Method of and system for controlling directional drilling

Abstract

A method of and system for controlling directional drilling determines a relationship between surface drill string orientation angle and drill bit face angle. The method uses the relationship to determine a predicted drill bit face angle. The method then uses the predicted drill bit face angle to achieve a target drill bit face angle by calculating a surface drill string correction angle. The correction angle may be displayed to a human driller. Alternatively, the correction angle may be provided as an input to an automated drilling machine.

Description

FIELD OF THE INVENTION

[0002] The present invention relates generally to the field of oil and gas well drilling. More particularly, the present invention relates to a method of and system for controlling directional drilling.

DESCRIPTION OF THE PRIOR ART

[0003] It is very expensive to drill bore holes in the earth such as those made in connection with oil and gas wells. Oil and gas bearing formations are typically located thousands of feet below the surface of the earth. Accordingly, thousands of feet of rock must be drilled through in order to reach the producing formations. Additionally, many wells are drilled directionally, wherein the target formations may be spaced laterally thousands of feet from the well's surface location. Thus, in directional drilling, not only must the depth but also the lateral distance of rock must be penetrated.

[0004] The cost of drilling a well is primarily time dependent. Accordingly, the faster the desired penetration location, both in terms of depth and lateral location, is achieved, the lower the cost in completing the well.

[0005] While many operations are required to drill and complete a well, perhaps the most important is the actual drilling of the bore hole. In order to achieve the optimum time of completion of a well, it is necessary to drill at the optimum rate of penetration and to drill in the minimum practical distance to the target location. Rate of penetration depends on many factors, but a primary factor is weight on bit. In mud motor bent sub directional drilling, the best indication of weight on bit is mud motor differential pressure.

[0006] As disclosed, for example in Millheim, et al., U.S. Pat. No. 4,535,972, rate of penetration increases with increasing weight on bit until a certain weight on bit is reached and then decreases with further weight on bit. Thus, there is generally a particular weight on bit that will achieve a maximum rate of penetration.

[0007] Drill bit manufacturers provide information with their bits on the recommended optimum weight on bit. However, the rate of penetration depends on many factors in addition to weight on bit. For example, the rate of penetration depends upon characteristics of the formation being drilled, the speed of rotation of the drill bit, and the rate of flow of the drilling fluid. Because of the complex nature of drilling, a weight on bit that is optimum for one set of conditions may not be optimum for another set of conditions.

[0008] Directional drilling has been a combination of art and skill as well as science and engineering. The direction of drilling is determined by the azimuth or face angle of the drilling bit. Face angle information is measured downhole by a steering tool. Face angle information is typically conveyed from the steering tool to the surface using relatively low bandwidth mud pulse signaling. The driller attempts to maintain the proper face angle by applying torque corrections to the drill string. However, because of the latency in receiving face angle information, the driller typically over- or under-corrects. The over- or under-correction results in substantial back and forth wandering of the drill bit, which increases the distance that must be drilled in order to reach the target formation. Back and forth wandering also increases the risk of stuck pipe and makes the running and setting of casing more difficult.

SUMMARY OF THE INVENTION

[0009] The present invention provides a method of and system for controlling directional drilling by determining a relationship between a first drilling control variable and drill bit face angle. The method and system of the present invention use the relationship to determine a predicted drill bit face angle. The method and system then use the predicted drill bit face angle to achieve a target drill bit face angle by calculating a surface drill string correction angle. The correction angle may be displayed to a human driller. Alternatively, the correction angle may be provided as an input to an automated drilling machine.

[0010] The method and system of the present invention determine the relationship between the first drilling control variable and the drill bit face angle by collecting drill bit face angle and control variable data. The method and system periodically perform linear regression of the drill bit face angle and first drilling control variable data, to obtain a mathematical model with drill bit face angle as response variable and first drilling control variable as an explanatory variable. The method and system determine the predicted drill bit face angle by solving the mathematical model for a measured first drilling control variable value.

