Errors inherent in Directional Surveying with MWD tools.

Traditionally there is a cone of error associated with directional surveys taken whilst drilling with any given survey tool to account for the inherent resolution within and accuracy of the tool.

However, there are many other more significant errors that are recognized to exist by certain sectors of the industry, but not generally accepted and accounted for in practice.

This article does not propose any one solution, or endorse any commercial product. However, when anti-collision and accurate well bore placement in a reservoir is required, then the errors discussed herein should be borne in mind.It is also hoped that this article will promote discussion and raise awareness of some very real issues in well-bore survey accuracy.

The main areas this article tries to evaluate are;

a)Real Hole Curvature.

b)Bent sub effect on Bent Housing motor BHAs

c)Stretch of Drill Pipe under its own weight.

d)Thermal Expansion.

e)Stretch of Drill Pipe due to hydraulics and buoyancy.

f)Axial misalignment of pipe in the well bore.

A) Real Hole Curvature between surveys.

If a man was walking along and was sensory derived apart from knowing the inclination of his foot (say every time 90 degrees), then he would have no clue if he was;Walking along a flat surface, walking up stairs, or walking down stairs. (fig 1).

Fig 1.

The same can be said for directional surveying. It is highly erroneous to assume a constant curve (as with the Minimum Curvature method), when the actual well path is very seldom constant. Failing to describe the well path between surveys can lead to potentially catastrophic errors.

Assume a Steerable motor is in the hole, and the following surveys are reported (fig 2);

Fig 2.

The natural assumption is that the TVD has not changed.

However if the motor BHA was dropping angle at a rate of 1 degree per 100ft and a slide of 15ft per stand was being conducted to compensate for this, the real situation would be as follows (Fig 3);

Fig 3.

This equates to an error of 0.7 ft per 93ft of drilled hole (a little over 7.5 ft per 1000ft).

The same situation occurs when drilling with the new generation of rotary Steerable systems, typically the strength of deflection is changed at a depth between survey stations, so again a compound curvature is produced between surveys.

So far there is no officially recognized solution to this problem; however one method I would suggest is the use of a “virtual” or “synthetic” survey to give reality to the survey. Even though there is no definite proof that the inserted survey is correct, it at least gives a more accurate result than the current practice of just recording the actual survey points.

Another way of describing the well bore better would be with the use of dynamic or “on the fly” surveys. Some types of MWD tools can produce an on-going survey whilst in drill ahead mode. As this data is normally from a single axis sensor it is considered to be not useful as a definitive survey, but is often used by Directional Drillers to spot trends whilst drilling ahead, however, this data could be harnessed to describe the well bore and tied onto the official surveys.

For simplicity here a simple build section is considered, however there will be similar errors in Northings and Eastings when the well is changing azimuth, and/or the well path calls for a compound change in inclination and azimuth.

If the well bore were to be modeled before drilling, using these “virtual” surveys, a more accurate well path could be described to estimate hole tortuosity. Similar, a more accurate picture could be built up using traditional Torque and Drag models to predict loads on equipment and Drilling Mechanic scenarios.

B) Bent Sub Effect.

When drilling with a Steerable Motor BHA, the MWD tool is not coincidental with the axis of the hole due to the effect of the bent housing which tends to offset the tubulars slightly.

This is recognized in low angle Kick-offs and compensated for by performing a “cluster shot”. This is a series of four surveys taken at the same depth, but with the pipe turned approx 90 degrees. By vector additionof the four surveys a bias can be calculated for any particular Tool-face. By knowing the tool-face when the survey is taken, the resulting survey can be corrected accordingly.

Example.

The four MWD surveys are taken;

1)10000ft56.5 Inc123.0 AziTool Face 75 deg

2)10000ft56.4 Inc124.6 AziTool Face 167 deg

3)10000ft55.8 Inc126.1 AziTool Face 248 deg

4)10000ft55.7 Inc125.3 AziTool Face 340 deg

These surveys may be represented graphically as follows;

Fig 4.

The vector addition of these points is (A to E) divided by 4 (Fig 4).

Mathematically this can be expressed as;

X1 = Inc1 x Sin Azi 1 (shot 1 above)Y1 = Inc 1 x Cos Azi 1 (shot 1 above)

X2 = Inc 2 x Sin Azi 2 (shot 2 above)Y2 = Inc 2 x Cos Azi 2 (shot 2 above)

X3 = Inc 3 x Sin Azi 3 (shot 3 above)Y3 = Inc 3 x Cos Azi 3 (shot 3 above)

X4 = Inc 4 x Sin Azi 4 (shot 4 above) Y4 = Inc 4 x Cos Azi 4 (shot 4 above)

X = (X1 + X2 + X3 + X4) / 4Y = (Y1 + Y2 +Y3 + Y4) / 4

Final Inclination = √(X2 + Y2)Final Azimuth = Arc Tan (X / Y).

