OA18455A - Method for determining a concentration of solid particles - Google Patents

Abstract

The present invention relates to a method for determining a concentration of solid particles in drilling fluid, wherein the method comprises determining (302), based on a received dimension, a plurality of wirelines, each determined wireline having a diameter. In addition, for each current wireline in the determined wirelines, the method comprises: - determining (304) if a solid particle or a part of a fluid is in the current wireline; - if it is determined that a solid particle is in the current wireline, determining (305) whether the current wireline is sealed; - reiterating said steps based on a reiteration criterion. The method further comprises determining (310) a volume of injected fluid into the fracture and comparing (311) said determined volume with a reference to determine if a fracturing criterion is met. If the fracturing criterion is met, it is possible to modify (312) the current concentration of solid particles.

Description

TOTAL SA

METHOD FOR DETERMINING A CONCENTRATION OF SOLID PARTICLES

BACKGROUND OF THE INVENTION

The présent invention relates to the domain of weil stabilization and more specifically tothedomain ofthe préventionofdrillingfluid loss duringa drilling.

The approaches described In this section could be pursued, but are not necessarily approaches that hâve been previously conceived or pursued. Therefore, unless otherwise indicated herein, the approaches described In this section are not prior art to the claims in this application and are not admitted to be prior art by inclusion in this section. Furthermore, ali embodiments are not necessarily intended to solve ali or even any of the problems brought forward In this section.

When drilling through a depleted réservoir, there is a high risk of loss of the drilling fluid (e.g. mud) due to the disturbance in situ stress generated by the pressure drop ofthe fluid In the réservoir.

In order to ensure both the stability of the drilling and well control, the density of drilling fluid may be maintain between two limit values:

- a lower limit to ensure the stability of the well walls, and

- an upper limit to ensure that the preexisting fractures in geological formations are not opened and that no additional fracture are created. Indeed, these fractures may lead to the loss of control of the drilling fluid in the well.

When drilling a depleted réservoir, the upper limit level may be lowered due to the réservoir pressure drop.

The difference/margin between the upper and the lower limîts, which Is commonly known as the Mud Weight Window may become very narrow or négative In the case of a heavily depleted réservoir with a cap rock in clay (shale) formation.

Therefore, there Is a need to increase the upper limit of the drilling fluid density by performîng wellbore strengthenlng and therefore to be able to drill the cap rock shale and to drill the depleted réservoir with a single drill diameter (drilling with a single drill diameter has a huge impact on the cost of drilling).

In order to Increase the upper limit, it is possible to add solid particles in the drilling fluid (i.e. to Increase the concentration of solid particles). These solid particles mayfiil the fractures as soon as they occur and/or may seal preexisting fractures when they are trying to reopen.

The amountZconcentration and the size distribution (PSD: particle size distribution) of solid particles to be added in the drilling fluid may be two key parameters (most of the time, the PSD are a predetermined parameter fixed by a provider of solid particles). Indeed, it is advantageous that the particle size in the slurry is important enough to create a bridge in the fracture, and that the number of particles (volumétrie content) is sufficient to quickly seal fractures before they spread.

To seal a fracture means that no fluid is abie to infiltrate into the fracture through the created bridge (or only a little part).

SUMMARY OF THE INVENTION

The Invention relates to a method for determining at least an adéquate concentration of solid particles In drilling fluid, wherein the method comprises:

ZaZ receiving a dimension of a section of a fracture;

/b/ receiving at least a current concentration of solid particles In the drilling fluid;

Id determining, based on the received dimension, a plurality of wirelines, each determined wireline having a diameter;

ZdZ for each current wireline in the determined wirelines:

Zd1 / determining if a solid particle or a part of a fluid Is in the current wireline based at least on the current concentration;

Zd2Z If it Is determined in step Zd1Z that a solid particle is in the current wireline, determining whether the current wireline is sealed;

Zd3Z reiterating steps /d 1 Z, Zd2Z and Zd3Z based on a réitération criterion; ZeZ determining a volume of injected fluid into the fracture based on itérations of step ZaZ where It Is determined that a part of a fluid is In the current wireline;

ZfZ comparing said determined volume with a reference volume to détermine if a fracturing criterion is met;

ZgZ if the fracturing criterion is met, modifyîng at least the current concentration of solid particles in the drilling fluid and reiterating steps ZcZ, ZdZ, ZeZ, ZfZ and ZgZ;

ZhZ if the fracturing criterion Is not met, outputting the current concentration of solid particles in the drilling fluid.

