EA014140B1 - Method for field scale production optimization - Google Patents

Abstract

A method for enhancing the allocation of fluid flow rates among a plurality of well bores in fluid communication with at least one subterranean reservoir bed is disclosed (24). An objective function and system equations are generated which utilize constraint violation penalties associated with soft constraints. The soft constraints are constraints which may be violated if necessary to obtain feasible solutions for optimizing the objective function and the system equations. The fluid flow rates are then allocated among the well bores (30) as determined by the optimizing of the objective function and system equations. The fluid flow rates among well bores (30), particularly those exhibiting similar fluid characteristics, may be related to one another. Initial flow rates of components (oil, gas, water) and pressure in the well bore (30) may be determined by an initial simulation run.

Description

The present invention relates generally to methods for controlling hydrocarbon production from a field with wells, and more particularly, to methods for optimizing production by improving the distribution of fluid flow rates in wells.

Optimization is known at the scale of the field, in which they seek to optimize or improve the production of produced fluids, including hydrocarbons, from a field that contains one or more underground reservoirs. Boreholes or boreholes connect reservoir layers to surface facilities in which collected produced fluids are collected and processed. Typically, these produced fluids contain oil, gas, and water components. To adjust the distribution of flow rates in the wellbores in the field, chokes or flow control devices are used. The management of individual relative quantities and coefficients for the production of various components of oil, gas and water for an individual well can be carried out by adjusting the throttle to change the pressure in the wellbore.

For the production and processing of produced fluids, ground facilities are needed. These objects may contain devices such as separators, pumps, storage tanks, compressors, etc. Ideally, the cost of this equipment is minimized by using the smallest and cheapest ground facilities as possible. However, the processing power of the fluid must be large enough not to unduly limit the current flow rate of economically required oil and / or gas. Therefore, ideally, the distribution of the fluid flow in the wells is optimized to maximize monetary returns while meeting production constraints, such as those imposed by the fluid processing capacities of surface facilities.

In the optimization methods used, the optimal distribution of fluid flows in the wells is predicted for a given set of production constraints. First, a reservoir simulator is used to mathematically model the flow of fluids through a field containing reservoir reservoirs and wells. The simulated flow is used to establish component production curves or production equations for each well, which describe how the production rate of one component, such as water, refers to the production rate of another component, i.e. oil. Typically, a goal function is created that seeks to optimize a task, such as maximizing oil production or minimizing water production. The objective function contains the flow rates of the well, which are predicted by modeling the reservoir. A set of production constraints is defined, such as oil production tasks or production constraints on gas or water for a field. Constraining equations are formed to fulfill the specified manufacturing constraints. Well fluid flow must adhere to these production constraints. Then, to determine the optimal distribution of production rates in wells, the objective function is optimized through a procedure defined as an optimizer. The optimizer uses the production component equations of the well component and the constraint equations in the optimization process.

The first drawback of conventional field-wide optimization schemes is that for these production constraints, it may not be possible to have feasible optimization solutions. For example, some level of oil production may be preferable when producing no more than a certain amount of water. An acceptable solution to the objective function with this set of constraints may not be possible. In this case, one or more constraints must be adjusted and the collector simulator and optimizer run again to determine when a feasible solution is possible. Such iterative runs when solving numerous optimizations of the objective function are computationally cumbersome and undesirable.

The second problem in some optimization schemes is that although a feasible solution to the optimization of the objective function can be obtained, the results cannot be put into practice. For example, in the first run or in the first time step, the optimizer may decide that the first well should produce at a high level, while the second well should essentially be shut. In the next step, the optimizer may suggest that the second well should produce at a high level, while the first well should essentially be shut. Therefore, if we follow the distributions proposed by the optimizer, then production from wells may fluctuate. It is generally more practical if production from wells having similar fluid flow characteristics is carried out at an agreed level. This should minimize fluctuations in the time steps in production from associated wells.

A third disadvantage is that creating equations or flow curves for a component for producing fluids from a wellbore can be computationally cumbersome. One way to calculate these production curves is to create a submodel of the wells and surrounding reservoirs and an iterative solution for the current production rates of components, i.e. oil, gas and water, when the chokes are open and the pressure drop between the reservoirs and wells increases. Usually for the formation of each data point related to the extraction of one component

- 1 014140 relative to another component for a given pressure drop in the wellbore, several Newton iterations must be performed. Again, the pressure drop in the well depends on how open the throttle regulating the well is. This process is repeated repeatedly until a sufficient number of data points are calculated, possibly 30-50 data points, so that an equation or a complete flow curve is obtained. The optimizer then uses equations or flow curves to optimize the objective function. Formation, to create equations or flow curves, data points using these many Newton iterations is computationally expensive.

The present invention provides solutions to the aforementioned disadvantages of conventional field-wide optimization schemes. First, to create an feasible solution, the objective function and associated restrictive equations are formed, which can be solved with a single run of the optimizer. Secondly, to prevent significant fluctuations in well production between time stages of reservoir simulation, restrictive equations can be created that require the dependence of current production from similar wells. Finally, an effective method for generating equations or flow curves of a well component relating to current flow rates between components of a well fluid is described.

SUMMARY OF THE INVENTION

The present invention provides a method for improving the distribution of fluid flow rates to several wells connected via fluid to at least one subsurface reservoir. A fluid flow is simulated using a numerical reservoir simulator in at least one underground reservoir and in several wells connected by fluid to the underground reservoir. Formation of the flow rate equations of the component in accordance with the simulated flow in the wells. Production constraints are selected with at least one of the manufacturing constraints, ideally being a soft constraint that, if necessary, could be violated during the optimization process to provide an acceptable solution. Constraining equations are also generated corresponding to production constraints.

An objective function is generated that corresponds to the fluid flow in the wells. The objective function may also contain penalties for violation of constraints that correspond to soft constraints and soft constraint equations. Then, the objective function is optimized using component production equations and restrictive equations to determine an improved distribution of fluid production over the wells. If necessary, soft constraints can be violated to obtain an acceptable solution for optimizing the objective function. The presence of fines for violation of restrictions provides the possibility of violating soft restrictions, while the corresponding restrictive equations continue to be satisfied. Then the fluid flow rates are distributed among the wells in accordance with the definition obtained by optimizing the objective function.

