CONTROLLER FOR SUPPRESSING SLUGS IN PETROLEUM PRODUCTION SYSTEMS

Abstract

The invention solves the problem of the difficulty of acquiring subsea variables by using a widely available surface variable, namely the pressure upstream of the choke valve. As surface variables have an unfavorable dynamic for use in conventional anti-slug controllers, which are based on the linear PID algorithm, the proposed controller uses a hybrid fuzzy-PID architecture, which compensates for the unfavorable dynamic of the controlled variable by means of heuristic interventions in the control action generated by the PID part of the controller. The heuristic action of the proposed controller allows it to be more robust than a conventional controller, even with a relatively slow control action, which makes it possible to apply the proposed algorithm in systems whose choke valve activation is slow. Thus, the two largest impediments for installation of conventional controllers, lack of subsea measurement and choke valve slowness, do not pose a problem for application of the proposed algorithm. This allows the proposed anti-slug controller to be used in offshore production systems without the need for physical intervention in the subsea or surface facilities.

Claims

1. A slug-suppressing controller (1), comprising a fuzzy interference system (FIS) (4) hybridized with a classic PID controller (5) to control a choke valve of an oil production system.

2. A slug-suppressing controller (1) of claim 1, wherein the slug-suppressing controller uses only a surface measurement, or a surface measurement with subsea measurements.

3. A slug-suppressing controller (1) of claim 1, wherein the PID (5) has variable overall gains.

4. A slug-suppressing controller (1) of claim 1, wherein the FIS (4) is responsible for adjusting the overall gain of the PID controller (5).

5. A slug-suppressing controller (1) of claim 3, wherein variable overall gain of the PID controller (5) decreases when the occurrence of slugging is detected.

6. A slug-suppressing controller (1) of claim 1, wherein the FIS (4) generates an additional restrictive choke valve-closing action, wherein the restrictive choke valve-closing action is a valve-closing action in addition to a closing action performed according solely to a PID (5) algorithm.

7. A slug-suppressing controller (1) of claim 1, wherein the FIS (4) generates a heuristic action for closing the choke valve during the period of positive control error (7) of the slugging cycle.

8. A slug-suppressing controller (1) of claim 1, further comprising a block to estimate a severity of the slugging (6).

9. A slug-suppressing controller (1) of claim 8, wherein the block to estimate the severity of the slugging (6) is based on determining the oscillation frequency.

10. A slug-suppressing controller (1) of claim 8, wherein the block to estimate the severity of the slugging (6) is based on determining the frequency of oscillation based on the following algorithm: a. Sampling the actual value of the measured variable X(n), adding it to a buffer size L; b. Calculating the average of the buffer X(1:L), storing it in X; c. Determining the sequence of average zero, X.sup.0(1:L), using the equation:
X.sup.0(1:L)=X(1:L)−X d. Calculating the variance of X.sup.0(1:L); if it is less than a threshold of σ.sup.2.sub.min, the system is considered to be stable and the algorithm returns frequency zero; e. Calculating the self-correlation for X(1:L), storing it in X.sub.x(1:L); f. Determining the index i of the element pertaining to X.sub.x(1:L), which has the greater value after the first crossover of zero; g. Calculating the period of oscillation T.sub.g from the second equation, in which T.sub.a is the sampling time:
T.sub.g=T.sub.a(i−1) h. Returning the value of the frequency in mHz, calculated as 1000/T.sub.g.

11. A slug-suppressing controller (1) of claim 1, wherein the FIS (4) includes two input variables: control error (6) and degree of slugging severity (8); and two output variables: overall gain of the PID (5) and restrictive action (9).

12. A slug-suppressing controller (1) of claim 10, wherein the restrictive action (9) is integrated with the exit of the PID (5).

13. A slug-suppressing controller (1) of claim 1, wherein the FIS (4) includes functions of triangular and trapezoidal pertinence in the entry variables and singleton functions in the output variables.

14. A slug-suppressing controller (1) of claim 11, wherein fuzzy inference rules (FIS) (4) are based on the restrictive action output variable (9), which denote the following behavior: a. If the system is not slugging, then the restrictive action (9) is unnecessary. b. If the system is slugging and the control error (7) is very negative, then the restrictive action (9) is necessary. c. If the system is slugging and the control error (7) is negative, then the restrictive action (9) is necessary. d. If the system is slugging and the control error (7) is zero, then the restrictive action (9) is necessary. e. If the system is slugging and the control error (7) is positive, then the restrictive action (9) is not necessary. f. If the system is slugging and the control error (7) is very positive, then the restrictive action (9) is not necessary.

