Hibo Ling ,Guobing Ding ,Xinpu Shen
a School of Mechanical and Electrical Engineering,Southwest Petroleum University,Chengdu,610500,China
b School of Petroleum Engineering,China University of Petroleum,Qingdao,266580,China
Keywords:Well wall strengthening Pressure sealing Stress cage Extended mud window Numerical simulation Natural crack Quasi-brittle Damage mechanics
ABSTRACT Aiming at the main problems in the design and analysis of well wall strengthening for fractured formations,a three-dimensional (3D) numerical simulation scheme is proposed.The three-dimensional finite element software is used to analyze the mechanical behavior of fractures and the pressure sealing process,and evaluate the stress cage effect.The main features of the model are as follows:(1) The equivalent fractures in the analytical model represent the function sum of the mechanical behavior of all fractures on the well wall,which is a functionally equivalent crack.(2) When evaluating the stress cage effect,the shape of the crack wedge filled with the plugging agent particles is formed by simulating the fractures opening process under the injection pressure,not a given regular shape.(3) In the model of calculating bull heading of block agent,the liquid pressure on the well wall is the injection pressure,which is a variation increased with time.The fluid pressure on the well wall in the stress cage calculation model is generated by the initial pore pressure.(4) The numerical evaluation of the stress cage effect is achieved by calculating the increase amplitude FX of the minimum hoop stress on the well wall.Using this model,several sets of injection pressure design values can be used for pressure plugging numerical simulation and stress cage effect evaluation calculation,and then the optimal and accurate quantitative value of“injection pressure,block agent particle size,safe mud window upper bound”are found through comparison.Finally,through an engineering example of horizontal well drilling pressure sealing in a shale gas reservoir developed by a fracture,we use the above theoretical tools to introduce the process and results of the numerical analysis of the extended mud window drilled in the shale gas fissure reservoir.
Well wall strengthening in fractured formations is the primary measure to increase the pressure tolerance of the wellbore to the drilling mud.Since the effect of well wall strengthening is mainly to increase the upper limit of the safe drilling mud window,the well wall strengthening is also called the extended mud window[1-4].
There are many reasons for strengthening the well wall in the project.One of them is that when drilling in a formation with natural fracture,high conductive fracture will cause mud loss[5].In general,the upper limit of the mud window,or Fracture Gradient,depends on the minimum horizontal principal stress.However,if the natural fracture is a high conductive fracture,that is,the fracture has a high perveance,mud loss will occur as long as the mud pressure exceeds the pore pressure.The mud upper limit at this time is much smaller than the minimum horizontal principal stress.In order to block these highly conductive natural fractures,pressure sealing is required,such as the mud leakage caused by the highconductivity fracture in the horizontal well drilling of the Pengshui shale block[6],and the later pressure sealing to reinforce the well wall.Another situation is that a weak fracture zone such as a minor fault is encountered during the drilling process.In order to reduce the complexity of casing construction and improve the pressure-bearing capacity of the fracture zone on the wall,it is necessary to strengthen the well wall.The reinforcement of the well wall in the fracture zone under the deep water rock salt in the Gulf of Mexico falls into this category.The similarity between the two cases is that there is mud leakage.The difference is that the fracture size is different in both cases.The distribution of cracks in shale formations is relatively regular,the crack size is relatively simple,and the number of cracks on the wall per unit length is relatively small,while in the fracture zone of rock salt,the crack size is different,and the number of cracks is also relatively large.
Pressure sealing is a process in which the plugging material(LCM)is pressed into the fracture and the sealing material particles are sent into the high-conductivity natural fracture or induced crack by a plugging injection pressure which is significantly higher than the upper limit of the drilling mud,that is,the minimum horizontal principal stress value.In this process,the crack opens and extends,plugs LCM into the crack and blocks the crack,thereby reducing the fracture flow conductivity and blocking the mud loss channel [7].
