EP1256693A1 - Method for determining by means of digital simulation the conditions of restoration, using reservoir fluids, of wells damaged by drilling operations - Google Patents

Abstract

Initial data are obtained by laboratory measurements of the initial (ki), damaged (kd) and restored (kf) permeability around the well as a function of distance (r) from the well wall. The damaged zone is discretized by a 3D cylindrical mesh forming blocks of small radial thickness relative to the well diameter. Fluid flows through the cakes are calculated to model evolution of the permeability Simulating the optimal conditions to impose on a well drilled through an underground formation at a particular angle, for the progressive removal using the formation's fluids of deposits or cakes which are formed in at least one zone at the periphery of the well after the drilling and completion operations, comprises resolving the diffusivity equation in the mesh modelling the fluid flows through the cakes, taking into consideration the initial measured data and modelling the evolution of the permeability as a function of the fluid flows (Q) through the cakes to deduce the optimal conditions to apply during operation of the well. The restoration of permeability is modelled at all points at distance (r) from the well wall considering that the permeability varies proportionally with the difference between the damaged permeability and the restored permeability. The coefficient of proportionality depends on an empirical law of variation of the permeability as a function of the quantity (Q) of fluid passing through the cakes.

Description

DESIGNATION OF THE TECHNICAL AREA

The present invention relates to a method for determining by simulation numerical optimal conditions to impose in a horizontal (or complex) well drilled through an underground deposit, to gradually eliminate (restore) by natural sweeping using production fluids from the deposit, deposits or cakes that have formed in at least one area around the periphery of the well, following drilling and completion operations.

Those skilled in the art know that a distinction is made between so-called internal cakes formed by invasion of the pores of the rock by mud and so-called external cakes a coating of mud on the external wall of the well.

STATE OF THE ART

Damage to the formations surrounding the horizontal wells (or complex), often open holes fitted for production, is a point critical for deep offshore oil fields where to get costs of acceptable development, only a limited number of wells are put into production very productive.

The tests which one can make to characterize the damage of formations in the vicinity of a well are of primary importance. They allow choose the most appropriate drilling fluid to minimize or reduce the deterioration of permeability in the vicinity of wells and also to optimize well cleaning techniques.

• Alfenore, J. et al, « What Really Matters in our Quest of Minimizing Formation Damage in Open Hole Horizontal Wells », 1999, SPE 54731 ;
• Longeron, D. et al, « Experimental Approach to Characterize Drilling Mud Invasion, Formation Damage and Cleanup Efficiency in Horizontal Wells with Openhole Completions » 2000, SPE 58737 ; ou
• Longeron, D. et al, « an Integrated Experimental Approach for Evaluating Formation Damages due to Drilling and Completion Fluids », 1995, SPE 30089.

During the past five years, the applicant has developed specific laboratory test equipment and procedures intended to characterize the damage to formations due to drilling during overpressure operations and to quantify the performance of various techniques. cleaning agents used in the industry as evidenced by the following publications

• Alfenore, J. et al, "What Really Matters in our Quest of Minimizing Formation Damage in Open Hole Horizontal Wells", 1999, SPE 54731;
• Longeron, D. et al, "Experimental Approach to Characterize Drilling Mud Invasion, Formation Damage and Cleanup Efficiency in Horizontal Wells with Openhole Completions" 2000, SPE 58737; or
• Longeron, D. et al, "an Integrated Experimental Approach for Evaluating Formation Damages due to Drilling and Completion Fluids", 1995, SPE 30089.

However, laboratory studies are often insufficient to they alone, to realistically model, the production conditions to apply in wells to best restore the permeability of formations surrounding, without provoking sand inflows. Modeling of restoration process of the formations surrounding a well have a large economic interest for the exploitation of fields.

THE METHOD ACCORDING TO THE INVENTION

The method according to the invention makes it possible to simulate the conditions as well as possible optimal to impose in a well drilled through an underground deposit at a any trajectory, for gradual elimination by fluids from the deposit, deposits or cakes that have formed in at least one zone at the periphery of the well, following drilling operations.

It involves the acquisition of initial data obtained by measurements in laboratory of the initial permeability values (ki) of the formations surrounding the well, the thickness of the cakes as well as the damaged permeability values (kd) and restored permeability (kf) of the area, depending on the distance (r) to the wall of the well, discretization of the area damaged by a 3D cylindrical mesh forming blocks of small radial thickness relative to the diameter of the well and the resolution in this mesh, of diffusivity equations modeling the flows fluids through cakes taking into account the initial measured data and by modeling the evolution of the permeability as a function of the flow rates (Q) of fluids flowing through cakes, and we deduce the optimal conditions to apply for the production of the well.

