**1. Introduction**

146 Acoustic Waves – From Microdevices to Helioseismology

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In drilling engineering, we must have solid understanding of the underground geological environment which is not only complicated and diversified but also someway concealed. Thus, in order to find an effective method of predicting it, a long-term research and practice must be required. In drilling engineering for oil & gas, problems including borehole deviation & its control, wellbore instability & its control, influence directly drilling quality & efficiency of a deep or complicated well for exploration and production of oil & gas fields. For instance, because of the complicated surface and underground conditions as well as the depth (over 5000 m) of oil & gas reservoirs in western China, such unstable factors such as hole deviation and instability often encountered with each other in deep drilling engineering. Because we did not have access to the geological parameters of the formations to be drilled including the rock drillability anisotropy and so on, huge economic loss had been caused and the steps to explore and produce oil & gas in western China had been seriously restricted. Hence, there are many researches and development programs to do for the right cognition and scientific evaluation of the geological environments, and for the further study of mechanism of the drilling process instability, and so on. The solution of these problems is the key to improve the performance of drilling & HSSE (health, safety, security, environment) and lower well construction cost.

The factors influencing the instability can be sorted into subjective category and objective category. In the objective category, there are the types of geological structure and in-situ stress, rock anisotropy, porosity, permeability, lithology, pressures, and mineral components, as well as rock strength and weak layer of the formation to be drilled, and so on. In the subjective category, there are the performance of down hole drilling system, the drilling parameters (weight and torque on bit, etc.), the drilling fluid performances (water loss, viscosity, rheological property and density) and its hydration on shale, the direction and open time of wellbore, the erosion and surge pressure of drilling fluid on the hole wall, the interaction between drillstring and hole wall. Thereby, in researches on the instability, the factors from the both categories should be taken into comprehensive consideration.

Whether in vertical drilling or in directional drilling, it is always a complicated academic and technological problem how to control the well trajectory exactly along the designed

Evaluation Method for Anisotropic Drilling Characteristics

original drilling direction and hole deviation.

**2.1 Definition of rock drillability anisotropy** 

the formations to be drilled.

drillability can be defined as:

( *I*r1 and *I*r2 ) which are defined as:

**e***s*

**2. Anisotropic drilling characteristics of the formation** 

of the Formation by Using Acoustic Wave Information 149

Although many theories have been proposed to explain the hole deviation since the 1950s (Gao et al, 1994), it is only the rock drillability anisotropy theory (Lubinski & Woods, 1953) that was recognized by petroleum engineers and widely applied to petroleum engineering because it can be used to quantify the anisotropic drilling characteristics of the formation and to explain properly the actual cases of hole deviation encountered in drilling engineering. The theory suggested that since values of rock drillability are not always the same in the directions perpendicular and parallel to the bedding plane of the formation, the formation will bring the bit a considerable force, which may likely cause changes on the

The orthotropic or the transversely isotropic formations are the typical formations encountered frequently in drilling engineering. The anisotropic effects of the formations (rock drillability) on the well trajectory must be considered in hole deviation control and directional drilling. Based on the rock-bit interaction model, the formation force is defined and modeled in this section to describe quantitatively anisotropic drilling characteristics of

Because of rock drillability anisotropy, the real drilling direction does not coincide with the resultant force direction of the drill bit (supposed that it is isotropic) on bottom hole. Besides calculating the drill bit force by BHA (bottom hole assembly) analysis, rock drillability

The formation studied here is typical orthotropic one, and the transversely isotropic

 represent unit vectors in the directions of inner normal, up-dip and strike of the formation respectively, as shown in Fig.1.There are different physical properties along different directions of them. γ in Fig.1 represents dip angle of the formation to be drilled. Rock drillability anisotropy of the formation can be expressed by rock drillability anisotropy index. If the components of penetration rate of the drill bit (isotropic) along inner normal, up-dip and strike of the orthotropic formation are noted as *R*dip , *R*str and *R*n respectively, correspondingly the net applied forces are *F* dip , *F* str and *F* <sup>n</sup> respectively, the rock

, **<sup>e</sup>***<sup>u</sup>*

and

anisotropy of the formation must be considered in hole deviation control.

n

*<sup>F</sup>* <sup>=</sup> , dip dip

*<sup>R</sup> <sup>D</sup>*

dip

n

dip

Rock drillability anisotropy of the orthotropic formation may be represented by two indexes

*<sup>D</sup>* <sup>=</sup> , str r 2

Dip angle and strike of the formation can be obtained from the analysis of well logging and geological structure survey. The values of *I*r1 and *I*r2 for the orthotropic formation can be

*<sup>D</sup> <sup>I</sup>*

*<sup>F</sup>* <sup>=</sup> , str str

n

*<sup>R</sup> <sup>D</sup>*

str

*<sup>F</sup>* <sup>=</sup> (1)

*<sup>D</sup>* <sup>=</sup> (2)

n *<sup>R</sup> <sup>D</sup>*

r 1

*<sup>D</sup> <sup>I</sup>*

evaluated by the experimental analysis or using the acoustic wave information.

n

formation discussed previously is regarded as its particular case. Let **e***<sup>d</sup>*

track to reach the underground targets. In rotary drilling, the forming of wellbore & its trajectory is the result of the rock-bit interaction. In this interaction, the drill bit anisotropy and its mechanical behavior (i.e. the drill bit force and tilt angle) are important factors that can directly affect the well trajectory. The mechanical behavior depends on by the bottom hole assembly (BHA) analysis. Accordingly, principal factors influencing the well trajectory generally contain BHA, drill bit, operating parameters in drilling, drilled wellbore configuration and the formations to be drilled. Of which the BHA, drill bit and operating parameters in drilling are the factors that can be artificially controlled, and the formation property (such as rock drillability and its anisotropy) is the objective factor which can not be changed by us. The trajectory can be predicted before drilling and also can be determined after drilling through surveys and calculations. Besides, the drilled wellbore will not only generate a strong reaction on the drill bit force and the drillstring deflection, but also will exert an influence on the anisotropic drilling characteristics of the formation. Due to the above-complicated factors, the hole deviation is always inevitable, which may seriously influence the wellbore quality and the drilling performance.