The dimension of the section of the fracture may be expressed as a surface, a diameter, a radius, etc.

If the received dimension Is a surface, It Is possible to détermine the wirelines so that ail wirelines grouped together forms a tube of the same surface as the received dimension. If the received dimension is a length, it is possible to do the same but after converting this length into a surface (for instance, by considering that the fractures hâve a rectangular or circular section).

The determined wirelines are only a représentation of the fracture for the modeling. No actual wireline exists in a fracture.

Steps Zd1/ to /d3/ are executed for every determined wirelines or for a subset of the determined wirelines. Each itération of such steps represents a given period of time.

The détermination of the step Zd1/ may be a random draw. For instance, if the concentration of the solid particles Is 10% in the drilling fluid, the probability of determining that a solid particle Is the wireline is 0.1 and the probability of determining that a part of the drilling fluid is the wireline is 0.9.

Once it is determined that a solid particle Is Inside the wireline, it Is possible to détermine the diameter of said particle: the determined diameter may be a predetermined value or may be a random value drawn in a distribution.

The determined volume may be used to détermine whether the fracture Is extending/increasing. Indeed, If the injected volume is greater than the fracture volume (for instance), the fracture opens and Increases to ailow the injection of the fluid. It Is also possible to take into account the seepage rate in the formation and thus to take into account the dérivative of the volume (e.g. when the volume of the fracture has been injected).

Then, it is possible to détermine a concentration of solid particles that are adéquate to quickly plug the existing fractures and thus:

- avoid the leakage of the mud during the drilling;

* en sure both the stability of the drilling and weli control.

In a possible embodiment, a sum of surfaces of sections of the wirelines may be equal to a surface of the section of the fracture.

Therefore, the modelling of the fracture by a plurality of fracture may be adéquate.

The method may also comprise receiving a distribution of dimensions of solid particles in the drilling fluid.

The détermination of step Zd1 / may be further based on the received distribution.

For instance, the distribution of dimensions may be a distribution of diameter/radius of solid particles.

The method may also comprise /g/ the détermination of adéquate ratio between several plugging matériels.

In addition, the détermination of step /d2/ may comprise the détermination of a dimension of the solid particle in the wireline.

This détermination may be based on a received distribution.

ln one possible embodiment, the wireline may be determined to be sealed if the determined dimension of the solid particle in the wireline is higher than a predetermined value function of the diameter of current wireline.

In another possible embodiment, the wireline may be determined to be sealed if the determined dimension of the solid particle In the wireline is within a predetermined interval around the diameter of current wireline.

Altematively or in combination with other embodiments, the wireline may be determined to be sealed if a number of solid particles determined to be ln the current wireline and matching a blocklng criterion is above a predetermined value.

For instance, the blocklng criterion may be that the dimension of the particle Is greater than X% of the diameter of the wireline (X being for instance75, 85 or 100). The number of particles needed to seal the wireline may be a function of the size of the particle or of the diameter of the wireline (e.g. If the critical size of the particle is 85% of the diameter of the wireline, 10 particles may be needed to seal the wireline; if the critical size of the particie is 70% of the diameter of the wireline, 5 particles may be needed to seal the wireline; if the size of the particle is 95% of the diameter of the wireline, 2 particles may be needed to seal the wireline; etc.).

In addition, the réitération criterion may comprise at ieast one condition in the following conditions:

- If the wireline is determined to be sealed ;

- if the number of réitérations for a current wireline exceeds a predetermined value;

- if the number of réitérations for ail wirelines exceeds a predetermined value.

Furthermore, the détermination of the volume of step /e/ may be based on a number of Itérations of step /a/ where it is determined that a part of a fluid is in the current wireline and based on a unitary volume that is injected for a single Itération.

