EP0816629B1 - Method and system for real time estimation of at least one parameter connected to the rate of penetration of a drilling tool - Google Patents

Description

The present invention relates to the field of measurements during drilling, in particular measures concerning the displacement of a drilling tool attached to the end of a drill string. The method according to the invention provides a solution for estimate in particular the instantaneous speed of rotation of the tool at the bottom of the well, said estimates being obtained by means of a calculation program taking into account measurements taken at the top of the drill string, i.e. substantially on the surface of the ground, generally by means of sensors or an instrumented fitting located in the neighborhood of the means for rotating the lining.

We know measurement techniques for the acquisition of information related to dynamic behavior of the drill string, which use a set of sensors bottom connected to the surface by an electrical conductor. In document FR-2 688 026, it two sets of measurement sensors are used connected by a logging type cable, one being located at the bottom of the well, the other at the top of the drill string. However, the presence of a cable along the drill string is troublesome for the operations of proper drilling.

We know the document EP-A-709546 which describes a predictive method of Downhole measurements following surface measurements, from an equation predictive obtained following collections of background and surface measurements. This method requires the collection of bottom measurements and two of the bottom well collection means.

We know from documents FR 2645205 or FR 2666845 of the surface placed at the top of the lining which determine certain malfunctions of drilling according to surface measurements, but without taking into account, so physical, dynamic behavior of the lining and the drilling tool in the well.

Between the bottom of a well and the soil surface, there is a string of rods along from which energy dissipative phenomena take place (friction on the wall, torsional damping, ...), conservative phenomena of flexibility, especially in torsion. There is thus a distortion between the measurements of the bottom and surface displacements which mainly depends on the intrinsic characteristics of the lining (length, stiffness, geometry), friction characteristics at the rods / wall interface and random phenomena.

This is why, the information contained in the surface measurements does not alone are not enough to solve the problem posed, that is to say knowing the instantaneous movements of the tool by knowing the instantaneous movements of the surface trim. The surface measurement information must be supplemented by independent information of another kind which takes into account the structure of the drill string and its behavior between the bottom and the surface: this is the role of the knowledge which establishes the theoretical relationships between the bottom and the surface.

The methodology of the present invention uses the conjunction of such a model, defined a priori, and surface measurements acquired in real time.

• on identifie les paramètres dudit modèle en prenant en compte les paramètres dudit puits et de ladite garniture,
• on linéarise ledit modèle autour d'un point de fonctionnement,
• on réduit ledit modèle linéarisé en ne conservant que certains des modes propres de la matrice d'état dudit modèle,
• on calcule, en temps réel, le déplacement de l'outil de forage à l'aide du modèle réduit et d'au moins un paramètre mesuré en surface.

Thus, the present invention relates to a method of estimating the effective displacement of a drilling tool fixed at the end of a drilling rig and rotated in a well by drive means located on the surface, in which we use a nonlinear physical model of the drilling process based on general mechanical equations. In the method, the following steps are carried out:

• the parameters of said model are identified by taking into account the parameters of said well and of said lining,
• we linearize said model around an operating point,
• said linearized model is reduced by retaining only some of the eigen modes of the state matrix of said model,
• the displacement of the drilling tool is calculated in real time using the reduced model and at least one parameter measured at the surface.

The model can take into account essentially the rotational displacements and said reduced model can calculate in real time the instantaneous speed of rotation of the tool of drilling, said parameter measured at the surface can be taken from at least: the speed of packing rotation or torque.

The reduced model can be refined by self-adaptive filtering which minimizes the difference between an actual measurement of a parameter related to the displacement of the lining in surface and the corresponding output obtained by said reduced model.

Filtering can take into account the torque measured at the surface or the speed of rotation measured at the surface.

The invention also relates to a system for estimating the effective displacement. of a drilling tool attached to the end of a drill string and rotated in a well by means of drive located on the surface, in which an installation of calculation includes means for non-linear physical modeling of the drilling process based on general mechanical equations. The parameters of said means modeling are identified by taking into account the parameters of said well and said lining, and the calculation installation includes means for linearizing said model around an operating point, means for reducing said linearized model so to keep only some of the eigen modes of the state matrix of said model, means for calculating, in real time, the displacement of the drilling tool using the means once linearized and reduced and means of measuring at least one parameter linked to the displacement of the lining on the surface.

The modeling means may take into account only the torsion, and the parameters can be the speed of rotation and / or the torque.

