrough moment in a production well. Commands are executed to: i) identify streamline tracking data; ii) calculating the average travel time in each cell of the network based on streamline tracking data; iii) the identification of the shortest or fastest streamline for a given production well, using the average travel time of the streamline in each cell of the network; iv) calculating the average flight time for the shortest or fastest streamline through each cell passed through the network using [computer processor]; and v) estimating the moment of fluid breakthrough in the producing well using fluid propagation simulation data and average transit time for the shortest or fastest flow line.

Additional aspects, advantages, and embodiments of the present invention will become apparent to those skilled in the art from the following description of various embodiments and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is described below with reference to the accompanying drawings, in which like elements are denoted by like reference numerals and in which:

FIG. 1 is a flowchart illustrating an embodiment of a method for implementing the present invention.

FIG. 2A illustrates the speed and direction of fluid propagation through a wide sand pocket.

FIG. 2B is the velocity and direction of fluid propagation through a narrow sand pocket.

FIG. Figure 3 illustrates an example of fluid propagation through the sand fraction of a facies model during the initial modeling phase.

FIG. 4A illustrates a synthesized 2D permeability model 2500 network cells (50 × 50) and a five-spot well pattern (1 injection well (I) and 4 wells producing (P ₁ -P _4)).

FIG. 4B illustrates a simulation of fluid propagation through the 2D permeability model of FIG. 4A from the injection well (I) with respect to the number of iterations (2500) that the simulation was launched.

FIG. 5 illustrates a possible distribution of streamlines in a five-point grid of wells in FIG. 4B.

FIG. 6 illustrates the travel time of a streamline along its arc lengths in a given network cell (i, j, k) of a 2D permeability model.

FIG. 7A illustrates the observed (measured) water cut curve for a production well P ₁ in FIG. 4A.

FIG. 7B illustrates the observed (measured) water cut curve for a production well P ₂ in FIG. 4A.

FIG. 7C illustrates the observed (measured) water cut curve for the production well P ₃ in FIG. 4A.

FIG. 7D illustrates the observed (measured) water cut curve for a production well P ₄ in FIG. 4A.

FIG. 8 is a functional diagram illustrating an embodiment of a system for implementing the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The subject matter of the invention is described with specificity, however the description itself is not intended to limit the scope of the invention. Thus, the patented subject matter can also be implemented in other ways, including other steps or combinations of steps similar to those described in this document, in combination with other modern or promising technologies. In addition, although the term ″ step ″ can be used in this document to describe the various elements of the applied methods, this term should not be interpreted as implying any specific order among or between the various steps disclosed in this document, unless otherwise expressly limited to this description in relation to a particular order. While the present invention can be applied in the oil and gas industry, it is not limited to this and can also be applied in other industries to achieve similar results.

The present invention includes systems and methods for estimating fluid breakthroughs at production well locations based on fluid propagation modeling. The present invention includes modeling a fluid distribution that is typically static and representing an invasion moment (s) for a fluid injected into an injection well (s) to reach a production well (-). Modeling makes it possible to fully consider facies modeling, which retains control over the lithological integrity of geological models by directly restricting modeling during facies distribution. The simulation also preserves the stochasticity of the propagation of the fluid front. Despite the static nature of this simulation, stochastic sampling of fluid front motion is performed using uniform distribution.

The present invention converts the fluid invasion moment (s) (specified by simulations in repetition units) into a physical time interval (specified, for example, in days, weeks, months ...) that is compatible with the well’s history of operation. Thus, the present invention provides new opportunities for quickly evaluating valuable characteristics of well productivity in a quick and cost-effective manner. For example, a quick and accurate estimate of fluid breakthrough moment (s) pertaining to a particular field model can be achieved before a complete inversion begins. Such an assessment will provide valuable information to well operators regarding the dynamics of well valves, especially in EOR water / gas injection projects in which managing oil and water / gas production offers significant economic benefits.

In order to achieve rapid evaluation points (s) fluid breakthrough (T ^BT), the present invention uses a combination of tracking the current line and the corresponding time of flight ( "TOF") during the simulation. Thus, the present allows a quick approximation of fluid breakthrough times by running simulations and one repetition of tracking the streamline in an automated model adaptation (″ AHM ″) that takes into account streamlines for the field model.