Before the pressure is plugged into the subsequent drilling process,the pressure is first reduced to the initial formation pressure and then the safe mud density required for drilling is applied.When the plugging pressure disappears and the bottom hole pressure returns to normal,the opened fracture is filled with LCM,which is equivalent to forming a wedge and wedged into the well wall,thereby increasing the circumferential compressive stress of the well wall.A surface layer with a higher circumferential compressive stress,that is,a stress cage,is formed near the surface of the well wall and hole bottom.
At the subsequent drilling,the upper limit of the mud window that the reinforced well wall can withstand,that is,the lost pressure,depends on the minimum value of the circumferential compressive stress within 360°of the wall surface.Under the normal bottom hole pressure,compared with the minimum value of the hoop stress when the crack is not opened,the increase of the minimum hoop stress is TFθ,which is the effect of the stress cage formed by the pressure sealing.When the particle size of the selected LCM is properly matched with the plugging pressure and the fracture aperture,LCM can not only smoothly enter the crack according to the design requirements,but also can form the stress cage according to the design requirements after the bottom hole pressure is relieved to achieve the purpose of strengthening the well wall and realize the expansion of the safe mud window.Conversely,when the particle size of the selected plugging material does not match the plugging pressure and the fracture aperture,the plugging cannot be achieved.For example,if the injection pressure is too small and the crack is not opened,the size of plugging material particle may be larger than the fracture aperture,so that the crack cannot be entered,and the stress cage cannot be formed,resulting in poor sealing effect.Or if the injection pressure is too large,the crack is too large and the length is too long,the sealing material cannot be blocked as required,the sealing effect is not good,and even the mud loss may be aggravated.
Therefore,the pressure sealing design needs to ensure the accurate prediction calculation of the following two factors:(1)sealing the injected fluid pressure and the corresponding fracture aperture;(2) evaluating the stress cage effect,that is,after the plugging pressure is replaced by the normal bottom hole pressure,the degree of improvement of the hoop stress of the well wall caused by the wedge formed by the plugging material relative to the original hoop stress.The former factor’s results are used to guide the design to select the maximum size of the plugging material particles;the latter factor’s results are used to determine the upper limit of the safe mud density window for subsequent drilling.Another problem involved here is the accurate determination of the geometric shape of the wedge to plug the fracture.This issue will be discussed in detail later.
For the purpose of realizing the above two prediction calculations,three-dimensional numerical simulation of the opening and expansion of natural fractures under the pressure sealing is required.In order to obtain accurate evaluation of the stress cage effect around the well wall,it is necessary to carry out threedimensional numerical simulation of the wedge formed by the plugging material entering the crack and the stress change caused by it [8,9].
Wang Gui [1]and Pu Xiaoping [10]studied the mechanism of drilling fluid plugging to improve the bearing capacity of the formation.Lu Xiaochuan and Fan Baitao [11]conducted a review of relevant literature before 2011,pointing out that “well wall reinforcement should actually be called an extended mud window”.Song Dingding and Qiu Zhengsong [12]used a two-dimensional finite element model to study the numerical solution of well wall strengthening based on the stress cage method.Li Jia and Qiu Zhengsong[13]used finite element numerical simulation to study the various influencing factors of well wall strengthening,including plugging material bridging position and leak off rate.
In the international community,there have been many reports on pressure sealing related engineering practices for many years.Lietard[14]used information such as the flow and pressure of mud loss during drilling to determine the width and length information of the natural fractures.Moreover,the size of the block agent particles was further determined,and the crack width data obtained by image logging was discussed.Caughron [15]and Edwards [16]reported in their literature in which they used single well analysis data to obtain natural fracture locations and to design optimized block agent particle size matching work.There are many other related literatures [17,18],which are not introduced here.The literatures show that pressure sealing and stress cages are an effective way to increase the upper limit of the extended mud window.At present,the problems existing in the analysis of pressure sealing are mainly as follows:(1) The existing work is mainly to simplify the analytical boundary of the model,these models are too simple,the difference with the actual engineering is large,and the evaluation of the effect of pressure sealing is not specific;(2)In the current numerical simulations,the description of the relevant mechanical models is not perfect,and the calculated results are quite different from the actual engineering.