Soft constraints may be prioritized with respect to which of the soft constraints should be the most difficult to violate, if necessary, in order to obtain an acceptable solution for optimizing the objective function. Fines for violation of restrictions in the objective function may be associated with weighted scale factors. Scale weights can be weighted according to prioritization for soft constraints so that breaking soft constraints with a higher priority is more difficult than breaking soft constraints with a lower priority.

Production rates between selected wells may be interdependent. In particular, wells exhibiting similar flow characteristics, for example, gas-oil ratio (SOC) or water-oil ratio (^ OK), may have interdependent well flow rates. Again, restrictive equations can be generated for these dependent well production rates. Then the improved distribution of production rates for dependent wells should be interdependent or interconnected.

According to another aspect of this invention, simulated wells comprise several completion elements and reservoir formations or reservoir formations comprise several reservoir elements. Run the reservoir simulator to determine the pressures in the elements of the reservoir and in the completion elements and to determine the flow of fluid in the completion elements of at least two components, i.e. oil and water caused by a drop in pressure between the elements of the reservoir and completion elements. Then, the flow rate data points of the fluid flow component are generated over the range of fluid flows for each well. Ideally, data points are generated by scaling and summing the fluid flows in the completion elements based on the flow rates of the component determined by the initial run of the simulator and depending on the extended range of pressure drops between the completion elements and the reservoir.

- 2 014140

An object of the present invention is to provide a method in which an objective function is created comprising at least one penalty for violation of restrictions corresponding to a soft restriction, which enables optimization of the objective function, while, if necessary, the soft restriction can be violated to obtain an acceptable solution for optimization.

Another objective is to formulate an objective function containing weighted fines for violations of restrictions that can be weighed accordingly, so that soft restrictions can be violated in the order of priority assignment.

Another task is to create a relationship between the current production rates for wells during optimization, so that after the optimization is performed, production rates for these wells are dependent, which leads to limited fluctuations in the production rate of these wells between time steps in modeling the reservoir.

Another task is to formulate the flow rate equations of the component, which are formed by scaling the flow rates of the component in individual completion elements based on flow rates originally determined during the simulation run of the reservoir, and depending on the range of changing pressure profiles in the well.

Brief Description of the Drawings

These and other objects, features and advantages of the present invention will become more apparent with respect to the following description, claims and the attached drawings, which illustrate:

FIG. 1 is a schematic drawing of a possible existing hydrocarbon field containing subsurface reservoirs that are fluidly coupled to the surface of the field with throttles used to control wellbore pressure and flow rates so that production from the field can be optimized;

FIG. 2 is a flow chart of a possible field-scale optimization method carried out according to this invention;

FIG. 3A and 3B show component production curves generated using the fast speed method of the present invention and component production curves generated using a computationally cumbersome Newton iterative method;

FIG. 4A and 4B are graphs depicting the dependence of well production between two wells having similar fluid characteristics.

A fluid connection is provided between the reservoirs 22 and 24 and the well 30, 32 and 34. The well 34 is connected only to the upper reservoir 22.

Throttles or well control devices 54, 56 and 60 are used to control fluid flow to and from respective wells 30, 32 and 34. As will be described more fully below, throttles 54, 56, and 60 also control pressure profiles in respective wells 30, 32, and 34. Although not shown, wells 30, 32, and 34 must be fluidly coupled to surface objects such as separators oil / gas / water, compressors, storage tanks, pumps, pipelines, etc. The flow rate of fluids through wells 30, 32, and 34 may be limited by the ability of the fluid to be processed by said surface facilities.

FIG. 2 is a flowchart illustrating the general steps used according to the field-scale optimization method of the present invention. Based on the principles contained in this description of the invention, specialists in the field of modeling reservoir formations can easily develop computer software to perform the method described in accordance with FIG. 2.

To simulate the fluid flow in the field 50, which contains reservoir reservoirs and wells (step 110), a reservoir simulator is used. Basically, to perform numerical modeling, such a reservoir model should contain thousands or even millions of individual elements. These individual elements include reservoir elements and well elements. Well elements contain certain completion elements that move the fluid back and forth between adjacent elements of the reservoir and other elements of the well that are fluidly connected to the throttle and ground objects (not shown).

On the model of the field, the initial and boundary conditions are determined. Said initial and boundary conditions include, for example, initial pressures and flow rates in reservoir elements and well elements, fluid components, viscosities, etc.

Then run a run (step 120) of modeling on the field model to calculate the characteristics of the fluid flow and reservoir for the time stage. In particular, fluid flow rates between reservoirs and wells are determined with respect to what are the pressures in the elements of the well and reservoir. Production wells will receive produced fluids from reservoirs containing oil, water and gas, which are delivered to the field’s onshore facilities. Injection wells may be used to create pressure in one or more reservoirs and / or to utilize water. also in

- 3 014140 wells, gas may be injected to provide for the production of a fluid carried out with gas. It will be apparent to those skilled in the art that many other operations affecting production can be simulated using a reservoir simulator, and these steps are included in the context of this invention.

The fluid flow rates of a component can be defined in terms of the flow of oil, gas, and water. Alternatively, the fluid components for which the flow is to be optimized can be composite components such as light (C ₃ -C ₄ ), medium (C ₅ -C ₈ ) and heavy (> Cd) hydrocarbons. As a possible embodiment, other possible combinations of components may contain non-hydrocarbon components such as H ₂ 8 and CO ₂ .

Then, component production equations for each well are calculated (step 130). These component flow equations describe the estimated flow of one fluid component relative to the flow of another fluid component over the expected range of flow rates for the well. Physically, throttles in a well can be opened or closed to increase or decrease the total output or inlet of fluid in relation to the well. When opening and closing the throttle, due to changes in pressure profiles in the well, the relative indicators of oil, gas and water extracted from the wellbore may be changed.

