Method for controlling reaming while drilling based on creep characteristics of salt rock

Abstract

The present invention discloses a control method for reaming while drilling based on the creep characteristics of salt rock, which relates to the technical field of automatic control. The method includes: Step 1: Considering the effects of effective stress, temperature, creep duration, and pore pressure on the creep deformation of salt rock, establishing a constitutive equation for the creep strain rate of salt rock, and calculating the creep strain rate of salt rock; Step 2: Establishing a salt rock dissolution-creep coupling model according to the creep strain rate; Step 3: Establishing a dynamic wellbore stability evaluation model to judge in real time whether the salt rock wellbore is stable during the reaming operation; Step 4: Establishing a reaming parameter optimization model, and calculating the corrected operation parameters and the corrected reaming trajectory vector according to the initial trajectory tangential unit vector and the initial drilling operation parameters. The present invention can effectively improve the wellbore stability, reduce the risk of non-uniform borehole expansion caused by creep, optimize the reaming trajectory control, reduce the potential safety hazards during construction, and improve the reaming efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of automatic control, and particularly to a control method for reaming while drilling based on the creep characteristics of salt rock. Background Art

[0002] During the construction of oil and gas drilling and underground engineering, reaming technology is widely used to increase the well diameter, optimize wellbore stability, and improve drilling efficiency. Especially in salt rock formations, due to its good plasticity and self-healing properties, reaming construction has the potential advantage of reducing the risk of wellbore instability. However, the special physical and chemical properties of salt rock formations, such as significant creep effects and high solubility, make the reaming while drilling construction face many challenges. In recent years, researchers and engineering practices at home and abroad have continuously explored salt rock reaming technology and wellbore stability control methods, and certain progress has been made. However, there are still many limitations in the existing technologies, resulting in the safety and controllability of reaming construction being difficult to meet the engineering requirements. Therefore, in-depth research on the control method for reaming while drilling based on the creep characteristics of salt rock to improve the stability and accuracy of the reaming process has important engineering value and economic significance.

[0003] Currently, reaming while drilling technology mainly uses three types of tools: mechanical reamers, hydraulic reamers, and eccentric reamers for construction. Mechanical reamers mainly rely on rotating cutting structures or telescopic reaming arms for reaming. This type of tool has certain advantages in stabilizing the wellbore size and is suitable for relatively stable formations. However, when constructing in salt rock formations, due to the creep characteristics of salt rock, the well diameter will continuously increase over time, resulting in problems such as over-expansion of the reamer or inability to maintain a uniform well diameter. In addition, mechanical reamers rely on mechanical structures to control the reaming process and are difficult to adaptively adjust in complex formation strain environments, and the reaming trajectory is prone to deviation. Hydraulic reamers control the expansion degree of the reaming cutter wings through hydraulic drive to achieve dynamic control of reaming while drilling. Hydraulic reamers can adjust the reaming size to a certain extent according to the downhole pressure changes and are suitable for environments with large formation stress changes. However, this technology still has limitations in salt rock formations. On the one hand, the adjustment mechanism of hydraulic reamers mainly relies on drilling fluid pressure control. However, due to the dissolution of salt rock, changes in the drilling fluid composition will affect the reaming effect, resulting in a decrease in wellbore support force. On the other hand, the control accuracy of hydraulic reamers is relatively low, and the reaming trajectory is easily affected by fluctuations in the drilling pressure and changes in the drilling fluid flow rate, making it difficult to ensure the precise controllability of the reaming trajectory. Eccentric reamers achieve directional reaming through an asymmetric reaming mechanism, can precisely adjust the reaming trajectory during drilling, and are suitable for scenarios where wellbore trajectory control is required. This technology performs well in conventional formations. However, in salt rock formations, due to the coupled dissolution-creep effect of salt rock, it is difficult for eccentric reamers to maintain a stable reaming trajectory. Creep causes continuous deformation of the wellbore wall, and the dissolution effect exacerbates the non-uniform expansion of the wellbore wall, resulting in a decrease in the guiding accuracy of the eccentric reamer and ultimately leading to deviation or even loss of control of the reaming trajectory. Summary of the Invention

[0004] In view of this, the present invention provides a control method for reaming while drilling based on the creep characteristics of salt rock. By constructing a salt rock dissolution-creep coupling model, a dynamic wellbore stability evaluation model, and a reaming parameter optimization model, intelligent control of the reaming process is achieved. This method can calculate the creep rate and dissolution rate of the wellbore in real time, dynamically optimize the bit rotation speed, drilling pressure, and drilling fluid flow rate, and combine a reaming trajectory correction strategy to ensure that the bit always advances along the target trajectory, ensuring the stability and accuracy of the reaming operation. Compared with the prior art, the present invention can effectively improve wellbore stability, reduce the risk of non-uniform wellbore expansion caused by creep, optimize reaming trajectory control, reduce construction safety hazards, improve reaming efficiency, and adapt to the dynamic evolution of complex salt rock formations, providing a high-precision, high-safety, and high-adaptability intelligent reaming control scheme for deep oil and gas exploration and reaming operations in other complex formations.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A control method for reaming while drilling based on the creep characteristics of salt rock, the method comprising:

[0007] Step 1: Considering the influence of effective stress, temperature, creep duration, and pore pressure on the creep deformation of salt rock, establish a constitutive equation for the creep strain rate of salt rock and calculate the creep strain rate of salt rock;

[0008] Step 2: Considering the contact area between the drilling fluid and the wellbore, the difference between the saturated solubility of salt rock and the salt ion concentration in the current drilling fluid, the rotation speed of the bit, and the circulation flow rate of the drilling fluid, establish a salt rock dissolution-creep coupling model according to the creep strain rate;

[0009] Step 3: Establish a dynamic wellbore stability evaluation model to judge in real time whether the salt rock wellbore is stable during the reaming operation;

[0010] Step 4: Establish a reaming parameter optimization model. According to the initial trajectory tangential unit vector and the initial drilling operation parameters, calculate the corrected operation parameters and the corrected reaming trajectory vector, and perform reaming while drilling control according to the corrected operation parameters and the corrected reaming trajectory vector.

[0011] Further, the initial drilling operation parameters include: initial bit rotation speed, initial drilling pressure, and initial drilling fluid flow rate.

[0012] Further, salt rock has time-dependent deformation characteristics. Even under stress, it will undergo continuous creep over time. During the reaming while drilling construction process, the creep characteristics of salt rock will cause changes in the wellbore diameter and result in the instability of the wellbore wall. The constitutive equation for the creep strain rate of salt rock is established through the following formula:

[0013] ;

[0014] Among them, is the creep strain rate of salt rock, with the unit of ; is a material constant, related to the mineral composition of salt rock, with the unit of ; is the effective stress, with the unit of MPa; is the stress exponent, dimensionless, with the value range from 3 to 5; is the creep activation energy, with the unit of kJ / mol; is the gas constant, with the value of 8.314, with the unit of J / (mol·K); is the absolute temperature, with the unit of K; is the time, with the unit of s; is the time hardening index, dimensionless, with the value range from 0.3 to 0.5; is the pore fluid pressure, with the unit of MPa; is the confining pressure, with the unit of MPa; is the pressure sensitivity index, dimensionless, with the value range from 0.8 - 1.2.

[0015] Furthermore, during the reaming construction, the drilling fluid continuously scours the salt rock wellbore. Since salt rock is easily soluble in water, salt rock dissolution occurs on the wellbore, resulting in an increase in the well diameter. At the same time, the creep behavior of salt rock will change the rock mass structure and surface microtopography, exposing more new surfaces and accelerating the salt rock dissolution rate. Through the following formula, a salt rock dissolution-creep coupling model is established based on the creep strain rate:

[0016] ;

[0017] Among them, is the salt ion concentration in the drilling fluid, with the unit of kg / m³; is the salt rock dissolution rate constant, with the unit of m / s; is the contact area, with the unit of m²; is the saturation solubility, with the unit of kg / m³; is the dissolution-creep coupling coefficient, with the unit of s, with the value range from 0.2 to 0.5; is the angular velocity of the drill bit rotation, with the unit of rad / s; is the drilling fluid flow rate, with the unit of m³ / s; is the annulus volume, with the unit of m³; represents the time derivative of the salt ion concentration in the drilling fluid.

[0018] Further, the salt rock dissolution rate constant is obtained through the following process: Immerse a salt rock sample with known mass and shape in drilling fluid or an aqueous solution, regularly measure its mass change, calculate the mass loss rate per unit time, and the salt rock dissolution rate constant is calculated using the following formula:

[0019] ;

[0020] where, is the dissolution contact area of the salt rock sample, with the unit of m²; is the mass loss of the salt rock per unit time, with the unit of kg / s; is the salt rock density, with the unit of kg / m³.

[0021] Further, the dynamic wellbore stability evaluation model in Step 3 is expressed using the following formula:

[0022] ;

[0023] where, is the wellbore stability factor, dimensionless, indicating stable, otherwise indicating unstable; is the circumferential stress of the wellbore, with the unit of MPa; is the pressure in the well, with the unit of MPa; is the yield strength of the salt rock, with the unit of MPa; is the creep influence coefficient, dimensionless, with a value range of 0.2 to 0.5; is the reaming operation time, with the unit of s; is the dissolution influence coefficient, dimensionless, with a value range of 0.4 to 0.8; is the saturation solubility, with the unit of kg / m³; is the reaming radius, with the unit of m; is the original drilling radius, with the unit of m.