• la figure 1 représente schématiquement les moyens mis en oeuvre pour une opération de forage,
• la figure 2 représente un exemple de diagramme d'un modèle physique en torsion,
• la figure 3 représente un diagramme d'un estimateur en boucle ouverte,
• la figure 4 représente un diagramme d'un estimateur avec recalage,
• la figure 5 représente schématiquement la méthodologie de la constitution de l'estimateur selon l'invention.
• la figure 6 illustre les résultats obtenus avec l'estimateur.

The present invention will be better understood and its advantages will become clear on reading the description of an example, in no way limiting, illustrated by the attached figures below, among which:

• FIG. 1 schematically represents the means used for a drilling operation,
• FIG. 2 represents an example of a diagram of a physical model in torsion,
• FIG. 3 represents a diagram of an open loop estimator,
• FIG. 4 represents a diagram of an estimator with registration,
• FIG. 5 schematically represents the methodology of the constitution of the estimator according to the invention.
• Figure 6 illustrates the results obtained with the estimator.

Figure 1 illustrates a drilling rig on which we will operate the invention. The surface installation comprises a lifting device 1 comprising a lifting tower 2, a winch 3 which allow the displacement of a drilling hook 4. Under the drill hook are suspended drive means 5 for rotating the assembly of the drill string 6 placed in the well 7. These drive means can be of the drive rod or kelly type coupled to a rotation table 8 and the mechanical motorizations, or of the type motorized drive head or "power swivel" suspended directly from the hook and guided longitudinally in the tower.

The drill string 6 is conventionally constituted by rods of drilling 10, of part 11 commonly called BHA for "Bottom Hole Assembly" mainly comprising drill rods, a drilling tool 12 in contact with the land being drilled. The well 7 is filled with a fluid, called a drilling fluid, which circulates from the surface at the bottom through the inner channel of the drill string and rises to the surface by the annular space between the walls of the well and the drill string.

For the implementation of the invention, an instrumented fitting can be inserted 13 between the drive means and the top of the lining. This fitting allows measure the torque, the speed of rotation, possibly the longitudinal displacement of the top of the filling. These so-called surface measurements are transmitted by cable or radio towards an electronic installation of recording, processing, display, not shown here. Instead of the connector 13, other sensors such as a tachometer on the rotation table to measure the speed of rotation and a measurement of the torque on the motorized device, if the accuracy of the measurements thus obtained is sufficient.

Part 11 of the BHA may more specifically include, drill collars, stabilizers, a shock absorber, and a second instrumented connector 14 which will not used only to experimentally control the present invention by allowing the comparison between the displacement of the drilling tool 12 actually measured by the instrumented fitting 14 and the estimated displacement thanks to the implementation of this invention. It is therefore clear that the application of the present invention does not use instrumented fitting placed at the bottom of the well.

The driller who conducts a drilling operation with the devices described in the Figure 1 has three main possible actions, which are therefore the command variables possible to control the drilling process. These are, the weight on the tool which is adjusted by the winch which controls the position of the hook, the speed of rotation of the table rotation or equivalent, and the flow of injected drilling fluid.

• un ensemble d'entraínement: organe de régulation et motorisation,
• un ensemble de tiges,
• un ensemble de masses-tiges,
• un terrain représentant le contact outil/roche.

To illustrate an example of the present invention, a model of the mechanical system composed of the following technological elements will be used:

• a set of drive: regulator and motor,
• a set of rods,
• a set of drill sticks,
• a terrain representing the tool / rock contact.

The described model will treat the drill string as a one-dimensional element vertical. Only rotational displacements will be considered, vertical displacements and lateral being neglected.

Figure 2 shows the block diagram of the model; here of twist. It's a model classic with finite differences which comprises several tens of meshes represented by blocks 20. Each mesh represents a part of the drill string, composed inter alia of drill rods and drill rods. It is a figured mass-spring-damping triplet by the diagrams referenced 21, 22, 23. Each block is provided with two inputs and outputs represented by the pairs of arrows 24 and 25 which represent the input and output and input and output rotational speeds. This representation shows the way to digitally connect several rods (or meshes) as we connect physically the packing rods.

Block 26 represents the boundary conditions at the head of the resulting drill string of the drilling rig.

