RU2081301C1 - Method for operating optimization of gas-lift wells - Google Patents

Abstract

FIELD: oil and gas industry. SUBSTANCE: according to method, measured are technological operating parameters of interacting wells, their operating modes are changed and procedures of determining their operating parameters are repeated until optimal functioning of interacting wells are achieved. Total oil output is measured through system of interacting wells and in each of wells being optimized gas flow rate is changed and determined in each well is dependence of oil output on changing of flow rate. Total oil output through separate groups of interacting wells is measured at various values of gas flow rate in separate wells. Determined is dependence of total oil output on changing of gas flow rate in each of interacting wells. Selected and changed are operating modes in each gas-lift well by maximization of arithmetical mean dependences of total oil output of interacting wells on gas flow rate in separate wells. Then measured is total oil output and it is compared with value obtained at previous stage of optimization until ensured is oil production increase through group of interacting wells. At limited availability of gas it is possible to cut off wells in order of decreasing their specific flow rates. At redistribution of gas availability between groups of interacting wells, its availability can be determined according to equality of deviations in changes of total oil output obtained at optimal distribution of gas with respect to changing gas availability for given group of wells. EFFECT: high efficiency. 2 cl, 7 tbl

Description

 The invention relates to the oil and gas industry, in particular to the field of gas lift oil production, and can be applied to optimize the operation of wells taking into account their interaction through the reservoir and (or) oil and gas collection and gas distribution systems.

 A known method of operating a system of gas lift wells (RD 39-2-885-83 "Methodology for selecting operating modes of gas lift wells in the conditions of a shortage of working agent"), in which the gas flow rate for gas lift wells is determined based on the dependence of flow rate on gas flow using the Lagrange multiplier method .

A known method of operating a system of gas lift wells (AS N 1091618 (USSR) MKI E 21 B 43/00,), including changing the gas flow rate and measuring the oil flow rate for each well, redistributing gas among the wells by increasing the gas flow rate for wells with large values Δf / Δx _i (the ratio of the change in the flow rate Δf when changing the gas flow rate to the value of the change in gas flow Δx _i ) by reducing the gas flow rate for wells with lower values of Δf / Δx _i , taking into account the existing total gas resource R.

 The prototype of the proposed technical solution is a method of operating a system of gas lift wells (Siemens US Optimization of the operation of continuously operating gas lift wells. Oil Engineer, 1972, N 10, 142 142), which uses the principle of maximizing oil production from a group of wells. The essence of this method is to set the same increments in gas flow for each well, to determine the well (s) that gives (them) the largest increase in oil production. For this well or group of wells, they give a new increment in gas flow rate until the corresponding increments in oil production remain maximum. After that, increments of the gas flow rate are set to another (s) well (s), which (s) currently have the largest increment in oil production.

Known methods have the following disadvantages:
they do not take into account the interaction of wells through the reservoir, which does not allow optimizing the group of wells interacting through the reservoir, since the previously obtained dependences of the flow rate on gas flow for each individual well f ₁ (x ₁ ) do not take into account their mutual influence through the systems of the oil production complex, i.e. abstract dependencies f ₁ (x ₁ ) do not fully reflect the actual state of the system of interacting wells;
they do not take into account the interaction of wells through the oil and gas gathering system, which does not allow to optimize the group of producing wells interacting through the net gas and gas gathering system;
do not take into account the interaction of the wells through the gas distribution system, which does not allow optimizing the group of gas-lift (in particular, compressor-free) wells having a common source of high pressure gas;
the optimization procedure used requires a large number of steps (steps) to approach the optimum, each of which is associated with labor costs by measuring changes in well flow rates;
with small changes in gas flow (when approaching the optimum), the influence of the relative errors of the procedure increases and does not allow close enough to approach the optimum, because It is known that existing metering systems have large errors.

 The aim of the invention is to increase the efficiency of the method by increasing the accuracy of the selection of optimal modes of gas lift wells, taking into account their interaction. The effectiveness of the method is determined by the minimum number of measurements of technological modes and a high degree of resistance to measurement errors when the optimal operating mode of a system of interacting wells is achieved.

The effect of the application of the method is expressed as:
additional oil production;
reduction of specific gas consumption;
reducing the cost of oil production;
reducing the time for the process of optimizing the operation of wells.