[0024] Further, the corrected operating parameters include: corrected drilling fluid flow rate, corrected bit rotation speed, and corrected drilling pressure, which are calculated using the following formula:

[0025] ;

[0026] where, is the initial bit rotation speed, with the unit of rad / s; is the initial drilling pressure, with the unit of kN; is the initial drilling fluid flow rate, with the unit of L / s; is the corrected bit rotation speed, with the unit of rad / s; is the corrected drilling pressure, with the unit of kN; For correcting the drilling fluid flow rate, in L / s; is the stability adjustment coefficient, dimensionless; is the comprehensive influence coefficient of dissolution-creep, in s, with a value range of 0.5 to 1.2; is the saturation solubility, in kg / m³; is the radius control gain coefficient, dimensionless, with a value range of 0.5 to 2.0; is the target reaming radius, in m; is the current reaming radius, in m.

[0027] Furthermore, the stability adjustment coefficient is calculated using the following formula:

[0028] ;

[0029] where is the reference stability adjustment coefficient, with a value range of 0.1 to 0.5.

[0030] Furthermore, the corrected reaming trajectory vector is calculated through the following formula:

[0031] ;

[0032] where is the corrected reaming trajectory vector, in m; is the curve length parameter along the well axis, in m; is the initial trajectory tangential unit vector, in m; is the tool face angle, in rad; is the characteristic length, in m, with a value range of 7 to 12.

[0033] By adopting the above technical scheme, the present invention produces the following beneficial effects: by introducing the well wall stability factor and the related evaluation model, the present invention can monitor the creep state and dissolution rate of the well wall in real time, so as to dynamically adjust the reaming parameters and ensure the stability of the well wall during the reaming process. The existing reaming method usually adopts static preset parameters for reaming, but ignores the dissolution-creep coupling effect of salt rock. Since salt rock will slowly deform under the action of long-term stress, even after the reaming is completed, the well wall may continue to deform, resulting in the expansion of the well diameter and the reduction of the well wall strength, and finally increasing the risk of well wall instability. The innovation of the present invention is that it can adjust the reaming parameters based on the well wall stability factor calculated in real time, so that the construction process can adapt to the evolution state of the well wall, thereby effectively avoiding the instability problem of the well wall caused by stress redistribution or local dissolution. By dynamically evaluating the stability state of the well wall, the drilling operator can adjust the construction parameters in time during the reaming process, reduce the risk of well wall damage, and improve the overall stability of the well wall. Secondly, the present invention can improve the accuracy of the reaming trajectory and ensure that the reaming operation is carried out strictly in accordance with the designed path. The application of existing reaming methods in salt rock formations is limited by the deformation of the wellbore caused by creep and the change in the wellbore diameter caused by dissolution, making it difficult to ensure that the drill bit drills according to the predetermined trajectory. When the wellbore wall undergoes local uneven deformation, the stress state of the drill bit may change, causing the reaming trajectory to shift, ultimately affecting the geometry of the wellbore. The present invention adopts an reaming parameter optimization model, combined with real-time calculated wellbore state data, to accurately adjust the movement direction of the drill bit, so that the reaming trajectory can be synchronously adjusted with the dynamic changes of the wellbore state. This real-time trajectory correction strategy avoids the loss of control of the reaming trajectory due to local deformation of the wellbore, ensures that the wellbore diameter after reaming meets the design requirements, and improves the accuracy of construction. In terms of construction safety, the present invention can reduce the risk of wellbore instability and improve the controllability of reaming operations. Since the creep behavior of salt rock will lead to long-term stress redistribution of the wellbore wall, if the construction parameters are not adjusted in time during the reaming process, stress concentration may occur in certain areas of the wellbore wall, ultimately causing local collapse or abnormal expansion of the wellbore diameter. The dynamic wellbore stability assessment model constructed by the present invention can calculate the stress state of the wellbore in real time, and adjust the drilling fluid flow rate, drill bit speed and drilling pressure according to the assessment results, so that the hole expansion operation is always kept in a stable state. In addition, the present invention adopts a dissolution-creep coupling control strategy to ensure that the flow state of the drilling fluid can adapt to the dissolution rate of the wellbore, preventing the local area from dissolving too quickly, resulting in a decrease in the local structural strength of the wellbore. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of a method for controlling hole expansion while drilling based on the creep characteristics of salt rock in an embodiment of the present invention. DETAILED DESCRIPTION

[0035] All features disclosed in this specification, or steps in all methods or processes disclosed, except for mutually exclusive features and / or steps, can be combined in any way.

[0036] Any feature disclosed in this specification (including any additional claims, abstract) can be replaced by other equivalent or similar-purpose alternative features, unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is only an example of a series of equivalent or similar features.

[0037] Example 1, refer to Figure 1 : A method for controlling hole enlargement while drilling based on the creep characteristics of salt rock, the method comprising:

[0038] Step 1: Considering the effects of effective stress, temperature, creep duration, and pore pressure on the creep deformation of salt rock, establish a constitutive equation for the creep strain rate of salt rock and calculate the creep strain rate of salt rock;

[0039] Salt rock is a rock material with significant rheological properties. Under the action of external forces, its deformation not only depends on the instantaneous stress response but also exhibits creep characteristics that develop over time. Creep is a time-dependent deformation process, which means that even under constant stress conditions, salt rock will still undergo slow and irreversible deformation, and this deformation is mainly affected by the combined action of effective stress, temperature, creep duration, and pore pressure. Therefore, during the process of reaming while drilling, if the creep behavior of salt rock cannot be accurately predicted, it will be difficult to maintain the stability of the wellbore diameter after reaming, and serious problems such as overexcavation and wellbore collapse may even occur. Based on this, the present invention first establishes a constitutive equation for the creep strain rate of salt rock in order to quantify the development rate of creep deformation and provide basic input data for subsequent dissolution-creep coupling analysis. When establishing the constitutive model, it is first necessary to consider the influence of effective stress on creep. Since salt rock is usually in a confining pressure environment, the pore fluid pressure inside it will weaken the external stress it bears. Therefore, the key stress determining the creep rate is not the applied confining pressure but the effective stress borne by the salt rock, that is, the difference between the applied total stress and the pore fluid pressure. As the drilling fluid circulates, the pore fluid pressure around the wellbore will change, thereby affecting the creep deformation rate. If the well pressure decreases and the pore fluid is discharged, resulting in an increase in effective stress, the creep of salt rock will intensify, causing the wellbore to tend to become unstable. Therefore, when constructing the creep constitutive equation, the effective stress needs to be taken as one of the core variables, and its influence on the creep strain rate is described by a power-exponential relationship. In addition, the creep behavior of salt rock is very sensitive to temperature. An increase in temperature will lead to enhanced ion activity in the crystal lattice, promoting micro-slip and plastic deformation, thereby accelerating the creep rate. During the process of reaming while drilling, due to the frictional heat generated by the drill bit and the change in the formation temperature gradient, the bottom hole temperature may rise significantly, further increasing the creep rate. In order to accurately characterize this temperature dependence, the model adopts the thermoactivation theory, that is, an exponential temperature factor is introduced into the constitutive equation to reflect the exponential influence of temperature changes on the creep rate. This part of the modeling enables the present invention to adapt to reaming operations at different well depths and different geothermal environments and achieve accurate prediction of the creep rate.

[0040] In addition to stress and temperature, the creep duration is also an important factor affecting the deformation process. During the reaming process, the wellbore wall is under high stress for a long time, and creep deformation increases with time. Especially in the early stage, the creep rate is relatively high and then gradually stabilizes. This characteristic is called the time-hardening effect. In the present invention, by introducing a time-hardening index to describe how the creep rate changes with time and determining the specific value of this index through experiments, the model can reasonably reflect the long-term deformation trend of salt rock. The consideration of the time-hardening effect enables the present invention not only to predict the creep deformation in a short time but also to be applicable to the evaluation of wellbore stability under a long drilling cycle, providing a scientific basis for long-term drilling operations. In addition, pore pressure also plays an important role in creep deformation. The pore structure inside salt rock is relatively small and the permeability is low, but there is still a certain fluid pressure. If the drilling fluid pressure is high, some fluids may infiltrate into the salt rock, resulting in a local increase in pore pressure, thereby reducing the effective stress and slowing down the creep rate. On the contrary, if the wellbore pressure decreases, the pore fluid is discharged and the creep rate increases. Therefore, in the present invention, by introducing a pore pressure sensitivity coefficient, the calculation formula of the creep strain rate is further corrected to enable it to maintain a high calculation accuracy under different fluid pressure conditions, thus effectively adapting to complex drilling environments.

[0041] Step 2: Considering the contact area between the drilling fluid and the wellbore wall, the difference between the saturated solubility of salt rock and the concentration of salt ions in the current drilling fluid, the rotation speed of the drill bit, and the circulation flow rate of the drilling fluid, establish a salt rock dissolution-creep coupling model according to the creep strain rate;

[0042] In actual construction, the dissolution rate of salt rock is not only affected by factors such as the chemical composition of the drilling fluid, the bottom-hole flow field, and temperature but is also controlled by creep deformation. Creep causes continuous microscopic fractures in the wellbore structure, increasing the contact area between the drilling fluid and the salt rock, exposing more fresh salt rock surfaces to the drilling fluid, and thus accelerating the dissolution process. At the same time, the change in the stress field caused by creep deformation also affects the permeability characteristics of the fluid, causing the dissolution rate to change dynamically with the progress of creep. Therefore, it is necessary to establish a coupling model to comprehensively consider the interaction mechanism between the two.