We model the restoration of permeability at any point at a distance (r) from the wall considering for example that the permeability varies in proportion to the difference between the damaged permeability (kd) and the restored permeability (kf), the proportionality coefficient dependent on an empirical law of variation of the permeability depending on the amount of fluids through the cakes.

The simulation carried out according to the method allows tank engineers to better predict the best exploitation plan for the deposit, avoiding disadvantages such as the coming of sand. It also allows drillers, account given known or estimated permeability data, to choose fluids more particularly suitable for drilling wells and installing equipment.

SUMMARY PRESENTATION OF THE FIGURES

• la Fig.1 montre les courbes de variation en fonction de la distance r à la paroi du puits endommagé, d'un premier coefficient multiplicateur c₁(r) de la perméabilité d'endommagement et d'un deuxième coefficient multiplicateur c₂(r) de la perméabilité restaurée ;
• la Fig.2 montre une loi empirique de variation d'un coefficient de variation de la perméabilité à la distance r de la paroi du puits endommagé, en fonction du débit de fluides Q_s au travers des cakes ;
• la Fig.3 montre un exemple de maillage radial pour la résolution des équations de diffusivité ;
• la Fig.4 illustre le calcul du flux F avec un maillage radial ;
• les Fig.5a et 5b illustrent le calcul de l'IP numérique respectivement sans cake externe et avec cake externe Cext, autravers d'une maille Wcell ;
• la Fig.6 montre schématiquement une portion de puits de longueur L et de rayon rw comportant 4 zones de profondeur r centrées autour du puits, avec des perméabilités k différentes 100mD ou 1000mD et un cake interne d'épaissseur r_int ;
• les Fig.7, 8 montrent les variations en fonction de la distance d au puits, des coefficients multiplicateurs respectivement de perméabilité endommagée C1(r) et de perméabilité restaurée ou de retour c2(r), qui ont été mesurées au laboratoire dans différentes zones et utilisées dans les exemples ;
• la Fig.9 montre la courbe de variation de la perméabilité c(r) dans le cake interne en fonction du volume cumulé q de fluide par unité de surface offerte à l'écoulement, mesuré au laboratoire et utilisée dans les exemples ;
• les Fig. 10a à 10c montrent respectivement les variations en fonction du temps t(d) exprimé en jours, des débits d'huile FR (en m3/j) dans différentes zones perforées le long du puits, correspondant à 3 simulations différentes SM1 à SM3, dans l'exemple 1 (cas a);
• les Fig. 11a et 11b montrent les variations en fonction du temps t(d) exprimé en jours, du coefficient de perméabilité c(r) du cake interne dans deux zones différentes le long du puits (exemple 1) ;
• la Fig. 12 montre la variation en fonction du temps du débit total FR(m3/d) dans le cas c de l'exemple 1, pour trois simulations différentes SM1 à SM3 ;
• la Fig. 13 montre la distribution du cake externe le long de la portion de puits, dans l'exemple 2 ;
• les Fig. 14a à 14c montrent respectivement, dans l'exemple 2, la distribution sur la longueur L(m) du puits, du cake externe (Fig.14a) et du débit FR le long du puits au temps t=0.5 j (Fig.14b) et au temps t=5j (Fig.14c);
• les Fig.15a à 15f montrent respectivement, dans l'exemple 2, la distribution sur la longueur L(m) du puits, du cake externe (Fig.15a) et du débit FR le long du puits, respectivement au temps t = 0.1j (Fig.15b), t = 0.3j (Fig.15c), t = 0 .5j (Fig.15d), t = 1j (Fig.15e), et t = 5j (Fig.15f);
• la Fig. 16 montre le débit total du puits FR en fonction du temps exprimé en jours, dans l'exemple 2, pour les deux cas c1 et c2 ; ;
• la Fig.17 est un tableau montrant un exemple de maillage avec NX mailles réparties le long du puits, progressivement plus épaisses en s'éloignant radialement de la paroi du puits (direction r(m)) ; et
• la Fig.18 est un tableau montrant la durée d'application t(d) exprimée en jours, d'une pression de fond de puits P(bar) imposée.