[0011] The method and system of the present invention also optimize rate of penetration. The method and system determine a relationship between rate of penetration and a second drilling control variable. The method and system determine a target second drilling control variable value, based upon the relationship between rate of penetration and the second drilling control variable. A driller maintains the control variable at the target control variable value. As in the case of the correction angle, the target second drilling control variable may be displayed to a human driller or inputted to an automated drilling machine.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] FIG. 1 is a pictorial view of a directional drilling system.

[0013] FIG. 2 is a block diagram of a directional driller control system according to the present invention.

[0014] FIG. 3 is a pictorial view of a display screen according to the present invention.

[0015] FIG. 4 is a flowchart of data collection and generation according to the present invention.

[0016] FIG. 5 is a flowchart of display processing according to the present invention.

[0017] FIGS. 6A-C comprise a flowchart of rate of penetration processing according to the present invention.

[0018] FIG. 7 is a flowchart of face angle processing according to the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0019] Referring now to the drawings and first to FIG. 1, a drilling rig is designated generally by the numeral 11. Rig 11 in FIG. 1 is depicted as a land rig. However, as will be apparent to those skilled in the art, the method and system of the present invention will find equal application to non-land rigs, such as jack-up rigs, semisubmersibles, drill ships, and the like.

[0020] Rig 11 includes a derrick 13 that is supported on the ground above a rig floor 15. Rig 11 includes lifting gear, which includes a crown block 17 mounted to derrick 13 and a traveling block 19. Crown block 17 and traveling block 19 are interconnected by a cable 21 that is driven by draw works 23 to control the upward and downward movement of traveling block 19. Traveling block 19 carries a hook 25 from which is suspended a top drive 27. Top drive 27 supports a drill string, designated generally by the numeral 31, in a well bore 33. According to an embodiment of the present invention, drill string 31 is coupled to top drive 27 through an instrumented sub 29. As will be discussed in detail hereinafter, instrumented top sub 29 includes sensors that provide torque and angular position information according to the present invention.

[0021] Drill string 31 includes a plurality of interconnected sections of drill pipe 35 a bottom hole assembly (BHA) 37, which includes stabilizers, drill collars, and a suite of measurement while drilling (MWD) instruments including a steering tool 53. As will be explained in detail hereinafter, steering tool 53 provides bit face angle information according to the present invention.

[0022] A bent sub mud motor drilling tool 41 is connected to the bottom of DHA 37. As is well known to those skilled in the art, the face angle of the bit of drilling tool 41 used to control azimuth and pitch during sliding directional drilling. Drilling fluid is delivered to drill string 31 by mud pumps 43 through a mud hose 45. During rotary drilling, drill string 31 is rotated within bore hole 33 by top drive 27. As is well known to those skilled in the art, top drive 27 is slidingly mounted on parallel vertically extending rails (not shown) to resist rotation as torque is applied to drill string 31. During sliding drilling, drill string 31 is held in place by top drive 27 while the bit is rotated by mud motor 41, which is supplied with drilling fluid by mud pumps 43. Although a top drive rig is illustrated, those skilled in the art will recognize that the present invention may also be used in connection with systems in which a rotary table and kelly are used to apply torque to the drill string The cuttings produced as the bit drills into the earth are carried out of bore hole 33 by drilling mud supplied by mud pumps 43.

[0023] Referring now to FIG. 2, there is shown a block diagram of a preferred system of the present invention. The system includes a mud pump pressure sensor 51. Pump pressure sensors are well known in the art. Preferably, they produce a digital pressure value at a convenient sampling rate, which in the preferred embodiment is five times per second although other sampling rates may be used. Pump pressure provides an indication of weight on bit. In relatively straight holes, weight on bit can be measured or computed directly. However, in highly deviated holes, direct measurement or computation of weight on bit is difficult if not impossible. Therefore, in the present invention, weight on bit is inferred from pump pressure or pressure differential (Delta_P). The driller applies weight to the bit effectively by controlling the height or position of hook 25 in derrick 13. The driller controls the position of hook 25 by operating a brake to control the paying out of cable from drawworks 23.

