In oil exploitation, many engineering problems, such as exploration, drilling, well completion, logging, oil recovery and well workover, are all related to the oil well itself. Control problems occur in various downhole production and operation processes. Taking the downhole control of drilling operations as an example, it involves a variety of control issues in safety control, quality control and cost control (Fig. 1). For each control problem, control tools or systems with one or more control modes can be developed. These are the research areas of downhole control engineering.

Fig. 1.

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	Fig. 1. Schematic diagram of downhole control classification in drilling operation.

The downhole control has its own inherent characteristics and difficulties, which are determined by the structures of the oil and gas well, the environment of downhole operation, and the properties of loads.

(1) Small radial size. An oil and gas well is an elongated hole that can reach several kilometers in length starting from the ground surface; however, its diameter is often within half a meter. Moreover, the size of the well decreases gradually as the increasing well depth, and the smallest borehole diameter can be less than 0.1 m. Since engineers cannot reach the bottom of the well to participate in the operation process, this control is in the form of remote control or closed-loop automatic control. In particular, the limitation of radial size makes downhole tools or systems difficult to design and manufacture.

(2) Coexistence of a variety of working media underground. Taking drilling as an example, solid (drill string) and liquid (drilling fluid) coexist downhole, and the drilling fluid in the actual working process is a multi-phase medium composed of non-Newtonian fluid, solid particles and even bubbles (under foam drilling conditions). The downhole system under multi- body coupling has complex physical properties.

(3) Extreme working conditions. Taking drilling as an example, the drill string works under conditions with high temperature (up to 200 ° C or more), high pressure (up to 100 MPa or more), strong vibration (up to 500 g (acceleration of gravity)), strong loads (maximum axial tension load can reach nearly 1000 tons), erosion and corrosion. Therefore, the components and control technology that can be used in the ground control equipment usually cannot be directly applied in the downhole control.

Due to the particularity of downhole control, the conventional control systems, mechanisms, components and mature methods, which can be effectively applied in other industries and ground projects, are difficult to be simply copied to downhole control. Under such circumstances, downhole control engineering has to investigate these special problems to form a set of special design methods and techniques.

1.3.1. Definition

Downhole control engineering is a discipline branch, which applies the perspectives and methods of engineering control theory to solve downhole engineering control issues in oil and gas wells. It is a combination of engineering control theory and downhole techniques in oil and gas well engineering. It is an application technology field with interdisciplinarity. From the engineering perspective, it involves drilling, well completion, well testing, well logging, oil production, well repair, and all other operations related to the downhole techniques of oil and gas wells. From the control perspective, it involves open-loop remote control and downhole closed-loop automatic control.

1.3.2. Research objects, purposes and properties

The research objects of downhole control engineering are all engineering control issues involved in various operating processes of oil and gas wells.

The purposes of studying downhole control engineering are to theoretically identify the physical properties of the downhole control issues and the basic laws of the control procedures, and develop and provide effective control systems, techniques and methods in practice, and solve engineering problems optimally from both technical and economical aspects.

Both the special structure of oil and gas wells and the extreme working conditions make the downhole control difficult and complex, and also determine the research properties of downhole control engineering, namely, it is a interdisciplinarity application technology field with high requirements on both theory and practicability.

1.3.3. Discipline characteristic

Downhole control engineering is an application technology field which integrates theoretical research, product development and experimental research. It features multi-specialty and multi-discipline, which can be summarized as follows: it takes downhole as the object, control as the goal, mechanics as the basis, machine as the subject, fluid as medium, computer as the means, and experiment as the support.

As a discipline branch, downhole control engineering consists of the following four basic parts.

1.4.1. Study on theoretical basis

The theoretical basis of downhole control engineering is downhole system dynamics and control signal analysis theory. As the downhole system is a complex system with multi-body coupling effects, a series of theoretical models should be established to describe the dynamic characteristics of the downhole system, the purpose of which is to determine the distributions and variations of important physical parameters (such as velocity, acceleration, stress, displacement, pressure, amplitude, and frequency, etc.), thus establishing the basic theory of downhole system dynamics. There are some special requirements on downhole-system control signals. It is necessary to study its occurrence and transmission process, and determine its dynamic quality and stability indicators, which can be further used to optimize the control signal.