[0043] In the present invention, the dissolution process of salt rock is mainly controlled by the solute transport mechanism, that is, the concentration gradient between the salt ion concentration in the drilling fluid and the saturated solubility of salt rock determines the driving force for dissolution. When the salt ion concentration in the drilling fluid is lower than the saturated solubility, the surface of the salt rock will continuously dissolve, and the dissolution rate depends on the concentration difference and the flow characteristics of the fluid. Since the flow of the drilling fluid at the bottom of the well is affected by the rotation of the drill bit and the circulation flow rate, its flow state determines the magnitude of the dissolution rate. Under high flow velocity and high shear conditions, the dissolved salt ions are quickly carried away, maintaining a large concentration gradient and keeping the dissolution process at a relatively fast rate; while under low flow velocity conditions, the salt concentration in the local fluid tends to saturate easily, resulting in a decrease in the dissolution rate or even a stagnation phenomenon. Therefore, in the present invention, by introducing parameters such as the drilling fluid circulation flow rate and the drill bit rotation speed, the calculation model of the dissolution rate is optimized to more realistically reflect the effect of drilling fluid dynamics on the dissolution of salt rock. In addition, the contact area of the wellbore is an important factor affecting the dissolution rate. In the traditional model, it is usually considered that dissolution mainly occurs on the original surface of the wellbore after reaming. However, in the present invention, by considering the influence of creep deformation on the dissolution rate, the dynamic change of the contact area is corrected, making the dissolution model more in line with the actual working conditions.

[0044] The mechanism by which creep affects the dissolution rate is mainly reflected in two aspects: first, creep deformation causes the microcracks of salt rock to expand continuously, thereby increasing the effective surface area for dissolution; second, the greater the creep strain rate, the more drastic the microstructural changes on the surface of the salt rock, thereby accelerating the dissolution process. In order to quantitatively describe this phenomenon, the present invention introduces a dissolution-creep coupling coefficient in the calculation of the dissolution rate, which reflects the enhancing effect of creep deformation on the dissolution rate and is calibrated by experimental measurement or numerical simulation. As creep proceeds, the microscopic damage on the surface of the salt rock gradually accumulates, resulting in a nonlinear growth of the dissolution area. Therefore, the setting of the coupling coefficient needs to consider the relationship between creep strain rate and time. Furthermore, since creep deformation is essentially a time-dependent process, the variation law of the dissolution rate in different time periods also needs to be dynamically adjusted. For example, in the early stage of creep, the well wall still maintains good integrity, and the dissolution rate is mainly controlled by the salt concentration gradient of the drilling fluid. When creep develops to a certain extent, the number of cracks increases, the dissolution rate is significantly increased, and finally reaches a new stable state. The present invention constructs a dynamic dissolution-creep coupling equation so that the dissolution rate can be calculated in real time during the hole expansion process, and the drilling fluid flow rate and circulation speed are adjusted according to the creep deformation rate, thereby ensuring the controllability of the dissolution process. In addition, the rotation speed of the drill bit also has an important influence on the dissolution rate during the hole expansion process. The rotation of the drill bit not only affects the flow field distribution of the drilling fluid at the bottom of the well, but also affects the creep rate of the salt rock. When the drill bit speed is high, the flow field at the bottom of the well is more intense, the scouring effect of the drilling fluid on the well wall is enhanced, and the dissolution rate is increased. At the same time, due to the shear stress generated by the rotation, the creep deformation may also be accelerated, further promoting the dissolution process. Under low speed conditions, the disturbance of the drilling fluid is weak, the dissolution rate is reduced, and the promoting effect of creep on dissolution is relatively small. Therefore, in the present invention, the drill bit rotation speed is used as a key parameter of the coupling model. By optimizing and adjusting it, the hole expansion efficiency can be improved while ensuring the stability of the well wall.

[0045] Step 3: Establish a dynamic wellbore stability assessment model to determine in real time whether the salt rock wellbore is stable during the hole expansion operation;

[0046] During the reaming operation, the wellbore is subjected to stress from the surrounding rock, which mainly manifests as circumferential stress, axial stress, and radial stress. Under stable formation conditions, the stress balance of the wellbore enables it to maintain integrity. However, due to the significant creep characteristics of salt rock, over time, the stress state of the wellbore material changes, causing the originally stable stress distribution to gradually deviate from equilibrium, resulting in a decrease in wellbore strength and ultimately possible instability. In addition, the pressure of the drilling fluid on the wellbore is also constantly changing. Especially in the case of high-flow velocity scouring or wellbore pressure fluctuations, it may further exacerbate the uneven stress on the wellbore. Therefore, the dynamic wellbore stability assessment model needs to comprehensively consider the influence of the surrounding rock stress field, drilling fluid pressure, creep strain rate, and dissolution process to accurately predict the stability change trend of the wellbore during reaming.

[0047] Creep deformation is one of the main factors affecting wellbore stability. The creep of salt rock causes the stress of the wellbore to gradually redistribute to the low-stress area. This stress redistribution process often leads to an increase in plastic deformation in local areas of the wellbore, reducing the overall load-bearing capacity of the wellbore. When the creep rate is small, the deformation of the wellbore is relatively slow and can still maintain a certain mechanical stability. However, with the prolongation of the reaming time, the cumulative effect of creep deformation gradually appears, resulting in a decrease in the yield strength of the wellbore material and ultimately possibly exceeding its load-bearing limit, leading to local collapse or uneven wellbore diameter expansion. Therefore, the present invention evaluates the degree of weakening of the creep deformation on the wellbore load-bearing capacity by calculating the creep strain rate in real time and combining it with the reaming operation time, so as to determine whether the stability of the wellbore under specific construction parameters meets the requirements. If the calculation results show that the creep strain rate is too large, which may lead to insufficient long-term load-bearing capacity of the wellbore, it is necessary to adjust the drilling parameters, such as reducing the bit rotation speed, adjusting the drilling fluid flow rate, or increasing the wellbore pressure, to mitigate the adverse effects of creep on the wellbore.

[0048] In addition to the creep effect, the dissolution process also affects the stability of the wellbore. Since salt rock is soluble in water, under the continuous scouring of the drilling fluid, the wellbore will gradually dissolve. Especially when there is a concentration gradient between the drilling fluid and the salt rock, the dissolution rate will increase, reducing the effective thickness of the wellbore and resulting in a decrease in the overall stiffness of the wellbore, thereby increasing the risk of wellbore deformation. More importantly, the dissolution process does not occur uniformly. Different regions of the wellbore may experience non-uniform dissolution due to different fluid flow fields, which will cause local stress concentration, making the stress in some weak parts exceed their yield strength and ultimately leading to local collapse or crack expansion. To accurately evaluate this influence, the wellbore stability assessment model of the present invention introduces a dissolution rate calculation parameter and combines it with the creep strain rate to analyze the influence of dissolution on the wellbore stress distribution. If it is found that the dissolution rate in a certain area is too high, which may lead to local instability, it is necessary to correspondingly adjust the salt concentration, flow rate, or circulation pressure of the drilling fluid to reduce the damage of the dissolution process to the wellbore stability.

[0049] To make the stability assessment results more accurate, the present invention uses the wellbore stability factor as a measurement index. This factor comprehensively considers the wellbore stress, creep rate, and dissolution rate, and is used to quantitatively judge whether the wellbore is in a safe state. If the stability factor is less than the set threshold, it indicates that the wellbore remains stable and the reaming operation can continue; if the stability factor is close to the critical value, it shows that there may be a high risk of wellbore instability, and construction parameters need to be adjusted to reduce the risk; when the stability factor exceeds the critical value, measures such as wellbore reinforcement, adjustment of drilling parameters, or suspension of reaming must be taken immediately to avoid the occurrence of wellbore instability accidents. Through this real-time assessment model, the reaming operation can achieve intelligent control based on the dynamic monitoring of wellbore stability, improving the safety and controllability of construction.

[0050] Step 4: Establish an optimized reaming parameter model. According to the initial trajectory tangential unit vector and initial drilling operation parameters, calculate the corrected operation parameters and corrected reaming trajectory vector, and perform real-time reaming control based on the corrected operation parameters and corrected reaming trajectory vector.

[0051] The core objective of optimizing reaming parameters is to improve reaming efficiency and ensure the uniformity of the wellbore diameter while maintaining wellbore stability. In the present invention, by calculating the wellbore stability factor in real time, the current stable state of the wellbore is judged, and the reaming parameters are adjusted accordingly. When the wellbore stability is high, the bit rotation speed and drilling pressure can be appropriately increased to improve reaming efficiency; when the wellbore tends to be unstable, the drilling pressure needs to be reduced, the bit rotation speed decreased, or the drilling fluid flow rate adjusted to reduce the disturbance to the wellbore and prevent wellbore collapse or abnormal expansion. In addition, since the creep deformation and dissolution rate change continuously over time, the optimization of reaming parameters must have the ability of dynamic adjustment, that is, the drilling parameters are continuously updated according to the real-time state of the wellbore, rather than using fixed parameters for reaming operations. The present invention establishes an optimized reaming parameter model, enabling the construction parameters to be adaptively adjusted according to the change of wellbore stability, so as to achieve precise control under complex formation conditions.