DESCRIPTION OF THE METHOD

With reference to FIG. 1, a flowchart illustrates an embodiment of a method 100 for implementing the present invention.

At step 102, fluid distribution modeling (″ FPS ″) is performed. One technique for performing FPS is based on an algorithm in the RGeoS software package developed by D. Renard. This FPS algorithm simulates the propagation of several fluids known in injection and / or production wells, which are provided with facies information known in the nodes of a regular network, and seeks to allow the fluid encountered in wells (e.g., in an injection well) to grow or expand spatially. The speed and direction of growth depends on the size of the sand pockets that can be filled. In FIG. 2, for example, the actual velocity and direction of fluid propagation through a wide sand pocket (FIG. 2A) and a narrow sand pocket (FIG. 2B) are shown. The larger the pockets 206, 208, there is faster growth. Velocity vectors 202, 204 are used in the FPS algorithm. This algorithm is designed to perform some modeling of a numerical variable using the Eden modeling technique. This technique provides a faster alternative solution for a multiphase fluid flow simulation program. This technique combines an example of a dual medium ″ black and white ″, where white represents sand and black represents clay with one or more injection wells and one or more production wells, as shown in FIG. 3. In this example, locations of sand facies 302, 304, 306 and two injection wells 307, 308 are shown.

Now, with reference to FIG. 4A, a synthesized 2D permeability model is shown with 2,500 grid cells (50 × 50) and a five-point grid of wells (1 injection well (I) and 4 production wells (P ₁ -P ₄ )). This FPS algorithm was used in 2500 repetitions, since one cell of this model is filled in one repetition. In FIG. 4B modeling fluid distribution through the 2D distribution model of FIG. 4A from the injection well (I) is shown relative to the number of repetitions (2500) by which this simulation was run. In FIG. 5 shows one possible distribution of streamlines in a five-point grid of wells in FIG. 4B.

In order to implement the FPS algorithm as a fast trusted estimate of the moment of fluid breakthrough in the AHM inversion in the water flooding curves, the transformation of the fluid invasion moment (s) into the physical time interval (-) should be considered with the following basic assumptions:

i) TOF streamlines are a key factor in normalization;

ii) tracking TOF from the production well (-) is the volume of the well drained; and

iii) tracking fluid from the injection well provides an estimate of the displacement.

To estimate the moment of fluid breakthrough in the production well, it is assumed that the following calculations are completed for this model of the field using any technique well known in the art to track flow lines from direct modeling of pressure and fluid velocity: a) calculation of the moment of fluid invasion ( that is, step 102); and b) a first repetition of streamline tracking and TOF calculation (i.e., step 106). These calculations will give a) the moment of invasion of the fluid from the FPS algorithm, given the number of repetitions of the simulation (taking 1 repetition per network cell); and b) the total number of streamlines passing through any cell in the field model network with coordinates (i, j, k).

In step 104, the results of the FPS data from step 102 are identified, which include the fluid invasion moment specified by the number of simulation repetitions required by the fluid to reach any production well (P _m ) from the injection well through one or more network cells representing a reservoir property model.

) для каждого сегмента линий тока ( $$\psi \begin{array}{c}i,j,k\\ m,n\end{array}$$

) в каждой ячейке сети, индекс ячейки сети и общее число ячеек сети, пересекаемых всеми линиями тока, соединяющими нагнетательную скважину с добывающей скважиной. $$$$

Со ссылкой на Фиг. 6, показано время пробега линии тока вдоль по ее длине дуги в данной ячейке сети 2D модели проницаемости. Индексы (n) и (m) пробегают все сегменты линий тока в каждой ячейке сети и во всех добывающих скважинах, соответственно (n=[1..N_SLN], а m=[l..N_p]). Время пробега для сегмента линий тока в каждой ячейке сети может быть вычислено посредством интегрирования ″медленности″ индикатора линии тока вдоль каждой траектории линии тока, используя следующее уравнение:In step 106, streamline tracking data is identified using any well-known technique that includes the number of streamline segments crossing each network cell (N _SLN ), travel time ( $$\partial \tau$$