1.4.2. Investigation on technological basis

The technological basis of downhole control engineering includes the downhole control mechanism with system design and the downhole parameter acquisition with transmission technology. For a variety of practical control signals applicable to downhole control, the corresponding signal generation, transmission, amplification and execution mechanisms must be designed. The typical structures of these mechanisms must be determined, and the structural libraries and characteristic simulation libraries for various types of signal control mechanisms must be established to reach the modular design level. Downhole parameters can be divided into state parameters and control parameters. State parameters are various geometric parameters and physical parameters that describe the working boundary and work process characteristics of the downhole system. Hence, many state parameters are used in the control process. It is necessary to study the measurement methods and means for different kinds of downhole state parameters and control parameters, as well as the methods and practical techniques of these parameter signals for the downhole short transmission and the two-way transmission between downhole and ground.

1.4.3. Product development

The application objective of this discipline branch is to research and develop a number of control tools and control systems required for different downhole operations to solve actual production problems. Mechanical-electrical-hydraulic integration is often the basic feature of the downhole control system. It is a comprehensive application of downhole control mechanism design techniques. Due to the diversity and practicality of the developed products, downhole control engineering will have a highly targeted professional application range and can generate great economic and social benefits, and is expected to form a new high-tech industry.

1.4.4. Laboratory construction and experimental research

The corresponding laboratory is a support for downhole control engineering. The theoretical analysis results need to be verified by experiments. The key structural parameters in the design are generally determined by experiments. In particular, the coefficients related to real fluid systems can only be worked out through experiments. Therefore, in the downhole system dynamics and signal analysis theory research, downhole control mechanism design research, downhole parameter acquisition and transmission technology research, and product development, experimental research has a non-negligible role.

The correlation among the above four parts is that, the product development is the main purpose of downhole control engineering research; the research of technological basis is the foundation of the product development; the research of theoretical basis is the basis of technical research; laboratory construction and experimental research are important means and support for the research of the theoretical basis, the research of the technological basis and the product development. The practical significance of the research of theoretical and technological basis is to form a modular design method, so that the product developers who did not engaged in the research of the theoretical and technological basis can complete the design and development of products by the approach of “ building blocks” according to the above hardware structure library and characteristic emulation library. This will reduce the difficulty of product development, improve the product design level and expand the application scope of downhole control engineering.

Drilling engineering originated in China in the 3rd century BC, when ancient Chinese ancestors collected brines via drilling, which even achieved a certain scale of production in Zigong, Sichuan Province^{[1, 2]}. The modern oil and gas well drilling engineering started in the West. In the 19th century, foreign industrial countries used cable drilling to drill oil and gas wells, which is the foundation for the development of the modern petroleum industry in the 20th Century^[3]. Between the late 19th and early 20th centuries, percussion drilling was replaced by rotary drilling as the main drilling method in the world. In the 1930s, downhole power drilling tools were invented, which accelerated the development of directional well technology in the 1950s to 1960s^{[4, 5]}. Since then, due to the introductions of engineering mechanics, computer technology and information technology, as well as the promotions of material science and downhole tools, the directional well technology for horizontal wells and extended-reach wells was further developed. The contemporary technology of oil well drilling engineering is a comprehensive system engineering which includes pre-drilling, drilling, completion, and oil and gas testing. It involves ground equipment, downhole tools, well trajectory control, drilling fluid and reservoir protection, measurement and testing, completion and cementing, and it is an application technology discipline involving several majors such as machinery, mechanics, chemistry and control.

2.1.1. Development of well types

The development of well types can clearly reflect the development history of the oil and gas well drilling engineering technology in the past century, namely, from vertical wells to directional wells (deviated wells), to cluster wells, to horizontal wells, to extended-reach wells, to other special process wells (such as sidetracked horizontal wells. multi-lateral wells, inverted cluster wells, etc.).

Before the 1950s, all the oil and gas wells worldwide were vertical. Due to the limitation of technical conditions, only vertical wells can be drilled to extract oil and gas in shallow layers.

From the 1950s to the 1970s, this was a period which experienced the rapid development and popularization of directional wells and cluster wells worldwide. Directional wells are mainly drilled to solve problems such as ground obstacles, land lease rights, emergency fire fighting and make use of the natural deflection law of the formation. The development of cluster wells is to drill multiple directional wells (or vertical wells) on a wellsite in accordance with certain planning and design in order to save land occupation, reduce environmental pollution, increase drilling efficiency and reduce drilling costs.