In FIG. 3A and 3B illustrate possible variations of the component production curves for the well. In FIG. The current gas flow rate in M8СР / О (millions of square cubic feet per day) relative to the current oil flow rate of 8ΤΒ / Ώ (barrels of the storage tank per day) is shown in Beyond. In FIG. ST shows the current water flow rate (8ΤΒ / Ο) relative to the current oil flow rate of 8ΤΒ / Ώ. The current gas flow rate relative to oil is relatively linear over a wide range of possible current oil flow rates. However, the current flow rate of water is non-linear with respect to the current flow rate of oil. A much larger amount of water is formed at higher oil production yields than at lower current oil production rates. High production yields correspond to the wide open throttle position.

In a preferred embodiment of this invention, a fast velocity method is used to generate individual points of component production data, which can then be used to quickly plot or generate component production equations. The method of fast speeds will be described in more detail below. It is obvious to those skilled in the art that other methods can be used in forming estimates as to how the production of one component can change relative to the current production rate of another component over the full range of well output.

The user must determine production constraints (step 140) for use with the field model. As a possible option, possible options for production constraints include (1) oil production at a given level; (2) gas production at a given level; (3) restricting gas production below a predetermined limit; (4) limiting water production below a predetermined limit; (5) limiting the injection of water to an amount related to water produced from a well; and (6) restricting gas injection above a predetermined limit to provide a gas lift. Additionally, these tasks and limitations can also be combined or scaled relative to each other.

Production restrictions may include hard or soft restrictions. Hard limits are restrictions that must not be violated. Soft restrictions are restrictions that, if necessary, can be violated to form an acceptable solution to the optimization problem. It may also be possible to determine the order in which it is preferable to violate, if necessary, soft restrictions to obtain an acceptable solution.

According to another aspect of the present invention, it may be determined (step 150) whether well flow rates of certain wells should be dependent. For example, wells having similar fluid characteristics, such as gas-oil ratio (SOC) or water-oil ratio (SOC), may be interdependent. The dependence of the current flow rates between wells should ensure the absence of arbitrary fluctuations in the current flow rates (or injection rates) between these wells between cycles.

Then form (step 160) restrictive equations from production constraints and in accordance with the dependent flow rates of the well. Form strict restrictive equations for those restrictions, the possibility of violation of which is not provided. Soft constraint equations are formed that correspond to soft constraints that contain fines for violation of constraints. Penalties for violation of constraints provide the ability to execute soft constraint equations, even when soft constraints must be violated to form an acceptable solution for optimization. The formation of this set of restrictive equations will be described in more detail below.

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At step 170, a goal function is created that seeks to optimize the task, such as oil production from field 50. The goal function ideally contains well component production rates as well as fines for constraint violations associated with soft constraint equations. With fines of soft constraints in the objective function, a weight scale factor can be associated. With appropriate weighting of the indicated weighting factors, priorities can be assigned for the order in which the corresponding soft constraints can be violated. Then, the objective function is optimized (step 180) by means of an optimization procedure (optimizer) to form an optimized distribution of fluid flow rates in the wells. To optimize the objective function, the optimizer uses the component debit equations calculated in step 130 and the constraint equations established in step 160.

Then, the optimized fluid flow rates and other fluid flow characteristics determined from the optimizer, for example fines for violation of restrictions, can be distributed to wells and reservoirs (step 190). Then, these optimized flow rates and characteristics can be set (step 200) as initial / boundary conditions at the next iterative time step in modeling the reservoir. Then, a large number of time steps are repeated steps 120-200 to provide improved field scale production until a sufficient period of time has elapsed, and then the simulation is completed. Now, the above steps will be described in more detail.

A. Creation of the objective function and restrictive equations.

1. The system of restrictive equations.

A linear programming system (bp) is a set of linear equations and linear constraints. A mixed integer programming system (M1P) is a set of linear or non-linear equations and constraints. In the present invention, in order to obtain an optimized objective function, it is preferable when it is necessary to find a solution for a set of nonlinear equations or constraints represented by piecewise linear functions, the LP system is improved by the M1P system. In this possible embodiment, to optimize the objective function, an open source software package is used in which the LR and M1P methods are used. In particular, in the present invention, a package called LF-§O1us is used, which is available at 1Bp: // split | C5.bsYap.ogd / 51aYc / ta111 / 1p-5o1us. They also use an alternative commercial solver program called XA, which is provided by §ip8C1 Software Technology Corporation, San Marino, CA. For specialists, it is obvious that other commercial L / MH optimizer packages can be used to optimize the objective function using fluid flow rates and restrictive conditions.

The constraint equations, the debit equations of the component, and the objective function are introduced into the optimizer. Then, the optimizer derives a feasible solution to the optimization problem containing an improved distribution of well production. Ideally, values are also inferred for violating all the soft constraints required to obtain a feasible optimization solution. Then the user can make appropriate changes to production restrictions or to the performance of ground facilities to reflect the value of breaking soft restrictions.

Search for the extremum of the objective function. A simple bp system can have the following form:

and subject to restrictions in the form

Στ [al-b {{,>, =} 0 (1) where ί is the index;

with ₁ - weight scale factor;

x ₁ - optimized parameters;

and ₁ is a constant factor and

B ₁ is a summable constant.

In one embodiment of this invention, the main variables are well flow rates. That is, flow rates in which components of fluid production, i.e., oil, water and gas, are extracted from the well. The flow rate equations of the component are preferably formed using the fast velocity method, which will be described below. The flow rate equations of a component describe how much of one component is transported through the well compared to the other component of the fluid. The current production rates of the components may remain linear relative to each other or may be non-linear in the possible range of well production yields. In the present invention, ideally, non-linear scaling is manipulated between the flow rates of a component or phase velocities through piecewise linear functions, defining the system as an M1P task. Production restrictions are set in the form of severe restrictions, the possibility of violation of which is not provided, and / or in the form of soft restrictions, for which, if necessary, the possibility of violation is provided to obtain a decision. Constraints may contain targets and production constraints. The target function is set according to the information provided by the user.