Other characteristics and advantages of the method and of the device according to the invention will appear on reading the following description of a non-limiting example of embodiment, with reference to the appended drawings where:

• Fig. 1 shows the variation curves as a function of the distance r to the wall of the damaged well, of a first multiplier coefficient c ₁ (r) of the damage permeability and of a second multiplier coefficient c ₂ (r ) restored patency;
• Fig.2 shows an empirical law of variation of a coefficient of variation of the permeability at distance r from the wall of the damaged well, as a function of the flow of fluids Q _s through the cakes;
• Fig.3 shows an example of a radial mesh for solving the diffusivity equations;
• Fig.4 illustrates the calculation of flow F with a radial mesh;
• Fig.5a and 5b illustrate the calculation of the digital IP respectively without external cake and with external cake Cext, through a Wcell mesh;
• Fig.6 schematically shows a portion of well of length L and radius rw having 4 depth zones r centered around the well, with different permeabilities k 100mD or 1000mD and an internal cake of thickness r _int ;
• Figs. 7, 8 show the variations as a function of the distance d to the well, of the multiplying coefficients of damaged permeability C1 (r) and restored permeability or return c2 (r) respectively, which have been measured in the laboratory in different zones and used in the examples;
• Fig. 9 shows the variation curve of the permeability c (r) in the internal cake as a function of the cumulative volume q of fluid per unit of surface area offered for flow, measured in the laboratory and used in the examples;
• Figs. 10a to 10c respectively show the variations as a function of time t (d) expressed in days, of the oil flow rates FR (in m3 / d) in different perforated zones along the well, corresponding to 3 different simulations SM1 to SM3, in Example 1 (case a);
• Figs. 11a and 11b show the variations as a function of time t (d) expressed in days, of the coefficient of permeability c (r) of the internal cake in two different zones along the well (example 1);
• Fig. 12 shows the variation as a function of time of the total flow FR (m3 / d) in case c of Example 1, for three different simulations SM1 to SM3;
• Fig. 13 shows the distribution of the external cake along the portion of the well, in Example 2;
• Figs. 14a to 14c respectively show, in example 2, the distribution over the length L (m) of the well, of the external cake (Fig. 14a) and of the flow FR along the well at time t = 0.5 j (Fig. 14b ) and at time t = 5j (Fig.14c);
• Fig.15a to 15f show respectively, in Example 2, the distribution over the length L (m) of the well, the external cake (Fig.15a) and the flow FR along the well, respectively at time t = 0.1 j (Fig.15b), t = 0.3j (Fig.15c), t = 0 .5j (Fig.15d), t = 1j (Fig.15e), and t = 5j (Fig.15f);
• Fig. 16 shows the total flow from the well FR as a function of the time expressed in days, in Example 2, for the two cases c1 and c2; ;
• Fig.17 is a table showing an example of a mesh with NX meshes distributed along the well, progressively thicker moving away radially from the wall of the well (direction r (m)); and
• Fig. 18 is a table showing the duration of application t (d) expressed in days, of an imposed downhole pressure P (bar).

DETAILED DESCRIPTION OF THE METHOD 1) Acquisition of laboratory data

• Alfenore, J. et al, « What Really Matters in our Quest of Minimizing Formation Damage in Open Hole Horizontal Wells », 1999, SPE 54731 ;
• Longeron, D. et al, « Experimental Approach to Characterize Drilling Mud Invasion, Formation Damage and Cleanup Efficiency in Horizontal Wells with Openhole Completions » 2000, SPE 58737 ; ou
• Longeron, D. et al, « an Integrated Experimental Approach for Evaluating Formation Damages due to Drilling and Completion Fluids », 1995, SPE 30089.

Damage testing of formations is of primary importance to minimize or reduce deterioration in permeability in the vicinity of wells by choosing the most appropriate drilling fluid and optimizing well cleaning techniques. During the past five years, the applicant has developed specific laboratory test equipment and procedures intended to characterize the damage to formations due to drilling during overpressure operations and to quantify the performance of various techniques. cleaning agents used in the industry as evidenced by the following publications:

• Alfenore, J. et al, "What Really Matters in our Quest of Minimizing Formation Damage in Open Hole Horizontal Wells", 1999, SPE 54731;
• Longeron, D. et al, "Experimental Approach to Characterize Drilling Mud Invasion, Formation Damage and Cleanup Efficiency in Horizontal Wells with Openhole Completions" 2000, SPE 58737; or
• Longeron, D. et al, "an Integrated Experimental Approach for Evaluating Formation Damages due to Drilling and Completion Fluids", 1995, SPE 30089.