Horizontal wells are special directional wells with a maximum well deviation angle of about 90° and a horizontal extension in the reservoir. In the process of transition from directional wells to horizontal wells, a technological stage of highly-deviated wells was experienced. Highly-deviated wells are directional wells with a maximum well deviation angle of more than 60° . Since the extensions of horizontal wells in the reservoir are several times or even hundreds times longer than the conventional vertical wells and directional wells, the production of horizontal wells can be several times or even more than ten times higher than that of conventional vertical wells and directional wells. In addition, horizontal wells can solve the water and gas coning, hence it can greatly increase the single-well output, promote oil and gas recovery, and achieve the results of fewer wells and higher production. Drilling directional wells means to solve the problems of the ground and the drilling engineering itself. The purpose of drilling horizontal wells is to solve the underground problems to increase production and recovery.

The application of horizontal drilling began in the 1950s, however, it was widely applied since the 1980s and it was further generalized in the 1990s. Between the 1980s and the 1990s, there was a stagnation period for more than 20 years, which was exactly a kind of “ scrutiny period” , just like the “ scrutiny period” of directional wells from the initial trial to large-scale development, which also lasted for more than 20 years. This “ scrutiny period” for a new technology is a reflection of calm analysis and review, a fine economic evaluation, a basic theory research, and the development and accumulation of a variety of supporting techniques. By a logical extension of this point, many “ emerging” technologies, especially significant technological advances, have such a “ scrutiny period” . This is a law.

Extended-reach wells are the further development of highly- deviated wells. They are characterized by long highly-deviated steady inclined section and large horizontal displacement. Its development trend is to combine with horizontal well technology to form extended-reach horizontal wells. The technology of extended-reach wells began with the offshore drilling in the late 1970s. Its purpose was to maximize the control area of oil to reduce the number of platforms. Since the 1980s and especially the 1990s, the technology of extended-reach wells has developed rapidly. At present, extended-reach wells with a horizontal displacement of more than 10 km have been drilled^[6], and the application field of this technology has been extended to onshore drilling, where extended-reach wells have been used to extract marine oil onshore and further reduce development costs.

Special drilling techniques such as sidetracked wells and multi-lateral wells (also known as multi-bore wells) are showing increasingly vigorous development. The short radius and medium-short radius horizontal wells sidetracked from old wells by combining the old well sidetracking technology and the horizontal well technology can significantly increase the recovery rate and reduce the drilling cost. Multi-lateral wells enable multiple-zone production in a single well and are receiving increasing attention. In addition, the U.S. and Canada combined mining (metal ore and coal) technology with oil drilling technology to drill multiple “ inverted cluster wells” using large-bore shafts and downhole artificial roadways, to produce extra-heavy oil by making use of gravity successfully.

At present, the technology for drilling straight wells is still developing, with emphasis on deep wells and ultra-deep vertical wells under complex geological conditions. There are already a large number of wells whose well depths exceed 7000 m worldwide. China drilled the Well Tashen 1, whose well depth reaches 8408 m. Germany set up the KTB project to study the physical and chemical properties of the continental crust. It planned to drill an ultra-deep well with 10 000 m and actually drilled 9 001 m. The former Soviet Union drilled a well with the depth 12 262 m (Well С г -3) in the Kola Peninsula for 17 years, which becomes a global open laboratory for the study of crust structure^[3].

Compared with the beginning of the 20th century, in oil and gas well drilling, significant changes have taken place in the surface equipment, downhole tools, drilling fluids, etc. Moreover, the technical links such as well trajectory measurement, control, reservoir protection, and well completion have been established, so that drilling engineering becomes a modern engineering science discipline.

From the development process of drilling engineering technology over 100 years, the following points can be drawn. Firstly, the demand of oil and gas exploration and development is always the strongest driving force for the advancement of drilling technology. Secondly, the evolution of well type shows that the drilling technology has shook off from the limitation of “ simply completing a hydrocarbon channel” and is increasingly becoming an important way to increase the encounter ratio and the recovery ratio. Thirdly, the development trend of drilling technology in the future is to drill the exact wells which can reduce the cost of tonnage oil and improve overall efficiency. Meanwhile, drilling along reservoirs and drilling multiple underground oil and gas targets in a well will be the important technical directions^{[6, 7]}. Fourthly, the key to meet the needs of drilling engineering is to improve the well trajectory control technology.

2.1.2. Development of trajectory control technology

Well trajectory control is one of the fundamental and key aspects of drilling engineering technology. The demand for oil and gas exploitation promotes the evolution and development of well type. The development of well type promotes the development of the theory and technology for well trajectory control, while the development of well trajectory control technology is the basis for the further development of well type.

