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![image.png](https://images.hive.blog/DQmeEjZmqGpkd2QkKfW5WFfh53LsxAickgwWPE5sXRLsziV/image.png)
[Image source](https://en.wikipedia.org/wiki/File:Inside_a_Mud_Logging_cabin.jpg)

There is a very important mathematical calculation in the oil industry when drilling an oil well, which must be taken into account by petroleum engineers when evaluating pressures. This mathematical calculation is called the corrected d exponent, a parameter that, once calculated, is widely used in mud logging activities and pore pressure analysis.

Mathematically speaking, the corrected d-factor is an extrapolation of certain drilling parameters such as:

- Drilling speed (ROP).
- Revolutions per minute of the drill string (RPM).
- Weight on the drill bit (WOB).
- Diameter of the drill bit (D).
- Drilling fluid density. 

Although the pore pressure of the producing reservoir is previously estimated, being able to calculate this corrected exponent d allows us to estimate the value of a pressure gradient for the constant evaluation of the pore pressure of the producing reservoir while we are drilling. 

All this is done because there are oil fields with very high pore pressures (overpressurized) that must be monitored in real time, and what better way to do this than to estimate it using the corrected d exponent. 

This is a mathematical correlation that is already calculated in the exploratory phase, but it is improved with real data from real-time well drilling parameters, hence its name, corrected d exponent. 

Drilling rate (ROP) is a very conclusive drilling parameter in how the calculation of the corrected d exponent can vary, since the way in which the lithological formations and the fluids contained in them are found makes it easier or more difficult to drill and, therefore, to estimate pore pressure in real time. 

### ***Calculation of the corrected exponent d (dc)***

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If the density of the drilling fluid is constant, i.e., it does not require changes, then dc is equal to:

<CENTER>![image.png](https://images.hive.blog/DQmaFtybeZYAnujER8uQi22N7BaPxPMFT9VZxnzCb5bp5rt/image.png)</CENTER>

Where:

R: Drilling speed measured in feet/hour.
N: Rotation speed of the drill string measured in revolutions per minute (RPM).
W: Weight on the drill bit measured in kilolbs. 
D: Diameter of the drill bit measured in inches. 

If the fluid density warrants changes, for example, if the drilling fluid density needs to be increased, then the same equation is used, only multiplied by the ratio between the original density and the new required density.

### ***Example of calculation of the corrected exponent d***

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An oil well is being drilled at a rate of 60 feet per hour (ROP). The rotation speed is 100 RPM. The weight on the drill bit is 15 KLb. The diameter of the drill bit is 8.5 inches. 

Data:

R: 60
N: 100
W: 15
D: 8.5

The solution is to apply the following equation:


![image.png](https://images.hive.blog/DQmQo3Kmj8TEC2TTtJ1y4NkwRQJfvwyFzwRhHHc6Z55S9bX/image.png)

For example, if you want to change a mud density from 9 lbs/gallon to 12 lbs/gallon, then the dc would be:


<center>![image.png](https://images.hive.blog/DQmbE4PUekmqsP8AVbch1B4Rtsm5J5DuADHTeYFqYgLx1Dh/image.png)</center>

Where:

dc: corrected exponent d with variable mud density.
d: corrected exponent d with constant mud density.
Do: original mud density.
Dn: new mud density.

![image.png](https://images.hive.blog/DQmZH5ke95w1EtiFVm2qjVgtHLZaY247v5LcAE74jCYYtmX/image.png)

In conclusion, the corrected d exponent gives us an idea of whether there are abnormal pressures in the reservoir we are drilling. However, it is important that if there is any change in the value of the corrected d exponent, a correct analysis can be performed based on the lithological characteristics of the area where the well is being drilled.   

### ***References***

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- Jorden, J.R. and Shirley, O.J.: "Application of Drilling Performance Data to Overpressure Detection", Journal of Petroleum Technology, p1387-1394, Vol.18, No.11, Nov 1966.

- (2010). Well Control for Completions and Interventions. 1st ed. Texas: Gulf Publishing.

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