METHOD AND DEVICE FOR STABILIZING A FAULT SYSTEM BY CONTROLLED INJECTION OF A FLUID

Abstract

The present invention relates to a method for stabilizing a fault system (1) comprising a first rock block (2) and a second rock block (4) defining a fault (6), said method comprising the following successive steps: a) providing a displacement command for the first rock block (2); b) measuring a displacement value for the first rock block (2); c) generating a fluid pressure control signal by applying a control law; d) injecting or pumping a fluid into said fault (6) according to the pressure control signal; and e) repeating the steps b) of measurement, c) of generation, and d) of injection, at a predetermined frequency. The invention also relates to a device for stabilizing such a fault system implementing the stabilization method.

Description

Title of the invention: METHOD AND DEVICE FOR STABILIZING A FAULT SYSTEM BY CONTROLLED INJECTION OF A FLUID Technical field of the invention

[0001] The present invention relates on the one hand to a method for stabilizing a fault system and on the other hand to a stabilization device implementing the stabilization method. State of the art

[0002] Methods for releasing seismic energy by moving a rock block at a fault or fault system are based on injecting a fluid into the Earth's crust.

[0003] Some of these methods are based on a control method, called "traffic light System", and are based on a decision variable, for example the amplitude of an earthquake, and a threshold value above which actions, for example stopping or extending the injection are carried out.

[0004] For example, from American document US 2018 / 231987, we know a method for controlling the release of seismic energy in which a fluid is injected into wells located along a fault. The injection of the fluid into the wells is determined from a thermal map comprising a plurality of data measured in the fault, such as potential energy, viscosity or previous seismic events.

[0005] Although these methods generally allow the dissipation of seismic energy accumulated at a fault, their implementation relies on the generation of small earthquakes which can damage buildings, production tools, or structures located nearby.

[0006] First of all, there is a need to limit the number of data to be measured to determine the injection of the fluid. There is also a need to determine data whose measurement offers sufficient precision to correctly inject the fluid. Presentation of the invention

[0007] The invention thus aims to provide a method for injecting a fluid into a fault in a controlled manner while limiting the magnitude of an earthquake to a threshold value, or even without generating an earthquake.

[0008] In this regard, there is proposed according to a first aspect of the invention a method for stabilizing a fault system comprising a first rock block and a second rock block defining a fault between them, said method comprising the following steps: following provisions:

[0009] a) providing a displacement instruction for the first rock block relative to the second rock block of said fault system, said displacement instruction being determined such that if a displacement of the first rock block relative to the second rock block in accordance with said instruction is produced, the energy accumulated in said fault system is progressively released;

[0010] b) measuring a displacement value of the first rock block relative to the second rock block of said fault system;

[0011] c) generation of a fluid pressure control signal by application of a control law and from a displacement error corresponding to the difference between the displacement setpoint and the measured displacement value;

[0012] d) injecting or pumping a fluid into or near said fault of said fault system, according to the pressure control signal; and

[0013] e) repeating step b) of measurement, c) of generation and d) of injection, at a predetermined frequency.

[0014] Thanks to the method according to the invention, it is possible to control the movement of the first rock block by injecting a fluid at a pressure determined by the control law and allowing the first rock block to follow a predetermined trajectory, corresponding to the movement instruction.

[0015] Thus, by controlling the movement of the first rock block, it is possible to avoid an abrupt movement triggering a sudden release of energy which could cause an earthquake.

[0016] Furthermore, the method according to the invention makes it possible to stabilize the fault system from a limited number of data to be measured. Indeed, it is possible to stabilize the fault system from a displacement value of the first rock block relative to the second rock block. This is all the more advantageous since this data can be measured with sufficient precision to generate a pressure control signal which guarantees the stability of the fault system.

[0017] By stabilization, the present invention aims to describe a method which tends to bring the fault system back to a state of equilibrium after having been moved away from the latter. Strictly speaking, the method aims to asymptotically stabilize, in the Lyapunov sense, the fault system.

[0018] By displacement, the present invention aims to describe a distance traveled, called sliding distance, by the first rock block relative to the second rock block, or a speed, called sliding speed, of the first rock block relative to the second rock block.

[0019] The displacement of the first rock block relative to the second rock block may correspond to the relative displacement of several points of the first block relative to several points of the second rock block.

[0020] The displacement of the first rock block relative to the second rock block may also correspond to the average displacement of points of the first rock block relative to points of the second rock block.