The modern well trajectory control theory and technology system is formed on the fusion of drilling engineering, engineering mechanics, machinery, control, computer, instrumentation, etc.. From the 1880s to the 1990s, the development of well trajectory control technology can be roughly divided into the following stages^[3].

(1) The first stage (before the 1950s), the well drilling was performed by experiences. In the 1920s, the problem of well deviation of vertical wells and its seriousness were realized ^[8]. In 1928, stabilizers were firstly used in drilling. Researchers and drilling engineers tried to apply the weight of drill collar to reduce well deviation, and used the elastic theory of the beam to analyze the bending and stability of the drill string in the vertical well, to explore the techniques for controlling well deviation, however there was no breakthrough.

(2) The second stage (from about 1950 to the early 1980s), the template and software for well deviation control were provided through theoretical analysis. In 1950, a famous American scholar Lubinski A proposed a mechanical model of the bending drill string in vertical well^[9], which was an important milestone in the history of well trajectory control research. Since then, a variety of theoretical algorithms have been developed, which can be divided into four kinds of representative methods, i.e., the differential equation method^[9], the finite element method^[10], the energy method^[11], and the vertical and horizontal bending method^{[8, 12]}. Their corresponding calculation charts and software have provided theoretical and technical supports for field application. At this stage, drilling engineering evolved from “ technology” to “ science“ . The analyses of the force and deformation of the bottom hole assembly, the analysis of interaction between the formation and the drill bit, and the prediction of borehole trajectory constitute the three major aspects of this “ science“ ; while the computer application is its external feature. Taking the analyses of the force and deformation of the bottom hole assembly as an example, in addition to the diversity of solving methods, the research evolved from one-dimension to three-dimension, from static to dynamic, and from small deformation to large deformation^{[8, 9]}. At this stage, the objects of the well trajectory control evolved from vertical wells to directional wells, cluster wells, and even horizontal wells. The control objectives evolved from the simple well deviation control to the controls of the rate of over-all angle change, the build-up rate and the rate of direction change.

(3) The third stage (from about the early 1980s to the 1990s), the well trajectory was controlled in real time based on the measurement information provided by the steering tool. Well trajectory measurement instruments experienced the development from hydrofluoric acid bottle inclinometers, to single-shot inclinometers, to multiple-shot inclinometers, cabled inclinometer, to measure while drilling. As the steering tool allowed the well trajectory control to enter into the third stage, the accuracy of the trajectory control decision had been greatly improved. At present, the most advanced steering tool is measure while drilling, it overcomes the shortcoming of the cabled inclinometer, which can only be used in the “ slide drilling” state; since measure while drilling can be used in the “ rotary drilling” state. The measure while drilling with high configuration can measure more than 10 parameters, which include not only the directional parameters such as well deviation, azimuth and tool face, but also the working parameters such as weight on bit, torque on bit, downhole vibration and annular temperature, as well as geological parameters such as natural gamma, formation resistivity, density, neutron porosity, etc. This kind of instrumentation system is commonly known as a logging-while-drilling tool.

The development from the first stage to the third stage is a major advance in well trajectory control technology, and it is the result of the introduction of engineering mechanics and computer technology into drilling engineering. However, the problems and difficulties in the well trajectory control technology cannot completely be solved only by mechanical models and calculation software. The reasons are as follows^[13].

(1) The mechanical models of bottom hole assembly (BHA) were built on simplifications and assumptions, the calculated results have a deviation from the actual results. For example, the inside wall of the wellbore is often assumed as a regular smooth cylinder, but this is not the case in the field, which affects the contact state of the drill string with the wellbore wall and may affect the obtained lateral force. Although some analyses of the BHA dynamics take the effects of torque and the variations of weight on bit into account, there is still a gap between the simplified load spectrum and the actual one. In addition, some of the input parameters of the BHA model have only nominal properties, such as weight on bit and torque on bit, which are currently replaced by the measurements shown on the surface instruments. However, for directional wells and horizontal wells, due to the prominent frictional resistance, the actual weight on bit and torque on bit are far from their nominal values, which inevitably affects the calculation result of the lateral force of the drill bit. Strictly speaking, all the lateral forces determined by mechanical models and method are only nominal.

(2) There are differences between the experimentally simulated anisotropy index of the formation and the actual downhole rock properties, such as confining pressure, the assumption of uniform and continuous rock anisotropy, etc. In addition, some of the experimental devices for measuring the transverse cutting index of the drill bit do not eliminate the effects of friction, which also causes systematic errors in the calculation results.