15. A slug-suppressing controller (1) of claim 11, wherein rules for fuzzy interference (FIS) (4) are based on the output variable of the overall gain from the PID (5), which denote the following behavior: a. If the system is slugging, then the overall gain is low. b. If the system is not slugging and the control error (7) is very negative, then the overall gain is high. c. If the system is not slugging and the control error (7) is negative, then the overall gain is high. d. If the system is not slugging and the control error (7) is zero, then the overall gain is low. e. If the system is not slugging and the control error (7) is positive, then the overall gain is average. f. If the system is not slugging and the control error (7) is very positive, then the overall gain is high.

16. A slug-suppressing controller (1) of claim 7, wherein the controller uses the degree of slugging severity (8) to create an instability alarm for the process.

17. A slug-suppressing controller (1) of claim 1, wherein the controller guarantees operation with stable and unstable setpoints.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0061] This invention will be described in more detail below, referencing the attached figures which, in a schematic manner not limitative of the inventive scope, show examples of its realization. The drawings include the following:

[0062] FIG. 1 shows a flowline-riser system in the process of slug formation;

[0063] FIG. 2 shows the cyclical process of formation of slugs in risers;

[0064] FIG. 3 shows a slug-attenuating device;

[0065] FIG. 4 shows a flowline-riser system with gas injection at the base of the riser;

[0066] FIG. 5 shows a flowline-riser system with gas reinjection;

[0067] FIG. 6 contains a Hopf bifurcation diagram for a flowline-riser system;

[0068] FIG. 7 shows the architecture of the slug-suppressing controller;

[0069] FIG. 8 shows the result of the verification test of the self-correction algorithm for estimating frequency;

[0070] FIG. 9 shows the diagram of the fuzzy interference system used in the slug-suppressing controller;

[0071] FIG. 10 shows functions pertaining to the linguistic variable “Control Error”;

[0072] FIG. 11 shows functions pertaining to the linguistic variable “Degree of Slugging Severity”;

[0073] FIG. 12 shows functions pertaining to the linguistic variable “Restrictive Action”;

[0074] FIG. 13 shows functions pertaining to the linguistic variable “Overall Gain”;

[0075] FIG. 14 shows the response surface of the FIS for the output variable “Restrictive Action”;

[0076] FIG. 15 shows the response surface of the FIS for the output variable “Overall Gain”;

[0077] FIG. 16 shows the responses of the most relevant variables from the suppression capacity test with initial opening of the choke at 40%;

[0078] FIG. 17 shows the responses of the most relevant variables from the suppression capacity test with initial opening of the choke at 100%;

[0079] FIG. 18 shows the outflow and valve-opening responses in the test with the PID controller based on the pressure at the top of the riser and prior opening of 40%;

[0080] FIG. 19 shows the influence of the limitation on actuation speed of the choke to the rapid controller signals;

[0081] FIG. 20 shows the outflow and valve opening for the tests in which the actuation is instantaneous (to the left) and slow (to the right). Dotted curves are for the FPID-P.sub.2 controller and continuous of the PID-P.sub.1;

[0082] FIG. 21 shows the responses of the outflow and valve opening in the stabilization test at the unstable point;

[0083] FIG. 22 shows a comparison of the average production obtained by the fuzzy controller, the reference controller, and the open-loop system;

[0084] FIG. 23 shows the responses of the outflow and valve opening in the noise production test;

[0085] FIG. 24 shows the responses of the outflow and valve opening in the response test to degrees of production (rapid choke);

[0086] FIG. 25 shows the responses of the outflow and valve opening in the response test to the degrees of production (slow choke);

[0087] FIG. 26 shows the responses of the outflow and valve opening in the response test to changes in operating conditions done with the PID controller based on pressure at the base of the riser;

[0088] FIG. 27 shows the responses of the outflow and valve opening in the response test to changes in operating conditions done with the controller described in this document.

DETAILED DESCRIPTION OF THE INVENTION

[0089] The invention is a controller for a slug suppressor (1) whose input is a variable from a system that is sensitive to slugging (2) and the output is a control action (3) that commands the opening of the choke valve. The algorithm used in the controller is the result of a hybridization of a fuzzy inference system (FIS) (4) and a classic PID control algorithm (5). A diagram illustrating the architecture of this controller is shown in FIG. 7.

[0090] The input variable (2) used in the controller must be sensitive to the passage of severe slugging, that is: the signal measured needs to reproduce the typical oscillations of this type of flow. Different from classic anti-slugging controllers, without compromising the efficacy of the controller, a variable is admitted, which is measured at the surface installation, such as the pressure upstream of the choke valve, which is easily obtained at production facilities.