[0021] The displacement of the first rock block relative to the second rock block may also correspond to the average displacement of a group of points of the first rock block relative to a group of points of the second rock block.

[0022] By fault, the present invention aims at a rupture zone deep in the rock, which can extend to an earth's surface.

[0023] It is because there is a correlation between the pressure of the fluid injected into the fault and the friction between the first rock block and the second rock block that it is possible to modify the friction between these blocks by adjusting the pressure of the injected fluid to move the first rock block along a predetermined trajectory.

[0024] The accumulated energy can thus be released gradually and without causing the slightest earthquake, up to a new stable equilibrium point where it may no longer be necessary to apply the stabilization process.

[0025] The movement instruction of the first rock block can be a speed instruction.

[0026] The speed setpoint of the first rock block may be a constant value. The speed setpoint of the first rock block may be defined by one or more ramps. The speed setpoint of the first rock block may be defined by one or more speed steps. The speed setpoint of the first rock block may be defined by the combination of at least one constant value, and / or a ramp and / or a step.

[0027] According to an exemplary implementation, the stabilization method may further comprise a step of determining said control law from a mathematical model representing the fault system and taking into account uncertainties linked to disturbances of said fault system, said mathematical model taking the following form:

[0028] x = Aox + AB (x, t) u + Bo(u + h (x, t))

[0029] where Ao and Bq are constant matrices representing the nominal part of the system, J is a state vector representing the displacement of the first rock block relative to the second rock block at at least one point of the fault, u is a vector of the system inputs representing the pressure control signal, AB (x, t) is a matrix representing uncertainties related to the influence of the input li on friction, h (x, t) is a function comprising uncertainties related to friction, the position and geometry of the fault, elastic, viscous and inelastic properties of the rock blocks, and the dependence of the fault system on phenomena multiphysics and multiscales which are not taken into account in the nominal model.

[0030] Advantageously, the mathematical model does not need to be updated or recalculated after each measurement or each injection. Indeed, it is only necessary to determine the state vector

[0031] According to another example, the step of determining the control law may comprise a step of determining a stability parameter 9 of said control law, said control law taking the following form:

[0032] u=-R'lBG0x

[0033] where R is a predetermined coefficient influencing the speed of the system,

[0034] the stability parameter 6 being the solution of the Riccati equation:

[0035] A?e + 3A() _ 3BoR-1Bq8 = - Q

[0036] where Q is a parameter which depends on a coefficient fi and R according to the following formula and conditions: [00371 e=e0+^ 2 he r' 12 he \

[0038] with

[0039] h(x,t) < fi || X ||

[0040] where ln is the identity matrix.

[0041] According to one example, the stabilization method may further comprise a step of estimating the state vector x of said mathematical model, by a state observer, from the measurement of the displacement value of the first rock block relative to the second rock block of said fault system.

[0042] The step of determining the stability parameter 9 can be carried out in real time after each measurement step b).

[0043] The step of determining the stability parameter 9 may precede the measurement step b).

[0044] According to another example of implementation, the measurement step b) may comprise a sub-step of determining a speed value of the first rocky block relative to the second rocky block, or a value of distance traveled by the first rocky block relative to the second rocky block.

[0045] The invention also relates, according to a second aspect, to a device for stabilizing a fault system comprising a first rock block and a second rock block defining a fault between them, said device comprising:

[0046] - a control unit configured to receive a movement instruction from the first rock block relative to the second rock block of said fault system, said displacement setpoint being determined such that if a displacement of the first rock block relative to the second rock block conforming to said instruction is produced, the energy accumulated in said fault system is gradually released;

[0047] - a measuring device configured to measure, according to a predetermined frequency, a displacement value of the first rock block relative to the second rock block of said fault system, said control unit being configured to generate a fluid pressure control signal by applying a control law and from a displacement error corresponding to the difference between the displacement setpoint and the measured displacement value; and

[0048] - an injection device configured to inject or pump a fluid into said fault or near said fault of said fault system, according to the pressure control signal.