2. Setting the target function.

Basically, the objective function corresponds to the mathematical expression = (2)

I у к where ΟΒ1 is the objective function, which should be optimized;

ί is the number of fluid components in the well fluid;

- weight scale factor for the production of the ί-th component of the fluid in the well;

_) - the number of wells;

S.],., - the amount of the ί-th component, extracted _) -th well;

k - the number of fines for violation of restrictions;

_k - weight scale factor for a fine for violation of the k-th restriction and

SUR _to - penalty for violation of the k-th restriction.

In particular, the most feasible objective function for the LF / M1P system may consist of a weighted sum of the current production rates of oil, water and gas in general for the selected set of wells. In the present invention, the objective function may also contain penalty variables for violation of restrictions (CMS _to ), corresponding to the use of soft restrictions. The usual objective function can be expressed in the following mathematical form:

= + + O) ί ί ί к where ΟΒί is the objective function, which should be optimized;

_o - weight scale factor for oil production;

with. | _{about |} - the amount of oil produced by the ί-th well;

- weight scale factor for gas production;

with. | _{d |} - the amount of gas produced by the ί-th well;

- weight scale factor for water production;

t · - the amount of water produced by the ί-th well;

_k - weight scale factor for (penalty for violation) of k-th (restriction) and

SUR _to - penalty for violation of the k-th restriction.

Weighted scale factors or well production parameters can be defined by the user. For example, a user may define:

ν _ο = 1.0; ν ₉ = -0.1 and N „= - 0.2

These weighted scale factors correspond to maximizing the current oil flow rate while trying to minimize gas and water flow rates. In this case, the objective function increases by 1.0 for each barrel of the storage tank per day (8ΤΒ / Ώ) of the extracted oil (· _ο1 ι = 1.0) and is fined 0.2 for every million ordinary cubic feet per day (M8SE / O) gas and 0.1 for every 8ΤΒ / Ο of produced water. In this case, the units of the objective function is the combination of the units 8ΤΒ / Ο and M8CE / O. Ideally, the components of the objective function are normalized to produce a dimensionless objective function.

Another preferred method for processing this unit mismatch in the objective function uses economic information, if available. For example, if oil revenues are 225 / 8ΤΒ / Ο, gas revenues are 35 / M8SE / E, and each 8ΤΒ / Ώ of water costs $ 3.5, then ν _ο = 22.0; and ₉ = 3.0 and N „= - 3.5

In this case, the units of the objective function are monetary units ($) and are consistent. It is preferable to scale the weighted scale factors so that o is 1.0, therefore, the previous values of the well production rate should be normalized to 22.0, which gives ν _ο = 1.0; m _d = 0.136 and and _k = -0.159

3. Production restrictions.

The restrictions may be based on physical restrictions, such as restrictions on production from the well, restrictions on the rate of injection, or restrictions on the speed of the gas lift. Alternatively, restrictions can be defined to suit technical preferences, such as production / injection tasks for a group of wells. Other restrictions, as an option, for example, may include gas to oil ratios (ΟΟΚ), water to oil ratios (^ ΟΚ.), And restrictions on a subset of wells or completions.

Limitations of the LP / MGR system are classified as hard and soft restrictions. For example, stringent restrictions may be imposed on a pair of wells so that the combined maximum oil production is 5,000 8ΤΒ / Ώ. The aforementioned stringent restrictions are converted into the following restrictions LR / M! P:

<Ф * ^О1А 5,000 <5,000 (4)

- 6 014140 where * is the amount of oil produced from the first well; and _ the amount of oil produced from the second well.

4. Prioritization for soft constraints.

Soft restrictions are restrictions, the possibility of violation of which is provided if, and only if, there is no other way to fulfill the soft restrictions, while obtaining an acceptable solution for the system. Ideally, this violation of the restrictions will be the minimum possible that is required to obtain a solution. Violations of restrictions can occur if there are conflicting restrictions / tasks in the system.

The following situation is considered where the field has the following restrictions, including the task of oil production and the restriction on water treatment for a group of wells:

Oil production task = 7,500 8ΤΒ / Ώ. (5) Water restriction> 5,000 8ΤΒ / Ώ.

Perhaps, and most likely, there should be a point in the simulation where a group of wells will not be able to produce 7,500 8ΤΒ / Ό of oil without producing more than 5,000 8ΤΒ / Ώ of water. There is a tendency to produce more water in wells during well depletion. In this case, the optimizer will not report the absence of a solution, but instead provide the possibility of violating one of the soft restrictions. Preferably, a flag will be set to indicate that the restriction has been violated. Initially, which restriction is selected for violation can be determined by the user, as in this preferred embodiment of this invention.

The indicated problem for oil and the constraint conditions for water are transformed into the following three soft constraint equations:

Limit + + ^^ 7,500

Limitation

2; Чр = 011 (6) ν ^ ΡΛΟΙΆ, utgp ς LLP

Limitation

At the end of the objective function, add penalty variables for violations of the restrictions of the RMS _to :

0Βσ = ... - Μι ονΡι - and ₂ ονρ ₂ СУР ₃ (7) is subordinate:

those _k > 0, where \ ν _(: is the k-th weighting coefficient associated with the penalty for violation of the k-th restriction; and

RMS _k > 0, where RMS _k is a fine for violating the k-th restriction, which is associated with the k-m restrictive equation.

It should be noted that this setting leads to the zeroing of the variables of the RMS, since they have negative weights in the objective function, which makes them equivalent to hard constraints every time their execution is possible, i.e. when oil production is 7,500 8ΤΒ / Ό and water production is less than 5,000 8ΤΒ / Ώ.

Assume that the conditions of the reservoir are such that 5,100 8ΤΒ / Ώ of water must be produced to produce 7,500 8ΤΒ / Ώ of oil. In this case, there are two possibilities:

reduce production and fulfill the water limit, but ignore the oil task or complete the oil task, but produce more water than meets the water limit.