[0052] The optimization of reaming parameters not only affects the stability of the wellbore, but also directly determines the accuracy of the reaming trajectory. Due to the directional characteristics of salt rock creep, the deformation of the wellbore during reaming is not evenly distributed. Instead, it is affected by multiple factors such as the in-situ stress state, the force exerted by the drill bit, and the flow state of the drilling fluid, which may cause the reaming trajectory to deviate and result in the reaming shape deviating from the design target. Traditional reaming methods mainly rely on mechanical guidance or manual correction to adjust the drilling trajectory. However, in a formation environment with high temperature, high pressure, and significant creep, this method often cannot achieve real-time adjustment, leading to the deviation of the reaming trajectory not being effectively corrected. The present invention proposes a method combining the optimization of reaming parameters and trajectory correction. While optimizing key parameters such as the rotational speed and weight on bit of the drill bit, a trajectory correction model is established. By calculating the deviation amount of the reaming trajectory in real time and combining with the wellbore stability factor, the movement path of the drill bit is adjusted, enabling the reaming trajectory to be dynamically corrected and approach the design trajectory.

[0053] The key to trajectory correction lies in accurately predicting the deviation trend of the reaming trajectory and adjusting the reaming parameters appropriately to bring it back to the target trajectory. In the present invention, by introducing the initial tangential unit vector of the trajectory, the ideal path of the reaming trajectory is defined, and based on the wellbore stability factor and creep deformation rate calculated in real time, the deviation direction and deviation amplitude of the reaming trajectory are predicted. When creep deformation causes the reaming trajectory to deviate to one side, the deviation can be corrected by adjusting the force direction of the drill bit or changing the angular velocity of the drill bit rotation, so that the trajectory is corrected in the opposite direction, pulling the reaming trajectory back to the target path. In addition, the present invention adopts a trajectory correction gain coefficient to control the amplitude of trajectory correction to avoid excessive adjustment causing additional wellbore disturbances. When the wellbore stability is relatively high, the intensity of trajectory correction can be relatively large to improve the adjustment speed of the reaming trajectory; while when the wellbore tends to become unstable, the intensity of trajectory correction should be reduced to prevent further instability of the wellbore caused by drastic parameter changes. In addition to the optimization of reaming parameters and trajectory correction, the present invention also introduces the concept of characteristic length to control the adjustment range of the reaming trajectory. The characteristic length determines the spatial scale of trajectory correction, that is, within what range the deviation of the reaming trajectory is adjusted. If the characteristic length is too short, the adjustment amplitude of the trajectory is small, which may make it difficult to quickly correct the reaming trajectory; while if the characteristic length is too long, the correction force of the trajectory is too large, which may cause instability of the wellbore. Therefore, the present invention calculates the characteristic length in real time during reaming and dynamically adjusts the range of trajectory correction in combination with the wellbore stability factor and creep deformation rate, enabling the adjustment of the reaming trajectory to quickly return to the target path without causing excessive disturbance to the wellbore structure.

[0054] Example 2: The initial drilling operation parameters include: the initial rotational speed of the drill bit, the initial weight on bit, and the initial drilling fluid flow rate.

[0055] Specifically, the initial bit rotation speed is a key parameter affecting the reaming efficiency and the stress state of the wellbore wall. The bit rotation speed determines the relative cutting speed between the bit and the salt rock, thereby affecting the mechanical load of the bit on the wellbore wall. When the bit rotation speed is low, the contact time between the bit and the wellbore wall is long, and the drilling amount per unit time is small, which may cause the drilling fluid to be unable to effectively carry away the cuttings, increase the accumulation of cuttings at the bottom of the well, thereby causing local stress concentration on the wellbore wall, aggravating the creep effect, and affecting the wellbore stability. When the bit rotation speed is too high, although the drilling efficiency is improved, the high-speed friction between the bit and the wellbore wall may cause the local temperature to rise, promote the increase of the salt rock creep rate, and accelerate the dissolution process of the wellbore wall, making it difficult to maintain the uniformity of the well diameter after reaming. Therefore, in the present invention, the setting of the initial bit rotation speed needs to comprehensively consider factors such as the creep rate, the bottom hole temperature, and the wellbore stability factor to ensure a moderate drilling rate, which can not only improve the reaming efficiency but also avoid the influence of aggravated creep on the wellbore stability. In addition, the present invention also combines a dynamic optimization strategy for the bit rotation speed, and during the reaming process, according to the real-time change of the wellbore stability factor, the bit rotation speed is finely adjusted, so that the drilling process can adapt to the dynamic evolution state of the wellbore wall, thereby ensuring the construction safety.

[0056] The initial drilling pressure directly determines the penetration force of the bit on the salt rock, thereby affecting the bit cutting efficiency and the stress state of the wellbore wall. Too small drilling pressure may cause the bit to be unable to effectively break the salt rock, resulting in a decrease in the drilling efficiency, and may cause local creep accumulation due to long-term action at the same position, forming local non-uniform deformation of the wellbore wall. Too large drilling pressure may cause the mechanical load borne by the salt rock to exceed its yield strength, triggering local wellbore collapse or crack propagation, and then affecting the wellbore stability. Therefore, in the present invention, the setting of the initial drilling pressure needs to consider the yield strength of the salt rock, the bottom hole stress state, and the wellbore stability factor to ensure that the drilling pressure can not only ensure the efficient cutting of the bit but also avoid the mechanical instability of the wellbore wall. In addition, since the wellbore creep will cause continuous stress redistribution, the initial drilling pressure may need to be adjusted over time after it is set. Therefore, the present invention combines a real-time drilling pressure optimization model and adjusts the drilling pressure in a timely manner based on the change trend of the wellbore stability factor to ensure that the force on the bit during the reaming process always remains within a reasonable range.

[0057] The initial drilling fluid flow rate affects the scouring effect of the drilling fluid on the wellbore, the dissolution rate of salt rock, and the ability of the drilling fluid to carry cuttings. In salt rock formations, the drilling fluid is not only used to cool the drill bit and lubricate the bottom hole, but also undergoes physicochemical reactions with the salt rock, resulting in the dissolution of the wellbore. When the drilling fluid flow rate is low, the salt ions dissolved from the salt rock may not be carried away in time, leading to intensified local dissolution and causing excessive wellbore expansion or wellbore instability. When the drilling fluid flow rate is too high, the scouring effect of the drilling fluid is enhanced, which may accelerate the dissolution of the wellbore and make it difficult to maintain a uniform wellbore diameter after reaming. Therefore, in the present invention, the setting of the initial drilling fluid flow rate needs to fully consider the dissolution rate of salt rock, the wellbore stability factor, and the creep rate to ensure that the drilling fluid can effectively control the wellbore dissolution process and meet the requirements of the drilling fluid's cuttings-carrying ability. In addition, the present invention adopts a dynamic optimization strategy for the drilling fluid flow rate, and during the reaming process, the drilling fluid flow rate is appropriately adjusted according to the wellbore stability factor and dissolution rate calculated in real time to reduce the adverse effects of the drilling fluid on the wellbore and improve the stability of the reaming operation.

[0058] Example 3: Salt rock has time-dependent deformation characteristics. Even under stress, it will undergo continuous creep over time. During the reaming operation while drilling, the creep characteristics of salt rock will cause changes in the wellbore diameter and result in wellbore instability. Through the following formula, a constitutive equation for the creep strain rate of salt rock is established:

[0059] ;

[0060] Where, is the creep strain rate of salt rock, with the unit of ; is a material constant related to the mineral composition of salt rock, with the unit of ; is the effective stress, with the unit of MPa; is the stress exponent, dimensionless, with a value range of 3 to 5; is the creep activation energy, with the unit of kJ / mol; is the gas constant, with a value of 8.314, with the unit of J / (mol·K); is the absolute temperature, with the unit of K; is the time, with the unit of s; is the time hardening exponent, dimensionless, with a value range of 0.3 to 0.5; is the pore fluid pressure, with the unit of MPa; is the confining pressure, with the unit of MPa; is the pressure sensitivity index, dimensionless, with a value range of 0.8 - 1.2.

[0061] Specifically, during the process of reaming while drilling, the creep characteristics of salt rock are the key factors affecting wellbore stability. Due to the time-dependent deformation characteristics of salt rock, even when the stress remains constant, its deformation will still continue to develop over time. This phenomenon is called creep. Creep not only affects the stability of the wellbore diameter size but also may lead to the redistribution of wellbore stress, causing the stress in some areas to exceed the yield strength, ultimately resulting in wellbore instability, collapse, or excessive expansion. Therefore, in the reaming while drilling control method of the present invention, by establishing a constitutive equation for the creep strain rate of salt rock, the accurate calculation of the creep deformation rate is achieved, providing basic support for the optimization of reaming parameters and the evaluation of wellbore stability. The core objective of the constitutive equation is to quantitatively describe the variation law of the creep strain rate of salt rock with factors such as time, stress, temperature, and pore pressure. Among them, the creep strain rate represents the creep deformation rate of salt rock per unit time, and its magnitude determines the degree of change in the wellbore diameter after reaming. To accurately describe the creep behavior, the constitutive equation considers five main control factors, namely effective stress, temperature, time hardening effect, pore pressure influence, and pressure sensitivity. These factors interact with each other and determine the dynamic evolution process of the creep rate.

[0062] First of all, the effective stress is the dominant factor controlling the creep rate. Its physical meaning is the difference between the confining pressure and the pore pressure, that is, the net pressure actually borne by the wellbore wall. In areas with relatively high stress, phenomena such as the slip of atoms or lattices inside the salt rock and the propagation of microcracks occur, resulting in an increase in creep deformation. Therefore, in the constitutive equation, the creep strain rate has a power-law exponential relationship with the effective stress, and the exponential parameter takes values between 3 and 5, which means that as the effective stress increases, the creep rate will increase non-linearly and accelerate. When the wellbore pressure decreases and the pore fluid is discharged, making increase, the creep deformation intensifies; while when the wellbore pressure increases, decreases, the creep rate decreases.

