Implementing the Minimum Curvature MethodImplementing the Minimum Curvature Methodfor Deviated Well Geometry Surveys in CE7for Deviated Well Geometry Surveys in CE7

Kevin Gerlitz, 2004The Problem

for Deviated Well Geometry Surveys in CE7for Deviated Well Geometry Surveys in CE7

The Problem

HRS uses the Tangential Method of applying dip and azimuth angles in deviated geometry surveys. While this is a valid method, it is also a simplistic method that assumes straight-line segments with constant angles along the well trajectory. Realistically, well paths are curved as the target well-bore trajectory is built up. The method of applying a minimum curvature to the well path takes into account the gradation of the angles in three dimensions along the well-bore trajectory and, hence, is a better approximation.

The SolutionThe Solution

This PPT illustrates a method of creating the well path using the minimum-curvature method. By using the Log Maths functionality in eLog, “minimum curvature”-equivalence angles can be derived from the recorded dip-azimuth deviation survey. Exporting these new deviation logs to a file and then importing the logs as the new deviated geometry will produce the same well-bore trajectory as a minimum curvature approach.

The Tangential Method

Description of MethodsDescription of Methods

The Tangential Method

The Tangential Method uses simple trigonometry to derive the displacements and assumes that the dip angle is held constant over the section:

Δ TVD = Δ MD cos I1

Δ N = Δ MD sin I1 cos A1

Δ E =ΔMD sin I1 sin A1Δ E Δ MD sin I1 sin A1

The Minimum Curvature Method

The Minimum Curvature Method effectively fits a spherical arc between points by calculating the “dog-leg” (DL) curvature from the 3D vectors and scaling by a Ratio Factor (RF).

DL = acos( cos(I2 – I1) – sinI1 sinI2 ( 1-cos(A2-A1) ) )DL acos( cos(I2 I1) sinI1 sinI2 ( 1 cos(A2 A1) ) )

RF = 2 tan( DL / 2) / DL

Δ TVD = ½ Δ MD ( cos I1 + cos I2 ) RF

Δ N = ½ Δ MD ( sin I1 cos A1 + sin I2 cos A2 ) RF

Δ E = ½ Δ MD (sin I1 sin A1 + sin I2 sin A2 ) RF

Creating the Minimum Curvature Equivalence AnglesCreating the Minimum Curvature Equivalence Angles

Given the equations for the two different methods for the calculating the TVD, we see that simply converting the dip angle, I, to the scaled and averaged angle (a “minimum curvature equivalence” angle as I call it) , Ø, is a simple substitution:

Δ TVD = Δ MD cos Ø = ½ Δ MD ( cos I1 + cos I2 ) RF

cos Ø = ½ ( cos I1 + cos I2 ) RF

Ø = acos( ½ ( cos I1 + cos I2 ) RF )( ( 1 2 ) )

For the horizontal displacements, the equations are non-linear and we have to make an approximation. Since we have already found the substitution of Ø incorporates the term of “½RF”, we can approximate the “minimum curvature equivalence” azimuth angle, θ, as a simple linear average:average:

Δ N = Δ MD sin Ø cos θ= ½ Δ MD ( sin I1 cos A1 + sin I2 cos A2 ) RF

Δ E = Δ MD sin Ø sin θ= ½ Δ MD ( sin I1 sin A1 + sin I2 sin A2 ) RF

sin θ ~ ½ ( sin A1 + sin A2 )

θ~ ½ ( A1 + A2 )

Other MethodsOther Methods

The Balanced Tangential Method

Δ TVD = ½ Δ MD ( cos I1 + cos I2 )

Δ N = ½ Δ MD ( sin I1 cos A1 + sin I2 cos A2 )

Δ E = ½ ΔMD ( sin I sin A + sin I sin A )Δ E = ½ Δ MD ( sin I1 sin A1 + sin I2 sin A2 )

The Average Angle MethodΔ TVD = Δ MD cos ½( I1 + I2 )

Δ N = Δ MD ½ sin (I1 + I2 ) ½ cos ( A1 + A2 )

Δ E = Δ MD ½ sin (I1 + I2 ) ½ sin (A1 + A2)

i f CThe Radius of Curvature MethodRv = 180 Δ MD / ( π (I2 - I1 ) )

Δ TVD = Rv ( sin I2 – sin I1 )

Δ H = Rv ( cos I1 – cos I2 )

Rh = 180 Δ MD / ( π ( A2 - A1 ) )

Δ N = Rh ( sin A2 – sin A1 )

Δ E = Rh ( sin A1 – sin A2 )

In order to implement the minimum curvature method, you need a well with some logs in your Geoview database

Implementing the Minimum Curvature Method in HRSImplementing the Minimum Curvature Method in HRS

database.

You then need to read in your deviation survey as a set of logs.

! Do not read this in as Deviated Geometry file.

Fill in the file reading parameters correctly for your ASCII file…

When you set the log types, do not set them to Dip and Azimuth since this will automatically create and apply the deviated geometry. Instead, provide a customized log type name such as Inclination and Direction (just type it in) and set the log amplitude units to degrees.

Here is the result of reading in the Dip and Azimuth logs.

In the Well Explorer page, you can edit the names of the logs. To make things easier in the process, edit the log names to Az (for the Azimuth log) and Inc (for the Deviation log). Do not forget to click on the Update button to save these edits.

Edit these log names now

Open an eLog project and select the Log Maths option…

Choose your input wells and output wells.

First, we’ll correct the dip angle. Select both the Inc and Az logs for the calculation. Choose the Inclination log type as your output log.

It is important to “Use the original domain values” and do not resample at this point.

This process will create an output log called Inclination_math

Make sure the variable names are correct, i.e., Inc and Az – if not, edit them here. Or you’ll have to debug the script yourself…

Here’s the script for calculating the new dip angle. Save the embedded file below to your system and load itfile below to your system and load it into the Log Maths script loading page. It’s an ASCII text file so you may want to open it in Notepad or a simple text editor if you want tosimple text editor if you want to look at it.

minCurveDip.prs

Here’s a graphic of the full script, if you care to

d iread it.

Here is the new Inclination log in blue overlaid on the original log in red. There should be only subtle differences.

Now apply the Log Maths function again to correct the Azimuth. You will need both the Inc and the Azlogs. Use the original Inclination log – not the newly created one. Make sure that your log type is set to the Direction log type.

Again, it is important to “Use the original domain values” and do not resample.

Here’s the embedded log maths script for the azimuth angle correction. Save it to your disk and load it as with the previous script.

PRS File

This is what the script for the azimuth angle correction looks like.

You should now have two new curves to compare with the original dip and azimuth logs.

Now we need to resample the new logs to a finer sample rate. We can use Log Maths to accomplish this.

We need to do this one log at a time. Make sure you select the new logs…

Rather than cluttering the well database with multiple logs, select the original log name in order to overwrite it…

The most important part in this process is to select to “Resample domain values at” a finer uniform sample rate…

In this case, the script is easy. We just need the output to be the same as the input. Because we selected the resampling option on the previous page, the only difference will be the sample interval.

Do the same process for the new azimuth angle log.

E t th l l d d t d di d i th lExport the newly resampled and corrected dip and azimuth logs to a file.

In the Well Explorer window, import the file as a Deviated Geometry file

Make sure you read it in correctly by filling in the parameters appropriately…

You can check the process by displaying both the TVD and the MD simultaneously along the vertical axes.

Or in the Table View of the Well Explorer window by selecting the Show both MD and TVDoption.