[0091] The input variable (2) is compared to a reference value (setpoint) to determine the control error (7), which in turn is used by the PID parcel (5) of the controller in determining the control action (3) that is applied to the choke valve. To offset the low performance of the PID algorithm (5) when using surface measurements, the controller uses a fuzzy interference system (FIS) (4) to incorporate heuristic knowledge into the controller's action.

[0092] In addition to the control error (7), the FIS (4) has an estimated degree of severity of the slugs (8) as an input, which value is calculated by an algorithm that estimates the severity of the slugs (6), which is responsible for translating the intensity of the slugs to which the system is submitted into a numeric value.

[0093] While other algorithms are used that estimate the severity of the slugs, the algorithm originally used in the implementation of the invention was based on the estimate of the fundamental frequency of the variable measured (2), as there is a monotonically increasing relationship between the severity of the slugs and the oscillation frequency of the variable measured (2). The advantage of this approach is that the estimated frequencies are independent of the variable observed, and its sensitivity to slugging.

[0094] Implementation of the estimated frequency in real time was based on calculating the self-correction of the variable measured, with the periodic exception (every T.sub.a seconds) of the following algorithm: [0095] 1. Show the actual value of the variable measured, X(n), adding to it a buffer of size L. [0096] 2. Calculate the average of the buffer X(1:L), storing it in X. [0097] 3. Determine the sequence of average zero, X.sup.0(1:L), using the equation:

X.sup.0(1:L)=X(1:L)−X [0098] 4. Calculate the variance of X.sup.0(1:L); if it is less than a threshold of σ.sup.2.sub.min, consider the system stable and the algorithm returns frequency zero. [0099] 5. Calculate the self-correction of X.sup.0(1:L), storing it in X.sub.x(1:L). [0100] 6. Determine the index i of the element pertaining to X.sub.x(1:L), which has the greatest value after the first cross through zero. [0101] 7. Calculate the period of oscillation using the following equation:

T.sub.g=T.sub.a(i−1) [0102] 8. The value of the frequency is returned in mHz, calculated as 1000/T.sub.g.

[0103] For this algorithm to be used successfully, it is important that a sample time, T.sub.a, be defined that is sufficiently small to sample at least 10 samples from the fastest slugging cycle in the system. Furthermore, the buffer size, L, must be capable of completely storing at least two slugging cycles.

[0104] The efficacy of the described algorithm was verified through a test in which the severity of the slugs at a simulated plant was increased gradually by means of opening the choke valve from 0 to 100% over 12 hours. The result of this test is presented in FIG. 8, in which the pressure upstream of the choke and the estimated frequency throughout the simulation are shown. In this graph, it can be seen that the estimated frequency grows as the severity of the slugging increases, which justifies the use of the oscillation frequency as the degree of severity of the slugging (8).

[0105] With both input variables, control error (7), and degree of severity of the slugs (8) determined, the FIS (4) performs two heuristic interventions in the controller: manipulation of the overall gain, k.sub.i, of the PID algorithm (5), and close of the choke valve in a specific way if the well is slugging. The name “restrictive action” (9) was given to this second action, which is added to the actions of the PID controller after an integration, because it acts by restricting the choke valve. An internal architectural diagram of the FIS (4) is presented in FIG. 9.

[0106] As usual, the rules of inference used in the FIS (4) were defined based on the human knowledge acquired through operation of these systems. In the case of the “restrictive action” output (9), the following rules of inference were used: [0107] 1. If the system is not slugging, then the restrictive action (9) is unnecessary. [0108] 2. If the system is slugging and the control error (7) is very negative, then the restrictive action (9) is necessary. [0109] 3. If the system is slugging and the control error (7) is negative, then the restrictive action (9) is necessary. [0110] 4. If the system is slugging and the control error (7) is zero, then the restrictive action (9) is necessary. [0111] 5. If the system is slugging and the control error (7) is positive, then the restrictive action (9) is not necessary. [0112] 6. If the system is slugging and the control error (7) is very positive, then the restrictive action (9) is not necessary.

[0113] The first rule arises from the fact that the FIS (4) helps stabilize the system by gradually closing the choke only during the occurrence of slugging, and restrictive action (9) is not necessary when the flow is stabilized.

[0114] The other rules define the following behavior: during the occurrence of the slugging cycle, the FIS (4) will tend to close the choke valve only when the control error is negative and it will not take action when the error is positive, since in this stage of the slugging cycle a tendency to self-regulation was seen. That heuristic closure is one of the biggest differentials of this controller.