Whether the LR / MGR system chooses to reduce production or fulfill the water restriction depends on the coefficients or weighted scale factors \ ν _1: SUR variables _k . Assume that the restriction on the volume of water is absolute and that it is possible to reduce oil production to fulfill the water restriction. In this case, it is assumed that ν ₁ = 1, ν ₂ = 1 and \\ ₃ = 2. which corresponds to restriction 3 (restriction on water production), which has a higher priority than the other two restrictions (oil production problem). It should be noted that the weighting scale factor \\ _{3 is} given more weight than the other two weighting scale factors and ν ₂ associated with oil production. With a decrease in well flow rates to meet the water production limit, it is assumed that when water production is exactly 5,000 8ΤΒ / Ώ, oil production decreases to 7,400 8ΤΒ / Ώ. In this case, the RMS must be different from zero to fulfill the restriction 1, so that RMS1 = 100 is exactly fulfilled. With this setting, due to certain values of the coefficients \ ν _1: SUR, the LF / MGR system should choose a reduction in flow rates rather than producing more water. For the two indicated cases, the elements of the objective function should look as follows.

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If we neglect the task of oil production and it will be possible to reduce oil production to comply with water restrictions, then. _ν = ΡΧΟΩ2 __ / y _L ln ⁺ Yar = t1 - /, 400, ivRLO02 _ with legs

Jarshichieg + 5 p ^ h> a1eg 5,000

Stekhov = 100 CTE ₂ = 0, = O paths

ATS = ... - 1СУЕ1 - 1СУЕ ₂ - 2СТГ ₃ = ... - 100

If the task of oil production should be completed, but the possibility of violating the restrictions on water production should be provided, then

Yar ^ a + I _{P = 0} 1 / = 7,500 (10) ^ RKOV! ^ РЯ0В2 _{! =} С 1 _П0

Chrzicht / th + + ρ ^ τναΐη 'd, gii

SUG1 = O, SUG ₂ = 0, C7; _: = 100

ATS = ... - 1STE1 - 1STE ₂ - 2STG ₃ = ... - 200

Since everything else remains the same, a decrease in flow rates leads to a higher value (+100) of the objective function, the optimizer ΕΡ / ΜΙΡ should prefer a decrease in flow rates. An identical approach can be used to handle η soft constraints and arrange them in the required priority order with respect to the violation.

If the order in which soft restrictions are to be violated is not defined and no priorities are assigned, then all weighted scale factors are equal and no preferences are set as to the possibility of violating which restrictions is provided first of all. In this case, ^ 1 = ^ 2 = ^:, = 1. As an option, the first soft limit can be given the lowest priority, the second soft limit is set to a slightly higher priority, and the third soft limit is set to the highest priority. In this possible embodiment, the weighting factors are then set to values corresponding to 10x10 ^p , where p is the order of priority in which soft constraints can be violated. For example, u1 = 10x10 ¹ ; «2 = 10χ10 ² and ig3 = 10x10 ³

The general equation for the objective function is

ATS = ... - ΉιΟν ?! - m ₂ RMS ₂ - ISMS; (12)

Then the objective function with weighted scale factors becomes the following: ATS = ...- 10x10 ¹ SUE1-10x10 ² SUEg-10x10 ³ STG ₃ (13)

Preferably, these coefficients are normalized to specify values between 0 and 1. Normalization is partially based on the possible range of the penalty for violation of restrictions.

Constraint 1: 0 <= θνΡ _ηοπη ι <= 1

STR _PST = (STR-STRR _ahp ) / (STRP-Sakh-SUR ^ n) (14) or, since ΟνΡ ^ π is always zero, _Μ1 = 10χ10 _ρ / (STR _so1 ) (15)

Parameters 0νΡ] _ί optimized jointly with the other parameters in the optimization system (current debits / injection rate). Since any positive value 0νΡ] _ί imposes a penalty through an objective function, the system attempts to maintain the zero values ΟνΡ ^ 0νΡ] _ί gets a positive value if, and only if, there is no other way to get a feasible solution.

It should be noted that if there are no conflicting problems for optimization, then all the variables ΟνΡ will be zero, and soft constraints will be equivalent to hard constraints.

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The operators used by soft constraints are transformed into Lp / MGR equations as follows. ________________________________________________________________________

Op Soft criteria limitations Op The equation bp / p > IATRN> 5000 Water flow rate Is becoming < ς „<500 0 < CA5RK <10000 Gas flow rate Is becoming > H _d > 10000 01Ь₽Е = 7500 Oil production Is becoming <and > 4ο <7500 and Cho> 7500

It should be noted that the operator (=) is the target operator and must satisfy the condition (it accordingly calls the action) if the left side of the criteria is not equal to the right side of the criteria.

5. Establishing the relationship between the flow rate of the well.

The LR / MGR systems are strictly mathematical and, accordingly, do not carry any physical concept underlying the variables, equations, and constraints. Therefore, in some cases, the results of LR / MGR, although mathematically justified, may not have much practical meaning. Such a case may occur when the optimizer LF / MGR decides to significantly contain only one well in the group of wells, which all have insignificant differences in properties. This can lead to large flow rate fluctuations for individual wells between time steps. To prevent such a case, the present invention provides the ability to establish the dependence of the flow rate of wells with similar characteristics.

If it is determined that the well production should be dependent, then in addition to the existing restrictive equations, additional restrictive equations are established that establish the dependence of certain well production. For example, if there are wells that have fluid characteristics, such as gas-oil ratios (UN) and / or water-oil ratios (\ νθΡ). which are within a predetermined range of each other, the dependence of the flow rates of these wells can be established. Like the soft constraint equations described above, these flow rate dependence equations can contain weighted scale factors that are close to each other and contain penalties for breaking the constraints.

Now according to FIG. 4 A, for example, a well production rate with a maximum OOK (d ₁ ) is set, and it is possible to find the production rate of a dependent well (p. | ₂ ) in a shaded area. This is achieved by adding the following restrictions to the system:

(16) ^ 1 / where q ₁ , p. | ₂ - flow rates, dependent on each other;

_{1 1} £, 2 2 £ - the maximum possible value of flow rates;

KUR - fine for violation of the flow rate;

and - the value that determines the severity of dependence.