The following sections of this paper will first introduce the simplified assumptions for the numerical simulation model of pressure sealing,then introduce the constitutive model of the crack mechanical behavior and the finite element model of the crack analysis,and give the calculation format of pressure plugging simulation and stress cage effect analysis.On this basis,the threedimensional finite element tool is used to study the opening and expanding behavior of natural fractures under the injection load,and the main mechanical mechanism of the pressure sealing process is clarified.The contents of the simulation include the opening and expansion process of the natural crack in the block agent injection process,and the evaluation of the stress cage effect.Finally,a successful engineering application example of the pressure sealing technology to block the crack development during the drilling of the Peng Page-1 section in the shale area of Chongqing will be given.
According to the above introduction,the purpose of this paper is to answer two basic questions of pressure sealing design in engineering practice:(1) Given the value of a plugging pressure,what is the fracture aperture? (2) After the plugging material is squeezed into the crack,what is the upper limit of the safe mud density that can be withstood by the formed wedges?
In order to obtain the numerical solution of the above two problems,it is necessary to establish a three-dimensional finite element model for numerical simulation and analysis.The focus of the analysis is on the mechanical behavior of crack plugging.For the sake of simplicity and without loss of generality,the following simplified assumptions are used in the following discussions:
(1) Assume that the well wall is a straight well section;
(2) Assume that the vertical stress is the maximum compressive stress;
(3) Assume that the crack is a vertical crack.
In addition,the model contains only one crack.When there are many cracks on the well wall,the crack is an equivalent crack of a plurality of cracks:the mechanical behavior of this equivalent crack in the practice of pressure sealing engineering is equal to the effect of all cracks actually present.Thus,the equivalent crack parameter can be used to check/calibrate the relevant parameter values based on the mud injection rate/injection pressure in the actual construction.Moreover,the data obtained from this equivalent crack design/analysis can guide the practice of pressure sealing engineering.Fig.1 shows a simplified model with an equivalent crack.The red dot of the figure gives a schematic representation of the location of the injection flow load/or injection pressure load at the crack opening.
The crack material constitutive model used in this model is a quasi-brittle crack model.Cracks in the finite element net are represented by pre-set crack elements.The opening and expansion of cracks are expressed by the principle of damage mechanics.There are many literatures on the study of fracture of quasi-brittle material [19-21].For ease of understanding,the material solid constitutive theory,the fluid flow and seepage constitutive theory used in the model are briefly described below.
Fig.2 shows a schematic diagram of the quasi-brittle fracture of a concrete material.The figure shows that there is a length of damage zone in front of the macroscopic fracture,and the fracture process of the material is completed in this damage zone [22].Therefore,the damage zone is also called the damage process area.In this damage zone,the material still has some connections and residual strength.The solid deformation in the model uses a linear elastic damage constitutive relationship.Fig.3 shows the Schematic diagram of the relationship among damage variable d,the effective stress,the initial stiffness K0and the crack opening displacement δ.
Fig.1.Illustration of the model with an equivalent crack.
Equation(1)gives the relationship between effective stress and l damage variable d:
Where d is a scalar damage variable,d=0 means no damage,and d=1 means the material has been completely damaged and has broken.
2.1.1.Damage initiation criteria
Here,the surface force-opening displacement relationship is used as the damage initiation criteria [23].As in equation (2),this relationship uses the peak intensity N and the fracture energy GTC:
Where σnis the normal stress on the crack surface,and σtand σsare the two shear stress components on the crack surface respectively.Nmax,Tmax,and Smaxare the strengths of the material in the normal direction of the crack surface and in the two tangential directions.
2.1.2.Damage evolution rate
Here,the energy-based damage evolution rate is used,and the damage evolution [16]is calculated using the Benzeggagh-Kenane(BK) [23]power law given by equation (3):
Where gshear=gii+giii,and gt=gi+gshearFig.4 shows the relationship between the fracture energy GTCand the maximum tensile strength N.