[0115] The PID parcel (5) of the controller will also tend to close the choke valve when the control error is negative, but it will tend to open it when the error is positive, which, depending on the characteristics of the slugging, may even aggravate the instability of the system. Thus it is necessary to reduce the actuation capacity of the PID controller (5) during the occurrence of slugging. This is done by manipulating the overall gain, k.sub.i, of the PID (5) by the FIS (4). The linguistic rules that define that manipulation for the gain k.sub.i are: [0116] 1. If the system is slugging, then the overall gain is low. [0117] 2. If the system is not slugging and the control error (7) is very negative, then the overall gain is high. [0118] 3. If the system is not slugging and the control error (7) is negative, then the overall gain is high. [0119] 4. If the system is not slugging and the control error (7) is zero, then the overall gain is low. [0120] 5. If the system is not slugging and the control error (7) is positive, then the overall gain is average. [0121] 6. If the system is not slugging and the control error (7) is very positive, then the overall gain is high.

[0122] Analysis of these rules shows that in addition to reducing the overall gain during the occurrence of slugging, the FIS action (4) improves the capacity of the PID algorithm (5) in rejecting disturbances due to the use of a non-linear overall gain, which increases with the error. The asymmetry between rules 3 and 5 arises from the fact that the controller may be more aggressive in closing the choke valve, as it is a stabilizing intervention.

[0123] With the objective of making implementation of the FIS (4) simpler, use of triangular and trapezoidal functions in defining the terms of the linguistic input variables and singleton functions in the terms of the output linguistic variables is recommended.

[0124] In the tests performed to validate the controller, for the “Control Error” (7) input variable, a universe of discourse was considered of −3 bar to 3 bar and five linguistic terms, which may be seen in FIG. 10. For the input variable “Degree of Severity of Slugging” (8), a universe of discourse was considered from 0 to 4 mHz (millihertz) and only two linguistic terms, as shown in FIG. 11. As in the tests performed, the oscillations were begun at a frequency of around 1.5 mHz, the linguistic term “degree of severity of slugging is low” has the same meaning as “system is not slugging,” therefore the term “degree of severity of slugging is high” means “system is slugging.”

[0125] In the same tests, the output linguistic variable “Restrictive Action” (9) was defined from two linguistic terms, as can be seen in FIG. 12. Finally, the output linguistic variable “Overall Gain” was defined by means of three linguistic terms, presented in FIG. 13.

[0126] Due to the use of singleton functions in the definition of the terms of the output variables, the process of defuzzification (the process of conversion from (imprecise) fuzzy sets into real precise values) degenerates into a simple weighted average of the support values for the singleton groups (they are the fuzzy groups in which a function of pertinence is just a point in the universe of discourse), such as in FIGS. 12 and 13), where the weight of each consequent is given by the higher degree of activation between the rules that activate it.

[0127] In FIG. 14 and FIG. 15, the response surfaces of the output variables from the FIS (4) described in this section are shown. These figures show that the system developed presents the desired behavior, which was described linguistically in the rules of FIS activation (4).

[0128] The proportional gain, K.sub.p, and the derivative gain, K.sub.d, of the PID algorithm (5) were constant and equal to 0.5%/bar for K.sub.p and 1200 s. %/bar for K.sub.d during all tests performed.

Performance Tests

[0129] With the objective of verifying the performance of the controller described in this document in various operating scenarios, several computer tests were run using a mathematic model of an offshore production system.

[0130] In these tests, the invented controller is called an “FPID-P.sub.2,” in reference to its hybrid fuzzy PID architecture, and to the use of pressure upstream of the choke valve (P.sub.2) as a measured variable. The results obtained were compared to classic PID controllers that use the pressure upstream of the choke valve (P.sub.2) as the controlled variable, and the pressure at the base of the riser (P.sub.1), called PID-P.sub.2 and PID-P1, respectively.

Suppression of Slugging

[0131] With the objective of verifying the invention's capacity to suppress slugging, a test was performed in which the initial opening of the choke valve is fixed at 40%, in which region the flow is characterized by the occurrence of severe slugging. After 2000 seconds of simulation, the loop is closed through the controller being evaluated, which acts on the system until the end of the test, at 5000 seconds.

[0132] The results for FPID-P.sub.2 and PID-P.sub.1 controllers are shown in FIG. 16, indicating the responses of the flow of liquid produced, the pressure upstream of the choke, and the opening of the choke valve.