Leakage pressure tests are performed with a filtration cell dynamic which can receive carrots with a diameter of 5 cm and a length up to 40 cm. The cell is equipped for example with five sockets pressure located 5, 10, 15, 20 and 25 cm from the entrance face of the carrot. The plugs pressure monitors monitor pressure drops across six sections of the carrot while circulating the mud and circulating the oil back in order to simulate the production of the well. In order to reproduce the dynamic process invasion of the mud and the mud filtrate, laboratory tests are carried out under representative well conditions (temperature, overpressure and rate of shear applied to mud, carrots saturated with oil and connate water, etc.). Of the oil is then injected in the opposite direction (return current) at a constant flow rate in order to simulate the production of the well. The evolution of return permeabilities is calculated, for each section, depending on the cumulative volume of oil injected. The final value stabilized return permeability is then compared to the initial permeability not deteriorated in order to assess the residual deterioration as a function of the distance by compared to the entrance face of the carrot. In general, it has been observed that a total amount of 10 to 20 PV (maximum one hundred PV) of oil injected was sufficient to obtain a stabilized return permeability value after damage with oil-based mud.

II - Simplified digital model to remove damage to neighborhood of the well

où p représente la pression, k, la perméabilité absolue, µ, la viscosité, c, la compressibilité et , la porosité. La viscosité µ et la compressibilité c dans le filtrat sont considérées comme identiques à celles observées dans l'huile qui sature le réservoir. On considère que la pression initiale dans le réservoir est hydrostatique au début de la production.Considering a well drilled in the petroleum zone with an oil-based mud, we admit that the properties of the oil in the tank are identical to those observed in the filtrate. The flow equation in the vicinity of the well is thus governed by a single-phase equation which is written as follows:

where p represents pressure, k, absolute permeability, µ, viscosity, c, compressibility and , porosity. The viscosity µ and the compressibility c in the filtrate are considered to be identical to those observed in the oil which saturates the tank. The initial pressure in the tank is considered to be hydrostatic at the start of production.

II. 1 Modeling of the internal filtration cake

The internal filtration cake reduces the permeability of the tank near the well. As noted above, the reductions in permeability to the end of the drilling period and at the end of a complete cleaning can be obtained from laboratory measurements. For modeling, we let's use the dimensionless permeability reduction factor to represent the variation in permeability. The use of the dimensionless form has the advantage of making it possible to group data by geological zones.

Let k _{i be} the initial permeability, k _d the permeability after damage and k _f the final return permeability; the permeability after damage and the final return permeability are generally a function of the distance to the well. c ₁ ( r ) = K _d ( r ) / K _i and c ₂ ( r ) = K _f ( r ) / K _i being the curves of the permeability reduction factor as a function of r before cleaning and after return fluid respectively (Figure 1), the variation in permeability in the vicinity of the well is generally limited by these two curves during the fluid return period. c ₁ (r) corresponds to the permeability curve after damage and c ₂ (r) corresponds to the stabilized return permeability curve.

As noted above, the variation in permeability in the area occupied by the internal filter cake during the fluid return period depends on the amount of oil produced flowing to the well. We use the following dimensionless form to describe this variation (Figure 2): vs 0 ( Q ) = K (Q) - K d K f - K d where Q is the total flow rate through the porous medium in the direction of flow divided by the porous surface (surface of the pores offered for flow). This curve represents the variation of permeability with respect to the flow through a unit of porous surface. It generally corresponds to a given direction of flow. In practice, the direction of flow is the radial direction towards the well. When Q = 0, there is no flow making it possible to clean the filter cake, the permeability corresponds to the permeability after damage with k (0) = k _d . So we have c ₀ (0) = 0. When Q is very large, the filter cake is completely cleaned, the permeability corresponds to the final return permeability with k (+ ∞) = k _f . In this case, we have c ₀ (+ ∞) = 1.

The permeability variation curve can be measured from laboratory data and can be considered as independent of the location in a core. Thus, a curve is used for each geological area. This curve is monotonous. Its maximum is generally reached for several m ³ (or several tens of m ³ ) of fluid crossed per unit of porous surface.