All CSDs are added to the objective function with a negative weight ov4 = ... ~ ^ m ₍₁₇ ) where in this certain possible variant those ₁ are chosen equal to -10.

and set:

This means that when ςι = ς * ι, then c. | ₂ should be in the range [d * _2tt , d * _2tax ]. The function £ is a simple linear function, as shown in FIG. 4B.

The present invention allows the user to change the threshold value of G, however, in most cases, 1 = 1.0 should act. With this setting, for a given 1 = 1.0, a well with a SOC of ₂ = 0.0 will not be independent and will have an independent scale rate of production, while at a different extremum, when OOK ₂ = OOK1, the shaded area in FIG. 4A should collapse in line, as shown in FIG. 4B, and the second wellbore will be forced to have a scale factor identical to the scale factor of wellbore 1.

- 9 014140

Another way to establish the dependence of the flow rate is to establish the dependence by scaling the flow rate in the group of wells by means of an identical coefficient. For example, the injection rates of all injection wells in the first group of injection wells and the current production rates of all production wells in the first group of production wells may be dependent. In this case, this dependence is not based on SOW or ^ OB; the dependence simply implies that when scaling a well’s production rate by a coefficient, other wells in the dependent group must scale by an identical coefficient.

For example, if a well in the first group of production wells is to cut production by half (possibly to fulfill another restriction), then all wells in the first group of production wells should cut production by half. Ideally, non-compliance with the rules for this dependence should have less weight in the LF / M1P system than certain restrictions. This means that flow dependencies may be violated to meet restrictions. Parameters can be used to determine the relative weights of constraints and flow dependencies in the LF / M1P system. The smaller (more negative) these coefficients, the greater the impact they should have on the system.

B. Formation of flow curves and component flow equations.

1. The method of fast speeds.

For the formation of equations and flow curves of a fluid component, the following fast velocity method is preferably used. The production curve refers to the comparison of the production of one component with the production of another. For example, when a throttle or valve is opened in a well, oil, water, and gas production should generally increase. The increase between any two of the components may be linear or non-linear over the entire range of fluid production. Again, according to FIG. ZA and 3B, gas and oil production is depicted mostly linearly, while water and oil production is mostly nonlinear. Flow curves are formed from a sequence of data points. Data points generated using the Newton-Raphson iterative procedure together with a subset of the reservoir model are indicated by x marks. Data points marked with a rhombus were created using the fast speed method. It should be noted that both methods provide similar results. However, the fast speed method is significantly more computationally efficient.

The fast speed method utilizes the fact that, at a fixed point in time, production from individual completion elements is generally linearly proportional to the pressure drop. The pressure drop is the pressure drop between the pressure in the well completion element and in adjacent elements of the reservoir. This is precisely the pressure drop that displaces fluids into and out of the completion elements during the corresponding production and injection operations. Using several different pressure drop profiles, a set of data points is generated for each well. Then ideally create a piecewise linear function that best fits these points. Then, from this piecewise linear function, the debit equation of the component that the optimizer should use is formed.

The full flow rate of the oil-water component is a piecewise linear function that is not linear. FIG. 5A-5B depict flow rates of individual completion elements for four different total production volumes for a well. Also depicted are pressure profiles for wellbore and reservoir elements for these various current flow rates. FIG. 5A-5B illustrate cases where oil production is successively reduced, as occurs when the wellhead air valve is closed. It should be noted that with a reduction in oil production, water production is reduced almost until the cessation of water production.

With a decrease in the current flow rate, the well pressure profile for the well should increase. It is assumed that the pressure profile of the reservoir at a given cycle remains constant. This should lead to a decrease in the pressure drop in the well, as the pressure profile of the well increases to the pressure profile of the reservoir. It should be noted that the pressure in deeper endings should be greater than in shallower endings due to the effects of hydrostatic pressure / gravity. Consequently, the pressure drop will be lower at greater depths, where the denser water lies below the less dense layers of oil and gas.

In the present invention, linear production scaling is used for individual completions. The total current production rate of component p, i.e., oil, water or gas, from a well is the sum of production rates from incoming completions

I _R t = Σ I _r , (19) ί "1 where c] rt is the total amount of flow from the well;

Psotr - the number of completion elements 8 in the well, etc.! - the amount of component flow from the ΐ-th wellbore.

- 10 014140

The basic flow rate of each component in each individual completion is obtained from the simulation run of the reservoir at a certain time stage and the level of production from the well. It is assumed that at a fixed point in time, the completion rate for each individual well completion element is linearly proportional to the pressure drop.

Accordingly, with a decrease in the pressure drop in the well by the number s, the individual completion rates will be accordingly reduced and a new full flow rate will be set

(20) where q * _r t is the new total amount of flow from the well;

C - decrease in pressure drop;

p _sotr - the number of completion elements in the well;

ΔΡ ₁ is the initial pressure drop in the ί-th completion element and q _p1 is the amount of phase flow from the ί -th well.

Accordingly, the amount of pressure change c required to reduce the oil flow rate from s. | to p. | *. set *

, Ch _in t ~ Ch _with t ^ R Cha (21) έί ΔΡ;

As illustrated in FIG. 6. This pressure change leads to a parallel change in the well pressure profile. With the calculated amount c, equation (20) can be used to calculate well production rates of other components. current in the well. An identical procedure can also be used for discharge rates. As discussed earlier. according to FIG. FOR and 3B. when repeating the specified process, several data points of the component stream can be formed. and a curve can be formed.

2. Creating a piecewise linear function.

Piecewise linear functions are formed for each of the wells. which best represent the specified dataset sets. formed by fast speeds.

Piecewise linear functions contain several line segments and break points. The number and location of break points is ideally selected using least squares data set alignment. formed by fast speeds. In this possible embodiment, the Levenberg-Marquardt least squares alignment method is used preferably to locate the discontinuity points (BSUPSGD-Magziag!). For experts it is obvious. that to represent the formed data points. which the optimizer should use. other methods of forming a curve or equation may be used.