[0133] It is seen that the FPID-P.sub.2 controller was successful in the task of stabilizing the flow from the system. However, when compared to the PID-P.sub.1 controller, a significantly slower control action (3) is noted in the FPID-P.sub.2 controller, which leads to the need for more time for complete suppression of slugging. That greater delay in suppression is due to less sensitivity of the variable seen by the FPID-P.sub.2.

[0134] With the objective of verifying whether these results repeat in other conditions, the test was repeated for a more severe situation, with an initial opening of the choke valve at 100%. The result of this second test is shown in FIG. 17.

[0135] As can be seen in the graph of this second test, the FPID-P.sub.2 controller was able to suppress the slugging more quickly than the reference controller, even with a significantly slower control action (3). This better performance is a consequence of the restrictive action (9) of the FPID-P.sub.2 controller, which closes the choke valve through a specific heuristic that is optimized for this type of problem. FIG. 17 shows that although the linear PID-P.sub.1 controller observes a better-quality variable (P.sub.i), it loses performance when the choke valve is opened in the positive pressure cycles, which characteristic is inherent to linear controllers.

[0136] Seeking to investigate the importance of the heuristic action implemented by the FIS (4) of the FPID-P.sub.2 controller, the same tests were repeated for the PID-P.sub.2 controller, which uses a classic PID algorithm and the pressure at the top of the riser as the controlled variable. The gains used in this controller were the same as those used in the PID parcel (3) of the FPID-P.sub.2 controller, with k.sub.i fixed at 0.01%/s.Math.bar. The results are shown in Table 1, where the symbol ‘-’ represents tests in which the PID-P.sub.2 controller was unable to stabilize the flow.

TABLE-US-00001 TABLE 1 Time necessary for suppression of slugging (FPID-P.sub.2 and PID-P.sub.2). Choke opening FPID-P2 PID-P2 20% 280s 285s 40% 830s — 60% 910s — 80% 930s — 100%  1270s  —

[0137] Analysis of Table 1 shows the crucial importance of heuristic action of the FPID-P.sub.2 controller, since a “pure” PID controller that also only observes the pressure at the top of the riser was only capable of suppressing slugging that was low in severity, which occurs very close to the opening at which the process is found to be in static stability (18%). In all other tests, the pure PID that observes the same surface variable as the FPID-P.sub.2, was incapable of suppressing the slugging present in the system.

[0138] FIG. 18 shows the flow of produced liquid and the control action of the PID-P.sub.2 controller throughout the test in which the opening of the choke was initialized at 40%. As discussed previously, the graphs show the complete inability of the controller to stabilize the flow.

Limit of Choke Actuation Speed

[0139] In the tests presented above, it was noted that the PID-P.sub.1 controller, based on subsea pressure, has a significantly faster control response than that of the FPID-P.sub.2 controller. For example, in the test presented in FIG. 17, the PID-P.sub.1 controller closes the choke valve from 100% to 40% in just 40 seconds. This action, which has an average speed of 1.5%/s, reaches instantaneous speeds of up to 3.26%/s at the start of the close.

[0140] Because of their large sizes, actuation of choke valves is usually slow, with complete closure or opening taking up to three minutes. This is a fundamental limitation to the use of anti-slugging controllers based on linear algorithms.

[0141] The consequence of the slowness on choke valve actuation in the control signal effectively delivered to the plant can be seen in FIG. 19, which shows the real openings of the valve when a sinusoidal control signal with maximum speed of 3%/s is applied to them. Three valves are included, one with instantaneous action, one that needs 60 seconds to perform a complete transition, and one that needs 120 seconds for a complete transition. The deformations presented in FIG. 19 show the reason that slow choke valves pose a huge challenge for use of anti-slugging controllers.

[0142] It is reasonable to assume that the invented controller is less sensitive to limitations in actuation speeds as it is a slower controller. With the objective of verifying this hypothesis, the tests performed in the previous section were repeated considering the choke valves that make a complete transition in 60, 90, 120 and 180 seconds. The times necessary to suppress the slugging by the FPID-P.sub.2 controller and the PID-P.sub.1 controller in each test are presented in Table 2.

