ROP fuzzy-logic model proposed for intelligent drilling in Iran, Malaysia
Rassoul Khosravanian
Behzad Choodar
Amirkabir University of Technology
Tehran
David A. Wood
DWA Energy Ltd.
Lincoln, UK
Bernt S. Aadnoy
Stavanger University
Stavanger
This article proposes a new improved fuzzy-logic approach to predict drilling rate-of-penetration (ROP) using a model built from available data for Ahvaz oil field in Iran and Kinabalu oil field in Malaysia.
Accurate ROP forecasts are important to drilling-cost optimization. Many factors affect ROP forecasting, including depth, bit type, bit hydraulics, rotary speed, rock properties, and depth.
Factors such as rock properties are uncertain and regional. Factors such as the depth of specific formations vary for individual wells. The relationships between these parameters are nonlinear, complex, and stochastic.
The industry widely uses a ROP model developed by A.T. Bourgoyne Jr. and F.S. Young Jr., although it sometimes provides insufficient accuracy.
The Bourgoyne and Young model requires the calculation of several parameters or coefficients based on field data. Other ROP forecasting methods involve artificial neural networks (ANNs) based on data for specific fields.
The proposed fuzzy-logic model outperformed the Bourgoyne and Young model, with mean errors of 2.56% for Ahvaz field and 3.01% for Kinabalu field.
Methodology
A fuzzy-logic model was easier to construct and more transparent than ROP forecasting models using ANNs or extreme learning machine algorithms. The fuzzy-logic model's simplicity and transparency makes it easy to modify for application in other fields and regions.
The proposed model provided accurate results with the limited case data presented, but it cannot be concluded that it will work in all situations. More work on larger data sets for different geological settings and different drilling techniques is needed.
Fuzzy-logic systems consist of four components:
• Fuzzy rules to outline the relationships between parameters.
• A fuzzy inference engine (mathematical formula) to link input variables to output values.
• Fuzzification to transform crisp input values into fuzzy-set membership.
• Deffuzification to generate a calculated output.
The authors built a fuzzy-logic model to predict ROP for Ahvaz and Kinabalu oil fields using data for the same seven variables as Bourgoyne and Young:
• Wellbore depth (D).
• Drillbit tooth wear (H).
• Jet impact force (Fj).
• Weight on bit (WOB).
• Drillbit rotation speed, rpm
• Equivalent circulating density (ECD).
• Pore-pressure gradient (ppg).
Fig. 1 shows the steps involved in constructing the fuzzy-logic ROP model.
Fuzzy-logic models deal with uncertainty by combining set membership functions (MF) with "if-then" rules. An appropriate MF is critical in fuzzy-model construction.
MF production can use subjective judgment and intuition, which provides an advantage in cases having little hard data.
The model proposed in this article involves a triangular MF form because it's simple to handle and quick to compute using the formulaic relationships shown in Equation 1.
Table 1 summarizes the descriptive statistics of the seven input variables for the fuzzy-logic drilling ROP model.
Researchers set up the fuzzy-model input and output variables in the fuzzy inference system (FIS) editor in MATLAB software, a proprietary programming language developed by MathWorks.
If-then rules
Rules consisting of a premise and a consequence, called if-then rules, determine the relationship between input and output in a fuzzy-logic model. If a premise occurs, then the consequence follows.
MFs represent premises and consequences. Fuzzy-logic reasoning involves compositional rules of inference. Output variables are derived by applying these rules of inference to the input variables.
Fuzzy sets and fuzzy logic can translate an entirely unstructured set of input data into a useful algorithm by applying an inference algorithm proposed by E.H. Mamdani and S. Assilian. This algorithm may be expressed as follows:
If XI is Ai1. . . and Xr is Air then Y is Bi for I = 1, 2, . . . , K
XI, Xr: Input variables
AiI, Air, Bi: Linguistic terms (fuzzy sets)
Y: Output variables, K: number of rules
A model's fuzzy-logic rules rest on available knowledge and data points. Researchers configured 30 rules to cover the possible cases for the proposed fuzzy-logic drilling ROP model.
The fuzzy-logic drilling ROP model used centroid defuzzification, the most commonly used method. The centroid method calculates the MF area.
Ahvaz field results
The authors established MFs and applied if-then rules to test their fuzzy-logic model. ROP forecasts calculated using the model were compared with wellbore measurements of ROP from Ahvaz oil field in Iran (Table 2).
The proposed model's measured and forecast ROP values were compared with ROP values calculated using the Bourgoyne and Young model. A statistical correlation coefficient (R2) helped demonstrate the model's high accuracy. Numbers ranging from 0 to 1 express the degree of membership in a fuzzy set as a degree of truth.
The ability of fuzzy sets to express gradual transitions from membership to non-membership provides meaningful representation of uncertainties (Equations 2-5).
The closer R2 is to 1 the more confidence researchers have in the model's ability to forecast the output variable based on input measures for the field.
R2 calculated for the fuzzy-logic drilling ROP model is 0.996 (Fig. 2), verifying the high performance of the fuzzy inference system built to infer ROP from the seven input variables used to define the if-then rules for the model.
The following formula calculated the fuzzy-logic drilling ROP model's error.
This yielded a low value of 2.56%, highlighting the model's accuracy in forecasting ROP for Ahvaz field (Table 1).
Table 3 shows the results derived from the model for Kinabalu field. The average error calculated for the Kinabalu model vs. field data was 3.01%.
Fig. 4 compares the measured and forecast ROP values for Kinabalu field.
The authors
Rassoul Khosravanian ([email protected]) is an assistant professsor in petroleum engineering at Amirkabir University of Technology, Tehran where he joined the faculty in 2001. He has more than 10 years' experience in offshore and onshore drilling, project management, and procurement engineering. He earned a BS in mining engineering from the University of Kerman in Iran, and an MS and PhD in industrial engineering from the Iran University of Science and Technology. His research includes economic evaluation of projects using various software. He belongs to SPE.
David A. Wood ([email protected]) is principal consultant of DWA Energy Ltd., UK. He specializes in integrating technical, economic, risk and strategic information to assist clients with asset evaluations and project planning. Wood has more than 35 years industry experience, previously working in senior technical and corporate positions with Phillips Petroleum, Amoco, Lundin Oil, and Canadian independents.
Bernt S. Aadnoy ([email protected]) is a petroleum engineering professor at the University of Stavanger. He previously worked for Phillips Petroleum, Rogaland Research, Statoil ASA, and Saga Petroleum. Aadnoy holds a mechanical engineering degree from Stavanger Tech, a BS in mechanical engineering from the University of Wyoming, an MS degree in control engineering from the University of Texas, and a PhD in petroleum rock mechanics from the Norwegian Institute of Technology.
Behzad Choodar ([email protected]) received a BS in petroleum engineering from the Amir Kabir University, Tehran, in 2015. His main areas of research include intelligent drilling, fuzzy logic, and ROP prediction.