Now according to FIG. 7A and 7B, segment k is specified. The coordinates of the endpoints of the segment are set (agk-1 / 32k) and (agk + 1 / E2k + 2) (22)

For least squares methods. such as Levenberg-Marquardt. requires the determination of the derivatives of this function y with respect to the parameters a. These derivatives are equal

& _tm1 __ ^x ~ ^a 2k-1,

E ^a 2k ~ ^a 2k-1 (23) do _ ( ^x ~ ~ ^a 2k} d ° 2k + 1 ( ^th 2k + 1

F '...

¹ —'--------------- ¹ >

& ^α 2ί + 2 ^a 2k + \ ~ ^a 2k-1

In a preferred embodiment, ideally, the corresponding number of break points is determined. as well as their optimal locations. An algorithm is used to select the number of break points. depicted in FIG. 8.

The first stage begins with a linear function (i.e. a single segment. Two endpoints. Therefore. 1 = 2). Χ ₁ ^{2 is} calculated for this linear function (χ2 ² ). Then a break point is added to the linear function. which makes it a piecewise linear function with two segments and three end points (1 = 1 + 1. i.e. 1 = 3). Break point coordinates are optimized to minimize χ1 ² . If alignment is improved by more than a factor of £ relative to the initial alignment. then add a new break point and repeat the process until significant improvement. In this algorithm continue

- 11 014140 add more break points only if this improves alignment by a factor of ί.

Better alignment can be achieved by decreasing ί due to the presence of more segments. This approach is mostly reliable. A check can be made to ensure that the discontinuity points are always in an acceptable region (first quadrant). This is ensured by penalizing (P) decisions that fall into unacceptable areas, as shown in FIG. nine.

3. Incorporation of piecewise linear functions into linear programming.

The incorporation of a piecewise linear curve into the LP installation requires the introduction of binary, additional continuous parameters and some restrictions. The following is a set of equations and variables to be added.

Break points:

(xy, yy) 4 = 1, 2 η (24)

Replace debit elements:

d = r1U1 + 32U2 +>. . + 2npn

Add restrictions:

Ζ1 <Υ1 Ζ2 <Υ! + Γ ₂ Ζ ₃ <γ ₂ + Υ3. . . Ζ _η -1 <γ _η - ₂ + γ _η -1 Ζ _η <γ _η -ι

U1 + y ₂ + ... + Vn-1 = 1, ζι + ζ ₂ + ... + ζ _η = 1, _(25}

4 = ΖιΧμ + ζ ₂ χ _μ +. ·. + _{R n} x _bn; y _r ε {0,1} ί-1, 2, ..., η-1, ζ _Γ> 0 1 = 1, 2, ..., η

Here μ is the dependent rate and μι is the control rate. Now, using a simple piecewise linear function with two segments, it will be demonstrated why such an installation leads to the correct behavior. It is assumed that the function has the form as in FIG. 10. The value of the function at x = 15 must be determined. The statement corresponding to this problem should be as follows:

£ (x) = ζιθ + ζ ₂ 3 + ζ ₃ 9 χ = ζι0 + ζ ₂ 20 + ζ ₃ 30

Ζχ <Υι g ₂ <y ₁ + y ₂ g ₃ <y ₂ (26) γι + γ ₂ = 1

Ζ1 + Ζ ₂ + Ζ ₃ = 1 y, e {0,1} 1 = 1, 2 ζ _χ > 0 ί = 1, 2, 3

The binary y indicates the segment to which x belongs. In this case, ₁ must be equal to one and ₂ must be equal to zero. First, a check is carried out to find out if _{2 can} ever equal one. If ₂ was equal to unity, then ₁ should be equal to zero, which means that ζ ₁ is equal to zero and ζ ₂ and ζ ₃ are non-zero. However, if ζ ₂ and ζ ₃ are nonzero, then x = 15 for the second equation can never be satisfied, respectively, ₂ cannot be equal to 1. Accordingly, if ₁ is equal to unity, then we obtain the following solution for ζ:

ζι = 0.25 ί (x} = 2.25 ζ ₂ = 0.75

The incorporation of equations and variables into equation (24) leads to the fact that the optimizer LP / M1P satisfies the debit curves of the component.

Although the description of this invention has been described with respect to its specific preferred embodiments and many details have been set forth to illustrate, it will be apparent to those skilled in the art that the invention is subject to change and that, without departing from the basic principles of the invention, the specific details discussed herein may be substantially changed.

Claims (19)