) for each segment of streamlines ( $$\psi \begin{array}{c}i,j,k\\ m,n\end{array}$$

) in each cell of the network, the index of the network cell and the total number of network cells crossed by all streamlines connecting the injection well to the producing well. $$$$

With reference to FIG. 6, the travel time of the streamline along its arc length in a given cell of the network of a 2D permeability model is shown. Indexes (n) and (m) run through all segments of streamlines in each network cell and in all production wells, respectively (n = [1..N _SLN ], and m = [l..N _p ]). The travel time for the streamline segment in each network cell can be calculated by integrating the “slowness” of the streamline indicator along each streamline path using the following equation:

(1) $$\partial \tau \left(\psi \begin{array}{c}i,j,k\\ m,n\end{array}\right)={\displaystyle \underset{\psi }{\int }\partial s\left(x\right)}dr$$

(one)

соответствует ″медленности″ индикатора линии тока (определяемой как обратное от скорости индикатора), $$dr$$

соответствует длине дуги сегмента линии тока ( $$\psi \begin{array}{c}i,j,k\\ m,n\end{array}$$

) между местами входа и выхода на ограничивающей поверхности ячейки сети с координатами (i, j, k).Where $$\partial s(x)$$

corresponds to the ″ slowness ″ of the streamline indicator (defined as the inverse of the indicator speed), $$dr$$

corresponds to the length of the arc of the streamline segment ( $$\psi \begin{array}{c}i,j,k\\ m,n\end{array}$$

) between the places of entry and exit on the bounding surface of the network cell with coordinates (i, j, k).

) вычисляют, учитывая все сегменты линий тока, пересекающих каждую ячейку сети, что может быть вычислено, используя следующее уравнение:At step 108, the average travel time of the streamline in each network cell ( $$\partial \tilde{\tau }$$

) are calculated, taking into account all segments of streamlines crossing each cell of the network, which can be calculated using the following equation:

(2) $$\partial \tilde{\tau }=\frac{\mathrm{one}}{N_{SLN}}{\displaystyle \sum _{n=\mathrm{one}}^{N_{SLN}}\partial \tau \left(\psi \begin{array}{c}i,j,k\\ m,n\end{array}\right)}$$

(2)

является временем пробега для каждого сегмента линий тока в каждой ячейке сети из этапа 106.where (N _SLN ) is the number of streamline segments crossing each network cell from step 106, and $$\partial \tau \left(\psi \begin{array}{c}i,j,k\\ m,n\end{array}\right)$$

is the travel time for each segment of streamlines in each cell of the network from step 106.

) в ячейках сети, пересекаемых линией тока между нагнетательной скважиной (I) и добывающей скважиной (P_m).At step 114, the shortest / fastest streamline is identified for each production well (P _m ) using the average travel time of the streamline in each cell of the network from step 108 and any well-known search algorithm. The shortest / fastest streamline is the streamline with the smallest sum of average travel times of streamlines ( $$\partial {\tilde{\tau }}^{\min }$$

) in the grid cells intersected by the streamline between the injection well (I) and the producing well (P _m ).

), пересекаемых кратчайшей/быстрейшей линией тока, идентифицированное на этапе 114, и их индексы из этапа 116 сохраняют.At 116, the total number of all network cells ( $${\widehat{N}}_{GC}{}^{\min }$$

) intersected by the shortest / fastest current line identified in step 114 and their indices from step 116 are stored.

) для кратчайшей/быстрейшей линии тока, идентифицированной на этапе 114, и общее число всех ячеек сети ( $${\widehat{N}}_{GC}{}^{\min }$$

), сохраненное на этапе 116, которое может быть вычислено, используя следующее уравнение:At step 118, the average TOF (<TOF> ^min ) for the shortest / fastest stream line identified at step 114 is calculated for each intersecting cell of the network using the smallest sum of average travel times of the stream lines ( $$\partial {\tilde{\tau }}^{\min }$$

) for the shortest / fastest stream line identified in step 114 and the total number of all network cells ( $${\widehat{N}}_{GC}{}^{\min }$$