(Also note that if y < 0, then add 180 to final azimuth. If X and Y are both zero, then the well is vertical). The actual Tool face angles have no part of the final calculation, but should be recorded to ensure the tool faces are spaced sufficiently to give a meaningful spread in the recorded surveys.

In the example above the final compensated survey = 56.08 Inclination and 124.76 Azimuth. The difference to taking a survey at an arbitrary tool-face can be seen.

By taking a cluster shot for every 10 degrees of inclination a bias can be built into the surveys to compensate for the axial misalignment from the steerable motor bent housing assembly.

Some operators choose to “sag correct” the directional surveys. This practice is to account for the misalignment of the MWD tool axis due to the placement of stabilizers (fig 5).

In the sketch below, which is a sample Steerable Motor BHA, it can be seen that the MWD tool would in fact “sag” in the direction of the arrow. This correction does not take into account the effect of the angular position of the bent housing Tool-Face, and so only gives a partial correction with regards to inclination measurement.

Fig 5.

C)Stretch due to pipe weight.

A sting of drilling tubulars will stretch due to its own weight. Also, as long as the Elastic Limit of the pipe is not exceeded, the Grade of pipe should have no effect on the strain (stretch) for a given stress (weight applied). To calculate the total effect different sections should be calculated and effects are cumulative.

Assuming the modulus of elasticity for steel as 30,000,000 lbs/sq.in.

Taking weight in AIR. (Buoyancy does not affect stretching due to weight, but for the sake of this effect may be considered as giving a piston effect to the tubulars)

Length change = (length of pipe x average weight) / (Mod of elasticity x CSA of pipe)

CSA of pipe = (OD2 – ID2) 0.7854

Eg.

5000 ft of drill pipe, 19.5 lb/ft

Total weight = 5000 x 19.5 = 97500

Average weight = 97500/2 = 48750 lbs

CSA = (5x5 – 4.23x4.23)0.7854 = 5.58 sq.in

Length change = (5000 x 48750) / (30000000 x 5.58) = 1.45 ft.

However, if the drill pipe had 500 ft of HWDP and 100ft 8” DC; 8” DC – say 150 lb/ft.Total weight = Pipe + HWDP + DC = 97500 + 25000 + 15000 = 137500Average weight = (97500 + 40000) / 2 = 68750 lbs

Length change is now = (5000 x 68750) / (30000000 x 5.58) = 2.05 ft.

However, there is also piston effect. Pressure differential acts on cross sectional areas. Can cause section under investigation to shorten or lengthen.

Length change due to piston effect = L x Force / (Mod of elasticity x CSA of pipe)

L = section length.

Force = differential force. = Force outside – Force inside.

Force inside = Inside area x hydrostatic, (lbs force)Force outside – Outside area x hydrostatic, (lbs force)

D) Temperature Effects.

Since the well bore is always at a temperature above ambient, thermal expansion of the pipe in the hole will take place.

From engineering tables the expansion of steel = Original Length x Expansion coefficient x ∆T.

A typical expansion coefficient for steel is 13 x 10^-6.

By using the above equation, an average elongation would seem to be 0.86 inches per 100ft of pipe per 100 degree increase in temperature (F).

So the total expansion due to thermal effect will be;

Te = ((Pipe length, ft)/100) x ((Temperature change, F)/100 F) x 0.86.

If we enter the MWD temperature at survey depth as this will be in a circulating condition we can assume temperature constant

We also need to know the ambient temperature – i.e. temp on deck when pipe is measured.

E)Stretch of Pipe due to Hydraulics and Buoyancy

According to the free-point when stuck formulae accepted by the industry;

1)Free point constant = Cross sectional area of pipe x 2500

And

2)Free point of pipe = (Stretch in inches x Free point constant) / Pull force.

In a drilling situation the pull force on the pipe can be equated to the buoyant weight of the BHA (x Cos Inclination in a tangent section).

Transposing formula 2) for stretch gives

Stretch in inches = (Free point of pipe x Free point constant) / Pull force

Therefore in a drilling situation the stretch in the pipe equates to;

Stretch in inches = (Length of pipe from BHA to surface x Free point constant) / Buoyant

Weight of BHA).