The permeability k at the distance r from the well during the fluid return period can be written in the following trivial form: k ( r , Q ) = ( k f ( r ) - k d ( r )) K r ( r, Q ) - K d ( r ) K f ( r ) - K d ( r ) + k d ( r )

Using the dimensionless curves defined above and taking into account equation (2), the permeability reduction factor c (r, Q) is expressed by: vs ( r , Q ) = ( vs 2 ( r ) - vs 1 ( r )) vs 0 ( Q ) + vs 1 ( r )

Initially, Q = 0, the reduction in permeability corresponds to that obtained after invasion of the filtrate (permeability after damage): c (r, 0) = c 1 (R)

At the end of the fluid return, when the quantity of fluid in flow Q is very large with c ₀ (Q) ≈ 1, the reduction in permeability corresponds to the restored state with the return permeability stabilized: c (r, Q) = c 2 (R)

Variation in permeability in the area occupied by the filter cake internal is modeled with equation (3). Unlike the internal filtration cake, the impact of the external filtration cake described below is modeled in the form of a wall coefficient in the discretized numerical model.

II.2 Meshing and numerical diagrams

A cylindrical mesh rx is used for the modeling of the flow of the fluid in the vicinity of a horizontal well (Figure 3): r is the radial direction, perpendicular to the axis of the well,  is the angular direction and x is the direction along the well. With this mesh, the limits of the well are discretized and meshes very small can be used to discretize the area occupied by the cake internal filtration. In general, the radius of the well is of the order of a few centimeters, and the thickness of the internal filter cake varies between a few centimeters and a few decimeters. In order to get a good description of the phenomenon of elimination of the filter cake, the meshes used in the vicinity of the wells vary between a few millimeters and a few centimeters.

For cylindrical meshes, a standard numerical diagram for the approximation of the flux between two points can be used to model F i +1/2 = T i +1/2 ( p i +1 - p i ) flow. For example, the flux between two neighboring meshes i and i + 1 in the radial direction is calculated by (Figure 4): with: T i +1/2 = 1 1 K r, i ln r l + 1/2 ri + 1 k r, i +1 ln r i +1 r i +1/2 Δ j Δ x k where j and k are the indices of the cells considered in the directions  and x, r _i represents the distance from the cell i to the well, r _{i + 1/2} is the distance from the interface of the cells considered to the well, k _{r , i} is the permeability of the mesh i in the radial direction, Δ and Δx are the lengths of the meshes in the directions  and x and Ti the transmissivity between meshes.

The term “well meshes” designating the meshes which discretize the limits of the well, the boundary conditions of the well are treated in the well meshes. The internal pressure of the well p _w and the flow rate of the well q _i over a mesh i considered can be linked by the following discretization formula (Figure 5a): q i = IP i (p i - p w ) with: PI i = 1 1 K r, i ln r w r i Δ j Dx k (10) where r _w is the radius of the well. This discretization at the limits of the well is similar to the approximation of the flow of the fluid between two meshes. However, for the discretization of the well limits, the discretization coefficient is designated by the digital productivity index IP and not by the transmissivity T, and the flow F is replaced by the flow rate of the well q _i . This notation is consistent with the commonly used digital well model, and the wall coefficient can be integrated into the term of the digital productivity index IP.

The permeability k _{r, i} varies during the return of fluid in the zone occupied by the internal filtration cake according to the formula presented in the previous section. Thus, the transmissivity and the digital productivity index IP also vary in the simulation during the fluid return period.

II.3 Modeling of the external filtration cake

The presence of the external filter cake can be taken into account in the discretization formula via the digital IP index. In the case of the presence of an external filtration cake of thickness d _e and of permeability k _e , the pressure of the well p _w corresponds to the pressure on the radius r _w - d _e and not on the radius r _w . The pressure drop is high through the external filter cake which is located in the area between r _w - d _e and r _w . Once again using equation (9) to connect the pressure of the well p _w , the pressure of the well mesh p _i and the flow rate of the well q _i , the discretization coefficient IP should integrate the impact of the filter cake external as follows (Figure 5b): PI i = 1 1 K r, i ln r w r i + 1 K e ln r w r w - d e Δ j Δ x k

It is assumed that the external filter cake is eliminated if the difference in pressure across its thickness is greater than a given threshold. So at the start of the fluid return, the numerical coefficient IP is calculated using equation (11) which incorporates the presence of the external cake if the latter exists. Once the difference pressure across the filter cake is above the given threshold, the index of digital productivity IP is calculated with equation (10).

The permeability k _e of the external filtration cake could generally be much lower than the permeability within the reservoir or in the area occupied by the internal filtration cake. Thus, in the presence of the external filtration cake, the numerical coefficient IP is very small.