Block 27 represents the friction law of the tool / ground contact determining the boundary conditions at the bottom of the well. This is a type power dissipator resistant couple. The different curves 28 represent a nonlinear law of tool / rock interaction, depending on the instantaneous speed of the tool (input 29) of the resisting torque (outlet 30) and weight on the tool (inlet 31).

This model is validated using data recorded on site using the instrumented bottom and surface fittings.

The drilling fluid and the well walls only intervene insofar as they generate a resistant friction torque. From experience, and using background measurements and surface, we can establish a friction law along the linear rods as a function of rotation speed.

The torsion model thus obtained is generally of high order, that is to say of around 50 to 100 to reproduce reality with sufficient finesse.

To obtain a quickly executable and robust model when changing drilling conditions, for example the change of land crossed, we proceed to steps below described.

We linearize the generally non-linear model. In the example above described, we linearize the model by choosing an operating point (a speed of rotation and a weight on the tool) representative of the actual drilling conditions. We can verify that the behavior of the torsional model of knowledge, once linearized, is correct in the vicinity of the operating point.

x = X-X ₀

X ₀= valeurs des états au point de fonctionnement

e = E-E ₀

E ₀= valeurs des entrées au point de fonctionnement

s = S-S ₀

S ₀= valeurs des sorties au point de fonctionnement

Linearization around an operating point consists in calculating the Jacobian of the non-linear state system. The linear state system obtained is then of the form: x = A. x + B. e s = C. x + D. e with:

x = X - X ₀

X ₀ = values of the states at the operating point

e = E - E ₀

E ₀ = values of the inputs at the operating point

s = S - S ₀

S ₀ = values of the outputs at the operating point

Modalization is done first by a change of base: z = P. x z = P. x

P est la matrice des vecteurs propres de la matrice d'état A,

Λ est la matrice diagonale des valeurs propres de la matrice d'état A.

After resolution we get: z = P -1 .AP z + P -1 .B. e z = Λ. z + B Λ . e s = CP z + D. e s = C Λ . z + D. e

P is the matrix of the eigenvectors of the state matrix A,

Λ is the diagonal matrix of the eigenvalues of the state matrix A.

After linearization, the torsion model retains the same high order. analysis eigen modes of the torsion model allows to quantify the contribution of each fashion on exits of interest. We only keep the relevant modes; that is to say those who have a notable influence on the dynamic behavior represented by said outputs.

• suppression des modes non ou peu observables sur les sorties mesurées,
• suppression des modes hautes fréquences, n'entrant pas dans la bande de fréquence de la commande ou de l'estimateur.

The scale model must reproduce the phenomena in a certain frequency band. The criteria for mode selection are therefore twofold and are based on concepts of observability:

• elimination of modes which are not or hardly observable on the measured outputs
• suppression of the high frequency modes, not entering the frequency band of the control or the estimator.

The reduction method used is the singular disturbance method. It consists in keeping from the state matrix and from the command matrix, the lines and the columns corresponding to the modes to keep. To keep static gains, the modes Rapids are replaced by their static value, which has the consequence of introducing a direct matrix.

The method assumes that the fast modes take their equilibrium in a time negligible, that is to say that they are established instantaneously (quasi-static hypothesis).

Figure 3 shows the block diagram of a loop-type estimation system opened. Block 40 shows diagrammatically the means for measuring surface parameters, here the speed of rotation of the lining Vms measured at the table or at the motorized injection head, and the torque Cms also measured at the surface. Block 41 represents the scale model which simulates the physical model of nonlinear torsion by calculating the transfer function between the input (Vms) and the outputs Ces, Cef and Vef representing respectively the torque of estimated area, estimated bottom torque and estimated bottom speed.

However, the transfer function is always an approximation of reality and any mismatch between the model and the actual drilling process can create a divergence between the estimated values and the real values by integration of the differences. Also, in most cases, it is advantageous to carry out a readjustment, or readjustment, using at least one comparison between a series of values from an estimated output and the same actually measured series. In this example, the linear estimator is readjusted from the surface torque.

According to the same principle and equivalently, it will be possible to enter the couple measured at the Cms surface and readjust from the comparison between the speed of rotation estimated and the speed of rotation measured at the surface.