The specified goal is achieved through the following solutions:
1.1. The total oil production is measured for individual groups of interacting wells at various gas flow rates for each of the optimized wells. The dependence of the total oil production on the change in gas flow rate for each well is determined and established.

 1.2. The technological regimes for each gas-lift well are selected and changed depending on its effect on the total oil production for a group of interacting wells (in particular, based on the solution of the convex programming problem with a separable objective functional, which is taken as the arithmetic average of the total oil production of the interacting wells on gas consumption for each individual well).

 1.3. Measure the total oil production in the group of optimized wells and compare it with the value at the previous stage. If the relative increase in total production is more than the relative measurement error of the flow rate, then the procedure described in clause 1.1, 1.2, 1.3 is repeated.

 This feature allows you to take into account the interaction of wells through the reservoir, the oil and gas gathering system and through the gas distribution system while reducing the number of steps and the relative error of the procedure for optimizing gas distribution in the system of gas lift wells.

 2. With a limited gas resource, wells may be sequentially and / or group shut-off in the decreasing order of their specific (oil production) gas consumption.

 This feature allows you to minimize losses during the optimization of wells.

 3. When redistributing gas between groups of interacting wells, it can be carried out according to the equality of the ratios of changes in the total oil production obtained at the optimal gas distribution to the change in gas resource for this group of wells.

 This feature allows you to optimally redistribute the existing resource of high-pressure gas between optimized groups of gas-lift wells.

 The optimization process is as follows.

 At various values of gas flow rate at separate interacting wells, their total oil production is measured. Then, the dependence of the total oil production on the change in gas flow rate for each of the interacting wells is determined. That is, the values of the target functional (total oil production or (and) the cost of oil production or (and) profit for a group of interacting wells) are determined for a selected value of control parameters (gas consumption for individual gas-lift wells). To do this, conduct experiments on a real object (well system). The need for this is due to the complexity of the complete mathematical model of the object and the lack of a priori information to determine the parameters of the model. Each step (step) of the optimization procedure is carried out experimentally on a real object, which is associated with significant time and material costs. Therefore, they reduce (minimize) the number of stages of the procedure, achieving a satisfactory value of the target functional (total oil production). Moreover, each stage of the procedure can be quite complex and require significant computational resources, but these costs are usually not comparable with the costs of obtaining field information. Therefore, the complexity of the procedures is justified if it allows to reduce the number of stages. In addition, the inevitable measurement errors taken at a real object should be taken into account. The technological regimes for each gas-lift well are selected and changed by maximizing the arithmetic dependences of the total oil production of the interacting wells on gas consumption in individual wells. The process of distributing high-pressure gas between gas-lift wells is formalized as the task of distributing a certain gas resource between n subsystems of a complex system in order to optimize the total oil production given by a smooth concave functional. If the functional of the problem is separable, i.e. the efficiency of each subsystem depends only on the resource allocated to this subsystem, but does not depend on its distribution between other subsystems, the solution of the problem does not present fundamental difficulties even with a large number of subsystems (optimization of the well system by characteristic curves, for example, by the Lagrange method). Moreover, the efficiency of the subsystem, depending on the resource allocated to it, is a function of one variable, the value of which is obtained as a result of an experiment conducted only on the corresponding subsystem (well). If the functional is not separable, the procedure is significantly complicated. In principle, there are many effective ways to minimize the concave function on a polyhedron. However, their use is impossible due to the fact that the target function is not known a priori, and its measurement is made with errors. In fact, the functional (total oil production) is not separable due to the interaction of the wells through the systems of the oil production complex, however, the components of the functional that describe the cross-connections between the subsystems are relatively small. Therefore, an iterative search procedure is carried out, in which at each stage a resource distribution with a separable functional is selected, depending on the state of the system achieved at the previous stage.