Fig.5 shows a schematic diagram of the thickness definition of crack element.The upper and lower bases of the element are shown in the figure,and the dimensions in the thickness direction are much smaller than those in the other two directions.The node degrees of freedom of this three-dimensional 8-node cohesive boundary element with pore pressure degrees of freedom include nodal displacement and pore pressure values on the nodes.It is therefore suitable for simulating the hydraulic fracturing process[15].Fig.6 shows the node number of the crack element.It has 12 nodes.In addition to the eight corner nodes,the four nodes on the mid-surface are dedicated to describing fluid flow and seepage calculations.
The fluid flow characteristics in the crack element are used to describe the fluid flow characteristics in the longitudinal and transverse directions inside the crack.The fluid flow in the longitudinal direction,that is,the tangential direction,determines the distance that the fluid injects into the crack and diffuses in the formation,and the lateral flow,that is,the flow in the normal direction,is liquid leakage.
The longitudinal,ie,tangential,fluid flow constitutive can be in Newton’s law.The seepage in the transverse direction,that is,the normal direction,is the liquid leakage,and the seepage law is Darcy’s law.Fig.7 shows a schematic diagram of the fluid flow and flow characteristics of a crack element.
Fig.2.Illustration of crack in rock formation.
Fig.3.Illustration of linear elastic damage.
Fig.4.Illustration of traction-separation response on the fracture surface.
Fig.5.Definition of cohesive crack element.
Fig.6.Definition of node number of a crack element.
The mathematical expression of the fluid flow constitutive volumetric flow rate density vector q in the Newton’s law is:
Where ktis the tangential flow coefficient,∇pis the pressure gradient along the tangential direction of the crack element.
The crack opening displacement d is:
Where tcurrand torigare the current thickness and initial thickness of the crack element,respectively,and ginitis the initial opening value of the crack element.Here,the current thickness of the crack element is calculated by the finite element,and the displacement discontinuity of nodes on the top face and bottom face is taken into account.
According to the Reynolds equation,the tangential flow coefficient ktis:
In equation (6),μ is the dynamic viscosity coefficient,and the perveance of the crack increases with the increase of the crack width.The plugging ability of the plugging material is formed after the plugging pressure is unloaded and the plugging material in the crack changes into the compressional wedge.The plugging material particles themselves are impermeable.
The seepage calculation of the crack surface in the normal direction is defined by the leakage coefficient.The leakage coefficient on the crack surface can be understood as the permeability coefficient of the mud cake on the crack surface.
The leakage coefficients of the top face and bottom face of the crack surface are ctand cb,respectively,and the corresponding leakage flow rates are:
qtand qbare the flow rates of the top face and bottom face respectively.piis the pore pressure on the mid-surface.ptand pbare the pore pressures of the top face and bottom face.
Fig.7.Flow within cohesive elements.
When the block agent is injected,a higher distribution pressure acts on both the well wall and the crack surface.The distribution pressure on the surface of the well wall is applied as a load.Its amplitude value over time is HP(t).The injection pressure load on the crack is applied to the crack opening,as shown in the red dot portion of Fig.1.Its amplitude value is also HP(t).Fig.8 is the geometry of the model,a sheet of three-dimensional space.Considering the symmetry,only the semicircular structure is taken for analysis.The model has a thickness of 0.127 m(5 inches),an outer radius of 3 m,and an inner radius(or wellbore radius) of 0.254 m(10 inches).
The numerical analysis format of pressure sealing fluid,LCM injection process and crack opening is:
(1) Setting the displacement boundary and initial earth stress state of the model;
(2) Simulating the drilling process:removing the borehole unit to form a stress concentration around the well wall;
(3) Application of blocking load:a distributed pressure load is applied to the surface of the well wall while a pressure boundary is applied at the crack opening.The amplitude value of both loads over time is HP(t).
Thus,the injection pressure-crack opening curve under the given conditions as shown in Fig.9 can be obtained.According to this injection pressure-crack opening curve,when an injection value is given,a crack opening value can be obtained.Thus,the plugging construction and material designer can design the maximum size of the LCM particles and the subsequent LCM particle size.