To perform the simulations we can use a modeling tool flows such as the ATHOS model for example (ATHOS is a model of numerical modeling developed by IFP). The discretization scheme used is a classic 5-point diagram to model the diffusivity equation in mesh cylindrical. In the meshes in the immediate vicinity of the well, a digital IP is used to connect the pressure in these meshes, the pressure at the bottom of the well and the flow flow to the well. As the permeability in the vicinity of the well changes during the disgorgement period, the transmissivities around the well and the PI also change according to the variation of the permeabilities.

The curves which define the multiplying coefficients of permeabilities as a function of the distance to the well, c ₁ (r) and c ₂ (r), are entered into the simulator in the form of tables of values. The corresponding values in each mesh are calculated from these curves using a linear interpolation as explained above. The cumulative pore volume of fluid passing through an interface between two meshes in the radial direction r is used to calculate the multiplying coefficient of transmissivity between these two meshes at each instant considered.

III Numerical results

We present two examples to illustrate the capabilities of the method which has been developed: the first concerns disgorgement of an internal cake without cake external and the second disgorgement in the presence of an internal cake and also an external cake.

Example 1: Disgorging in the presence of the internal cake alone

We consider a part of a horizontal well with a length of 20 m, which crosses 4 zones alternately representing two different types of heterogeneity (Figure 6). The permeabilities k of the corresponding media, initially without any damage, are 1000 and 100 mD. The length of each medium crossed is 5 m. The permeability values in the cells where the internal cake is formed due to the damage are entered manually in the data set. The curves, by zones, of the multiplier coefficient of the damaged permeability as a function of the distance from the wall of the well c ₁ (r) are given in Figure 7. The curves of the return permeability c ₂ (r) are presented in the Figure 8. These curves are discontinuous because the data provided by laboratory on only a few points. The greater the number of points, the better the laboratory curve is represented. The variation in permeability during cleaning as a function of the quantity of fluid flowing through the unit of porous surface, c ₀ (V), is shown in Figure 9. In practice, the maximum plateau can be reached with a few cubic meters of fluid passed per unit area.

As we have seen, a cylindrical mesh is used for the simulations. The tank is very large in the radial direction with an outside radius of 1750 m where the boundary condition is zero flow. On the borders at both ends of the well, the condition is also of zero flux. The numbers and mesh sizes in the directions r and x are given in Fig. 17 ( = 360 °). The well is discretized in 80 meshes along its length. Each zone of constant permeability is thus discretized in 20 meshes of 0.25 m. The initial pressure in the tank at the level of the well is approximately 320 bar.

a). Un débit de 20m³/j est imposé au puits pendant 1.5 jours. L'écoulement au voisinage du puits simulé avec la méthode présentée ci-dessus tenant compte de la variation de la perméabilité en cours du temps est notée SM1. Cette simulation est comparée à deux autres simulations en utilisant le modèle d'écoulement classique avec des perméabilités inchangées, égales d'une part aux perméabilités après endommagement c₁(r), et d'autre part aux perméabilités retour c₂(r). Ces deux simulations sont notées SM2 et SM3. Les résultats de simulations sont présentés pour les mailles des puits 31 et 40 situées au milieu et à la limite d'une des zones peu perméables, et pour les mailles 41 et 50 situées en limite et au milieu de la zone plus perméable suivante. La Figure 10 montre les débits d'huile au niveau de ces mailles pour les trois scénarios simulés : SM1, SM2 et SM3. Les simulations avec des perméabilités fixées, SM2 et SM3, donnent des débits constants par maille, ce qui est normal puisque la limite dans la direction r n'est pas atteinte pour le temps court simulé (1.5 jours). Par contre, les débits varient quand on modélise les variations de perméabilités dans le cake interne pendant la remise en production. Au temps 0, ces débits sont identiques à ceux des simulations avec les perméabilités consécutives à l'endommagement. Ensuite, ils se différencient en raison des perméabilités qui augmentent dans le cake interne suite au nettoyage par l'huile de la formation. Très rapidement, au bout d'une journée, ces débits rejoignent ceux simulés avec les perméabilités retour.Les variations de perméabilité dans les mailles 31 et 50 sont présentées aux Fig.11a, 11b respectivement. Ces variations correspondent à celles dans les deux zones. Les perméabilités dans les états d'endommagement et de retour sont aussi représentées. La variation de perméabilité au cours du nettoyage est bornée par ces valeurs. Au bout d'un jour, la perméabilité dans la zone la plus perméable (maille 50) rejoint presque la valeur de perméabilité retour, et celle dans la zone moins perméable (maille 31) ne change pas beaucoup. Mais, comme la variation entre la perméabilité d'endommagement et celle de retour est très faible dans la zone peu perméable, les résultats de simulation dépendent principalement de la variation de perméabilité dans la zone la plus perméable. Sur les résultats présentés à la Fig.10, les débits augmentent dans les zones plus perméables et ils rejoignent très rapidement ceux de la simulation SM3. Les débits dans les zones peu perméables diminuent car les simulations sont faites avec un débit total imposé au puits.Avec cette modélisation, nous pouvons également obtenir la variation de vitesse locale due au dégorgement du cake.