) stored in step 116, which can be calculated using the following equation:

(3) $${〈TOF〉}^{\min }=\frac{\mathrm{one}}{{\widehat{N}}_{GC}^{\min }}{\displaystyle \sum _{u=\mathrm{one}}^{{\widehat{N}}_{GC}^{\min }}\partial {\tilde{\tau }}_u^{\min }}$$

(3)

where index (u) is the number of runs on all indexes of the network cells intersected by the shortest / fastest current line. The difference between the “fastest” and “slowest” current lines from the distribution of streamlines related to each production well (P _m ) corresponds to the difference between a uniform and non-uniform spatial distribution of formation properties, such as, for example, voids. The difference between the distribution of streamlines in FIG. 5 shows that the producing wells P ₂ and P _{3 are} connected to the injection well (I) through clearly different geological formations than the producing wells P ₁ and P ₄ , which can be compared with the underlying structure of the voids.

At step 120, method 100 determines whether all network cells intersected by the shortest / fastest current line have been considered. If all intersected cells of the network have not been considered, then method 100 returns to step 118. If all intersected cells of the network have been considered, then method 100 proceeds to step 124. Alternatively, steps 118 to 120 can be performed simultaneously for each intersected cell network.

At step 124, an estimate of fluid breakthrough time for each production well (Pm) is calculated by combining streamline tracking data from step 106 with FPS data from step 104, which can be calculated using the following equation:

(4) $$T^{BT}={〈TOF〉}^{\min }\times \frac{t_{INV}^{i,j,k}}{N_p}\times \frac{N_{SLN}^m}{N_{xyz}}$$

(four)

) представляют собой общее число ячеек сети, пересекаемых всеми линиями тока, соединяющими нагнетательную скважину (I) с добывающей скважиной (P_m), а ( $$t_{INV}^{i,j,k}$$

)представляют собой время вторжения флюида из этапа 104.where (N _xyz ) and (N _p ) are the total size of the reservoir model and the total number of production wells, respectively, (<TOF> ^min ) is the average TOF for the shortest / fastest streamline calculated in step 118, ( $$N_{SLN}^m$$

) represent the total number of grid cells intersected by all streamlines connecting the injection well (I) to the producing well (P _m ), and ( $$t_{INV}^{i,j,k}$$

) are the fluid invasion times from step 104.

At step 126, method 100 determines whether all production wells have been reviewed. If not all production wells (P _m ) have been considered, then method 100 returns to step 104. If all production wells (P _m ) have been considered, then method 100 ends. Alternatively, steps 104 to 126 may be performed at a time for each production well (P _m ).

EXAMPLE

With reference to the synthesized 2D permeability model in FIG. 4A, the observed (measured) watering curves for the model configuration in FIG 4A are given in FIG. 7A, 7B, 7C and 7D for each of the four production wells (P ₁ , P ₂ , P ₃ and P ₄ ).

Date / time data points along the x axis in FIG. 7A-7D corresponding to physical dates related to the water injection plan (water breakthrough data points) are presented below in Table 1.

Table 1 Data point Physical Date (dd / mm / yyyy) one 17/9/2000 2 6/6/2001 3 2/19/2002 four 10/10/2002 5 7/24/2003 6 4/4/2004 7 12/25/2004 8 9/9/2005

The observed moments of water breakthrough derived from FIG. 4A are given in Table 2 below. Moreover, Table 2 lists the water intrusion moments calculated by the FPS algorithm, the water breakthrough moments (T ^B7 ) calculated using the method proposed in FIG. 1 and the error corresponding to the result obtained by the method proposed in FIG. one.

table 2 Manufacturer Observed T ^BT (days) Invasion Time (reps) T ^BT proposed method (days) Accuracy (days /%) P1 263 2272 281.41 18.41 / + 7% P2 121 2027 124.63 15.73 / + 3% P3 263 2268 239.33 -23.67 / -9% P4 1043 2491 1105.58 62.58 / + 6%

The results show that the method proposed in FIG. 1, is able to quickly predict the moment of fluid breakthrough with an error of less than 10% for a given five-point grid of wells. The error achieved can be different (more / less) when the fluid distribution is applied through an area with significantly greater geological complexity, and the dynamic model combines a significantly larger number of production wells.