TABLE-US-00002 TABLE 2 Time necessary for suppression of slugging for different speeds of choke valve actuation (FPID-P.sub.2 and PID-P.sub.1) Opening Complete Transition Time of the Choke Valve of the 60s 90s 120s 180s Choke FPID-P.sub.2 PID-P.sub.1 FPID-P.sub.2 PID-P.sub.1 FPID-P.sub.2 PID-P.sub.1 FPID-P.sub.2 PID-P.sub.1 20% 280s  36s 280s  46s 280s 78s 270s 114s 40% 830s 292s 830s 1687s 830s — 830s — 60% 911s 344s 910s — 910s — 910s — 80% 930s 674s 930s — 930s — 930s — 100%  1270s  1364s  1260s  — 1260s  — 1261s  —

[0143] Analysis of Table 2 confirms the hypothesis that the FPID-P.sub.2 controller is not very sensitive to the limitation on the actuation speed of the choke valve. In truth, there was no loss of controller performance at all, as it was able to suppress the slugging in nearly the same interval of time in all tests. On the other hand, the effect of limiting actuation speed was catastrophic for the PID-P.sub.1 controller, with loss of suppression capacity in most of the tests in which the choke valves take 90 seconds or more to make a complete transition.

[0144] FIG. 20 shows the responses of liquid outflow and opening of the choke valve for two tests in which the choke valve is initiated at 40% opening, with an instantaneous actuation of the valve and another with slow actuation, in which 180 seconds are necessary for a complete transition to occur. Analysis of the graphs shows that the FPID-P.sub.2 controller was practically immune to the slowness of the choke valve. The only observable difference occurs right after 2500 seconds, when a slight alleviation of the control action is seen in the test in which the choke valve is slow. On the other hand, the action of the PID-P.sub.1 controller was completely disfigured, resulting in an operation contrary to what was expected, with intensification of the severity of the slugging after activation of the controller.

[0145] This test shows that although the FPID-P.sub.2 controller observes a variability with low sensitivity and non-minimum phase, the pressure upstream of the choke, its capacity to detect the slugging, and to act heuristically not only offset this deficiency, but in some cases ensure performance that is superior to that of linear controllers that observe controllers more suitable to anti-slugging control.

Stabilization of an Unstable Point of Operation

[0146] Verification of the capacity of an anti-slugging controller to stabilize a stable point is quite simple and consists of awaiting stabilization of the flow, and then disconnecting the controller, keeping the choke valve fixed in the last position defined by the algorithm. If the flow remains stable after disconnection, the controller merely automates the static choking; on the other hand, if the system begins to oscillate again, the controller was in fact stabilizing an unstable point of operation.

[0147] In order to verify the stabilization capacity of the FPID-P.sub.2 controller, a test was performed in which the choke valve was initialized at 50% of opening, with the controller being turned on at 2000 and turned off at 10,000 seconds. The results of this test are shown in FIG. 21.

[0148] The results show that after disconnecting the controller at 10,000 seconds, the system again presented oscillations, even without the introduction of any disturbance. It can therefore be concluded that the invention's controller is in the class of controllers that in fact stabilize unstable points of operation, and therefore allow gains in oil production.

Production Gains

[0149] Seeking to establish the limits of production gain provided by the FPID-P.sub.2 controller, a test was performed in which the initial setpoint of the controller was adjusted to a high value, corresponding to a 10% opening of the choke valve (statically stable region). In this test, whenever the system goes into a permanent regime, the setpoint is decreased by 0.2 bar. This process continues until a very low setpoint causes the system to enter into unstable operation, marking the close of the test. For each point of stable operation obtained in the test, the liquid output at the exit from the riser and the average opening of the choke valve are determined.

[0150] The results obtained in the testing of the FPID-P.sub.2, the PID-P.sub.2 and PID-P.sub.1 controllers are presented in FIG. 22, where the average outflows in the open-loop system are compared, assuming the occurrence of slugging for choke valve openings larger than what is critical (18%). This graph shows that the FPID-P.sub.2 controller was able to stabilize the system at average choke valve openings of up to 34%, with corresponding production of 9.35 kg/s, which is a gain of 4.1% of production in relation to the best case of static choking, in which the production is 8.98 kg/s. The FPID-P.sub.2 controller also outperformed the PID-P.sub.2 controller, which had maximum outflow of 9.13 kg/s. On the other hand, performance of the FPID-P.sub.2 controller was less than that of the PID-P.sub.1 controller, which was able to stabilize production at a value of 9.46 kg/s, a 5.3% gain over the best case of static choking.

[0151] Therefore, the invented controller provides a lower gain in production when compared to the controller that has access to flowline pressure. This disadvantage is a direct consequence of use of a controlled variable with less sensitivity and non-minimum phase in the FPID-P.sub.2 controller, because in the absence of slugging, the controller behaves like a PID (3) controller based on this variable, and is therefore subject to the same limitations as linear controllers.

Rejection of Disturbances

[0152] In order to verify the behavior of the FPID-P.sub.2 controller against typical disturbances in a production system, two more tests were performed.