[0063] Secondly, the temperature has an impact on creep deformation described by the thermal activation effect. The creep of salt rock belongs to thermally activated deformation. An increase in temperature will lead to an increase in the activity of ions in the salt rock lattice, promoting the acceleration of creep deformation. Therefore, the constitutive equation uses the Arrhenius exponential term to describe the influence of temperature on creep, where is the creep activation energy, is the gas constant, is the absolute temperature. This term indicates that the creep rate increases exponentially with the increase of temperature, which means that in deep high-temperature formations, salt rock creep is more significant than in shallow formations. Therefore, during the reaming process, if the temperature effect is not considered, it may lead to an underestimation of creep deformation, thereby affecting the accuracy of hole diameter control. The present invention precisely calculates the creep rate by measuring the bottom-hole temperature in real time and combining with this mathematical model, and then dynamically adjusts the reaming parameters to ensure the construction stability.

[0064] The time factor is also one of the important control variables of creep deformation. During the reaming process, the wellbore wall bears stress for a long time, and the creep deformation accumulates with time, and its rate gradually decreases. This phenomenon is called the time hardening effect. In the constitutive equation, the time influence term adopts a power exponential form , where takes values between 0.3 and 0.5. This exponent indicates that the creep rate gradually decreases over time, but does not completely stop. Even if the stress in the well remains constant, creep deformation will still occur continuously. This characteristic is crucial for the reaming construction because after reaming, the wellbore wall may still experience creep deformation for a long time. If this influence is ignored, it may lead to a continuous increase in the reaming diameter in the later stage of construction, affecting the wellbore quality. Therefore, the present invention not only calculates the creep rate in real time during the reaming construction process, but also considers the prediction of creep deformation after construction to ensure that the wellbore wall size remains stable in the long term after reaming.

[0065] In addition, the change of pore pressure will also affect the creep rate. In a high pore pressure environment, the microcracks inside the salt rock are supported by the fluid, reducing the effective stress and making the creep rate decrease; while in a low pore pressure environment, the closure of microcracks and lattice rearrangement lead to an increase in effective stress, making the creep deformation intensify. The constitutive equation describes this influence through the pressure-sensitive term , where takes values of 0.8 - 1.2, indicating the degree of influence of pore pressure on creep. A higher value indicates that creep is more sensitive to changes in pore pressure, and a lower value means that creep is mainly controlled by stress and temperature. This model can accurately predict the creep deformation rate under different wellbore pressure conditions, thereby guiding the optimization and regulation of drilling fluid pressure and preventing wellbore instability problems caused by pressure changes.

[0066] Through the establishment of this constitutive equation, the present invention can calculate the creep strain rate of salt rock in real time and optimize the reaming parameters in combination with the wellbore stability factor. Compared with traditional creep analysis methods, the present invention for the first time systematically models creep stress, temperature, time hardening, pore pressure and pressure sensitivity, making the calculation of creep rate more accurate. This model can not only provide optimization suggestions for the reaming process before construction, but also adjust drilling parameters in real time during construction to ensure the stability of the reaming trajectory and reduce the out-of-control phenomenon of wellbore deformation caused by creep. In addition, this method is particularly applicable to deep high-temperature salt rock formations. In such formations, the creep rate is significant, and it is difficult for traditional empirical methods to accurately predict deformation. The mathematical model of the present invention can dynamically adjust the reaming construction strategy, making the wellbore diameter control more refined and improving construction safety.

[0067] Example 4: During reaming construction, the drilling fluid continuously scours the salt rock wellbore. Since salt rock is easily soluble in water, salt rock dissolution will occur on the wellbore wall, resulting in an increase in the wellbore diameter. At the same time, the creep behavior of salt rock will change the rock mass structure and surface microtopography, exposing more new surfaces and accelerating the salt rock dissolution rate. Through the following formula, a salt rock dissolution-creep coupling model is established based on the creep strain rate:

[0068] ;

[0069] where is the salt ion concentration in the drilling fluid, with the unit of kg / m³; is the salt rock dissolution rate constant, with the unit of m / s; is the contact area, with the unit of m²; is the saturation solubility, with the unit of kg / m³; is the dissolution-creep coupling coefficient, with the unit of s, and its value range is from 0.2 to 0.5; is the angular velocity of the drill bit rotation, with the unit of rad / s; is the drilling fluid flow rate, with the unit of m³ / s; is the annulus volume, with the unit of m³; represents the time derivative of the salt ion concentration in the drilling fluid.

[0070] Specifically, during the reaming operation, the dissolution and creep behaviors of salt rock jointly affect the stability of the wellbore and the change in well diameter. Therefore, it is necessary to establish a salt rock dissolution-creep coupling model to accurately describe their interaction. Salt rock is a water-soluble formation. Under the continuous scouring of drilling fluid, its surface will dissolve, causing the well diameter to gradually increase. At the same time, the creep behavior of salt rock changes the microstructure of the wellbore, generating new exposed surfaces that directly contact the drilling fluid, further accelerating the dissolution process of salt rock. Therefore, dissolution and creep do not occur independently but promote each other. In regions with high creep rates, the dissolution rate is often faster, and vice versa. In the present invention, by establishing a mathematical model, the chemical action of drilling fluid, the characteristics of the bottom-hole flow field, and the creep behavior of salt rock are systematically modeled, so as to achieve accurate calculation of the salt rock dissolution rate and combine the correction of the dissolution rate by the creep deformation rate, enabling the reaming operation parameters to be optimized and adjusted according to the real-time calculation results.

[0071] The dissolution-creep coupling model adopted in the present invention describes the change process of the salt ion concentration in the drilling fluid over time. The core of this equation lies in accurately calculating the salt rock dissolution rate and making corrections in combination with the influence of creep deformation. In this equation, the dissolution rate of salt rock is mainly controlled by three aspects: dissolution kinetics, the flow characteristics of drilling fluid, and creep behavior. First of all, the dissolution kinetics is jointly determined by the dissolution rate constant of salt rock and the difference between the salt ion concentration in the drilling fluid and the saturation solubility. When the salt ion concentration is lower than the saturation solubility , the surface of the salt rock will continuously dissolve. The greater the concentration gradient, the faster the dissolution rate. However, as the salt ion concentration in the drilling fluid increases, this concentration gradient gradually decreases, and the dissolution rate tends to decline. This phenomenon conforms to the typical dissolution kinetics law. Therefore, in the mathematical model of the present invention, a concentration gradient term is introduced to describe this dissolution driving force, enabling the calculation of the dissolution rate to be updated in real time according to the ion concentration of the actual drilling fluid and ensuring the accuracy of the model.

[0072] Secondly, the flow characteristics of the drilling fluid affect the dissolution rate of salt rock, mainly reflected in the contact area, the angular velocity of the drill bit rotation, and the flow rate of the drilling fluid. The contact area between the drilling fluid and the wellbore directly determines the surface area of the salt rock that can be dissolved per unit time. A larger contact area means more dissolution occurs, thus accelerating the increase in the well diameter. And the angular velocity of the drill bit rotation affects the flow field characteristics at the bottom of the well. At high rotation speeds, the shearing action of the drill bit on the bottom of the well is enhanced, making the flow of the drilling fluid more intense, increasing the scouring effect on the wellbore, and thus increasing the dissolution rate. In the present invention, by introducing terms, the influence of the rotation speed on the dissolution rate is characterized, ensuring that the model can maintain calculation accuracy at different drill bit rotation speeds. In addition, the flow rate of the drilling fluid and the annulus volume together determine the renewal rate of the drilling fluid, that is, the ability of the drilling fluid to carry dissolved salt ions. If the flow rate is large, the dissolved salt ions can be quickly carried away, maintaining the dissolution rate at a high level; if the flow rate is small, the dissolved salt ions remain in the bottom hole area, increasing the local salt concentration and thus inhibiting further dissolution. Therefore, the present invention uses the flow rate / volume ratio term to describe the renewal rate of the drilling fluid, ensuring that the model can dynamically adjust the dissolution rate according to different fluid circulation conditions.

[0073] Finally, the influence of creep deformation on dissolution is corrected by the coupling term which characterizes the promoting effect of the creep rate on the salt rock dissolution process. Creep changes the microstructure of the salt rock wellbore, resulting in the continuous exposure of fresh surfaces, increasing the dissolution area and thus accelerating the dissolution process. Through experimental research and numerical simulation, the present invention has determined that the value range of the dissolution-creep coupling coefficient is in , indicating that the higher the creep rate, the greater the increase in the dissolution rate. The introduction of this coupling coefficient enables the model to dynamically respond to changes in the creep deformation rate and automatically correct the dissolution rate in the high creep rate region, thereby more accurately predicting the change trend of the hole diameter after reaming. In addition, this model can also be used for construction parameter optimization, that is, during the reaming process, when the calculated dissolution rate is too high, the drill bit rotation speed can be appropriately reduced or the drilling fluid flow rate can be adjusted to control the dissolution process and ensure the stability of the wellbore.