(3) The existing control method basically relies on the dynamic analysis of the BHA to determine the drilling assembly. Once the drilling assembly is applied in the wellbore, the characteristics of the entire drilling system have been generally determined, and only the partial regulation can be performed, such as changing the weight on bit, varying the rotation speed or adjusting the tool face. If the mechanical properties of BHA are not accurately estimated or if the actual drilling trajectory deviates significantly from design due to the effects of strata and other random factors, drilling assembly has to be replaced. In particular, for the horizontal wells with oil sheet, the stringent requirements on the well trajectory often require frequent tripping and replacement of drilling assembly, leading to the increase of drilling costs.

The mechanical model error, the measurement parameter error, the difficulty in acquiring some important calculation parameters in actual operation, the unchangeable BHA structure and characteristics, and the traditional control methods, all of them seriously restrict the effectiveness precision of well trajectory control technology, which makes it difficult to meet the accuracy and efficiency requirements of well trajectory control for ultra-thin oil reservoirs and complex structural wells.

How to overcome the error caused by the mechanical model of BHA in the actual drilling process? How to implement high-precision control when there are no accurate parameters available? How to timely change the inherent structure and inherent mechanical properties of BHA in drilling? How to drill into the target area when changes occur in the target location (caused by geological errors)? How to control the bit direction underground to make it accurately drill into the reservoir? These important issues caused deep thinking of the author and his colleagues in the mid-late 1980s.

Considering that every major advance in drilling technology is the result of the introduction and combination of other disciplines and new technologies, meanwhile considering the commonality of drill bit and aircraft in attitude and trajectory control, and considering the successful application of engineering cybernetics in missile guidance^[14], the author came up with the idea of introducing engineering control theory and aircraft guidance technology into oil and gas well drilling engineering to develop well trajectory control theory and technology. After a period of analogy, analysis and in-depth research, the author proposed a new research direction, namely, the well trajectory control theory and technology, in 1988, and hoped for “ downhole closed-loop control“ and “ use of means to solve problems” . The road in the beginning was difficult and cautious. From the judgment of the nature of the problem to the introduction or establishment of a new concept, from the thinking and definition of the connotation of the new field to the decomposition of a series of research topics, and from the deduction and determination of the system model, equations and boundary conditions to the conception and design of a patent program, the process was accompanied by repeated wandering, self-examination, self-questioning and self-verification and was basically conducted and completed in an “ amateur” manner. At the end of 1991, the author discovered from technology news reported that some foreign counterparts were also working on or were beginning to work on this direction, and they also adopted the “ closed-loop control” concept and formulation, which further strengthened the confidence of the author in continuing this research direction.

Specifically, it includes the dynamics model of the downhole system (drillstring-inner fluid-annular fluid); the load properties of the downhole system and the initial and boundary (state of bottom hole and borehole wall) conditions; quantitative description of several physical fields (pressure field, velocity field, flow rate field, and dynamics field) of the downhole system; dynamic analysis and stability evaluation method of downhole control signals; analysis of downhole control signal transmission process, analyses of transfer function and frequency spectrum characteristics; and screening of downhole practical control signal.

Specifically, it includes the design methods and principles of signal generation, transmission and actuating elements; the design and analysis of generation, transmission and actuating elements of various practical control signals; the computer simulation of the generation, transmission and actuating elements of various practical control signals; the overall design method and principle of the downhole control system; the system synthesis and modular design methods for different control signals; the intelligent basic algorithm and system simulation of the downhole control system; the dynamic debugging method and technical evaluation of downhole control system; structural module library and simulation software library for various control signal subsystems (organizations); a variety of parameter acquisition methods and device (sensor) design; and the methods to improve the signal transmission characteristics (frequency and quality).

With respect to product development, the control tools and systems should be developed according to the control requirements of various downhole operations (such as drilling, well completion, well testing, logging, oil recovery, and workover). For example, for the drilling process, a variety of open-loop remote-controlled downhole tools and closed-loop automatic control tools and instrument systems are mainly being developed based on the geometric guidance and geo- steering of the well trajectory.

The laboratory should be capable of testing the results of the above-mentioned various theoretical studies, determining critical structural dimensions, assembling and tuning experimental prototypes, etc. Because of the particularity of the structure and working conditions of oil and gas wells, it is necessary to study the corresponding effective experimental methods and form relevant technical standards and operating procedures, and it is also necessary to design and develop special experimental equipment according to experimental requirements.