b). Une différence de pression de 1 bar est imposée pendant 1.5 jour. La Fig.12 montre la variation en fonction du temps t exprimé en jours, des débits simulés FR (exprimés en m3/j) correspondants au puits. Dans le cas de perméabilité inchangée (SM2 et SM3), les débits diminuent avec le temps. Par contre, la modélisation d'un dégorgement progressif donne un débit croissant jusqu'à un jour environ, avant de diminuer. L'augmentation de débit pendant la période initiale est due à l'augmentation de perméabilité dans le cake interne au cours de la remise en production.Les résultats dans les mailles de puits 31, 40, 41 et 50 sont très similaire aux ceux du cas a. Les débits avec la modélisation du nettoyage de cake au temps t=0 sont égaux à ceux simulés avec les perméabilités d'endommagement, et ensuite ils varient et rejoignent les débits simulés avec les perméabilité de retour.Dans cet exemple, nous observons que le nettoyage du puits est assez rapide quel que soit le scénario modélisé. Dans tous les cas, les résultats de simulation du dégorgement progressif SM1 sont très proches au bout d'un jour de ceux obtenus avec les perméabilités retour SM3. Il est possible de fournir les détails des résultats aux temps courts, comme par exemple les débits le long du puits, les pressions et les vitesses au voisinage du puits, pour mieux connaítre ce qui se passe au cours du dégorgement. Toutefois, les performances du puits aux temps longs, après quelques jours, sont quasi identiques, quelles que soient les configurations étudiées, sachant que les aspects géomécaniques ne sont pas pris en compte. Dans cette hypothèse, il semble donc que les impacts du cake interne sur la performance du puits soient très limités en temps et qu'il suffise en général d'étudier cette performance en considérant la perméabilité restaurée, c'est-à-dire celle de la configuration notée SM3.

Two simulations were made with different conditions imposed on the well:

at). A flow of 20m ³ / d is imposed on the well for 1.5 days. The flow in the vicinity of the well simulated with the method presented above taking into account the variation of the permeability over time is noted SM1. This simulation is compared to two other simulations using the classical flow model with unchanged permeabilities, equal on the one hand to the permeabilities after damage c ₁ (r), and on the other hand to the return permeabilities c ₂ (r). These two simulations are noted SM2 and SM3. The results of simulations are presented for the meshes of wells 31 and 40 situated in the middle and at the limit of one of the not very permeable zones, and for meshes 41 and 50 located in limit and in the middle of the next more permeable zone. Figure 10 shows the oil flows at these meshes for the three simulated scenarios: SM1, SM2 and SM3. The simulations with fixed permeabilities, SM2 and SM3, give constant flow rates per mesh, which is normal since the limit in the direction r is not reached for the simulated short time (1.5 days). On the other hand, the flows vary when we model the variations in permeabilities in the internal cake during the return to production. At time 0, these flows are identical to those of simulations with the permeabilities consecutive to the damage. Then, they differentiate due to the permeabilities which increase in the internal cake following the cleaning by oil of the formation. Very quickly, at the end of a day, these flows reach those simulated with the return permeabilities. The variations in permeability in the meshes 31 and 50 are presented in Fig. 11a, 11b respectively. These variations correspond to those in the two zones. The permeabilities in the damage and return states are also shown. The variation in permeability during cleaning is limited by these values. After one day, the permeability in the most permeable zone (mesh 50) almost reaches the return permeability value, and that in the less permeable zone (mesh 31) does not change much. But, as the variation between the damage permeability and that of return is very weak in the not very permeable zone, the results of simulation depend mainly on the variation of permeability in the most permeable zone. On the results presented in Fig. 10, the flows increase in the more permeable zones and they very quickly join those of the SM3 simulation. The flows in areas with low permeability decrease because the simulations are made with a total flow imposed on the well. With this modeling, we can also obtain the local speed variation due to disgorgement of the cake.

