Using Nonlinear Least Squares Method & Techniques to Predict Drilling Performance Based on Learning Curve Equation
Authors: Amer Mustafa , Aman Beshir , Radhwi Asem 
Published: January 2023

The Drilling Performance Curve (DPC) is a simple yet powerful tool to assess the drilling performance in any given area where a consecutive series of similar wells have been drilled.

Have shown the Drilling Performance Curve as a valid measure of drilling performance, it provides an indicator of relative improvement over a campaign, and position on learning curve can provide a measure of process maturity.

Brett and Millheim has proven that Learning Curve Theory (LCT) mathematically describes the ability of organizations to improve their performance over time. It has been used under many different names - the progress curve, the experience curve, etc.

All the information that is needed to perform the analysis is the sequence numbers of the well and the time it takes to reach a given depth.

The expression relating the sequence in which a well was drilled and the total activity duration is given by:

T = C 1 * e c 2 ( 1 − n ) + C 3

Where:

T: Time required to drill the nth well,

n: Well number in an area of uniform geology,

C1: Constant reflecting how much longer the initial well takes to drill than the idealized final well,

C2: Constant reflecting the speed with which the drilling organization reaches the minimum drilling time for an area,

C3: Constant reflecting the idealized minimum drilling time for the area.

Defining the value of the three constants; C1, C2, and C3, is the most critical step in the process as it affects the accuracy of the total duration predications for future wells.

In this paper, Nonlinear Least Squares Method is used to estimate the parameters in the nonlinear equation shown above.

Based on the operation classification and coding reported in the daily morning report, well operation durations were collected at many different levels of granularities such as: well, hole sections, major operations, and activity levels. LCT equation was applied at these predefined levels of operation time breakdown and Nonlinear Least Squares Method was utilized to calculate the value of the equation three constants that will be used to predicate future wells duration.

It was found that, LCT is a good practical tool for performance monitoring and predication with highly accurate results up to 90 % where the experience gaining by the involved teams is the key fact consideration in this technique in addition to the technology technical limitations.

The degree of detail collected in our drilling data allows more variety of drilling performance evaluation. Learning curve calculation is performed by the system on well level and can be decomposed into different levels of analysis covering from total well duration down to action duration level. The proposed technique allows any codes combinations as well.

LCT was found to be an objective, neutral tool to measure the performance of the organization and different teams at many different levels with a very high accuracy while using Nonlinear Least Squares Method to estimate the LCT equations parameters.