Breaking down for the three sections of hole;

a)Length of pipe to kick-off point

b)For the build section I estimate; Length of build section x cosine of tangent / 2

c)Length of pipe in tangent multiplied by cosine of tangent angle.

Therefore the correction to be made to survey depth = ((a+b+c) x Free point constant)) / Buoyant weight of BHA

As Cross Sectional Area is know for both Drill Pipe and HWDP they can both be modeled.

I assume that under the forces involved, and the smaller lengths the BHA component stretch is negligible.

Notes.

The above ignores friction factors and unusual hole conditions.

F) Axial misalignment of Pipe in the Well Bore.

Basic assumptions.

When taking a survey, the drill string is in tension and so the drill pipe is pulled against the hole wall on build and drop off sections.

This will be on the high side of the hole in build sections, and on the low-side of the hole in drop sections.

Across a theoretical tangent section, the pipe will either be pulled diagonally across the hole, or lie flat along the bottom of the hole if there is no drop off section. (Fig 6)

Fig 6.

The Radius of curvature during build sections is:180/ (Build Rate * Pi)

And the arc length of a circle is:(2*Pi*r)*Ǿ/360

(Where Ǿ is the angle subtended by the two defining radii, or in our case the difference between the two inclinations).

Reasoning.

The length of the arc can be equated to the course length between surveys. By noting the difference in inclination an initial theoretical radius of curvature can be calculated. By then substituting the radius of curvature, less the hole radius a correction factor can be derived that can be applied to the course length.

Fig 7.

The above tables illustrate my initial findings (fig 7). Going from 0 Inclination to 0.98 Inclination, this method estimates 0.15m in 157m of MD. (0.95m per 1000m of drilled hole). This is taken in 17 ½” hole size.

Conclusion.

Though each of the above may seem small when taken individually, their cumulative effect can be quite significant.

Service companies have invested lots of time, effort and financial resources in the accuracy and precision of their MWD tools, but all this goes to waste when compared to the possible gross errors in current running practices.

I am not aware of any company of commercial product that is handling these errors at present, but would suggest there is a need to take these errors into account when drilling in areas that have small tightly defined targets.

As a proof I suggest that operators consider “retro-correcting” surveys in areas where the geology has been a surprise. The only factor that cannot be calculated after the drilling phase is the Bent sub effect, as that needs to be done in “real time” whilst drilling the well.

Perhaps it was not the formation that moved after all, but errors in the surveying practice.

Fig 8. Summation of potential survey errors.

Relief Well Drilling.

One of the most exacting applications in Directional Drilling is that of relief well drilling. I have personally been involved with 2 successful relief well operations in recent years, both of which involved the use of Magnetic Ranging tools.

However, if the above corrections we were conducted in tandem with the ranging tools on these wells, I feel time and, of course, money could have been saved in achieving the intersection.

Running logging tools on wire line creates yet another unknown in the true depth measurement. It is well known that at the end of logging runs there are both the “loggers’ depths” and the “drillers’ depths”. When the tool is a magnetic ranging tool, then the confusion further clouds the accuracy.

On a wire line logging run in Indonesia a little over 2 years ago, by applying the calculations stated above to the drilling BHA, and the correction stated in (f) “axial misalignment in the well bore” to the wire line depth data, the difference between the 2 depths was reduced from a little over 36ft to just under 3ft (total depth of well 13900ft).This represents a reduction from 0.26% to 0.02%.

The one wild card in the depth corrections for wire line is to depth correct for cable stretch, as data on the cable is not readily available. If any company can provide data on this topic, I would be very grateful.

By analyzing the target well data in terms of surveys, BHA components, MWD logs (temperature etc), a more accurate file can be generated on the final spatial position of the well bore where intersection is required to take place. By then applying the same logic and analysis models to the object (relief) well the well bore can be positioned closer to the target well before the expensive ranging tools are deployed.

There will always be the cone of error around any definitive well position, but with the application of the above corrections, this position can be identified and correctly focused on for the purposes of the relief well operation. The use of mathematical models will never (and should never, due to the number of variables involved), replace the tools in the field; however by the use of these models and balancing them with good sense and judgment, a great deal of time will be saved to accomplish the goal of a successful intersection.

About the author.

Chris Henderson is the Directional Drilling Coordinator for Weatherford Drilling Services in Beijing, China. He has 39 years experience in the oil industry, of which 26 years have been directly involved with Directional Drilling and has worked for both operator (Dutch Shell) and various service companies. He has Shell Round One and Round Two drilling certificates and holds a Bsc in Mechanical Engineering from Salford University, England.