[0024] Referring still to FIG. 2, the system of the present invention includes a hook speed/position sensor 52. Hook speed sensors are well known to those skilled in the art. An example of a hook speed sensor is a rotation sensor coupled to crown block 17. A rotation sensor produces a digital indication of the magnitude and direction of rotation of crown block 17 at the desired sampling rate. The direction and linear travel of cable 21 can be calculated from the output of the hook position sensor. The speed of travel and position of traveling block 19 and hook 25 can be easily calculated based upon the linear speed of cable 21 and the number of cables between crown block 17 and traveling block 19. According to the present invention, hook speed provides an indication of rate of penetration (ROP).

[0025] The system of the present invention includes a steering tool 53, which produces a signal indicative of drill bit face angle. Typically, steering tool uses mud pulse telemetry to send signals to a surface receiver (not shown), which outputs a digital face angle signal. However, because of the limited bandwidth of mud pulse telemetry, the face angle signal is produced at a rate of once every several seconds, rather than at the preferred five times per second sampling rate. For example, the sampling rate for the face angle signal may be about once every Twenty seconds.

[0026] The system of the present invention also includes a drill string angle sensor 54, which provides an indication of the angular orientation of the drill string entering the well bore. The drill string angle sensor is included in instrumented top sub 29 illustrated in FIG. 1. Substantial reactive torque is stored in the form of twists or wraps in the drill string. Thus, the angular orientation of the drill string entering the well bore is not the same as the face angle of the drill bit. Also, due to the elastic nature of the drill sting and contact with the wall of the well bore, there are delays between the time torque is applied to the drill string at the surface and when the face angle changes at the bottom. Moreover, a particular angular change of drill string orientation at the surface does not necessarily produce the same face angle change at the bottom of the hole. The drill string angle sensor is coupled to the top drive to provide a digital signal at the preferred sampling rate of five times per second.

[0027] In FIG. 2, the digital outputs of sensors 51-54 are received at a processor 55. Processor 55 is programmed according to the present invention to process data received from sensors 51-54. Processor 55 receives user input from user input devices, such as a keyboard 57. Other user input devices such as touch screens, keypads, and the like may also be used. Processor 55 provides visual output to a display 59. Processor 55 may also provide output to an automatic driller 61, as will be explained in detail hereinafter.

[0028] Referring now to FIG. 3, a display screen according to the present invention is designated by the numeral 63. Display screen 63 includes a target Delta_P display 65 and a current Delta_P display 67. According to the present invention, a target Delta_P is calculated to achieve a desired rate of penetration. Target Delta_P display 65 displays the target Delta_P computed according to the present invention. Current Delta_P display 67 displays the actual current Delta_P.

[0029] As will be explained in detail hereinafter, the method and system of the present invention constructs a mathematical model of the relationship between Delta_P and rate of penetration for the current drilling environment. The mathematical model is built from data obtained from pump pressure sensor 51 and hook speed/position sensor 53. When a statistically valid model is created, the present invention calculates a target Delta_P, which is displayed in target Delta_P display 65. After the system of the present invention has built the model, the system continually tests the validity of the model against the data obtained from pressure sensor 51 and hook speed/position sensor 53. The system of the present invention continuously updates the model; however, the system of the present invention uses one model as long as the model is valid. If conditions change such that the current model is no longer valid, then the system of the present invention fetches the current updated model.

[0030] According to one aspect of the present invention, a driller attempts to match the value displayed in current Delta_P display 67 with the value displayed in target Delta_P display 65. According to another aspect of the present invention, the driller may turn control over to automatic driller 61. If the driller has turned control over to automatic driller 61, the driller continues to monitor display 63. If the model becomes invalid, then a flag 69 will be displayed. Flag 69 indicates that the model does not match the current drilling environment. Accordingly, flag 69 indicates that the drilling environment has changed. The change may be a normal lithological transition from one rock type to another or the change may indicate an emergency or potentially catastrophic condition. When flag 69 is displayed, the driller is alerted to the change in conditions.

[0031] Display screen 63 also includes a target face angle display 71 and a current face angle display 73. Target face angle is a value that is input according to the directional drilling plan for the well. As will be explained in detail hereinafter, current face angle is either the last face angle measured by the steering tool, or a face angle value predicted from a mathematical model of face angle as a function of surface drill string angle.