Since the linear elastic damage constitutive model is used in the model,when the sealing pressure is unloaded after the crack is pressed,the open crack will reclose.Therefore,the above model can only simulate the crack opening process and cannot be used to analyze the stress cage effect.In order to simulate the wedge formed by the plugging material which is squeezed into the crack and the stress cage effect,a separate model must be built.
Fig.8.Geometry of the model.
Fig.9.Diagram of injection pressure vs.crack opening during LCM plugging.
This paper proposes the following stress cage effect analysis calculation format:
(1) The distribution pressure formed by the normal mud is applied to the surface of the well wall as shown in Figs.1 and 8.This pressure does not change over time;
(2) An injection pressure load PS is applied at the crack opening to open and expand the crack.In order to distinguish the injection pressure of the crack wedge during the stress cage analysis phase and the injection pressure HP during the pressure sealing phase,the current injection pressure is referred to directionless pressure PS.The value of PS is greater than the value of HP.
(3) Calculate the crack opening degree caused by PS so as to reach the same crack opening degree caused by the given injection pressure HP during the pressure sealing process,and then keep the opening degree unchanged,which simulates the wedge formed by the plugging material entering the crack;
(4) Calculate the distribution of hoop stress at each point on the surface of the well wall and the evaluation of the stress cage effect obtained compared with the initial state before the well wall reinforcement on the basis of (3).
(5) When the given plugging pressure HP is not only a point but a series of values,it is necessary to repeat (3) and (4) to obtain a series of well wall strengthening effects formed by pressure plugging of different parameters.Designers can choose the best solution to achieve the lowest cost and best pressure plugging.
Based on the principle of integrated pressure plugging and stress cage analysis,the entire analytical calculation process can be represented by the flow chart of Fig.10 below.
The shale gas reservoir of the Pengshui shale gas block is located in the Ordovician Wufeng Formation-Lower Silurian Longmaxi Formation shale below TVD=2100 m[24-27].During the drilling process,when the drill bit just entered the shale reservoir,a serious mud loss occurred in the well wall:the mud pressure at the time of the mud loss was substantially equal to the hydrostatic pressure.In this paper,the pressure plugging and well wall strengthening effect given above are used to analysis workflows and calculate the extended mud window that is strengthened by the well wall when drilling in a shale gas reservoir with a very developed fracture.
The design goal of the pressure sealing construction is to create an expanded mud window with a width of 0.5 g/cm3(equal to 4.16 ppg)at a true vertical depth(TVD)of 2150 m in target stratum.This requires strengthening the well wall to increase the mud pressure tolerance of 1.66 ppg based on the original breakdown pressure.This is equivalent to an increase in the pressure bearing capacity of 4.285 MPa after well wall is enhanced.
Fig.10.Flowchart of the hydraulic plugging simulation and stress cage effect calculation.
Fig.11 shows the corresponding log data,from left to right:gamma ray,acoustic wave,density.
The image log data shows that the induced crack is mainly a vertical crack.Therefore,the format of the initial stress can be judged as ‘normal fault stress format’,that is,the vertical stress is the maximum principal stress.
The red curve in the second grid of Fig.11 is the pore pressure,whose value is close to the hydrostatic pressure,which is calculated from the sonic log data using empirical formulas.Limited to the data,only the pore pressure value of the true vertical depth TVD=2160 m can be obtained.The minimum horizontal principal stress Sh is obtained by the Mathew-Kelly method and is the blue line in the middle of the grid in Fig.11.Generally speaking,this Sh is the breakdown pressure (also called the closing pressure)calculated from the ground stress,which is the upper limit of the mud window.
If the pore pressure PP is used as the lower mud limit and FG is the upper limit of the mud,the mud window range is 0.3 g/cm3,which is equal to 2.5 ppg.This value is neither too large nor too small and does not affect the construction.
The problem is:due to the presence of high conductive fracture,as long as the mud exceeds the pore pressure,there is a significant mud loss,so there is no mud window,and the window range is zero.It is necessary to carry out pressure sealing of natural cracks,and use stress cage technology to strengthen the well wall and increase the upper limit of mud.