The fracturing (fracture propagation) criterion may comprise at least one condition In the following conditions:

- if the determined volume is higher than a predetermined volume;

- if the dérivative of the determined volume is higher than a predetermined value ;

- if the dérivative of the determined volume is higher than a predetermined value for itérations higher than a given itération number.

A second aspect relates to a computer program product comprising a computer readable medium, having thereon a computer program comprisjng program Instructions. The computer program is ioadable into a data-processing unit and adapted to cause the data-processing unit to carry out the method described above when the computer program Is run by the data-processing unit.

Other features and advantages of the method and apparatus disclosed herein will become apparent from the following description of non-limiting embodiments, with reference to the appended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The présent invention is illustrated by way of example, and not by way of limitation, In the figures of the accompanying drawings, in which like reference numerals refer to similar éléments and In which:

- Figure 1 is a représentation of a sealed fracture in a well;

- Figure 2 is a représentation of the model used for modeling the formation of the plug;

- Figure 3a is a flow chart describing a possible embodiment of the présent

Invention;

- Figure 3b présents various functions that relate an injected volume In the fracture to the time;

- Figure 4 Is a possible embodiment for a device that enables the présent invention.

DESCRIPTION OF PREFERRED EMBODIMENTS

Figure 1 Is a représentation of a sealed fracture 102 In a well 101.

By adding solid particles having predesigned size distribution and volumétrie content, it Is possible to prevent fracture propagation while drilling above the fracture Initiation pressure.

The solid particles added In the drilling fluid may hâve two rôles:

- plugglng the fracture entry as rapidly as possible at the beginning of fracture Initiation in order to reduce the fracture’s conductivity at its entry and then to stop the fracture propagation;

- Increasing the hoop stress by placing the some particles inside the fracture. The wellbore strength to sustain the drilling fluid pressure Is then enhanced.

For instance, the fracture 102 may hâve a length of l_t(e) (arrow 104) and an opening (width) of e(t) (arrow 103s) (L»(e) may be, for instance, ruled by the relation given bySneddon, 1945).

In particular, the fracture may be sealed by a plug 103p that comprises a set/conglomerate of solid particles: this plug 103p may create a hermetic or semihermetic seal (with a permeability K). The size of the plug is noted Lt(e) or L_b.

The opening e(t) may détermine the size of solid particles to be added in the drilling fluid.

The volume of fracture 102 may détermine the volumétrie concentration of the solid particles to be added. The différence between injection volume V_inj (arrow 105c) and seepage volume V_teak (105a and 105b) may be less than the fracture volume, otherwise (i.e. after having filled the fracture volume, q_leak < q_lnj, with q_leatc the seepage rate and q_lnj the injection rate), the fracture continues to propagate.

The injection volume may be function of the permeability K of the plug 103p at the entry of the fracture (the permeability may be a constant value or a value function of cumulated LCM). The injection rate q,_nj through the fracture entry (LCM bridge) may be calculated with the relationship:

_ K(0 ?ecd ~ ?b ^qi*> - -μ ~^e where P_ecd the drilling fluid pressure, P_b the pressure in the fracture (for instance,

P_b = aP_ecd with a In the range [0.95, 0.99]), μ the viscosity of the drilling fluid without any solid particles, e the fracture width, L_b being thickness of the bridge, for instance in the range (1mm, 2mm],

In addition, the seepage rate throught the fracture's walls into the formation may be computed as:

L·²

Qleak — 4rrC_t —3-5 ^CP where C_L Is the fracture leak-off coefficient which is function of the formation (106) permeabilityand t_p Isthe time afterthe opening ofthe fracture.

Thanks to the above formula, it is then possible to détermine the limit value of for which q_inJ = q_lealc (and the corresponding opening value e).

Nevertheless, due to the uncertainties of various parameters Involved in fracture length Ζγ calculation, sensitlvity calculation may be carried out using analytical solution. For instance, thousands simulations may be realized with random sampling of input data.

Therefore, no single value of L_r is determined: a distribution of limit values L_r / e may thus be determined.