[0032] Display screen 63 also includes an angular correction display 77. Angular correction display 77 displays a recommended angular correction to apply to the drill string with the top drive in order to bring the current face angle to the target face angle. The angular correction value is calculated from a model constructed according to the present invention. The angular correction value is expressed in degrees from the current angular orientation of the drill string.

[0033] Display screen 63 also displays a moving plot 79 of rate of penetration. The target rate of penetration is indicated in plot 79 by circles 81 and the actual rate of penetration is indicated by triangles 83. By matching actual Delta_P to target Delta_P, the plot of actual rate of penetration, indicated by triangles 83, will be closely matched with the plot of target rate of penetration, indicated by circles 81, as long as the mathematical model is valid.

[0034] Referring now to FIGS. 4-7, there are shown flow charts of processing according to the present invention. In the preferred embodiment, four separate processes run in a multitasking environment. In FIG. 4 there is shown a flow chart of the data collection and generation processing of the present invention. The system receives hook rate of penetration, Delta_P, drill string orientation and face angle values from sensors 51-54, at block 101. The preferred sampling rate for hook ROP, drill string orientation and Delta_P is five times per second. Because of bandwidth limitations, face angle values are received at the rate of about once every sixteen seconds. The system calculates average ROP, drill string orientation and Delta_P over a selected time period, which in the preferred embodiment is ten seconds, at block 103. Then the system stores a face angle value and the average ROP, drill string orientation and Delta_P values with time stamps, at block 105 and returns to block 101.

[0035] Referring now to FIG. 5, there is shown display processing according to the present invention. The system displays the current average Delta_P, which is calculated at block 103, at block 107. The system displays the current average ROP, which is also calculated at block 103 of FIG. 4, at block 109. The system displays the current face angle, which as will be explained in detail hereinafter is a forecasted current value, at block 111. The system displays a target Delta_P, which is calculated according to the present invention, at block 113. The system also displays a target ROP, which also is calculated according to the present invention, at block 115. The system also displays a target face angle, which is input according to the directional drilling plan, at block 117. Finally, the system displays an angular correction, which is also calculated according to the present invention, at block 119. Then, the system tests, at decision block 121, if a flag is equal to zero. If so, processing returns to block 107. If the flag is not equal to zero at decision block 121, the system displays a flag at block 123 and display processing returns to block 107.

[0036] Referring now to FIG. 6, and particularly to FIG. 6A, there is shown a flow chart of the building of a drilling model and calculation of target rate of penetration and Delta_P according to the present invention. In the preferred embodiment, FIG. 6 processing is performed once every five seconds. First, the system cleans the data stored according to FIG. 4 processing and populates a data array, at block 131. Data cleaning involves removing zeroes and outliers from the data.

[0037] The clean data are stored in a data array. The data array includes an index column, a Delta_P column, and an ROP column. The data array also includes a first lagged ROP column and a second lagged ROP column. The first lagged ROP is denoted ROP(t-1) and the second lagged ROP is denoted ROP(t-2).

[0038] After populating the data array with clean data, at block 131, the system performs multilinear regression analysis using ROP(t) as the response variable and ROP(t-1), ROP(t-2) and Delta_P(t) as the explanatory variables, at block 133. Multiple linear regression is a well-known technique and tools for performing multilinear regression are provided in commercially available spreadsheet programs, such as Microsoft® Excel®, or commercially available mathematical or statistical tool kits, such as MATLAB®, available from MathWorks, Inc. Multiple linear regression produces a mathematical model of the drilling environment. The mathematical model of the drilling environment is an equation of the form:

ROP (t)=α+β1ROP(t-1)+β2ROP(t-2)+β3Delta—P(t),  (1)

[0039] where α is the intercept, β1 and β2 are lagged ROP coefficients and β3 is the Delta_P coefficient.