[0049] According to an exemplary embodiment, the control law can be determined from a mathematical model representing the fault system and taking into account uncertainties linked to disturbances of said fault system, said mathematical model taking the following form:

[0050] x = Aox + AB(x, t)u + Bq (u + h(x, t))

[0051] where Aoet Bq are constant matrices representing the nominal part of the fault system, A is a state vector representing the displacement of the first rock block relative to the second rock block, u is a vector of the model inputs representing the pressure control signal, AB ( x, t ) is a matrix representing uncertainties related to the influence of said pressure control signal on friction, h ( .x, t ) is a function comprising uncertainties related to friction, to the position and geometry of the fault, to elastic, viscous and inelastic properties of the rock blocks, and to the dependence of the fault system on multiphysical and multiscale phenomena which are not taken into account in the nominal part of said mathematical model.

[0052] According to another exemplary embodiment, the control unit may comprise a state observer configured to estimate the state vector x of said mathematical model from a measurement of the displacement value of the first rock block relative to the second rock block of said fault system by the measuring device.

[0053] According to one embodiment, the device may comprise a plurality of injection devices and a plurality of measuring devices.

[0054] According to one example, the control unit may be configured to generate a fluid pressure control signal for each injection device of said plurality of injection devices such that the displacement values ​​of the first rock block measured by the plurality of measuring devices are substantially equal to the displacement setpoint.

[0055] According to another example, which may be complementary to the example described above Alternatively, the control unit may be configured to generate a fluid pressure control signal for each injection device of said plurality of injection devices such that the average of the displacement values ​​measured by the plurality of measuring devices is substantially equal to the displacement setpoint.

[0056] According to one embodiment, the control unit can be configured to calibrate the setpoint according to technical limitations of the fluid injection device.

[0057] Indeed, the fluid pressure control is limited by the capacity of the fluid injection device. For example, if a movement instruction requires a fluid pressure control that is too high in view of the capacity of the fluid injection device, the control unit can provide a new instruction based on these technological limits.

[0058] This is all the more interesting in the case where the setpoint is a distance. Indeed, the control unit can be configured to estimate a minimum time to reach the setpoint based on the capabilities of the fluid injection device. Brief description of the figures

[0059] We will now continue the description of the invention by describing an exemplary embodiment, given below for illustrative and non-limiting purposes, with reference to the appended drawings in which: - [Fig.l] schematically represents a fault system comprising a first rock block and a second rock block defining a fault in which a control device according to the invention is installed, and - [Fig.2] represents the architecture of the servo device of [Fig.l]. Detailed description

[0060] [Fig.l] schematically represents a fault system 1 formed by a first rock block 2 and a second rock block 4 defining a fault 6, as well as a control system 10 of the speed of the first rock block 2 relative to the second rock block 4.

[0061] The fault system 1 may be subjected to stresses acting on the first rock block 2 and / or the second rock block 4 and generally tending to move the rock blocks relative to each other, on either side of the fault 6.

[0062] The fault system 1 is said to be stable when it is in a state of static equilibrium, that is to say that the resultant of the stresses exerted on the first rock block 2 and on the second rock block 4 is zero, or when it remains close to the state of static equilibrium under weak disturbances.

[0063] Fault system 1 is said to be unstable when it is no longer in the state of static equilibrium and / or when it does not tend to return to this state of static equilibrium under low disturbances.

[0064] In this case, the stresses tend to move one of the first rock block 2 or the second rock block 4 relative to the other of the first rock block 2 or the second rock block 4. This phenomenon can lead to an accumulation of energy by elastic deformation of the rock blocks 2 and 4, without however causing a displacement of the first rock block 2 relative to the second rock block 4.

[0065] If the stresses present exceed a resistance threshold of the rock blocks 2 and 4, these can cause a sudden displacement of the first rock block 2 or of the second rock block 4, respectively relative to the second rock block 4 or to the first rock block 2. This sudden displacement can result in the rapid release of the accumulated energy and generally leads to an earthquake.

[0066] In other words, during an earthquake, one of the first rock block 2 or the second rock block 4 has a relatively high speed compared to the other of the first rock block 2 or the second rock block 4, when the stresses are too high.

[0067] For the sake of clarity, only the relative movement of the first rock block 2 will be described in the remainder of the description. However, it will be clearly understood that one of the first rock block 2 or the second rock block 4 may be fixed while the other of the first rock block 2 or the second rock block 4 moves, that both rock blocks 2 and 4 may move in the same direction and at different speeds, or that the rock blocks 2 and 4 move in different directions.

[0068] The first block 2 and / or the second block 4 comprises a well 5 having a first end opening here onto an earth surface 3 and a second end opposite the first end opening into or near the fault 6.