b). A pressure difference of 1 bar is imposed for 1.5 days. Fig. 12 shows the variation as a function of time t expressed in days, of the simulated flows FR (expressed in m3 / d) corresponding to the well. In the case of unchanged permeability (SM2 and SM3), the flow rates decrease over time. On the other hand, the modeling of a gradual disgorgement gives an increasing flow until about one day, before decreasing. The increase in flow during the initial period is due to the increase in permeability in the internal cake during the return to production. The results in the wells 31, 40, 41 and 50 are very similar to those of the case. at. The flows with the modeling of cake cleaning at time t = 0 are equal to those simulated with the damage permeabilities, and then they vary and join the simulated flows with the return permeability. In this example, we observe that the cleaning of the well is quite fast whatever the scenario modeled. In all cases, the simulation results of the progressive disgorgement SM1 are very close after one day to those obtained with the return permeabilities SM3. It is possible to provide details of results in short time, such as flows along the well, pressures and velocities in the vicinity of the well, to better know what happens during the disgorgement. However, the performance of the long-time well, after a few days, is almost identical, whatever the configurations studied, knowing that the geomechanical aspects are not taken into account. In this hypothesis, it therefore seems that the impacts of the internal cake on the performance of the well are very limited in time and that it is generally sufficient to study this performance by considering the restored permeability, i.e. that of the configuration noted SM3.

Example 2. Presence of a non-uniform external cake along the drain

We consider the same well geometry as in the previous example. In this example, the reservoir is homogeneous with a permeability of 1000 mD in the porous medium. The external cake does not have a homogeneous presence along the well. In some places, there is no external cake, and in places where the external cake is present, it has a kext permeability of 1 mD and a thickness r _ext of 4 mm as in the previous example. The distribution of the presence of the external cake is given in Fig. 13. The pressure difference necessary for the removal of the external cake is always fixed at 0.5 bar.

Two types of boundary conditions are used in the simulations. For the first case, a pressure of 318.2 bar is imposed at the bottom of the well, i.e. pressure difference between the tank and the well of 1.8 bar. For the second case, we impose several consecutive levels of pressure to arrive at a fall total pressure of 1.8 bar (Table 2).

Figures 14 and 15 show the distribution of the external cake and the distribution of the flow along the well for these two cases at different production times. In the first case, the flows are uniform along the well, because the external cakes are completely torn from the start. In the second case, the flow distribution varies as a function of time, since the external cakes are torn non-uniformly at different times. In addition, there are always external cakes that cannot be removed after 5 days. Fig. 16 shows the production of the well for these two cases. In the first case, the production of the well is higher, because all the external cakes are torn from the start. However, the maximum local flow along the well is always less than 3m ³ / m.day . In the second case, the well flow is lower, but the local flow can be very strong with a maximum of 4.5m ³ / m.day . Cakes still cannot be pulled out in some places. The performance of the well is greatly reduced in this case. This example shows that the disgorging procedures can influence the performance of the well even in a homogeneous tank.

Although it seems tempting to want to impose a large pressure difference between the well and the formation, since it is the procedure that allows the most quickly and most uniformly the external cake which limits the flow rate of the well, it can be dangerous to the integrity of the well to act so if the formation is unbound and that sand inflows are likely to occur with the consequence that plugging the well. It is one of the interests of the present invention to be able to define the best disgorgement procedure for the well without causing the risk mentioned when we know the speed of the fluid from which the sand loses its cohesion.

Claims (2)

Method for simulating the optimal conditions to be imposed in a well drilled through an underground deposit at any trajectory, for the gradual elimination by deposits of cakes that have formed in at least one zone, by fluids from the deposit the periphery of the well, following drilling and completion operations, characterized in that it comprises acquisition of initial data obtained by laboratory measurements of thickness and cakes as well as values of damaged permeability (kd) and restored permeability (kf) of the area surrounding the well, as a function of the distance (r ) at the well wall, depending on the value of the initial permeability (ki) of the formation around the well; the discretization of the damaged area by a 3D cylindrical mesh forming blocks of small radial thicknesses relative to the diameter of the well; and the resolution in this mesh of the diffusivity equation modeling the flows of fluids through cakes taking into account the initial data measured and by modeling the evolution of permeability as a function of the flow rates (Q) of fluids flowing through cakes, to deduce the optimal conditions to apply for the production of the well. Method according to claim 1, characterized in that the restoration of the permeability is modeled at any point at a distance (r) from the wall, considering that the permeability varies in proportion to the difference between the damaged permeability (kd) and the restored permeability (kf), the proportionality coefficient depending on an empirical law of variation of the permeability as a function of the quantity (Q) of fluids through the cakes.

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