SYSTEM DESCRIPTION

The present invention may be implemented through computer-executable sequences of instructions, such as program modules, commonly referred to as software applications or computer-executable applications. The software may include, for example, routines, programs, objects, components, data structures, and so on, which perform separate tasks or implement separate abstract types of data. The DecisionSpace® interactive environment, which is commercial software provided by Landmark Graphics Corporation, can be used as an interface application for implementing the present invention. This software can also interact with other code segments to run various tasks in response to data received in combination with a source of received data. The software can be stored and / or transferred to any type of storage device, such as a CD-ROM, a magnetic disk drive, a memory device on a DEM and a semiconductor memory device (for example, various types of ROM or RAM). In addition, this software and its results can be transmitted over various transmission media, such as optical fiber, metal wire, and / or through any of a variety of data transmission networks, such as the Internet.

Moreover, those skilled in the art will appreciate that this invention can be applied with a variety of computing device configurations, including hand-held devices, multiprocessor systems, microprocessor or programmable consumer electronics, minicomputers, mainframes, and the like. Any number of computing devices and computer networks are suitable for use with the present invention. The present invention can be applied in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules can be located on both local and remote computer storage devices, including memory storage devices. The present invention may thus be implemented using various hardware, software, or a combination thereof, in a computing device or other processing system.

With reference to FIG. 8, a functional diagram illustrates an embodiment of a system for implementing the present invention on a computer. The system includes a computing unit, sometimes called a computing system, that comprises a storage device, application programs, a client interface, a video interface, and a processing module. The computing unit is just some example of a suitable computing environment and is not intended to offer any limitations regarding the scope of use or functionality of the present invention.

The storage device primarily stores application programs, which can also be described as program modules containing computer-executable instructions executed by a computing unit for implementing the present invention described herein and shown in FIG. 2. The storage device thus comprises a fluid breakthrough moment estimation module that provides the method shown and described with reference to FIG. 1, and combines the functionality of the remaining applications shown in FIG. 8. The fluid breakthrough moment estimation module, for example, can be used to perform many of the functions described with reference to method 100 in FIG. 1. The Decision Space® interactive environment can be used, for example, as an interface application for implementing the module for estimating the moment of fluid breakthrough and use the results of method 100 in FIG. one.

Although the computing unit is shown as having a generalized storage device, the computing unit typically includes various computer-readable media. By way of example, and not limitation, a computer-readable medium may comprise a computer storage device. A computer storage device may include a computer storage device in the form of a volatile and / or non-volatile storage device, such as read-only memory (ROM) and random access memory (RAM). A basic input / output system (BIOS), containing basic routines that help transfer information between elements in a computing unit, for example, during startup, is usually contained in ROM. RAM typically contains data and / or program modules that are immediately available and / or currently being processed by the processing module. By way of example, and not limitation, the computing unit includes application programs, other program modules, and program data in the operating system.

The components shown in the storage device may also be included in another removable / non-removable volatile / non-volatile computer storage medium or they may be implemented in a computing unit via an application programming interface (″ API ″) or cloud computing that may reside on a separate computing unit connected to the computing unit through a computing device or data network. By way of example only, a hard disk drive can read from or write to a non-removable non-volatile magnetic medium, a magnetic disk drive can read from or write to a removable, non-volatile magnetic disk, and an optical drive can read from or write to a removable, non-volatile optical a disc, such as a CD-ROM or other optical media. Other removable / non-removable, volatile / non-volatile computer storage media that may be used in an exemplary operating environment may include, but are not limited to, magnetic tapes, flash memory cards, universal digital disks, digital video tapes, solid state RAM , solid state ROMs and so on. The devices and associated computer storage media discussed above provide storage of machine-readable instructions, data structures, program modules and other data for the computing unit.

The user can enter commands and information into the computing unit through a user interface, which can be input devices, such as a keyboard and a positioning device, usually called a “mouse,” a ball pointer, or a touchpad. Input devices may include a microphone, a lever indicator, a satellite dish, a scanner, and the like. These and other input devices are often connected to the processing module via the system bus, but they can be connected via another interface and bus structures, such as a parallel I / O port or universal serial bus (USB).

