It is important to note that our industry standard systematic error models have not traditionally modelled for the effect of survey interval. It is very hard to quantify what the effect of missing data might have been and so the error models have been published with the caveat that adequate surveys must be taken to accurately reflect the geometry of the wellpath.
Clearly if the minimum curvature algorithm were applied to the survey on the left where the inclination and azimuth are identical at the start and end of the curve, a simple straight line path would be assumed whereas the reality is better represented by the surveys on the right. I conducted a study using some of Shell’s survey database a few years ago. I removed every second survey from some high intensity gyro surveys and recalculated. Then I removed more and plotted the errors against the survey interval. The actual positional error grew in a quadratic. Here is one example plot.
On the x axis is the survey interval and the scatter on the y axis represents positional errors from the original surveyed position. The green histogram is a set of average positional errors for each survey interval in 10ft increments.
The approximate equation relating these is of the order of .3 x (Interval/100)^2 which has an interesting effect. If this is even close to correct then reducing our survey interval from 90ft to 30ft reduces our positional error by a factor of 9 not 3. Similarly, we might expect that missing a 90ft survey will increase our positional error due to lack of surveys by a factor of 4 rather than 2.
What should we do about this? Some companies would argue that a simple additional inclination and azimuth error should be added in proportion to their respective changes from one survey to the next. For example, we might add .1 x azimuth change as an azimuth error and perhaps 0.1 x inclination change as an inclination error.
The shorter the interval, the smaller the change and therefore the smaller the error applied. Since the md difference is also proportional to the interval, this has a square term on interval just like the study shows. Others would argue that as we are trying to model missing data, we might generate misleading uncertainty models and we should cover this by best practice.
Most companies agree that when the dogleg severity exceeds 3 degs / 100ft it is good practice to survey every single rather than every stand.However, there are some occasions where the lack of surveys has to be remedied long after the event.
Sometimes when a well is misplaced in TVD, it is necessary to re-analyse the MWD survey to obtain a better estimate of TVD. This is done by including the slide sheet information. The technique can only be used as a rough guide to the likely TVD adjustment required but has often explained poor production results or severe disagreement between gyro and MWD depths.
Using the slide sheet in below figure as an example:
Looking at the data for BHA 6, we can see a few points where surveys were taken and several changes from rotating to oriented (sliding) mode. The lengths and toolfaces are listed for each slide. Whilst these values will only be approximate it is possible to then estimate the wellbore attitude at the points where the slides began and ended.
Firstly if we take the total curvature generated over the BHA run by measuring the angle changes between surveys (see minimum curvature described above in chapter 7) we can work out the dogleg severity capability of this assembly. If we then apply that curvature on the toolfaces quoted, it is possible to determine a fill in survey at the beginning and end of each slide by using the approximation that the inclination change will be:
DLS x length x cos(Toolface) and the azimuth change will be the DLS x length x sin(Toolface) / sin(Inclination)
- where DLS means dogleg severity in degrees per unit length. This allows us to complete surveys at the start and end of each slide and minimum curvature will then be more valid when joining the points.
This assumes that:
- The DLS is unchanged during the run
- The curvature all happens when sliding
- The toolface was constant during the slide
These assumptions are very simplistic but the analysis will generally give a better idea of TVD than the assumption that the sparse surveys can be safely joined with 3D constant arcs.
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