Figure 2 Is a représentation of the mode! 200 used for modeling the formation of the plug.

The opening 201 of the fracture Is modeled as N virtual thin wirelines (202) as shown in Figure 2: each wireline may hâve a diameter function or equal to the fracture opening (or fracture width). The drilling fluid / solid particles may circulate into these wirelines (arrow 203).

The dimension of the section of the wirelines may be Identical (e.g. having the same diameter) or may be drawn according to a given distribution. The addition of sections of ali wirelines may be, for instance, sensibly equal to the surface of the opening of the fracture.

When a solid particle enters a wireline, this particle may seal the wireline:

- if the size of the particles is close to the dimension of the wireline (i.e. within a range around the dimension of the wireline, e.g. particle 204). If the particle is too small (e.g. particle 206), nothing happen. If the particle is too big (e.g. particle 205), the particle cannot enter the wireline and the particle is not considered to hâve any Impact on the flow ln the wireline;

- this sealing may happen only after a predetermined number of times a particle close to the dimension of the wireline enters the wireline (the predetermined number of time may be fonction of the size of the particles and/or of the dimension of the fracture/wireline, for instance, if the size of the particle is slightly bigger than the dimension of the wireline, only one particle may seal the wireline while If the size of the particle is slightly lower than the dimension of the wireline, two or three particles may be need to seal the wireline).

Figure 3a Is a flow chart 300 describing a possible embodiment of the présent invention. Part of this flow chart can represent steps of an example of a computer program.

When receiving the dimension of the opening e of the fracture (301, this opening value e may be computed as described in relation of Figure 1), it Is possible to détermine (step 302) a plurality of wlrelines as detailed above in relation of figure 2. Each wireline w has a diameter d_w. The diameter d_w may be a constant fonction of the width of the fracture. The diameter of each wireline may be determined from the mean volume of a single particular calculated from the volume of ail particles generated divided by total number of particles In ail wirelines.

In addition, it is possible to obtain a distribution 303 of the solid particles that is expected to be added Into the drilling fluid. Most of the time solid particles provided by industrial hâve a known distribution (for instance the percentage of particles having a diameter below 10% of the mean diameter and the percentage of particles having a diameter below 90% of the mean diameter are known, the distribution being a logarithmic distribution, for example). Concentration of the solid particles associated with a given distribution Is also provided (for instance, ln part per billion or ppb or ln percentage).

It is possible to receive a plurality of distribution and a plurality of concentration as it is possible to add in the drilling fluid a plurality of industrial predetermined solid particles. Therefore, it Is possible to create a mix with said particles from different types / different Industrial providers.

Therefore, a génération of a flow In each wireline is computed (step 304). In order to do so, a first wireline (with a diameter d_w) is selected. It is then determined (random draw according to the concentration(s) and the distribution(s) of the solid particles in the drilling fluid) if the substance that enters the wireline is a solid particles or a part of the drilling fluid:

- if the substance is a part of the drilling fluid, the wireline is not sealed (test 305, output KO) and a counter Vrec is incremented (step 315) : this counter V_rec represent a value proportional to the volume of drilling fluid entering the fracture ;

if the substance is a solid particle having a diameter d_sp (the diameter of the solid particles Is, for Instance, randomly drawn into the solid particle diameter distribution(s)), the diameter d_sp Is compared to the diameter of the wireline d_w in order to détermine if the particle seals the wireline, (test 305).

- if d_sp Is “too big compared to d_w (for instance d_sp>5.d_w. or d_sp being bigger than a predetermined number of times d_w), the particles Is considered as being rejected (the particles do not enter into the wireline) and is not blocked into the wireline;

- if d_sp Is “too” small compared to d_w (for instance d_sp<0.85*d_w. or d_sp being smaller than a predetermined number of times d_w), the particles is not blocked into the wireline;

- otherwise, the particle may be blocked Into the wireline (e.g. if ~^E-<x1, the solid particle seals instantaneity the wireline, t^e<x2. the solid particle seals the wireline after two passages of such solid (f particles, -p- <x₃, the solid particle seals the wireline after three passages of such soiid particles, etc. with x_lt x_2t x₃, etc. being predetermined values). If it is determined that the particle does not seal the wireline at that current itération (test 305, output KO), a number of Itérations (see above) may be noted (step 306) in a memory or in a database to be able to détermine if the wireline is to be sealed during a next itération.