1. A method for improving the distribution of fluid flow rates over several wells connected via fluid to at least one subsurface reservoir includes: (a) modeling a fluid stream containing several components in at least one subterranean reservoir and in several wells that are fluidly coupled to at least one subterranean reservoir; (b) selecting production constraints containing at least one hard constraint, wherein at least one hard constraint is observed and at least one soft constraint, wherein at least one soft constraint may be violated; (c) generating system equations containing component flow equations corresponding to the simulated fluid flow in the wells and restrictive equations containing at least one soft restriction equation associated with at least one soft restriction, at least one soft restriction equation comprises penalty for violation of restrictions (RMS), which provides the ability to perform soft restrictions at least one soft restrictive equation; (i) the formation of an objective function corresponding to the flow of fluid in the wells and a fine for violation of restrictions; (e) optimization of the objective function using the optimizer and system equations to determine an improved distribution of fluid flow rates across several wells, at least one soft constraint, if necessary, may be violated to obtain a physically feasible optimization solution, and at least a violation one hard restriction will lead to the impossibility of obtaining a physically acceptable solution; (1) the distribution of fluid flow rates over several wells as defined in step (e). 2. The method according to claim 1, in which the production restrictions contain several soft restrictions that may be violated; system equations contain several soft constraint equations that correspond to soft constraints, each of the soft constraint equations contains a corresponding penalty for violation of constraints (RMS), which makes it possible to fulfill the corresponding soft constraint by this soft constraint equation; and the objective function corresponds to the fluid flow in the wells and fines for violation of restrictions, while, if necessary, soft restrictions can be violated to obtain a physically feasible optimization solution. 3. The method according to claim 2, in which the soft constraints prioritize the difficulty of breaking soft constraints. 4. The method according to claim 3, in which, in the objective function, fines for violation of the constraints of the corresponding soft constraint equations are associated with weighted coefficients that are weighted in accordance with the priority assignment for the soft constraints associated with the corresponding soft constraint equations to make the violation more difficult soft restrictions with higher priority. 5. The method according to claim 1, in which the objective function corresponds to a mathematical expression ί 1 to where OB1 is the objective function that must be optimized; ί is the number of fluid components; - weight scale factor for the production of the го-th (component) of the fluid in the well; - number of wells; μ ,, is the amount of the ί-th component produced by the _) -th well; k is the number of fines for violations of restrictions associated with soft restrictions; those _k - weighted scale factor for a fine for violation of the k-th restriction and SURK - a fine for violation of the k-th restriction. 6. The method according to claim 2, in which the objective function corresponds to a mathematical expression 0В4 = Σ ^ ίΣφ, -Σ » ₄ ίΤΡ _Α ί 1 к where ОВ1 is the objective function, which should be optimized; ί is the number of fluid components; - weight scale factor for the production of the го-th (component) of the fluid in the well; - number of wells; - 13 014140 ς, ι - the amount of the ί-th component, extracted _) -th well; k - the number of fines for violations of restrictions associated with production restrictions; \ ν _1: - weight scale factor for a fine for violation of the k-th restriction and SUR _to - penalty for violation of the k-th restriction. 7. The method according to claim 6, in which the soft constraints are prioritized with respect to the difficulty of breaking soft constraints and the weighting factors ν associated with the fines for breaking the constraints of the RMS _{to the} corresponding soft constraint equations are weighted in accordance with the priority setting for the soft constraints so that make it more difficult to violate soft restrictions with a higher priority. 8. The method according to claim 1, further comprising comparing the characteristics of the fluid flow in at least two wells and, if the characteristics are within a predetermined range relative to each other, establishing a relationship between the flow rates of the fluid of at least two wells by generating equations flow rates in system equations so that at least two wells have dependent distributed flow rates. 9. The method according to claim 1, in which the wells contain several elements of completion and at least one underground reservoir contains several elements of the reservoir, which are connected through fluid to the elements of completion; the fluid flow modeling step comprises determining pressures in the reservoir elements and in the termination elements and comprises determining the corresponding fluid flow rates of the component in the termination elements due to a pressure drop between the reservoir elements and the termination elements; and the component debit equations are formed from the component debit data points, which are created by scaling and summing the component fluid flows in the completion elements of each well based on the component debit rates determined in the simulation of the fluid flow and depending on the change in pressure drop between the completion elements and reservoir. 10. The method according to claim 9, in which the data points of the flow rate of the component is formed using the following mathematical expression: , hundred dr _ _s Σ —GB-Ϋρί where c] * |, t is the new total amount of flow from the well; Psotr - the number of completion elements in a particular well; DR, is the initial pressure drop in the ΐ-th element of completion; c - change in pressure drop relative to the initial simulated pressure drop for the completion element, etc.! is the initial simulated amount of component flow from the ΐth termination element. 11. A method for improving the distribution of fluid flow rates over several wells connected via fluid to at least one subsurface reservoir includes: (a) modeling a fluid stream containing several components in several wells and in at least one subsurface reservoir, wells comprise several completion elements, and at least one subsurface reservoir contains several reservoir elements that are connected by means of a fluid with completion elements, as well as determining the pressures in the elements of the reservoir and in the completion elements and determining the corresponding flow rates of the component in the completion elements, ovali pressure drop between the elements of the reservoir and the elements of completion; (b) generating data points for the component’s flow rate for the wells over a range of fluid flows by scaling and summing the component fluid flows in the completion elements based on the production rates of the component determined in step (a) and the change in pressure drop between the completion elements and the reservoir; (c) generating flow rate equations for the component for the wells based on data points for the respective wells; (ά) the formation of constraint equations corresponding to production constraints; (e) the formation of an objective function corresponding to the fluid flow in the wells; - 14 014140 (ί) optimization of the objective function using the optimizer and restrictive equations and component flow equations to determine an improved distribution of fluid flow rates over several wells and (e) distribution of fluid flow rates over several wells in accordance with the definition in step (ί). 12. The method according to claim 11, further comprising forming piecewise linear functions from data points for each of the wells and generating production rate equations for the component from piecewise linear functions. 13. The method of claim 12, wherein the component debit equations comprise binary variables for describing the piecewise linear function and the optimization step comprises using mixed integer programming. 14. The method according to claim 11, in which the flow rates of at least between two wells are dependent on each other. 15. The method according to claim 11, in which the optimizer uses at least one of linear programming and mixed integer programming when optimizing the objective function. 16. The method of claim 15, wherein the optimizer uses mixed integer programming to optimize the objective function. 17. The method according to claim 11, in which the data points of the flow rate of the component is created using the following mathematical expression: , "SotrDR-s where d * _r t is the new total amount of flow from the well; Isotr ^{- the} number of completion elements in a particular well; ΔΡ ₁ - initial pressure drop in the ί-th element of completion; c is the change in pressure drop relative to the initial simulated pressure drop for the completion element, and d _p1 is the initial simulated amount of component flow from the ίth completion element. 18. A method for improving the distribution of fluid flow rates over several wells connected via fluid to at least one subsurface reservoir includes: (a) modeling a fluid stream containing several components in at least one subterranean reservoir and in several wells that are fluidly coupled to at least one subterranean reservoir; (b) the formation of equations of dependence of the flow rate between at least two wells; (c) the formation of an objective function corresponding to the flow of fluid in the well; (b) optimizing the objective function using flow rate equations to determine an improved distribution of fluid flow rates across multiple wells, with at least two wells having dependent flow rates; and (e) the distribution of fluid flow rates over several wells as defined in step (b). 19. The method according to p. 18, in which the characteristics of the fluid flow between at least two wells are compared and cause the formation of equations of dependence of the flow rate, if the compared flow characteristics of the fluid are within a predetermined range from each other.