[0040] After the system has performed multilinear regression at block 133, the system searches for a potential optimum weight on bit based upon the Delta_P coefficient β3. The Delta_P coefficient β3 represents the slope of the line in the hyper plane that relates Delta_P to rate of penetration. In the neighborhood around the optimum weight on bit, the slope β3 is about equal to zero. Thus, it is a goal of the present invention to drill such that the Delta_P coefficient β3 is close to zero. However, negative Delta_P coefficients β3 are to be avoided. The greater the positive value of Delta_P coefficient β3, the further the system searches into the data array to find a potential optimum weight on bit. The system tests, at decision block 135, if Delta_P coefficient β3 is strongly negative, which in the preferred embodiment is less than −0.5. If so, the system sets the maximum data array search depth at 1, at block 137. Then the system sets Delta_P equal to the Delta_P corresponding to the maximum ROP value in the search depth, at block 139. Since the search depth is 1, there is only one candidate Delta_P. If at decision block 135, the Delta_P coefficient β3 is not strongly negative, the system tests, at decision block 141, if the Delta_P coefficient β3 is weakly negative, which in the preferred embodiment is between 0 and −0.5. If so, the system sets the maximum data array search depth equal to 5, at block 143. If not, the system tests, at decision block 145, if the coefficient β3 is weakly to moderately positive, which in the preferred embodiment is between 0 and 1. If so, the system sets the maximum data array search depth equal to 10, at block 147. If not, which indicates that the Delta_P coefficient β3 is strongly positive, the system sets the maximum data array search depth equal to 15, at block 149. Then, the system uses the maximum data array search depth set at blocks 143, 147, or 149 to find the indices with the four highest ROP(t), at block 151. Then, the system sets the Delta_P equal to the average Delta_P(t) for the four highest ROP(t) values, at block 153. The system then uses the Delta_P value determined at block 139 or block 153 to determine a target Delta_P based upon the Delta_P coefficient β3.

[0041] Referring to FIG. 6E, the system tests, at decision block 155, if Delta_P coefficient β3 is greater than a positive Delta_P incrementer determiner. The incrementer determiner is selected to keep the Delta_P coefficient β3 in the neighborhood of zero. If the Delta_P coefficient β3 is greater than the incrementer determiner, then the system sets the target Delta_P equal to the Delta P determined at block 139 or block 153 plus a Delta_P increment value, at block 157. If not, the system tests, at decision block 159 if the Delta_P coefficient β3 is less than (more negative) than the negative Delta_P incrementer determiner. If so, the system sets the target Delta_P equal to the Delta_P determined at blocks 139 or 153 minus the Delta_P increment value, at block 161. If the Delta_P coefficient β3 is between the positive Delta_P incrementer determiner and the negative Delta_P incrementer determiner, the system sets, at block 163, target Delta_P equal to the Delta_P determined at blocks 139 or 153. The target Delta_P determined at blocks 157, 161 or 163, may be higher than a preset Delta_P limit. Delta_P limit is set according to engineering and mechanical considerations. The system tests, at decision block 165, if target Delta_P is greater than the Delta_P limit. If so, system sets target Delta_P equal to the Delta_P limit, at block 167.

[0042] Referring now to FIG. 6C, after determining target Delta_P, the system calculates a target rate of penetration based upon the target Delta_P and the model of equation (1), at block 171. There are engineering reasons for limiting rate of penetration. For example, the drilling fluid system may be able to remove cuttings at only a certain rate. Drilling above a certain rate of penetration may produce cuttings at a rate greater than the ability of the fluid system to remove them. Accordingly, in the present invention, there is a preset rate of penetration limit. The rate of penetration limit may be a theoretical maximum rate of penetration, or some percentage, for example 95% of the theoretical maximum. The system tests, at decision block 173, if the target ROP is greater than the ROP limit. If not, the system sets the target ROP equal to the calculated target ROP, at block 175. If the calculated target ROP is greater than the ROP limit, then the system sets the target ROP equal to the ROP limit, at block 177. Then, the system calculates target Delta_P based upon the ROP limit and the model of equation (1), at block 179. The system then tests, at decision block 181, if the target Delta_P calculated at block 179 is greater than the Delta_P limit. If so, the system sets target Delta_P equal to the Delta_P limit, at block 183.