It Is also possible to follow simpler rules (for instance, the wireline is sealed if N solid particles having a diameter above a given value enters the wireline (N a predetermined integer >0); the wireline is not sealed in the other cases).

If the wireline is seaied (see above), a flag may be set in relation to this wireline (step 307).

Once the current wireline Is sealed, and if at least one wireline has not been sealed (test 308, output KO), a new wireline (which has not been sealed) is selected as the current wireline (step 309) and the above steps (304 to 308) are reiterated.

Once the current wireline is sealed, and if ali wirelïnes has been sealed (test 308, output OK), the volume injected V_(nj ln the fracture is determined (step 310). This volume is function of the volume V_rec Incremented in step 315 (for Instance V_lnj ~ Vrec.Uv where U_v is the unitary volume injected per itération (i.e. unitary period of time)).

The test 308 may also take in account a maximal number of itérations: if the number of Itérations is the maximal number of itérations, it is possible to quit the itération loop (the number of itérations may, Indeed, be linked to the determined volume ln step 310).

This volume (determined in step 310) may be a unique value but may also be a function of the time (representing the évolution of the injected volume with the time / the Itération number).

The volume may thus be compared with a threshold value V», representing, for instance, the volume of the fracture 102 (determined, for instance, thanks to the value e and Lf). If the volume computed in step 310 Is a function (e.g. 351, Figure 3b), the value compared with the threshold value Vm may be the maximal value of the function (e.g. 356, Figure 3b). If the threshold value Vth Is lower than the compared value (test 311, output KO), It is possible to modify the distribution of solid particles and/or the concentration(s) of the solid particles (step 312, for instance by increasing the concentration(s) by a predetermined amount) and to reiterate above steps. If the threshold value Vm Is bigger than to the compared value (test 311, output OK), the current distribution and the current concentration of the solid particles may be output.

In another embodiment, and if the volume computed ln step 310 Is a function (e.g.

352 or 353, Figure 3b), It is possible to détermine the dérivative value of the function for a value of the function corresponding to the threshold value Vth (e.g. respectively 354 or 355). This dérivative value is related to the maximal flow into the fracture. If the dérivative value is bigger than a predetermined value (test 311, output KO, meaning that the flow In the fracture Is too Important), It Is possible to modify the distribution of solid particles and/or the concentration of the solid particles (step 312, for Instance by Increasing the concentration by a predetermined amount) and to reiterate above steps. If the dérivative value Is lower than the predetermined value (test 311, output OK), the current distribution and the current concentration of the solid particles may be output. It Is also possible to systematically modify the current distribution and/or the current concentration, for Instance by dichotomy, to détermine the values of concentratlon(s) and distribution(s) for which the dérivative value Is close enough to the predetermined value.

The predetermined value compared to the dérivative value may be function of the flowofthe seepage volume Vieak (105a and 105b, Figure 1).

Figure 4 Is a possible embodiment for a device that enables the présent Invention.

In this embodiment, the device 400 comprise a computer, this computer comprising a memory 405 to store program Instructions loadable into a circuit and adapted to cause circuit 404 to carry out the steps of the présent Invention when the program Instructions are run by the circuit 404.

The memory 405 may also store data and useful Information for carrying the steps of the présent invention as described above.

The circuit 404 may be for Instance:

- a processor or a processing unit adapted to Interpret instructions in a computer language, the processor or the processing unit may comprise, may be associated with or be attached to a memory comprising the Instructions, or

- the association of a processor / processing unit and a memory, the processor or the processing unit adapted to Interpret Instructions In a computer language, the memory comprising said Instructions, or

- an electronic card wherein the steps of the invention are described within silicon, or

- a programmable electronic chip such as a FPGA chip (for « FieldProgrammable Gâte Array »).