e_i, F_i, R заданные неотрицательные числа. Проверяют, что

, и, значит, решение существует. Здесь f(x) интерпретируют как оценку эффективности работы системы, состоящей из n подсистем (скважин), x_i как ресурс газа, выделяемый i-ой подсистеме (скважине или группе скважин), а R как суммарный ресурс. Применительно к системе газлифтных скважин n - количество скважин, x_i расход газа на i-ой скважине, f(x) суммарная добыча нефти по системе взаимодействующих скважин, R суммарный ресурс газа высокого давления. Выбирают произвольный вектор (распределение ресурса газа) x ∈ S.To do this, consider the problem
f (x) _ → max, x ∈ S (1)
where x ∈ R ⁿ , f (x) is a smooth concave function,

e _i , F _i , R are given non-negative numbers. Verify that

, and, therefore, a solution exists. Here f (x) is interpreted as an estimate of the performance of a system consisting of n subsystems (wells), x _i as the gas resource allocated to the i-th subsystem (well or group of wells), and R as the total resource. In relation to a system of gas lift wells, n is the number of wells, x _{i is the} gas flow rate at the i-th well, f (x) is the total oil production from the system of interacting wells, R is the total resource of high-pressure gas. Choose an arbitrary vector (gas resource distribution) x ∈ S.

Таким образом, функции f_i(x, y) представляют зависимости суммарной добычи от расхода на отдельных газлифтных скважинах.Denote

Thus, the functions f _i (x, y) represent the dependence of the total production on the flow rate in individual gas-lift wells.

Then, the resource R is distributed according to the following functional F (x, y):
F (x, y) _ → max, x ∈ S (3),
the resulting set of gas resource distribution options is denoted by X (y).

A distribution x from S is optimal in problem (1) if and only if x belongs to the set of gas distributions X (x). An iterative sequence x ^{k + 1} ∈ X (x ^k ) is determined that starts (starts) from an arbitrary current state of the system x ^o ∈ S and converges to the optimal distribution. If f (x) is representable in the form
f (x) = ∑f _i (x _i ) + h (x) (4)
where h describes the relationship (interaction) between the wells, the convergence of the procedure is ensured provided that h and its derivatives are sufficiently small and f _i (x _i ) is strictly convex. Under these conditions, x ^k approaches the optimal distribution with a geometric progression rate with the denominator q <1. The conditions imposed on h and providing the condition q <1 mean that the cross-connections between the subsystems (wells) defined by the function h are relatively small.

The proposed optimization method can use the quadratic functional f:
f (x) = 1/2 x ^T Qx + b ^T x + c (5)
The choice of exactly the quadratic functional is explained by the fact that the characteristic curves of gas lift wells are well approximated by quadratic dependencies. Each step of the proposed method consists in maximizing on S functions of the form (5) with the diagonal matrix Q and allows an effective numerical solution. To illustrate this, we present some results of numerical simulations performed by the authors on an IBM PC.

The matrix Q was specified in the form Q = Q ₁ -Q ₂ , where O _{1 is a} diagonal, Q _{2 is a} symmetric matrix. Matrix elements were selected using a random number sensor. The optimal distribution x and the corresponding value of the functional f = f (x) were determined by the gradient projection method from some initial point. Then, iterations were performed from the same starting point using the proposed method. Table 1 shows the calculation results for 4 variants of the problem for various values of n and R. For control, the maximum value was also calculated by the standard gradient projection method. The last column of the table shows the number of iterations of the proposed optimization method required to find the maximum. Note a very small number of iterations. For comparison, we note that, using the gradient projection method in the 4th embodiment, the functional value of 149.9487 was achieved in 8 iterations.

We note two circumstances arising from the results of numerical modeling:
1) the rapid convergence of the considered method, a satisfactory approximation to the optimum is achieved in just 2 3 stages;
2) convergence takes place, despite the fact that the quantity q, which determines the theoretical rate of convergence, is greater than 1 (from 1.09 to 17.35) in the above examples.

 It follows from the latter that, in practice, the convergence of the optimization procedure can take place with a significantly greater interaction between the wells than is guaranteed by theory.

 When solving problem (8) with a separable functional at each of the stages of optimization, the Lagrange multiplier is determined. These factors converge to the Lagrange multiplier of the original problem (1).

It is known that the Lagrange multiplier characterizes the increment of the total oil production at the optimal gas distribution if the gas resource changes. Namely, if we consider the optimal value of the functional f (x) in problem (1) as a function of the resource R, then the Lagrange multiplier df (x) / dR. Based on this, the proposed method of gas redistribution between groups of wells is based. Several groups of wells are distinguished in such a way that there is no mutual influence between wells belonging to different groups (or so little that they can be neglected). For each i-th group, for a given gas resource R _{i, the} optimal distribution of this resource and the corresponding value of the Lagrange multiplier are determined. For each of the groups of wells, the restrictions are set, R _i -ΔR _i , R _i + ΔR _i to change the resource. Within the framework of these restrictions, the resources of the allocated groups of wells are changed in magnitude, while maintaining the constant value of the total resource R.