A monitor or other type of display device may be connected to the system bus via an interface, such as a video interface. A graphical user interface (″ GUI ″) can also be used with a video interface to receive commands from the user interface and send commands to the processing module. In addition to the monitor, computers can also include other peripheral output devices, such as a speaker system and a printing device, which can be connected through the interface of the output peripheral devices.

Although many other internal components of the computing unit are not shown, those skilled in the art will recognize that such components and their wiring are well known.

Although the present invention has been described with reference to the present preferred embodiments, those skilled in the art will understand that this is not intended to limit the present invention to these embodiments. It follows that it is contemplated that various alternative embodiments and modifications may be made to the disclosed embodiments without departing from the spirit and scope of the invention as defined by the appended claims and their equivalents.

Claims (20)

1. A method for estimating the moment of fluid breakthrough in a production well based on fluid distribution modeling data, comprising:
identification of current line tracking data;
calculating the average travel time of the streamline in each cell of the network based on the tracking data of the streamline;
identification of the shortest or fastest streamline for the producing well using the average travel time of the streamline in each cell of the network;
calculating the average flight time for the shortest or fastest streamline through each intersected network cell using a computer processor; and
Estimation of the moment of fluid breakthrough in the production well, using fluid distribution simulation data and the average transit time for the shortest or fastest flow line. 2. The method according to claim 1, wherein the fluid propagation simulation data comprises a fluid invasion time, represented by the number of simulation repetitions required to reach the production well from the injection well through one or more network cells representing a reservoir property model. 3. The method of claim 1, wherein the streamline tracking data comprises the number of streamline segments intersecting each network cell, travel time for each streamline segment in each network cell, indices for each network cell, and the total number of network cells intersected by all streamlines connecting the injection well to the producing well. 4. The method according to p. 3, in which the average travel time of the current line in each cell of the network is calculated by the formula
$$\partial \tilde{\tau }=\frac{\mathrm{one}}{N_{SLN}}{\displaystyle \sum _{n=\mathrm{one}}^{N_{SLN}}\partial \tau \left(\psi \begin{array}{c}i,j,k\\ m,n\end{array}\right)}$$

, (2)
where N _SLN is the number of streamline segments intersecting each network cell, and $$\partial \tau \left(\psi \begin{array}{c}i,j,k\\ m,n\end{array}\right)$$

is the travel time for each segment of streamlines in each network cell. 5. The method according to claim 1, in which the shortest or fastest streamline for the producing well is a streamline with the smallest sum of the average travel times of the streamline in the network cells intersected by the streamline between the injection well and the production well. 6. The method according to claim 5, in which the average transit time for the shortest or fastest stream line is calculated for each intersected network cell using the smallest sum of the average travel times of the stream line for the shortest or fastest stream line and the total number of network cells crossed by the shortest or fastest current line. 7. The method according to p. 6, in which the average flight time for the shortest or fastest stream line is calculated by the formula
$${〈TOF〉}^{\min }=\frac{\mathrm{one}}{{\widehat{N}}_{GC}^{\min }}{\displaystyle \sum _{u=\mathrm{one}}^{{\widehat{N}}_{GC}^{\min }}\partial {\tilde{\tau }}_u^{\min }}$$

,
Where $${\widehat{N}}_{GC}^{\min }$$

represents the total number of all network cells crossed by the shortest or fastest current line, $$\partial {\tilde{\tau }}_u^{\min }$$

represents the smallest sum of average travel times for the shortest or fastest streamline, and u represents the number of runs across all network cell indices crossed by the shortest or fastest current line. 8. The method according to p. 2, in which the moment of breakthrough of the fluid in the producing well is estimated by the formula
$$T^{BT}={〈TOF〉}^{\min }\times \frac{t_{INV}^{i,j,k}}{N_p}\times \frac{N_{SLN}^m}{N_{xyz}}$$