[0043] After completing steps 175 or 183, the system calculates a predicted ROP(t) and confidence interval at block 185. The predicted ROP is calculated by solving equation (1) for the actual current Delta_P, ROP(t-1) and ROP(t-2). The system tests, at decision block 187, if the current ROP is within the confidence interval. If so, the system sets the flag equal to zero, at block 189, and processing returns to block 131 of FIG. 6A. If, at decision block 187, the current ROP is not within the confidence interval, the system sets the flag equal to 1, at block 153.

[0044] Referring now to FIG. 7, there is shown a flow chart of face angle processing according to the present invention. A target face angle is determined according to directional drilling plan to achieve the desired path through the earth to reach a target location. The target face angle may be periodically recalculated. The system of the present invention cleans the face angle and drill string orientation data and populates a data array, at block 201. The data array is similar to that used in connection with determining the rate of penetration model. Then, as indicated at block 203, the system determines the relationship between surface drill string orientation and bit face angle. The system of the present invention may determine the relationship between drill string orientation and bit face angle by performing multiple linear regression using Face_Angle(t) as the response variable and Face_Angle(t-1), and Drill_String_Orientation(t) as explanatory variables, at block 203. The multiple linear regression step of block 203 produces an equation similar to equation (1) and of the form:

Face_Angle(t)=σ+μ1Face_Angle(t-1)+μ2Drill_String_Orientation(t),  (2)

[0045] where σ is the intercept, μ1 is the lagged face angle coefficient, and μ2 is the Drill_String_Orientation coefficient. The system then sets the current face angle equal to the actual current face angle or a forecast face angle based upon the model, at block 205.

[0046] Alternatively, the system may forecast a face angle based upon an Exponentially Weighted Moving Average (EWMA) or Box-Jenkins technique. As is well known to those skilled in the art, EWMA is a statistic for monitoring a process that averages the data in a way that gives less and less weight to data as they are further removed in time. The EWMA statistic is calculated as follows:

EWMA (t)=λY(t)+(1−λ)EWMA(t-1)  (3)

[0047] where Y(t) is the observed value at time t, and λ is a weighting constant having a value greater than zero and equal to or less than one. The weighting constant λ determines the rate at which older data enter into the calculation of the EWMA statistic. A λ value close to one gives more weight to recent data and less weight to older data. Similarly, a λ value close to zero gives more weight to older data and less weight to recent data. Usually a λ value between 0.2 and 0.3 yields a good balance between more recent and less recent data.

[0048] After the system has determined the relationship between drill string orientation and face angle, the system calculates an angular correction necessary to achieve the target face angle, at block 207. From Equation (2), 1$\begin{array}{cc}\mathrm{Drill\_String}\mathrm{\_Orientation}\left(t\right)=\frac{\mathrm{Face\_Angle}\left(t\right)-{\mu }_1\mathrm{Face\_Angle}\left(t-1\right)}{{\mu }_2}& \left(4\right)\end{array}$

[0049] According to the present invention, angular correction is expressed as the difference between the current drill string orientation and the target drill string orientation calculated by Equation (4). After calculating the angular correction at block 207, the system displays the angular correction, at block 209.

[0050] From the foregoing, it may be seen that the present invention is well adapted to overcome the shortcomings of the prior art. The system of the present invention builds mathematical models of the relationships between Delta_P and rate of penetration as well as drill string orientation and face angle, for the current drilling environment. The system continuously updates the mathematical models to reflect changes in the drilling environment. The system of the present invention enables a driller to optimize rate of penetration and control the direction of drilling simultaneously.

Claims

1. A method of controlling directional drilling, which comprises: determining a relationship between a first drilling control variable and drill bit face angle; determining, based upon said relationship, a target first control variable value to achieve a target face angle; and, correcting current first drilling control variable to said target first drilling control variable to achieve said target face angle.

2. The method as claimed in claim 1, wherein determining said relationship between said first drilling control variable and said drill bit face angle comprises: collecting drill bit face angle and first drilling control variable data.

3. The method as claimed in claim 2, wherein determining said relationship between said first drilling control variable and said drill bit face angle comprises: performing linear regression of said drill bit face angle and said first drilling control variable data, to obtain a mathematical model with drill bit face angle as a response variable and first drilling control variable as an explanatory variable.