[0074] Compared with the traditional salt rock dissolution model, the dissolution-creep coupling model of the present invention incorporates the influence of creep deformation into the calculation of the dissolution rate for the first time, making the dissolution rate prediction more in line with the actual reaming construction conditions. Traditional methods usually assume that salt rock dissolution is only determined by the flow field and chemical action of the drilling fluid, ignoring the problem of fresh surface exposure caused by creep deformation, so it is difficult to accurately predict hole diameter changes under high creep formations or long-term drilling conditions. By introducing the creep coupling factor, the present invention has established a dynamic dissolution model that changes with time, which can not only calculate the change of the drilling fluid salt concentration in real time, but also adaptively adjust the dissolution rate according to the creep deformation situation, making the model more adaptable to complex formation conditions and improving the accuracy and reliability of the prediction.

[0075] Example 5: The salt rock dissolution rate constant is obtained through the following process: Immerse a salt rock sample of known mass and shape in the drilling fluid or aqueous solution, regularly measure its mass change, calculate the mass loss rate per unit time, and then the salt rock dissolution rate constant is calculated using the following formula:

[0076] ;

[0077] Among them, is the dissolution contact area of the salt rock sample, with the unit of m²; is the mass loss of the salt rock per unit time, with the unit of kg / s; is the density of the salt rock, with the unit of kg / m³.

[0078] Specifically, during the reaming while drilling process, the dissolution rate of the salt rock has an important influence on the wellbore stability and the control of the reaming trajectory. Therefore, accurately determining the dissolution rate constant of the salt rock is a key step in establishing the salt rock dissolution-creep coupling model. The present invention proposes an experimental determination method to obtain the salt rock dissolution rate constant , and calculates its dissolution rate in the drilling fluid or aqueous solution by measuring the mass loss of the salt rock sample, so as to provide accurate input data for the numerical modeling of the salt rock dissolution behavior during the reaming process. The basic principle of this method is based on dissolution kinetics, determines the relationship between the dissolution rate and the contact area of the salt rock in a specific fluid environment, and calculates the dissolution rate constant through experimental data regression, so as to be used for the dynamic dissolution prediction and construction parameter optimization of the reaming while drilling operation.

[0079] During the experiment, first select a salt rock sample with a known mass and shape to ensure that its dissolution behavior can represent the characteristics of the actual wellbore salt rock. The salt rock sample is usually processed into a regular shape (such as a cylinder or a cube) to facilitate the calculation of the dissolution contact area . Then, immerse the sample in the drilling fluid or aqueous solution with a specific composition, and control the experimental conditions, including temperature, flow rate, solution composition, to simulate the real downhole environment. During the experiment, regularly measure the mass change of the salt rock sample , record the mass loss rate per unit time , and thus calculate the dissolution rate. Finally, through the regression analysis of the experimental data, calculate the salt rock dissolution rate constant , and this value can be used for the calculation of the salt rock dissolution rate during the reaming while drilling process, and further optimize the construction conditions such as the drilling fluid parameters and the bit rotation speed.

[0080] During the experiment, the determination of the dissolution rate constant is affected by multiple factors, including temperature, drilling fluid composition, flow rate and wellbore stress state. First, the temperature has a greater influence on the dissolution rate. As the temperature increases, the dissolution rate of the salt rock usually shows an exponential growth. Therefore, it is necessary to strictly control the temperature during the experiment to ensure the accuracy of the experimental data. Second, the composition of the drilling fluid determines the chemical kinetics of the dissolution reaction. For example, a drilling fluid with a high salt concentration will inhibit dissolution, while a drilling fluid with a low salt concentration will accelerate dissolution. Therefore, different drilling fluid compositions need to be set during the experiment to determine The variation law under different chemical environments. In addition, the flow rate is also an important factor affecting the dissolution rate. In a high-flow-rate environment, the dissolved salt ions are more easily carried away, thus maintaining a high concentration gradient and making the dissolution rate faster; while in a low-flow-rate condition, the dissolution products accumulate locally, reducing the concentration gradient and resulting in a decrease in the dissolution rate. Therefore, different flow rate conditions need to be simulated during the experiment to obtain the value range.

[0081] The experimental determination method proposed by the present invention is more accurate and applicable than the traditional dissolution rate estimation method. The traditional method usually uses theoretical model derivation or formation empirical parameters, which are difficult to apply to complex downhole environments. The present invention can provide more reliable input data by experimentally determining the dissolution rate of actual salt rock samples, ensuring more accurate prediction of the wellbore dissolution behavior during the reaming process. In addition, the experimental determination method can adjust parameters according to different drilling fluid systems, formation pressures, and temperature conditions, making the calculation more in line with the actual working conditions and improving its application value in the reaming construction.

[0082] In the application scenario of the present invention, the dissolution rate constant can be directly used in the salt rock dissolution-creep coupling model, combined with the creep strain rate and the drilling fluid flow parameters to calculate the real-time change of the salt rock dissolution rate during the reaming process. During the construction process, by real-time monitoring the salt ion concentration of the drilling fluid , combined with the dissolution rate calculation model, the drilling fluid flow rate and composition can be dynamically adjusted to control the wellbore dissolution rate and ensure the wellbore stability. For example, when the calculated is too large, it may mean that the wellbore dissolution is too fast, and during the construction process, it is necessary to appropriately increase the salt concentration of the drilling fluid or reduce the drilling fluid flow rate to inhibit the dissolution process; while when is too small, it is necessary to increase the drilling fluid flow rate to increase the dissolution rate of the wellbore and avoid uneven expansion of the wellbore due to insufficient dissolution, thereby affecting the stability of the reaming trajectory.

[0083] Example 6: The dynamic wellbore stability evaluation model in step 3 is expressed by the following formula:

[0084] ;

[0085] Wherein, is the wellbore stability factor, dimensionless, indicates stable, otherwise it indicates unstable; is the circumferential stress of the wellbore, in MPa; is the pressure in the well, in MPa; is the yield strength of salt rock, with the unit of MPa; is the creep influence coefficient, dimensionless, with the value range from 0.2 to 0.5; is the reaming operation time, with the unit of s; is the dissolution influence coefficient, dimensionless, with the value range from 0.4 to 0.8; is the saturated solubility, with the unit of kg / m³; is the reaming radius, with the unit of m; is the original drilling radius, with the unit of m.

[0086] Specifically, the wellbore stability factor adopted in the present invention As an important index to measure the wellbore stability, this factor is calculated by a mathematical formula, comprehensively considering the circumferential stress of the wellbore, the wellbore pressure, the creep cumulative effect and the wellbore diameter change caused by dissolution. Among them, As a dimensionless parameter, it is used to quantitatively describe the stability condition of the wellbore. When it indicates that the wellbore is still in a stable state and the reaming operation can continue; when it indicates that the wellbore may have entered an unstable state and the construction parameters need to be adjusted to reduce the risk of instability. Compared with the traditional static wellbore stability analysis method, the dynamic model of the present invention can calculate the stable state of the wellbore in real time and make predictions in combination with the time evolution characteristics of the reaming process, making the reaming operation safer and more accurate. The core of this model lies in the stress analysis of the wellbore, and the circumferential stress term describes the stress state of the wellbore material. The circumferential stress is the main tensile stress borne by the wellbore material, while the wellbore pressure is the support pressure from the drilling fluid. The difference between the two represents the net tensile stress borne by the wellbore. The physical meaning of this term is to measure the stress safety margin of the wellbore, that is, the ratio between the tensile stress borne by the wellbore and the yield strength of salt rock. If this term is large, it means that the wellbore is subjected to a large tensile stress and there may be a risk of tensile failure; if this term is small, the wellbore is still in a safe state and will not be damaged due to the action of tensile stress. Therefore, this term is used to measure the mechanical stability of the wellbore and provide a theoretical basis for the adjustment of the drilling fluid pressure during the reaming process.

[0087] The creep influence term describes the weakening effect of creep deformation on the wellbore stability. During the reaming construction process, the creep deformation of salt rock gradually accumulates with time, resulting in a decrease in the bearing capacity of the wellbore material and finally may reach the yield state. The creep strain rate is calculated by the creep constitutive equation, which depends on factors such as effective stress, temperature and time, and reflects the deformation rate of salt rock under given construction conditions. The reaming operation time The cumulative effect of creep deformation is further described, that is, the creep deformation continues to develop over time, resulting in a gradual decrease in the wellbore stability. The creep influence coefficient ranges from 0.2 to 0.5 and is used to adjust the degree of influence of creep on stability. In an environment with a high creep rate it takes a higher value, and in an environment with a low creep rate it takes a lower value. By introducing this item, the wellbore stability evaluation model of the present invention can dynamically predict the change of the wellbore bearing capacity under the action of creep and perform real-time parameter optimization during the reaming process, such as reducing the drilling pressure or adjusting the drilling fluid pressure, so as to slow down the influence of creep on the wellbore stability. The dissolution influence item describes the influence of salt rock dissolution on the wellbore stability. During the reaming process, the drilling fluid continuously scours the wellbore, causing the salt rock to dissolve and resulting in an increase in the wellbore diameter. Since the dissolution process occurs locally and there are differences in the dissolution rates in different regions, it may cause uneven expansion of the wellbore, leading to local stress concentration and thus increasing the risk of wellbore instability. This model uses the ratio between the salt concentration of the drilling fluid and the saturation solubility to measure the magnitude of the dissolution driving force. If the salt concentration of the drilling fluid is low, the dissolution rate is fast and the wellbore is greatly affected by dissolution; if the salt concentration of the drilling fluid is close to saturation, the dissolution rate decreases and the influence on the wellbore is small. In addition, the wellbore diameter change rate directly characterizes the degree of wellbore diameter change after reaming. If the reaming radius is much larger than the original wellbore diameter , it indicates that the dissolution effect of the wellbore is strong and local instability may be caused. The dissolution influence coefficient ranges from 0.4 to 0.8 and is used to adjust the degree of influence of dissolution on stability. In an environment with a high dissolution rate it takes a higher value, and in an environment with a low dissolution rate it takes a lower value. By calculating the dissolution influence item in real time, the present invention dynamically adjusts the salt concentration, flow rate and flow velocity of the drilling fluid during the reaming construction process to control the dissolution rate and ensure the overall stability of the wellbore.