[0069] Alternatively, the first end of the well 5 may open onto an underground space such as a tunnel for example.

[0070] The control system 10 comprises a fluid injection device 12, a measuring device 14 and a control unit 16 in communication with the fluid injection device 12 and the measuring device 14.

[0071] The communication between the control unit 16 and the injection device 12, and the detection device 14 can be wired and / or wireless.

[0072] The fluid injection device 12 is configured to inject a fluid, for example water, under pressure near the fault 6 or directly into the fault via the well 5.

[0073] The injection device 12 is also configured to pump fluid from the fault 6 or from an area located near the fault.

[0074] The injection device 12 can be installed at one end of the well 5 or between the first and second end of the well.

[0075] The measuring device 14 is configured to measure data at a point on the fault 6, in particular the displacement of the first rock block 2 relative to the second rock block 4.

[0076] In the example shown in [Fig.l], three measuring devices 14 are arranged at distinct points of the fault 6, so as to measure data at three distinct points of the fault 6.

[0077] According to a variant not shown, a single measuring device 14 can be configured to measure data at several distinct points of the fault 6.

[0078] By displacement, the present invention aims to describe a distance traveled by the first rock block 2 relative to the second rock block 4, or a speed, called sliding speed, of the first rock block 2 relative to the second rock block 4.

[0079] The measuring device 14 is also configured to measure the pressure of fluid injected by the fluid injection device 12.

[0080] The data measured by the measuring device 14 may include the sliding speed of the first rock block 2, the distance traveled by the first rock block 2, movements of the first rock block 2 and / or of the second rock block 4 on the earth's surface 3, deformations of the blocks 4 and 6 and more generally measurements linked to sliding in the fault 6.

[0081] The measuring device 14 can thus comprise one or more sensors, including a displacement sensor, a deformation sensor, a geophone, an accelerometer, an inclinometer, a stress and pressure sensor and more generally any kind of sensors making it possible to measure the relative displacement between the first rock block 2 and the second rock block 4 at at least one point of the fault 6.

[0082] The data can also be measured by a satellite system such as GPS (Global Positioning System) or INSAR (IN-terferometric Synthetic Aperture Radar) system.

[0083] In the example shown, the system 1 comprises several wells 5 and the control system 10 comprises for this purpose a plurality of injection devices 12 and measuring devices 14, each injection device 12 and each measuring device 14.

[0084] Each injection device 12 and each measuring device 14 is in communication with the control unit 16.

[0085] [Fig.2] illustrates a functional diagram of the control system 10 applied to the system 1 formed by the first rock block 2 and the second rock block 4, which is here represented by a block.

[0086] The injection device 12 and the measuring device 14 are also shown. by blocks.

[0087] The control unit 16 is represented by a block delimited by dotted lines and comprises a comparator 162 and a corrector 164.

[0088] The comparator 162 is configured to compare a displacement setpoint D of the first rock block 2 with a displacement of the first rock block 2 relative to the second rock block 4, measured by the measuring device 14 at a point on the fault 6.

[0089] The instruction D may be an instruction for the distance traveled by the first rock block 2 relative to the second rock block 4 or a speed instruction for the first rock block 2 relative to the second rock block 4.

[0090] The comparator 162 is configured to determine a displacement error ed which corresponds to the difference between the displacement setpoint D and the measured displacement of the first rock block 2.

[0091] The corrector 164 receives as input the displacement error ed generated by the comparator 162.

[0092] The corrector 164 is configured to determine and output a pressure control signal U from the displacement error ed. The pressure control signal U determined by the corrector 164 is intended to minimize the displacement error ed.

[0093] The pressure control signal U is sent to the injection device 12 which processes it and injects or pumps fluid from the pressure control signal U.

[0094] The control unit 16 can be configured to display an error message if the displacement setpoint D causes the generation of a pressure control signal exceeding the capabilities of the injection device 12. Furthermore, the control unit 16 can be configured to calculate and display a maximum setpoint admissible by the injection device 12 taking into account the technical and technological limits of the injection device.

[0095] Depending on the pressure of the fluid injected or pumped into or from the fault 6 of the system 1, the first rock block 2 moves relative to the second rock block 4, more or less quickly.

[0096] The displacement of the first rock block 2 is measured at a point on the fault 6 by the measuring device 14 which generates at least one signal Y corresponding to the displacement of the first rock block 2 relative to the second rock block 4.