 Then measure the total oil production and compare it with the value at the previous stage of optimization until an increase in oil production is ensured for a group of interacting wells.

 In order to reduce losses in oil production directly in the optimization process, when their specific gas consumption decreases, the limited gas resource turns off the wells in sequence.

 Consider the implementation of the method on the example of five interacting gas lift wells connected to one satellite station N 19 of the Pravdinskoye field. We will arbitrarily denote them by serial numbers 1, 2, 3, 4, 5.

 That is, by changing the gas flow rate in a separate well (using a gas flow regulator, a throttle is installed on a given technological insert), for example, from 4000 to 6800 cubic meters. m in well N 3 (see table. 4), measure the change in total oil production. At the same time, due to the interaction of the wells, the change (increment) in oil production for an individual well N 3 does not coincide with the change in the total production (6.2 instead of 4.6, see Table 3). They do the same with all interacting wells, and this procedure is repeated in various modes (from minimum to maximum). (See tab. 2, 3, 4, 5, 6).

 The technological parameters of the system when changing the mode for well N 1, see table. 2.

 The technological parameters of the system when changing the mode for well N 2, see table. 3.

 The technological parameters of the system when changing the mode for well N 3 see table. 4.

 The technological parameters of the system when changing the mode for well N 4 see table. 5.

 The technological parameters of the system when changing the mode for well N 5 see table. 6.

 Then, the dependence of the total oil production on the change in gas flow rate for each of the interacting wells is determined. That is, they build the dependence of the total (for all interacting wells) oil production from gas flow for each individual well. Thus, five dependencies are obtained for this particular example.

 After that, the technological regimes for each gas-lift well are selected and changed by maximizing the arithmetic average of the total oil production of the interacting wells from gas consumption in individual wells.

 To maximize the arithmetic mean of the dependences of the total oil production, proceed as follows: according to the obtained dependencies, they are determined by simply summing the values of the function for the given arguments and dividing by the number of optimized wells. For example, at gas flow rates in wells, respectively (300, 100, 4000, 0, 2000), the arithmetic average total oil production is 24.8, and at (5000, 3000, 6800, 5500, 5100) it is 32.0.

 To maximize this value, the authors use the Lagrange multiplier method, the found modes for the wells are respectively equal (4100, 3100, 5000, 1900, 5900) (with a limit on the total gas flow rate of 20,000).

 Then measure the total oil production and compare it with the value at the previous stage of optimization. So, at the second stage of optimization, the value of the arithmetic average of total oil production is equal to the maximum with the corresponding values of gas consumption equal to (3400, 2400, 5900, 2300, 6100). The measured value of total oil production in the second stage is 31.6, more than in the first, 29.8. That is, the increase in oil production is 1.8. This procedure is repeated until an increase in oil production in the group of interacting wells is provided.

 As can be seen from table 7, despite the fact that the estimated production rate for optimization by the existing method is greater than the proposed one, the actual production rate of the proposed method for a group of five wells is 1.6 t / d more.

 An even greater effect will be with a greater gas shortage and when shutting off the wells.

Claims (3)

 1. A method of optimizing the operation of a system of gas lift wells, including measuring the technological parameters of the interacting wells, changing their technological regimes and repeating the operation of determining technological regimes until the optimal operation of the interacting wells is achieved, characterized in that the total oil production is measured for individual groups of interacting wells at different values gas flow rate in individual wells, determine the dependence of total oil production on changes in gas flow rate per From the interacting wells, the technological regimes for each gas-lift well are selected and changed by maximizing the arithmetic average of the total oil production of the interacting wells from gas consumption in individual wells, then the total oil production is measured and compared with the value at the previous optimization stage until the oil production span is provided for a group of interacting wells.  2. The method according to claim 1, characterized in that, with a limited gas resource, the wells are alternately shut off in descending order of their specific gas consumption.  3. The method according to claims 1 and 2, characterized in that when redistributing the gas resource between the groups of interacting wells, it is established by the equality of the ratios of the changes in the total oil production obtained at the optimal gas distribution to the change in the gas resource for this group of wells.

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