This computer comprises an input Interface 403 for the réception of data used for the above method according to the invention and an output interface 406 for 5 providing the distribution and or the concentration of the solid particles to be used In the drilling fluid.

To ease the interaction with the computer, a screen 401 and a keyboard 402 may be provided and connected to the computer circuit 404.

Expressions such as comprise, include, incorporate, contain, is and hâve 10 are to be construed in a non-exclusive manner when interpreting the description and its associated claims, namely construed to allow for other items or components which are not expiicitly defined also to be présent. Reference to the singular is also to be construed in be a reference to the plural and vice versa.

A person skilled in the art will readily apprecîate that various parameters disclosed 15 in the description may be modified and that various embodiments disclosed may be combined without departing from the scope of the invention.

Claims (11)

1. A method for determining a concentration of solid particles in drilling fluid, wherein the method comprises:

/a/ receiving a dimension of a section of a fracture (301 );

/b/ receiving at least a current concentration of solid particles in the drilling fluid (303);

/c/ determining (302), based on the received dimension, a pluralîty of wirelines, each determined wireline having a diameter;

/d/ for each current wireline in the determined wirelines:

/d1/ determining (304) If a solid particle or a part of a fluid Is in the current wireline based at least on the current concentration;

/d2/ if it is determined in step /d1 / that a solid particle is In the current wireline, determining (305) whether the current wireline is sealed;

/d3/ reiterating steps /d1 /, /d2/ and /d3/ based on a réitération criterion; /e/ determining (310) a volume of Injected fluid into the fracture based on itérations of step /a/ where it is determined that a part of a fluid is in the current wireline;

/f/ comparing (311 ) said determined volume with a reference to détermine if a fracturing criterion is met;

/g/ if the fracturing criterion is met, modifying (312) at least the current concentration of solid particles in the drilling fluid and reiterating steps /c/, /d/, /e/, /f/ and /g/;

/h/ if the fracturing criterion is not met, outputting the current concentration of solid particles in the drilling fluid.

2. A method according to claim 1, wherein a sum of surfaces of sections of the wirelines is equal to a surface ofthe section of the fracture.

3. A method according to one of the preceding claims, wherein the method further comprises:

- receiving a distribution of dimensions of solid particles in the drilling fluid (303);

and wherein the détermination of step /d1/ is further based on the received distribution.

4. A method according to one of the preceding ciaims, wherein the détermination of step /d2/ comprise the détermination of a dimension of the solid particle in the wireline.

5. A method according to claim 4, wherein the wireline is determined to be sealed If the determined dimension of the solid particle in the wireline is higher than a predetermined value fonction of the diameter of current wireline.

6. A method according to claim 4, wherein the wireline is determined to be sealed if the determined dimension of the solid particle in the wireline is within a predetermined interval around the diameter of current wireline.

7. A method according to one of the preceding claims, wherein the wireline is determined to be sealed if a number of solid particles determined to be in the current wireline and matching a blocking cri te ri on is above a predetermined value

8. A method according to one of the preceding claims, wherein the réitération criterion comprises at least one condition in the following conditions:

- if the wireline Is determined to be sealed ;

- If the number of réitérations for a current wireline exceeds a predetermined value;

- if the number of réitérations for ail wirelines exceeds a predetermined value;

9. A method according to one of the preceding claims, wherein the détermination of the volume of step /e/ is based on a number of itérations of step /a/ where it is determined that a part of a fluid is in the current wireline and based on a unitary volume that is injected for a single itération.

10. A method according to one of the preceding claims, wherein the fracturing criterion comprises at least one condition in the following conditions:

- if the determined volume is higher than a predetermined volume;

- if the dérivative of the determined volume is higher than a predetermined value ;

- if the dérivative of the determined volume is higher than a predetermined value for itérations higher than a given itération number.

11. A non-transitory computer readabie storage medium, having stored thereon a computer program comprising program instructions, the computer program being loadable into a data-processing unit and adapted to cause the data-processing unit to carry out the steps of any of claims 1 to 10 when the computer program Is run by the 10 data-processing device.