The pore pressure of the target stratum true vertical depth TVD=2150 m is PP=27.3 MPa,the minimum horizontal principal compressive stress Sh=-32.0 MPa,the maximum horizontal principal compressive stress SH=-42.5 MPa,and the vertical stress Sv=-54.5 MPa.The effective stress values for the corresponding stress components are:Sx=Sh=-4.7 MPa;Sy=SH=-15.2 MPa;Sz=Sv=-27.2 MPa.
Fig.12 gives information on natural fractures.According to the measurement results,there are two kinds of natural fractures in the reservoir,one is a high conductive fracture and has a high conductivity.The other is a low conductive fracture with poor conductivity.The azimuth angles are from northeast to southwest.The natural fracture angle is shown in Fig.12.The high-conductivity natural fracture angle is 80°-90°,and the low-conductivity natural fracture angle is generally 40°-70°.
Fig.11.Logging data obtained with the vertical well section and resultant curves of 1D analysis.
Fig.13 shows the distribution of Poisson’s ratio near the target stratum,where purple is the value of the vertical Poisson’s ratio and blue is the value of the transverse Poisson’s ratio.In a formation with a true vertical depth of more than 2000 m,the vertical Poisson’s ratio is significantly larger than the transverse Poisson’s ratio,indicating that the maximum horizontal principal stress is close to but less than the vertical stress component.
According to the dip angle of the high conductive fracture,it can be judged that the minimum horizontal principal stress is the smallest principal stress component,and the vertical stress is the largest stress component.
There is no information on the natural fracture opening degree in the information above.According to the published literature,the natural fracture opening degree of the shale gas reservoir is about 1 mm [8].The equivalent fracture width in this model is 1 mm.
This simulation will be conducted using the model of the straight well and vertical crack shown in Fig.1.
The initial conditions involved in the model include:initial porosity ratio 0.125,initial pore pressure 27.3 MPa,effective stress value of initial earth stress:σx=-4.7 MPa;σy=-15.2 MPa;σz=-27.2 MPa,the shear stress component is zero.The x-axis of the coordinate axis is along the direction of the minimum horizontal principal compressive stress,the y-axis is along the direction of the maximum horizontal principal compressive stress,and the zaxis is along the vertical direction.
The normal zero displacement constraint is applied to the outer surface,the symmetry plane,the top face and bottom face,and the seepage boundary on the symmetry plane is impermeable.The seepage boundary of the outer surface is the far-field pore pressure value,the pore pressure boundary of the well wall surface and the pressure boundary condition by block agent injection in crack opening.
The loads in the model are:initial earth stress and gravity loads,and fluid pressure loads on the surface of the well wall.The injection pressure from the crack opening is applied as a pressure boundary condition.
The material parameter values given in Table 1 and Table 2 are used.Table 1 gives the material parameter values for the crack model.S1 is the opening strength of the natural fracture in the normal direction;S2 and S3 are the strengths of the two tangential directions of the fracture,respectively.G1,G2 and G3 are the fracture energies of the crack in a single mode,respectively,and Kn,Kt1,and Kt2 are the stiffness values in normal and two tangential directions,respectively.In Table 2,E is the elastic modulus and ν is the Poisson’s ratio.The behavior of the formation solid matrix is considered elastic behavior.
Table 1 Values of parameters used for cohesive crack model.
Table 2 Values of parameters of formation model.
Fig.14 shows the curves that crack opening degree changes with injection pressure during the block agent injection phase.As can be seen from Fig.14,when the injection pressure is increased from 20 MPa to 90 MPa,the value of the natural crack opening degree is increased from 1 mm to 3.5 mm.
Fig.12.Information of natural fractures obtained with image logging data.
Fig.13.Values of Poisson’s ratio for the section around the target formation.
Fig.15 shows the changes of crack opening degree FW during the directionless pressure PS changes.Fig.16 shows the hoop stress distribution along the surface of the well wall.This result which corresponds to the pressure on the well wall is only the initial formation pore pressure value.The set of hoop stresses value which corresponds to opening degree of a natural crack is from 1.238 to 2.414 mm,and the aperture width corresponds to the intrusion of the block agent.