[0088] Example 7: The corrected operating parameters include: corrected drilling fluid flow rate, corrected bit rotation speed and corrected drilling pressure, which are calculated using the following formula:

[0089] ;

[0090] where is the initial bit rotation speed, with the unit of rad / s; is the initial drilling pressure, with the unit of kN; is the initial drilling fluid flow rate, with the unit of L / s; is the corrected bit rotation speed, with the unit of rad / s; The weight on bit for correction, unit: kN; The drilling fluid flow rate for correction, unit: L / s; The stability adjustment coefficient, dimensionless; The comprehensive influence coefficient of dissolution-creep, unit: s, value range: 0.5 to 1.2; The saturated solubility, unit: kg / m³; The radius control gain coefficient, dimensionless, value range: 0.5 to 2.0; The target reaming radius, unit: m; The current reaming radius, unit: m.

[0091] Specifically, the stability adjustment term is used to optimize parameters according to the stability of the wellbore wall. When the wellbore wall stability factor is large, it indicates that there is a high risk of instability of the wellbore wall. At this time, it is necessary to reduce the bit rotation speed, the weight on bit and the drilling fluid flow rate to reduce the disturbance to the wellbore wall, thereby improving the safety of the wellbore wall. is the stability adjustment coefficient, and its value range is calibrated by experiments, usually between 0.1 - 0.5. A larger value indicates that the influence of the change in wellbore wall stability on the reaming parameters is more significant, while a smaller value indicates that the adjustment of the reaming parameters is more conservative. This adjustment strategy enables the present invention to reduce the risk of instability in real time and improve the stability of the reaming construction, and is particularly applicable to salt rock formations with high creep rates or high dissolution rates. Secondly, the comprehensive influence term of dissolution-creep is mainly used to correct the influence of creep deformation and dissolution process on the reaming parameters. Creep deformation reflects the continuous deformation rate of the wellbore wall. If the creep deformation is large, the wellbore wall structure may have been affected by a large stress redistribution, and it is necessary to appropriately reduce the bit rotation speed and the weight on bit to reduce additional disturbance to the wellbore wall. In addition, the ratio of the salt ion concentration of the drilling fluid to the saturated solubility reflects the dissolution degree of the salt rock. If this ratio is low, it indicates that the drilling fluid still has strong dissolution ability, which may cause the well diameter to expand too fast. At this time, it is necessary to appropriately adjust the drilling fluid flow rate to slow down the dissolution rate. is the comprehensive influence coefficient of dissolution-creep, and its value range is 0.5 - 1.2 s, indicating the influence intensity of creep and dissolution on the adjustment of the reaming parameters. A larger value indicates that the dissolution-creep effect is significant and the correction amplitude of the reaming parameters is large, while a smaller value indicates that the influence of creep and dissolution on the reaming parameters is weak and the adjustment amplitude is small. Through this correction, the present invention can adaptively adjust the drilling parameters to adapt to the dynamic influence of creep and dissolution on the wellbore wall and improve the accuracy of the reaming construction.

[0092] Finally, the reaming radius error correction term is mainly used to ensure that the reaming radius meets the design requirements. During the reaming process, affected by creep deformation and dissolution, the wellbore diameter may deviate from the target size, resulting in over-reaming or under-reaming. The present invention calculates the reaming radius error based on the deviation between the target reaming radius and the current reaming radius and corrects the parameters using a quadratic relationship. When the reaming radius error is large, the correction amplitude of this term is large, indicating that the bit rotation speed, weight on bit, and drilling fluid flow rate need to be adjusted to make the reaming radius return to the target value; when the reaming radius error is small, the correction amplitude of this term is small, indicating that the reaming parameters can remain relatively stable. is the radius control gain coefficient, and its value range is 0.5 - 2.0, which is used to adjust the influence degree of the reaming radius error on parameter adjustment. A larger value indicates being more sensitive to the reaming radius deviation and requires larger parameter adjustment, while a smaller value indicates a milder adjustment to the reaming radius deviation. Through this correction term, the present invention enables the reaming parameters to be adjusted at any time to ensure that the reaming radius meets the design requirements and improve the reaming quality.

[0093] Example 8: Stability adjustment coefficient It is calculated using the following formula:

[0094] ;

[0095] wherein, is the reference stability adjustment coefficient, and its value range is from 0.1 to 0.5.

[0096] Specifically, the exponential term in this formula reflects the influence law of the wellbore stability factor on the stability adjustment coefficient. Since reflects the stability degree of the wellbore wall, when is larger, it indicates that the wellbore wall tends to be unstable, and at this time, larger adjustments to the drilling parameters are required to reduce the risk of instability. Therefore, the present invention adopts a stability adjustment model in the form of exponential decay, so that when the wellbore wall is relatively stable ( is smaller), changes little, maintaining the relative stability of the reaming parameters; while when the wellbore wall tends to be unstable ( is larger), increases rapidly, thereby enhancing the adjustment intensity of the reaming parameters, timely reducing the weight on bit, bit rotation speed, or drilling fluid flow rate to reduce the possibility of wellbore wall instability. During the reaming process, the stability of the wellbore wall is comprehensively affected by creep deformation, dissolution rate, and drilling parameters. If no real-time adjustment is made, when the wellbore wall stability factor When it gradually increases, the stress state of the wellbore may enter the plastic yield zone, which may lead to local damage of the wellbore or abnormal expansion of the well diameter. Therefore, the stability adjustment coefficient of the present invention By dynamically adjusting the adjustment range of the reaming parameters, the stability of the reaming process is ensured, so that the construction parameters remain stable under the condition of wellbore stability, and active adjustment is carried out when the wellbore tends to be unstable to reduce risks.

[0097] At (that is, the wellbore is very stable), At this time , indicating that the adjustment range of the reaming parameters is very small, and the reaming process can remain relatively stable without frequent adjustment of the construction parameters. When increases (that is, the wellbore tends to be unstable), rapidly decays to close to 0. At this time approaches , that is, the adjustment range of the reaming parameters reaches the maximum to ensure the wellbore stability. If is small (the wellbore is stable), then is close to 0, indicating that the adjustment range of the reaming parameters is very small, and the reaming process basically maintains the current construction parameters. If is large (the wellbore tends to be unstable), then rapidly increases, indicating that the reaming parameters need to be adjusted by a large margin to reduce the adverse impact on the wellbore. Determines the adjustment range of the reaming parameters. When is small, is approximately 0, making still close to the initial value , that is, the reaming parameters basically remain unchanged. When increases, rapidly increases, so that the reaming parameters are significantly adjusted to reduce the possibility of wellbore instability. This adaptive adjustment strategy enables the reaming construction to optimize the parameters according to the real-time wellbore state, thereby improving the construction safety.

[0098] Example 9: Calculate the corrected reaming trajectory vector through the following formula:

[0099] ;

[0100] wherein, is the corrected reaming trajectory vector, with the unit of m; is the curve length parameter along the well axis, with the unit of m; is the initial trajectory tangential unit vector, with the unit of m; is the tool face angle, with the unit of rad; is the characteristic length, with the unit of m, and the value range is from 7 to 12.

[0101] Specifically, the reaming trajectory correction method of the present invention takes the wellbore stability factor as the core, and this factor reflects the real-time stable state of the wellbore. When the wellbore tends to be unstable, creep deformation and dissolution cause the wellbore diameter change to intensify, and the reaming trajectory is prone to deviation. Therefore, a larger amplitude of trajectory correction is required to redirect the drill bit back to the target path. When the wellbore is in a stable state, excessive trajectory adjustment may introduce unnecessary disturbances and affect the stability of the reaming operation. Therefore, the correction amplitude should be reduced accordingly. The present invention makes the intensity of trajectory correction as the weight coefficient of trajectory correction, so that the intensity of trajectory correction can be adaptively adjusted according to the real-time stability of the wellbore. If is small, it indicates that the wellbore is relatively stable. At this time, the intensity of trajectory correction is small, and the reaming trajectory basically remains on the original set trajectory; if is large, it indicates that the instability trend of the wellbore increases, then the intensity of trajectory correction increases to ensure that the drill bit can deflect to the correct direction in time and prevent the further deterioration of wellbore instability.

[0102] In addition, the adjustment of the reaming trajectory must consider the motion characteristics of the drill bit. Therefore, the present invention introduces a rotation matrix to describe the change of the drill bit motion direction. During the reaming operation, the motion direction of the drill bit is affected not only by the mechanical state of the wellbore, but also by the combined action of the weight on bit, the rotary speed of the drill bit, and the drilling fluid flow rate. Therefore, it is difficult to accurately predict the motion trajectory of the drill bit relying solely on a single mechanical model. The present invention constructs a rotation matrix to make the direction of trajectory correction consistent with the actual motion direction of the drill bit, ensuring the rationality of trajectory adjustment. The introduction of the rotation matrix enables the trajectory adjustment to be adaptively adjusted in three-dimensional space, avoiding excessive or insufficient trajectory correction caused by single-direction adjustment and improving the accuracy of the reaming operation.