[0097] The measuring device 14 also generates a signal corresponding to the pressure injected or pumped into or from the fault 6 by the injection device 12.

[0098] The Y signals generated by the measuring device 14 are sent to the control unit 16.

[0099] In particular, the signal Y corresponding to the displacement of the first rock block 2 is sent to comparator 162 to calculate the displacement error ed.

[0100] The control unit 16 can be configured according to several configurations, in particular when the system comprises a plurality of wells 5.

[0101] For example, in a first configuration, the control unit 16 generates a pressure control signal U for each injection device 12, so that the displacement of the first block 2 at each well 5 follows the displacement setpoint D. In other words, the displacement setpoint D is identical, at each point of the fault 6 and in each well 5. This has the effect of causing a homogeneous displacement of the first rock block 2.

[0102] In a second configuration, the control unit 16 generates a pressure control signal U for each injection device 12, so that the average of the displacements of the first block 2 at the level of the wells 5 is substantially equal to the displacement setpoint D. In other words, the displacement setpoint D corresponds to the average of the displacements of the first block 2 at the level of each well 5 and at each point of the fault 6 located near an injection device.

[0103] For example, in order to illustrate the configurations of the control unit described above, it is considered that the displacement setpoint D is a speed setpoint given here as an example equal to 2 mm / s. The displacement setpoint D is determined so as to gradually release the energy accumulated in the fault system 1. This can for example be achieved by setting a displacement setpoint value D which is approximately 1000 times lower than a sliding speed of the first rock block relative to the second rock block, called seismic, for which the fault system 1 is unstable. Thus, the speed setpoint of 2 mm / s given as an example can be determined if the seismic sliding speed is substantially equal to 2 m / s.

[0104] In the first configuration, the control unit 16 generates a pressure control signal U for each injection device 14 so that the first rock block 2 moves at a speed of 2 mm / s relative to the block 4 while in the second configuration, the control unit 16 generates a pressure control signal U for each injection device 14 so that the average of the speeds of the first block at the three wells 5 is substantially equal to the displacement setpoint D.

[0105] We will now explain in more detail the principles which are the basis of the operation of the control system 10 for the movement of the first rock block 2.

[0106] The injection device 12 is controlled by a control law which develops pressure control signals U from the signal Y received from the measuring device 14. The control law as well as the methodology for adjusting this control law will therefore be described in detail in the rest of the description.

[0107] First, a mathematical model, hereinafter called a fault model, of fault system 1 is used.

[0108] In the present embodiment, a particular form of fault model has been chosen. Other forms of fault models may be used without, however, departing from the scope of the invention.

[0109] The fault model can thus be written in the form of a system of equations of ordinary derivatives called equations of state:

[0110] x = A(x, t)x + B(x, t)u + g(x, t) (1) [YES] y = Cx

[0112] with x the state vector of the system corresponding to the displacement of the first rock block 2 relative to the second rock block 4 at at least one point, u the vector of the inputs of the system corresponding to the pressure control signal, A' the vector of the outputs, A a matrix representing phenomena of elasticity, viscosity or inelasticity, B a matrix representing the influence of pressure changes on the dynamics of the system through friction and C is the output matrix of the system.

[0113] Matrices A and B can be decomposed into a nominal part and a part

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120] disturbed with uncertainties related to fault system 1. The nominal part can be determined by identification, for example by stimulating fault system 1 by injecting a small amount of fluid into one or more wells 5, or with other already known geophysical data. In addition, a state observer configured to estimate state x from signal Y can be used. Thus, we can write the matrices A and B as follows: A(x, t) = Ao + AA( x. t) (2) where Ao and Bo are constant matrices representing the nominal part of the system while AA and AB are matrices representing perturbations of the fault system 1 evolving over time and correspond in the fault model to uncertainties. In particular, the matrix AA ( x, t ) represents uncertainties related to the position and geometry of the fault, to elastic, viscous and inelastic properties of rock blocks 2 and 4, to tectonics and geology as well as other perturbations that are not taken into account in the nominal model, while the matrix AB(x, t) represents uncertainties related to the influence of input 11 on friction. After substituting equations (2) and (3) into equation (1), we obtain an equation of state of the type: with + ( AA ( a, t) a + g( a, t) ) where jA is the Moore-Penrose inverse of o the matrix Bü, h ( x, t ) including uncertainties, friction-related disturbances and the dependence of fault system 1 on multiphysical and multi-scale phenomena which are not taken into account in the nominal model.