As can be seen from Fig.16,the minimum value of the hoop stress amplitude occurs at the crack opening,and the value is the minimum horizontal principal compressive stress Sh.When the crack opening degree increases from the initial value to 1.28 mm,the effective stress value of the minimum horizontal principal compressive stress increases from the initial 4.7 MPa-9 MPa,which corresponds to an increase of the total compressive stress component value to 33 MPa,and an increase of the bearing capacity generated by the stress cage effect to 4.3 MPa.When the crack opening degree is increased to 2.424 mm,the total compressive stress component value is increased to 62.3 MPa,and the bearing capacity generated by the stress cage effect is increased to 30.1 MPa.
According to the numerical results given in Figs.15 and 16,it can be concluded that when the crack opening degree caused by the block agent reaches 1.285 mm,the target of the mud window expansion of 1.66 ppg is reached;the mud pressure required to achieve the above opening degree target is 15 ppg,which is equivalent to a mud density of 1.81 g/cm3;for the purpose of achieving a crack opening degree of 1.285 mm,the recommended block agent particle size o 100-500 μm.
This paper first briefly summarizes the relevant literatures on the extended mud window required for fractured formation drilling,and then introduces the implementation measures for extended mud window,including the pressure sealing process of natural fractures and the stress cage effect evaluation process.Aiming at the main problems in the design and analysis of well wall reinforcement,the flow of three-dimensional numerical simulation and crack mechanics behavior analysis of pressure sealing process and stress cage effect evaluation using ABAQUS three-dimensional finite element software is proposed,and a practical engineering application is given.The process and numerical analysis results of using the above theoretical tools to calculate the extended mud window of shale gas fissure reservoir drilling are introduced by engineering example.Numerical results show that:
(1) Pressure sealing squeezes the block agent particles into the crack and seals the natural cracks exposed on the well wall,thereby preventing the mud loss during the drilling process.The equivalent crack in the analytical model represents the sum of the mechanical behavior of all cracks on the well wall.The crack width from the image logging is referenced when determining the width of the equivalent crack,but the final value is determined by combining the ‘phenomena simulation’.
(2) The stress cage effect is formed when the block agent particles are squeezed into the crack to reduce the bottom hole pressure.The larger the diameter of the block agent particle that is squeezed into the natural crack,the more obvious the effect of the stress cage,and the upper limit of the mud window is more obvious.The shape of the crack wedge filled with the block agent particles when evaluating the stress cage effect is formed by simulating the crack opening process under the injection pressure,not a given regular shape.The evaluation results of the stress cage obtained in this way are consistent with the actual situation.This is the main difference between the paper and the existing literatures.
(3) In the model in which I calculate the squeeze of block agent in the process,the fluid pressure on the well wall is the injection pressure,which is a variation increased with time.The fluid pressure on the well wall in the stress cage calculation model is generated by the initial pore pressure.The initial pore pressure is a constant that does not change with time.This is one of the differences between the numerical models’ displacements of the two different processes of the“clogging process” and the “stress cage effect evaluation”.
Fig.14.Variation of fracture opening vs.injection pressure.
Fig.15.Variation of fracture opening vs.directionless pressure.
Fig.16.Stress cage effect:variation of hoop stress distribution around borehole with values of crack width.
(4) The numerical evaluation of the stress cage effect is realized according to the increase range Δσθof the minimum hoop stress on the well wall.This calculation process is performed for a given injection pressure and the resulting crack opening degree.In order to obtain the best construction effect that is economical and efficient,the model can be used to perform pressure sealing numerical simulation and stress cage effect evaluation calculation for several sets of injection pressure design values,and then compare and find the optimal and accurate quantified values of “injection pressure,maximum particle size of block agent and the upper limit of the safe mud window”.Numerical examples show the validity and practicability of theoretical results and models.
Acknowledgements
Thanks to the general project of national natural science foundation of China (11272216) for the financial support of this paper.
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