4. The method as claimed in claim 3, wherein determining a target first control variable value to achieve a target face angle includes: solving said mathematical model for a measured first drilling control variable value.

5. The method as claimed in claim 1, wherein correcting a current first drilling control variable to said target first drilling control variable to achieve a target face angle. calculating a surface drill string correction angle to achieve said target face angle.

6. The method as claimed in claim 5, including displaying said correction angle.

7. The method as claimed in claim 5, including inputting said correction angle to an automatic drilling machine.

8. The method as claimed in claim 1, wherein said control variable is surface drill string orientation.

9. The method as claimed in claim 1, including: determining a relationship between rate of penetration and a second drilling control variable; determining a target second drilling control variable value, based upon said relationship between rate of penetration and said second drilling control variable, to achieve an optimum rate of penetration; and, maintaining said second drilling control variable at said target second drilling control variable value.

10. The method as claimed in claim 9, wherein determining said relationship between rate of penetration and said second drilling control variable includes: collecting rate of penetration data.

11. The method as claimed in claim 10, wherein determining a relationship between rate of penetration and said second drilling control variable includes: performing linear regression of said rate of penetration data and said second drilling control variable data, to obtain a mathematical model with rate of penetration as response variable and second drilling control variable as an explanatory variable.

12. The method as claimed in claim 9, wherein maintaining said second drilling control variable at said target second drilling control variable value includes: displaying said target second drilling control variable value.

13. The method as claimed in claim 9, wherein maintaining said second drilling control variable at said target second drilling control variable value includes: inputting said target drilling control variable value to an automatic drilling machine.

14. The method as claimed in claim 9, wherein said second drilling control variable is pressure differential.

15. A directional drilling control system, which comprises: means for determining a relationship between a first drilling control variable and a drill bit face angle; means for predicting, based upon said relationship, a target first drilling control variable to achieve a target drill bit face angle; and, means for determining a correction to said target first drilling control variable to achieve a target face angle.

16. The system as claimed in claim 15, wherein said means for determining said relationship between said drilling control variable and said drill bit face angle comprises: means for collecting drill bit face angle and first drilling control variable data.

17. The system as claimed in claim 16, wherein said means for determining said relationship between said first drilling control variable and said drill bit face angle comprises: means for performing linear regression of said drill bit face angle and said first drilling control variable data, to obtain a mathematical model with drill bit face angle as response variable and first drilling control variable as an explanatory variable.

18. The system as claimed in claim 17, wherein said means for predicting said predicted drill bit face angle includes: means for solving said mathematical model for said first drilling control variable value.

19. The system as claimed in claim 15, wherein said means for determining a correction to said target first drilling control variable to achieve a target face angle includes: means for calculating a surface drill string correction angle to achieve said target face angle.

20. The system as claimed in claim 19, including a display for displaying said correction angle.

21. The system as claimed in claim 15, including: means for determining a relationship between rate of penetration and a second drilling control variable; means for determining a target control variable value, based upon said relationship between rate of penetration and said second drilling control variable, to achieve an optimum rate of penetration.

22. The system as claimed in claim 21, wherein said means for determining said relationship between rate of penetration and said second drilling control variable includes: means for collecting rate of penetration data.

23. The system as claimed in claim 22, wherein said means for determining a relationship between rate of penetration and said second drilling control variable includes: means for performing linear regression of said rate of penetration data and said second drilling control variable data, to obtain a mathematical model with rate of penetration as response variable and second drilling control variable as an explanatory variable.

24. The system as claimed in claim 21, including a display for displaying said target second drilling control variable value.

25. The system as claimed in claim 21, including: an automatic drilling machine arranged to receive said target control variable value.

26. A method of drilling, which comprises: determining a relationship between surface drill string angular orientation and drill bit face angle; determining, based upon said relationship, a target surface drill string angular orientation to achieve a target face angle; correcting current surface drill string angular orientation to said target surface drill string angular orientation to achieve said target face angle; determining a relationship between rate of penetration and a drilling control variable; determining a target drilling control variable value, based upon said relationship between rate of penetration and said drilling control variable, to achieve an optimum rate of penetration; and, maintaining said drilling control variable at said target second drilling control variable value.