[0103] The amplitude of trajectory correction is not only affected by the wellbore stability, but also related to the change of reaming operation parameters. The rotary speed of the drill bit, the weight on bit, and the drilling fluid flow rate are important factors determining the reaming trajectory. If these parameters change, the motion state of the drill bit will also change accordingly, thus affecting the reaming trajectory. The present invention adopts a parameter ratio correction strategy, that is, calculates the change amplitude of the corrected rotary speed of the drill bit, the weight on bit, and the drilling fluid flow rate relative to the initial value, and corrects them through a trajectory adjustment matrix. The advantage of this method is that the adjustment amplitude of the reaming parameters can be directly fed back to the trajectory correction, enabling the trajectory adjustment to be synchronized with the optimization of the reaming parameters, avoiding the accumulation of deviation of the reaming trajectory, and improving the controllability of the operation. For example, when the rotary speed of the drill bit increases, the drilling efficiency of the drill bit improves. However, if the reaming trajectory deviates, at this time, the weight on bit or the drilling fluid flow rate can be adjusted for compensation, so that the trajectory correction can dynamically adapt to the change of the drill bit motion state and ensure that the drill bit always advances along the target reaming trajectory.

[0104] Since the creep and dissolution of salt rock can cause continuous changes in the wellbore diameter, the present invention also introduces a dissolution-creep influence term to correct the adjustment amplitude of the reaming trajectory. The rate of creep deformation is calculated from the creep strain rate and the dissolution rate is determined by the ratio between the salt ion concentration in the drilling fluid and the saturation solubility . When the creep rate is high or the dissolution rate is fast, the morphological changes of the wellbore wall are more significant, and the deviation of the reaming trajectory may be more obvious. Therefore, a larger trajectory correction is required. When the creep rate is low or the dissolution rate is slow, the deformation of the wellbore wall is small, and the intensity of trajectory correction should be reduced accordingly. The present invention controls the influence range of trajectory correction through an exponential decay function, so that when the creep and dissolution rates of the wellbore wall are high, the adjustment amplitude of trajectory correction increases, and when the creep and dissolution rates are low, the trajectory adjustment amplitude decreases, thus ensuring the stability of the reaming operation. The introduction of the exponential decay function enables the trajectory correction to adapt to different downhole environments and ensures the stable progress of the reaming operation under various complex working conditions.

[0105] In addition, the present invention also introduces a characteristic length to control the smoothness of the trajectory correction. The characteristic length determines the spatial scale of the trajectory correction. If takes a large value, the smoothness of the trajectory adjustment is high, and the reaming trajectory correction is relatively slow, which is suitable for environments with high wellbore wall stability. If takes a small value, the amplitude of the trajectory adjustment is large, which is suitable for environments with fast wellbore wall creep and strong dissolution. In the present invention, the value range of the characteristic length is between 7 and 12 m, which can be optimized and adjusted according to different working conditions to ensure that the correction of the reaming trajectory can meet the construction requirements without causing additional disturbance to the wellbore wall.

[0106] The present invention is not limited to the foregoing specific embodiments. The present invention extends to any new feature or any new combination disclosed in this specification, as well as any new method or process step or any new combination disclosed.

Claims

1. A method for controlling underreaming while drilling based on the creep characteristics of salt rock, characterized in that The method includes the following: Step 1: Considering the effects of effective stress, temperature, creep duration, and pore pressure on the creep deformation of salt rock, establish a constitutive equation for the creep strain rate of salt rock and calculate the creep strain rate of salt rock. Step 2: Considering the contact area between the drilling fluid and the wellbore wall, the difference between the saturated solubility of salt rock and the concentration of salt ions in the current drilling fluid, the rotation speed of the drill bit, and the circulation flow rate of the drilling fluid, establish a salt rock dissolution-creep coupling model based on the creep strain rate. Step 3: Establish a dynamic wellbore stability evaluation model to judge in real time whether the salt rock wellbore is stable during the reaming operation. Step 4: Establish an optimized reaming parameter model. According to the initial tangential unit vector of the trajectory and the initial drilling operation parameters, calculate the corrected operation parameters and the corrected reaming trajectory vector, and conduct real-time reaming control based on the corrected operation parameters and the corrected reaming trajectory vector. Salt rock has the characteristics of time-dependent deformation. Even under stress, it will undergo continuous creep over time. During the real-time reaming construction process, the creep characteristics of salt rock will cause changes in the well diameter and result in the instability of the wellbore wall. Through the following formula, establish a constitutive equation for the creep strain rate of salt rock: ； Among them, is the creep strain rate of salt rock, with the unit of ; is a material constant, related to the mineral composition of salt rock, with the unit of ; is the effective stress, with the unit of MPa; is the stress exponent, dimensionless, with the value range from 3 to 5; is the creep activation energy, with the unit of kJ / mol; is the gas constant, with the value of 8.314, with the unit of ; is the absolute temperature, with the unit of K; is the time, with the unit of s; is the time hardening index, dimensionless, with the value range from 0.3 to 0.5; is the pore fluid pressure, with the unit of MPa; is the confining pressure, with the unit of MPa; is the pressure sensitivity index, dimensionless, with the value range from 0.8 - 1.

2.

2. The control method for reaming while drilling based on the creep characteristics of salt rock according to claim 1, wherein The initial drilling operation parameters include: the initial drill bit rotation speed, the initial drilling pressure, and the initial drilling fluid flow rate.

3. The control method for reaming while drilling based on the creep characteristics of salt rock according to claim 2, characterized in that, During the reaming construction, the drilling fluid continuously scours the salt rock wellbore wall. Since salt rock is easily soluble in water, salt rock dissolution will occur on the wellbore wall, resulting in an increase in the well diameter. At the same time, the creep behavior of salt rock will change the rock mass structure and surface micro-topography, exposing more new surfaces and accelerating the dissolution rate of salt rock. Through the following formula, establish a salt rock dissolution-creep coupling model based on the creep strain rate: ； Among them, is the salt ion concentration in the drilling fluid, with the unit of kg / m³; is the salt rock dissolution rate constant, with the unit of m / s; is the contact area, with the unit of m²; is the saturation solubility, with the unit of kg / m³; is the dissolution-creep coupling coefficient, with the unit of s, and its value range is from 0.2 to 0.5; is the angular velocity of the drill bit rotation, with the unit of rad / s; is the drilling fluid flow rate, with the unit of m³ / s; is the annulus volume, with the unit of m³; represents the time derivative of the salt ion concentration in the drilling fluid.

4. The control method for reaming while drilling based on the creep characteristics of salt rock according to claim 3, wherein The salt rock dissolution rate constant is obtained through the following process: Immerse salt rock samples with known mass and shape in the drilling fluid or aqueous solution, regularly measure their mass changes, calculate the mass loss rate per unit time, and the salt rock dissolution rate constant is calculated using the following formula: ； wherein, is the dissolution contact area of the salt rock sample, with the unit of m²; is the mass loss of the salt rock per unit time, with the unit of kg / s; is the density of the salt rock, with the unit of kg / m³.

5. The control method for reaming while drilling based on the creep characteristics of salt rock according to claim 4, characterized in that The dynamic wellbore stability evaluation model in Step 3 is expressed using the following formula: ； Among them, is the wellbore stability factor, dimensionless, indicating stability, otherwise indicating instability; is the circumferential stress of the wellbore, with the unit of MPa; is the pressure in the well, with the unit of MPa; is the yield strength of salt rock, with the unit of MPa; is the creep influence coefficient, dimensionless, with the value range from 0.2 to 0.5; is the reaming operation time, with the unit of s; is the dissolution influence coefficient, dimensionless, with the value range from 0.4 to 0.8; is the saturation solubility, with the unit of kg / m³; is the reaming radius, with the unit of m; is the original drilling radius, with the unit of m.

6. The control method for reaming while drilling based on the creep characteristics of salt rock according to claim 5, wherein The corrected operation parameters include: the corrected drilling fluid flow rate, the corrected drill bit rotation speed, and the corrected drilling pressure, which are calculated using the following formula: ； Among them, is the initial bit rotation speed, with the unit of rad / s; is the initial bit weight on bit, with the unit of kN; is the initial drilling fluid flow rate, with the unit of L / s; is the corrected bit rotation speed, with the unit of rad / s; is the corrected bit weight on bit, with the unit of kN; is the corrected drilling fluid flow rate, with the unit of L / s; is the stability adjustment coefficient, dimensionless; is the comprehensive influence coefficient of dissolution-creep, with the unit of s, and the value range is from 0.5 to 1.2; is the saturated solubility, with the unit of kg / m³; is the radius control gain coefficient, dimensionless, and the value range is from 0.5 to 2.0; is the target reaming radius, with the unit of m; is the current reaming radius, with the unit of m.

7. The method for controlling reaming while drilling based on the creep characteristics of salt rock according to claim 6, wherein Stability adjustment coefficient Calculated using the following formula: ； Among them, is the reference stability adjustment coefficient, and its value range is from 0.1 to 0.

5.

8. The reaming control method while drilling based on the creep characteristics of salt rock according to claim 7, wherein Calculate the corrected reaming trajectory vector through the following formula: ； Among them, is the corrected reaming trajectory vector, with the unit of m; is the curve length parameter along the well axis, with the unit of m; is the initial trajectory tangential unit vector, with the unit of m; is the tool face angle, with the unit of rad; is the characteristic length, with the unit of m, and the value range is from 7 to 12.

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