The estimation technique is based on the filtering principles of Luenberger and Kalman ("Automatic linear systems" by P. De Larminat and Y. Thomas-Flammarion science; Paris IV, 1975). The principle of a linear estimator can be illustrated by FIG. 4 where the measurement of the torque Cms and the estimated value Ces are compared in the means 42, the difference between these two values being injected into an adapter 43 in real time. The objective here is to reconstruct the exits as faithfully as possible rather than having an exact model. This is why a state registration is carried out. Like the outputs are directly linked to the states, state registration consists in performing a weighting between the states predicted by the model at time t and the states reconstructed from only measured outputs. This weighting is not a simple average, but it takes into account the degree of precision of the estimates of the states obtained by its two channels independent. As specified above, the measured torque can be used as input Cms and perform the readjustment by the rotation speed.

Once readjusted the states of the model which represent the dynamics of the process drilling, all outputs, whether measured or not, can be recalculated.

This estimate is not only interesting for unmeasured variables like Cef and Vef, it also applies to the measured variables (for example Cms or Vms) which were used for registration. The estimated value Ces is the equivalent of a filtered value on the basis of a model: this is why we generally use the term filtering (filtering Luenberger, Kalman filtering ...).

The state registration technique, as described above, introduces a slaving of Cms measured on these estimated.

This closure eliminates the risk of divergence mentioned above, when the model is simulated in open loop (figure 3).

There is thus a desensitization of the estimated variables with respect to imperfections of the model. In this context, we no longer need to have a perfect model: a model approached is sufficient.

In addition, only one measurement is available here, the torque C, for performing the readjustment: it does not seem possible to readjust a large number of states from this measured. This is why, the model of nonlinear torsion is not suitable in spite of its greater accuracy.

There is therefore a compromise to be made between the precision and the order of the system. he look for the minimum order model that meets precision tolerances desirable, and that is also easy to adjust and robust.

• il faut sauvegarder les modes propres de vibration en torsion qui sont prépondérants dans les sorties à ré estimer ;
• pour des raisons de cohérence et de stabilité numérique, il faut rejeter les modes de fréquences élevées supérieures à f_max = f_e/2 où fe est la fréquence d'échantillonnage des entrées et des sorties. On peut préciser ces notions en prenant par exemple le cas d'un train de tiges composée de 800m de tiges 5" (127 mm) et de 200m de masses-tiges 8" (203,2 mm) pour lequel le système d'acquisition a une fréquence d'échantillonnage de 10 Hz.

The choice of the order of the reduced model depends on the following qualitative criteria:

• it is necessary to save the eigen modes of vibration in torsion which are predominant in the outputs to be re-estimated;
• for reasons of consistency and numerical stability, it is necessary to reject the high frequency modes greater than f _max = f _e / 2 where fe is the sampling frequency of the inputs and outputs. We can clarify these concepts by taking for example the case of a drill string composed of 800m of 5 "(127mm) rods and 200m of 8" (203.2mm) drill collars for which the acquisition system has a sampling frequency of 10 Hz.

The modal study of the knowledge model, discretized into 35 meshes, locates the five first modes at 0.344 Hz, 1.86 Hz, 3.61 Hz, 5.37 Hz, 7.12 Hz.

f _max being equal to half the sampling frequency, f _max = 5 Hz. But taking into account the possibilities of the anti-aliasing filters, the maximum observable frequency is 2.8 Hz.

It is therefore superfluous to choose a reduced model of order greater than 4 (two modes) if you want to integrate the model at the sampling rate fe.

The final choice of reduction order can be made by comparing the results obtained with a model reduced to order 2 and a model reduced to order 4.

In addition, it should not be forgotten that the reduced estimation model must, preferably meet the technological constraints of real time.

• génération du modèle réduit,
• implantation des filtres passe-haut,
• agrégation des filtres passe-haut et du modèle réduit, l'ensemble devient le modèle d'estimation,
• calcul des gains de recalage,
• construction de l'estimateur complet.

The estimator is therefore constructed according to the following steps:

• generation of the reduced model,
• installation of high-pass filters,
• aggregation of high-pass filters and the reduced model, the whole becomes the estimation model,
• calculation of registration gains,
• construction of the complete estimator.

The methodology for the construction of the estimator according to the invention can be illustrated by FIG. 5. Block 50 represents a physical model representing a rotary drilling process, for example illustrated in Figure 2. This model takes into account account for a determined operating situation, in particular by receiving the mechanical characteristics of the drill string used, symbolization referenced 51, well and surface conditions, symbolization referenced 52, and friction laws, symbolized by reference 53. Block 54 represents the main torsion model once linearized and reduced as described above. All these steps gathered under the DF brace run in delayed time compared to the progress of the process rotary drilling, the other steps gathered under the TR brace are executed in time real.