[0121] After obtaining the state representation of the fault model, the control law can be synthesized to generate a pressure control signal U that stabilizes the fault system 1 mathematically represented by equation (4).

[0122] Assuming that the uncertainties are zero, i.e. that the fault model corresponds to the nominal fault model, the fault model can be written as follows:

[0123] x = Aox + Bou (5)

[0124] A control law stabilizing such a linear system represented by equation (5) can thus be written in the form:

[0125] u = - R^B^dx = - Kx^

[0126] where K is a gain matrix, R is a predetermined coefficient influencing the speed of the system and & is a stability parameter to be determined to establish the stability of the fault system 1.

[0127] The purpose of the control law is to allow the minimization of the relative displacement error ed of the first rock block 2 with respect to the second rock block 4, while guaranteeing that the fault system 1 is asymptotically stable in the Lyapunov sense.

[0128] In this control law, G is a parameter subsequently called the stability parameter to be determined and which is the solution of the Riccati equation: [°129] Aq9 + 9A0 - -Q^

[0130] where Q is a positive definite matrix.

[0131] We will thus show how to determine the stability parameter 0 so as to generate a pressure control signal U which guarantees the asymptotic stability of the fault system 1.

[0132] For fault system 1 to be asymptotically stable in the Lyapunov sense, we show that it verifies Lyapunov's theorem. Thus, we choose a function, called Lyapunov's candidate, which verifies the conditions of the theorem and advantageously includes the stability parameter 0. In this way, it is possible to define the value of the stability parameter G so that system 1 is asymptotically stable by applying the control law thus synthesized. Such a function verifying the conditions of Lyapunov's theorem and integrating the stability parameter 6 can be written:

[0133] V(x)=xT0x&)

[0134] with U ( x ) which is strictly positive for each non-zero x.

[0135] By definition, the fault system 1 represented mathematically by equation (4) is asymptotically stable if the derivative with respect to time of the Lyapunov candidate, denoted V ( x ) is negative.

[0136] By deriving the Lyapunov candidate V ( x ) in equation (8), we obtain:

[0137] y (x) _ xTffx + xTf)x 'XT0X' (9)

[0138] As we are looking for a control law that allows us to asymptotically stabilize the fault system 1 by taking into account its disturbances, we substitute the equation of the fault model including the uncertainties (4) in the equation of the derivative of the Lyapunov candidate (9):

[0139] . - / tit ' tittitt V (x) = x1 (A^e + 8A0 - BB^Bçe)x +xT3B0R~lBJ03x- 2xT3Boir AB + ' 0 0 ' 8x + 2xT3BJt (10)

[0140] The matrix Bq can be determined so that the matrix BqR1 A BT is always positive semi-definite. In this way, the third term of equation (10) is a negative number.

[0141] We can simplify the equation by setting:

[0142] z = Æ->«gJto(ll)

[0143] Thus, by substituting the Riccati equation (7) and equation (11) into equation (10) as well as considering that the third term of equation (10) is negative, we obtain the following inequality:

[0144] y (x) < -xTQx - zrz + 2z?Ril2h(^

[0145] In order to show that the disturbances do not influence the stability of fault system 1, we pose:

[0146] h(x,t) < fi || X || (13)

[0147] with h (x, t) the function comprising the uncertainties of the fault model, which is a Lipschitzian function and fi a positive real coefficient which can be called here the Lipschitz constant.

[0148] We thus seek to show that the fault system 1 represented mathematically by the fault model equation (4) is asymptotically stable, even if the uncertainties take a value equal to that of the coefficient fi. The coefficient fi is determined so as to be much greater than the value of the uncertainties to ensure the robustness of the fault system 1.

[0149] In this way, we can calculate the stability parameter 0 with the coefficient fi while guaranteeing the asymptotic stability of the fault system 1, since the coefficient fi limits the function including the uncertainties.