[0153] In the first test, the effect of production with high-frequency (noise) variations on the capacity of the controller (1) to keep the system stable was considered. These variations were modeled using the following equation:

W.sub.T=k.sub.p(P.sub.ra+P.sub.σ+P.sub.l)

where: [0154] W.sub.T is the total outflow from the well. [kg/s] [0155] k.sub.p is the constant of well productivity [kg/(s.Math.bar)] (Constant) [0156] P.sub.ra is the apparent static pressure in the reservoir. [bar] (Constant) [0157] P.sub.α is an independent Gaussian stochastic and average null process. [bar] [0158] P.sub.l is the pressure at the wellhead. [bar]

[0159] A value equivalent to 20% of the apparent pressure of the reservoir, P.sub.ra, used in the model of the producing well, was used as variance of the Gaussian noise. This modeling is equal to a reservoir with fluctuations in its static pressure, which causes fluctuations in the gas and liquid outflows, even with a constant pressure at the wellhead.

[0160] The results of the test for both controllers operating at the setpoint limit are presented in FIG. 23, where it can be seen that both controllers are capable of suppressing slugs and maintaining system stability, even when outflow fluctuations are present. However, maintenance of stability can only be assured with operation at average valve openings that are slightly smaller than those attained in the production scenario without fluctuations.

[0161] The smaller valve opening causes the maximum production attained by the FPID-P.sub.2 controller to fall from 9.35 kg/x to 9.33 kg/s, and by the PID-P.sub.1 controller from 9.46 kg/s to 9.44 kg/s. However, these reductions do not imply greater gains in production, as the stability of the open-loop system was also affected by the fluctuations, becoming stable only for openings smaller than or equal to 16%, which corresponding production is 8.73 kg/s. Thus, the production gains become 6.9% for the FPID-P.sub.2 controller, and 8.1% for the PID-P.sub.1 controller. The fluctuations, also present in the surface pressures, were not interpreted as slugging by the FPID-P.sub.2 controller, thus not triggering the unnecessary use of the restrictive action (9), which would close the choke valve gradually.

[0162] In the second test, the types of disturbances considered were degrees, which model some typical disturbances of oil production systems, for example the start of production of another well in systems in which the riser is shared, or even sudden changes in the characteristics of the reservoir or production system.

[0163] The system disturbance was the same used in the previous test, with the stochastic process Pa being replaced by a deterministic signal given by an ascending step to 5000 seconds and to a descending step to 1000 seconds. Both steps have amplitude equivalent to 20% of the apparent pressure of the reservoir, P.sub.ra, used in the model of the producing well. The results are shown in FIG. 24.

[0164] An analysis of the graphs shows that although the FPID-P.sub.2 controller has had good regulatory performance in the ascending step, which is stabilizing, it was unable to maintain system stability in the descending step, making actuation of the restrictive action necessary (9) to reestablish stability after the occurrence of two slugs. If this heuristic action is not provided by the FIS (4), the system would be unstable indefinitely, because at the moment of the negative step, the opening of the choke was approximately 40%, in which situation a PID controller based on the top pressure is not capable of stabilizing, as can be seen in the test in FIG. 18.

[0165] Another interesting observation is that after application of the ascending step, the opening of the choke and production were greater in the test with the FPID-P.sub.2 controller, contrary to all of the results obtained up to that moment. Furthermore, in the test with the PID-P.sub.1 controller, there was action to close the choke valve after application of the step, causing an unnecessary loss in production, given that increases in the pressure in the reservoir enable stabilization of the system at greater valve openings. This behavior can be explained by greater robustness of the setpoint of the controllers based on the pressure from the top, since this magnitude is less sensitive to disturbances imposed on the production system.

[0166] The last point to observe from this test is that, again, the PID-P.sub.1 controller presented an exaggeratedly rapid response, with an almost instantaneous opening of the choke valve at the moment of application of the ascending step. As discussed above, the actuation of these valves is usually slow, making this type of actuation impossible. To verify the effect of the limitation on actuation speed to the regulatory capacity of the system, the tests were repeated with a more realistic choke valve, which causes a complete transition in 180 seconds. The results of this test are shown in FIG. 25.

[0167] The realistic consideration of slowness in choke actuation drastically affected the capacity of the PID-P.sub.1 controller to regulate the system, because although it was capable of stabilizing the system in the initial situation, in which the choke valve was only 20% open, the stability was indefinitely lost after application of the first step, in an instant in which the choke was 45% open. This result exemplifies the importance of an anti-slugging controller being able to stabilize a system for any initial conditions, and it excludes the idea that a simple manual restriction of the valve before activation of the automatic controller can eliminate the disadvantage of a low stabilization capacity.