The well trajectory control is the process which forces drill bit to break through formations along the designed track forward by applying reasonable techniques. The anisotropic drilling characteristics of the drill bit & the formation and their interaction effects are the factors which will cause a direct influence on the well trajectory control. Thereby, it is a complicated scientific and technological problem for us how to make the cognition, evaluation and utilization of anisotropic drilling characteristics of the formation, as well as the prediction & control of mechanical action of the drill bit on the formations.

Rock drillability anisotropy of the formation to be drilled has significant effects on the well trajectory control so that it is very important to evaluate it. Definitions of rock drillability anisotropy and acoustic wave anisotropy of the formation to be drilled are presented in this chapter. The acoustic velocities and the drillability parameters of some rock samples from Chinese Continental Scientific Drilling (CCSD) are respectively measured with the testing device of rock drillability and the ultrasonic testing system in laboratory. Thus, their drillability anisotropy and acoustic wave anisotropy are respectively calculated and discussed in detail by using the experimental data. Based on the experiments and calculations, the correlations between drillability anisotropy and acoustic wave anisotropy of the rock samples are illustrated through regression analysis. What's more, the correlation of rock drillability in directions perpendicular to and parallel to the bedding plane of core samples is studied by means of mathematical statistics. Thus, a mathematic model is established for predicting rock drillability in direction parallel to the formation bedding plane by using rock drillability in direction perpendicular to the formation bedding plane with the well logging or seismic data. The inversion method for rock anisotropy parameters (ε,δ) is presented by using well logging information and the acoustic wave velocity in direction perpendicular to the bedding plane of the formation is calculated by using acoustic wave velocity in any direction of the bedding plane. Then, rock drillability in direction perpendicular to the bedding plane of the formation can be calculated by using acoustic wave velocity in the same direction. Thus, rock drillability anisotropy and anisotropic drilling characteristics of the formation can be evaluated by using the acoustic wave information based on well logging data. The evaluation method has been examined by case study based on oilfield data in west China.

track to reach the underground targets. In rotary drilling, the forming of wellbore & its trajectory is the result of the rock-bit interaction. In this interaction, the drill bit anisotropy and its mechanical behavior (i.e. the drill bit force and tilt angle) are important factors that can directly affect the well trajectory. The mechanical behavior depends on by the bottom hole assembly (BHA) analysis. Accordingly, principal factors influencing the well trajectory generally contain BHA, drill bit, operating parameters in drilling, drilled wellbore configuration and the formations to be drilled. Of which the BHA, drill bit and operating parameters in drilling are the factors that can be artificially controlled, and the formation property (such as rock drillability and its anisotropy) is the objective factor which can not be changed by us. The trajectory can be predicted before drilling and also can be determined after drilling through surveys and calculations. Besides, the drilled wellbore will not only generate a strong reaction on the drill bit force and the drillstring deflection, but also will exert an influence on the anisotropic drilling characteristics of the formation. Due to the above-complicated factors, the hole deviation is always inevitable, which may seriously

The well trajectory control is the process which forces drill bit to break through formations along the designed track forward by applying reasonable techniques. The anisotropic drilling characteristics of the drill bit & the formation and their interaction effects are the factors which will cause a direct influence on the well trajectory control. Thereby, it is a complicated scientific and technological problem for us how to make the cognition, evaluation and utilization of anisotropic drilling characteristics of the formation, as well as the prediction & control of mechanical action of the drill bit on the

Rock drillability anisotropy of the formation to be drilled has significant effects on the well trajectory control so that it is very important to evaluate it. Definitions of rock drillability anisotropy and acoustic wave anisotropy of the formation to be drilled are presented in this chapter. The acoustic velocities and the drillability parameters of some rock samples from Chinese Continental Scientific Drilling (CCSD) are respectively measured with the testing device of rock drillability and the ultrasonic testing system in laboratory. Thus, their drillability anisotropy and acoustic wave anisotropy are respectively calculated and discussed in detail by using the experimental data. Based on the experiments and calculations, the correlations between drillability anisotropy and acoustic wave anisotropy of the rock samples are illustrated through regression analysis. What's more, the correlation of rock drillability in directions perpendicular to and parallel to the bedding plane of core samples is studied by means of mathematical statistics. Thus, a mathematic model is established for predicting rock drillability in direction parallel to the formation bedding plane by using rock drillability in direction perpendicular to the formation bedding plane with the well logging or seismic data. The inversion method for rock anisotropy parameters (ε,δ) is presented by using well logging information and the acoustic wave velocity in direction perpendicular to the bedding plane of the formation is calculated by using acoustic wave velocity in any direction of the bedding plane. Then, rock drillability in direction perpendicular to the bedding plane of the formation can be calculated by using acoustic wave velocity in the same direction. Thus, rock drillability anisotropy and anisotropic drilling characteristics of the formation can be evaluated by using the acoustic wave information based on well logging data. The evaluation method has been examined by case

influence the wellbore quality and the drilling performance.

study based on oilfield data in west China.

formations.