[0150] Thus, we integrate the coefficient fi into the Q term of the Riccati equation (7), to determine on the one hand the stability parameter 0 as a function of the coefficient fi, and on the other part of the stability of the fault system 1 by the Lyapunov theorem: 101511 e=e o+ / f R , / 2 IV 14)

[0152] where Qq is a positive matrix having an influence on the speed of the control system and which can be determined arbitrarily while 4 is an identity matrix of size n. Substituting equation (14) into equation (12), we have: 101531 V(x) < || R'12 || 2 xrx-zTz + 2zTRv2h 101541 V\x) s || S1'2 || 2 || x || 2- || z || 2 + 2 / i || R"2 || || z || || x || 101551 v\x) < -xTQox- (fi || R1'2 || || x || - || z || )2 <15)

[0156] Since the matrix Qq is positive, the first term of inequality (15) is negative. It The same is true for the second term of this inequality (15).

[0157] It is thus shown according to Lyapunov's theorem that the fault system 1 represented mathematically by the fault model defined by equation (4) is asymptotically stable with equation (14).

[0158] Thus, solving the Riccati equation (7) with equation (14) makes it possible to obtain a value of the stability parameter 7 which allows the control law (6) to generate a pressure control signal U stabilizing the fault system 1, even in the presence of disturbances. The control law is thus synthesized.

[0159] As shown previously, the parameter S of the control law resides in the choice of the value of the coefficient which limits the function comprising the uncertainties and which has an influence on the robustness of the control law.

[0160] The stability parameter 7 thus determined guarantees the robustness of the control law in view of uncertainties. The calculation of the parameter of 0 can be carried out in real time, or prior to the control process.

[0161] The comparator 162 of the control unit 16 calculates the difference between the output value of the fault system 1 measured by the measuring device 1 and the predetermined displacement setpoint D, according to the following formula:

[0162] ed=Cx-D

[0163] Thus, it is possible, by a change of variable from the equation system (1), to make one of the first rock block 2 or the second rock block 4 follow the instruction D.

[0164] Due to the form of the control law used, the corrector 162 is here a linear corrector. Other forms of control law can be used, for example non-linear.

[0165] In summary, the invention relates to a method for closed-loop control of the movement of the first rock block 2 relative to the second rock block 4, by injection of fluid by a fluid injection device 12 controlled by a pressure control signal U generated by a corrector 164 as a function of a displacement signal Y measured by a measuring device 14 and a predetermined displacement setpoint D.

[0166] A control law is determined from a mathematical model of the fault system 1 taking into account disturbances and uncertainties applying to the fault system 1. The disturbances of the fault system 1 result in uncertainties in the mathematical model representing it. The control law is configured to produce a pressure control signal U as a function of the measurements of the displacement of the first rock block 2.

[0167] The determined control law is used in the corrector 164 to produce the pressure control signal U then sent to the injection device 12 as a function of the measured displacement signal Y received from the measuring device 14 and the predetermined displacement setpoint D.

[0168] The pressure control signal U thus determined from the control law guarantees asymptotic stability of the fault system 1 in the Lyapunov sense.

[0169] It is understood that the principle underlying the invention, a system for controlling the movement of a rock block, can be applied in practice for controlling the movement of a rock block in ways other than those detailed above. In particular, the type of fault model may be different, and the methods for determining the control law and the stability parameter S may also be different.

Claims

Claims

1. Method for stabilizing a fault system (1) comprising a first rock block (2) and a second rock block (4) defining a fault (6) between them, said method comprising the following successive steps: a) providing a displacement setpoint (D) of the first rock block (2) relative to the second rock block (4) of said fault system (1), said displacement setpoint (D) being determined so that if a displacement of the first rock block (2) relative to the second rock block (4) in accordance with said setpoint (D) is produced, the energy accumulated in said fault system (1) is gradually released; b) measuring a displacement value of the first rock block (2) relative to the second rock block (4) of said fault system (1); c) generation of a fluid pressure control signal (U) by application of a control law and from a displacement error (ed) corresponding to the difference between the displacement setpoint (D) and the measured displacement value; d) injecting or pumping a fluid into or near said fault (6) of said fault system (1), according to the pressure control signal (U); and e) repetition of steps b) of measurement, c) of generation and d) of injection, at a predetermined frequency.

2. Stabilization method according to claim 1, characterized in that it further comprises a step of determining said control law from a mathematical model representing the fault system (1) and taking into account uncertainties linked to disturbances of said fault system (1), said mathematical model taking the following form: x = Aox + AB ( x, t ) u + B0(u + h(x, t) ) where Ao and B(i are constant matrices representing the nominal part of the fault system (1), x is a state vector representing the displacement of the first rock block (2) relative to the second rock block (4) at at least one point of the fault (6), u is a vector of the model inputs representing the pressure control signal (U), AB ( x, t) is a matrix representing uncertainties related to the influence of said pressure control signal (U) on friction, h ( x, t ) is a function with uncertainties related to friction, position and geometry of the fault (6), elastic, viscous and inelastic properties of the rock blocks (2, 4), and the dependence of the fault system (1) on multiphysical and multi-scale phenomena which are not taken into account in the nominal part of said mathematical model.