[0168] In turn, the FPID-P.sub.2 controller, which does not present loss of stabilization capacity as a function of slow actuation of the choke valve, practically maintains the response of the prior test, with only two events of slugging occurring again after the descending step.

Operation with an Unstable Setpoint

[0169] For a production system modeled for this invention, the setpoints have lower limits, below those at which the linear controllers tend to induce the occurrence of slugging. Furthermore, it is always recommendable to operate with a setpoint that is a little greater than its limit, thus avoiding small disturbances or changes in the characteristics of the process destabilizing the system, even if this implies a small reduction in production.

[0170] In the case of the PID-P.sub.1 controller, the limit setpoints were determined in the previous tests as 67.8 bar in the modeling without fluctuations, and 68.0 bar in the modeling in which fluctuations were considered in the outflow from the well. Although the reduction of the setpoints below these values lead to slugging in the system, this is not the only way that a closed-loop production system may become unstable, as the changes in the characteristics of the plant may cause a stable setpoint to become unstable. Within the context of oil production, the change that can most easily cause this phenomenon is the reduction of the outflow from the well, caused by the natural depletion of the reservoir, and by problems in the well itself, such as obstruction of the piped region.

[0171] To verify the behavior of the FPID-P.sub.2 and PID-P.sub.1 controllers during the occurrence of changes in the characteristics of the process, a test was set up in which the apparent pressure of the reservoir is slightly reduced from 112.5 bar to 110 bar after stabilization of the flow. The responses of the outflow and the control signal to the PID-P.sub.1 controller are presented in FIG. 26, in which it can be seen that the PID-P.sub.1 controller was not able to stabilize the system after the small reduction in the apparent pressure of the reservoir because its setpoint ceased to be stable. In a real situation, the solution to this problem requires an operator to perceive the lack of control of the process, to identify the well that is slugging, and to adjust the setpoint of the controller.

[0172] One way of preventing these situations from occurring frequently is to adjust a setpoint that is farther away from the stability limit, thus preventing small variations in the process conditions from leading to instability. The problem of this solution is that it implies a decrease in production.

[0173] The same test was done with the FPID-P.sub.2 controller, obtaining the results presented in FIG. 27, in which the outflow from the exit can be seen, the pressure at the top of the riser, the control signal, and the degree of slugging severity (8).

[0174] Before activation of the controller, marked by the line traced at 2000 seconds, the estimator continuously indicated the occurrence of slugging at an intensity of 1.8. After activation, this signal commands the heuristic close of the choke valve, as can be seen in the fourth chart, stabilizing the system.

[0175] After stabilization, the PID parcel (5) of the controller seeks the pressure setpoint normally, until at 10,000 seconds there is a decrease in the apparent pressure of the reservoir, leading to the occurrence of slugging, which is reflected in the top pressure, and promptly detected by the slugging severity estimator (6), which again acts heuristically in closing the valve until stabilization.

[0176] After the new stabilization, the PID parcel (5) of the controller again pursues the setpoint, which is now unattainable because it became unstable after the change in pressure, again leading to the formation of slugging, which is promptly detected and suppressed.

[0177] As the setpoint of the controller is constant, the process continues indefinitely, with generation of small slugs in the form of wavelets in the outflow from the exit point. In the top pressure, the only variable that the controller in fact sees, the deformation is much more significant, with deviations of up to 2 bar in relation to the setpoint. This exemplifies as a non-linear control action (3), which apparently harms the system by going against the classic objective of minimizing the error, and in truth this favors the control objective. This type of action, which cannot be implemented by a linear controller, allows this controller to perform well even being dependent on a low-quality variable for control purposes.

[0178] In this test, the average outflow obtained was 8.71 kg/s, slightly lower than the maximum outflow attainable with a stable setpoint, which became 8.74 kg/s after reduction of pressure in the reservoir, but significantly higher than the maximum outflow obtained through the static choking technique, 8.35 kg/s for the new conditions of the reservoir. This shows that from the production point of view, operation with an unstable setpoint is not a huge problem, and it may be preferable in relation to an operation whose setpoint is far away.

[0179] Naturally, operating with an unstable setpoint is not the ideal situation, but if this happens, the loss of performance of the FPID-P.sub.2 controller is significantly less than that seen with the PID-P.sub.1 controller. In addition, as the invented controller (1) has a slugging-severity estimator (6), it may be used to create an alarm on the operation screen, indicating an unstable operation and the need to readjust the setpoint.