Block 55 is directly what has been called the estimator. Means of measure 56 placed on the top of the drill string give the torque measurements and speed of rotation at the top of the rods, i.e. at the surface. These surface measurements are taken into account in the estimator, as described above, to give a estimation of the displacement values of the drilling tool, in particular the speed of rotation of the Vef drilling tool.

The present invention is advantageously implemented on a construction site drilling in order to have as precise an estimate as possible of the rotation speed of the drilling tool in real time, using only surface measurements, in particular the rotational speed of conventional means for rotating the gasket drilling, and a surface installation equipped with electronic and computer means. It is very interesting to have an estimate of the background parameters in order to detect, and even to prevent known malfunctions, for example the so-called behavior of "stick-slip" characterized by very sensitive variations in the speed of rotation of the tool at bottom while it is driven through a drill string set rotation from the surface at a substantially constant speed. Tool speed can vary between a practically zero speed and a value of the speed of rotation very higher than the speed applied to the surface. This may have consequences detrimental to the life of the tools, increasing the mechanical fatigue of the train of rods and the frequency of connection breaks.

Figure 6 shows a record F of the speed of rotation of a tool drilling, recording made from bottom sensors, for example using means described in document FR / 92-02273. Said means allow measurements of rotational speed and surface torque, synchronized with speed measurements of rotation and torque at the bottom. Area measurements are used as inputs to the estimator according to the invention, and after having carried out all the necessary calculation steps, we obtain the record S corresponding to the speed of the tool at the bottom estimated by the estimator according to the invention. In FIG. 6, the diagrams F and S are plotted with, in abscissa the time and on the ordinate the speed of rotation of the tool. We can thus compare the measurement actually performed F with the values S obtained by the estimator according to the invention.

It is clear that the dysfunction of "stick-slip" that appears at time 80 s is distinctly estimated on diagram S, which allows the driller to be warned of the existence of this malfunction thanks to the estimator and without the need for measurement measures background in real time. We can notice on this figure, that between 0 and 20 seconds, there is a bad estimate which is explained by the fact of the initialization of the auto filtering adaptive. This observation shows all the interest of the registration loop.

It should also be understood that the present invention is also applicable to the estimate of the instantaneous speed of rotation of elements included in the gasket drilling, elements which can be located at a certain distance from the drilling tool.

Claims (5)

1. A method designed to estimate the effective displacement of a drill bit (12) fastened to the end of a drill string (6) and driven into rotation in a well (7) by surface driving means (8), wherein a non-linear physical model (50) of the drilling process based on general mechanics equations is used, characterized in that the following stages are carried out:

   the parameters of said model are identified by taking account of the parameters of said well and of said string (51, 52, 53),

   said model is linearized about a working point,

   said linearized model is reduced while keeping only some of the specific modes of the state matrix of said model,

   the displacement of the drill bit is computed in real time by means of the reduced model (54) and of at least one parameter measured at the surface, and in that said model takes essentially account of the rotational displacements and said reduced model performs real-time computation of the instantaneous rotational speed of the drill bit, said parameter measured at the surface being selected at least from the rotational speed of the string or the torque measured at the surface.
2. A method as claimed in claim 1, wherein the reduced model is fined down by means of self-adaptive filtering which minimizes the difference between a real measurement of a parameter linked with the displacement of the string at the surface and the corresponding output obtained by said reduced model.
3. A method as claimed in claim 2, wherein said filtering takes account of the torque measured at the surface.
4. A method as claimed in claim 3, wherein said filtering takes account of the speed measured at the surface.
5. A system designed to estimate the effective displacement of a drill bit (12) fastened to the end of a drill string (6) and driven into rotation in a well (7) by surface driving means (8), wherein a computing unit (9) comprises means intended for non-linear physical modelling of the drilling process based on general mechanics equations, characterized in that parameters of said modelling means are identified by taking account of the parameters of said well and of said string, in that the computing unit comprises means designed for linearization of said model about a working point, means for reducing said linearized model so as to keep only certain specific modes of the state matrix of said model, means for real-time computation of the displacement of the drill bit by means of the modelling means once linearized and reduced and means for measuring at least one parameter linked with the displacement of the string at the surface (13): rotational speed and/or torque, and wherein the modelling means only take account of the torsion.

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