3. Stabilization method according to claim 2, characterized in that the step of determining the control law comprises a step of determining a stability parameter 0 of said control law, said control law taking the following form: u = -R^B^x where R is a predetermined coefficient influencing the speed of the fault system (1), the stability parameter 6 being a solution of the Riccati equation: A^e + qa^ - eB^B^e = - q where Q is a parameter which depends on a coefficient and R according to the following formula and conditions: e=e0+^ il il 3 with h(x, t) < / 3 || X || where / is the identity matrix and Qq is a positive definite matrix.

4. Method for identifying the system according to claim 2 or 3, characterized in that it further comprises a step of estimating the state vector x of said mathematical model, by a state observer, from a measurement of the displacement value of the first rock block (2) relative to the second rock block (4) of said fault system (1).

5. Stabilization method according to any one of claims 1 to 4, characterized in that the measurement step b) comprises the determination of a speed value of the first rock block (2) relative to the second rock block (4), or of a value of distance traveled by the first rock block (2) relative to the second rock block (4).

6. Device for stabilizing a fault system comprising a first rock block (2) and a second rock block (4) defining between them a fault (6), said device comprising: - a control unit (16) configured to receive an instruction

7.

8. (D) displacement of the first rock block (2) relative to the second rock block (4) of said fault system (1), said displacement setpoint (D) being determined so that if a displacement of the first rock block (2) relative to the second rock block (4) in accordance with said setpoint (D) is produced, the energy accumulated in said fault system (1) is gradually released; - a measuring device (14) configured to measure, according to a predetermined frequency, a displacement value of the first rock block (2) relative to the second rock block (4) of said fault system (1), said control unit being configured to generate a fluid pressure control signal (U) by applying a control law and from a displacement error (ed) corresponding to the difference between the displacement setpoint (D) and the measured displacement value; and - an injection device (12) configured to inject or pump a fluid into said fault (6) or near said fault (6) of said fault system (1), according to the pressure control signal (U). Stabilization device according to claim 5, characterized in that the control law is determined from a mathematical model representing the fault system (1) and taking into account uncertainties linked to disturbances of said fault system (1), said mathematical model taking the following form: X — Aax + AB (x, t}u + B0(u + h(x, t) ) where Ao and Bq are constant matrices representing the nominal part of the fault system (1), J is a state vector representing the displacement of the first rock block (2) relative to the second rock block (4) at at least one point of the fault (6), 11 is a vector of the model inputs representing the pressure control signal (U), AB ( x, t ) is a matrix representing uncertainties related to the influence of said pressure control signal (U) on friction, h ( x, t ) is a function comprising uncertainties related to friction, the position and geometry of the fault (6), elastic, viscous and inelastic properties of the rock blocks (2, 4), and the dependence of the fault system (1) on multiphysical and multiscale phenomena which are not taken into account in the nominal part of said mathematical model. Stabilization device according to claim 7, characterized in that the control unit (16) comprises a state observer configured to estimating the state vector A of said mathematical model from a measurement of the displacement value of the first rock block (2) relative to the second rock block (4) of said fault system (1) by the measuring device (14).

9. Stabilization device according to any one of claims 6 to 8, characterized in that it comprises a plurality of injection devices (12) and a plurality of measuring devices (14), the control unit (16) being configured to generate a fluid pressure control signal (U) for each injection device (12) of said plurality of injection devices (12) so that the displacement values ​​of the first rock block (2) measured by the plurality of measuring devices (14) are substantially equal to the displacement setpoint (D).

10. Stabilization device according to any one of claims 6 to 9, characterized in that it comprises a plurality of injection devices (12) and a plurality of measuring devices (14), the control unit (16) being configured to generate a signal (U) for controlling the pressure of a fluid for each injection device (12) of said plurality of injection devices (12) so that the average of the displacement values ​​of the first rock block (2) relative to the second rock block (4) measured by the plurality of measuring devices (14) is substantially equal to the displacement setpoint (D).

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