,
where N _xyz and N _p are the total size of the reservoir model and the total number of production wells, respectively, <TOF> ^min is the average transit time for the shortest or fastest flow line, $$N_{SLN}^m$$

represent the total number of grid cells intersected by all streamlines connecting the injection well to the producing well, and $$t_{INV}^{i,j,k}$$

represent fluid invasion time. 9. The method of claim 1, further comprising repeating the steps of claim 1 for each production well. 10. The method of claim 1, wherein the reservoir property model is a permeability model. 11. A permanent storage device materially carrying computer-executable instructions for estimating a fluid breakthrough moment in a production well based on fluid distribution simulation data; instructions are executed to implement:
identification of current line tracking data;
calculating the average travel time of the streamline in each cell of the network based on the tracking data of the streamline;
identification of the shortest or fastest streamline for the producing well using the average travel time of the streamline in each cell of the network;
calculating the average flight time for the shortest or fastest streamline through each intersected network cell; and
Estimates of fluid breakthrough in a production well using fluid propagation simulation data and average transit time for the shortest or fastest streamlines. 12. The program carrier device according to claim 11, wherein the fluid propagation simulation data comprises a fluid invasion time represented by the number of simulation repetitions required to reach the production well from the injection well through one or more network cells representing a reservoir property model. 13. The program medium device according to claim 11, wherein the streamline tracking data comprises the number of streamline segments intersecting each network cell, travel time for each streamline segment in each network cell, indices for each network cell, and the total number of network cells, crossed by all streamlines connecting the injection well to the producing well. 14. The device media program according to p. 13, in which the average travel time of the stream line in each cell of the network is calculated by the formula
$$\partial \tilde{\tau }=\frac{\mathrm{one}}{N_{SLN}}{\displaystyle \sum _{n=\mathrm{one}}^{N_{SLN}}\partial \tau \left(\psi \begin{array}{c}i,j,k\\ m,n\end{array}\right)}$$

, (2)
where N _SLN is the number of streamline segments intersecting each network cell, and $$\partial \tau \left(\psi \begin{array}{c}i,j,k\\ m,n\end{array}\right)$$

is the travel time for each segment of streamlines in each network cell. 15. The program carrier device according to claim 11, wherein the shortest or fastest streamline for the producing well is the streamline with the smallest sum of the average travel times of the current line in the network cells intersected by the current line between the injection well and the producing well. 16. The program carrier device according to claim 15, wherein the average transit time for the shortest or fastest current line is calculated for each intersected network cell using the smallest sum of the average travel times of the current line for the shortest or fastest current line and the total number of network cells crossed by the shortest or the fastest current line. 17. The device of the program carrier according to claim 16, in which the average flight time for the shortest or fastest streamline is calculated by the formula
$${〈TOF〉}^{\min }=\frac{\mathrm{one}}{{\widehat{N}}_{GC}^{\min }}{\displaystyle \sum _{u=\mathrm{one}}^{{\widehat{N}}_{GC}^{\min }}\partial {\tilde{\tau }}_u^{\min }}$$

,
Where $${\widehat{N}}_{GC}^{\min }$$

represents the total number of all network cells crossed by the shortest or fastest current line, $$\partial {\tilde{\tau }}_u^{\min }$$

represents the smallest sum of average travel times for the shortest or fastest streamline, and u represents the number of runs across all network cell indices crossed by the shortest or fastest current line. 18. The device of the program carrier according to claim 12, in which the moment of breakthrough of the fluid in the producing well is estimated by the formula
$$T^{BT}={〈TOF〉}^{\min }\times \frac{t_{INV}^{i,j,k}}{N_p}\times \frac{N_{SLN}^m}{N_{xyz}}$$

,
where N _xyz and N _p are the total size of the reservoir model and the total number of production wells, respectively, <TOF> ^min is the average transit time for the shortest or fastest flow line, $$N_{SLN}^m$$

represent the total number of grid cells intersected by all streamlines connecting the injection well to the producing well, and $$t_{INV}^{i,j,k}$$

represent fluid invasion time. 19. The device of the program carrier according to claim 11, further comprising repeating the steps of claim 1 for each production well. 20. The device media program according to claim 11, in which the model of the properties of the reservoir is a model of permeability.

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