Trust-Region Approach To Find Constants of Bourgoyne and Young Penetration Rate Model in Khangiran Iranian Gas Field

Abstract

Abstract Up to now, authors have proposed several drilling rate models. Bourgoyne and Young model represents a general relation between penetration rate and some drilling variables. In this model, there are eight constants, which are dependent to the formation type and must be found from previous drilling data. Bourgoyne and Young recommended multiple regression method to solve these eight unknowns but this method is limited to the number of data points and recommended ranges for drilling parameters. In this research, by writing a computer program, three other mathematical methods were applied on nine wells data of Khangiran gas field to find each formation constants. Results of applied four methods were compared to each other and it was found that trust-region method is the best mathematical method to find Bourgoyne and Young penetration model constants and in many situations, results of other three methods were not meaningful. Since, this method has not limitations of recommended method, it can be applied easily to predict penetration rate when e few data points are present and when drilling parameters are not in the recommended ranges. Introduction Penetration rate prediction is always one the most important issue among drilling engineers, because it makes the possibility to select optimum drilling parameters to achieve the minimum cost per foot. Scientists have suggested several mathematical equations to relate the drilling rate and major controllable and uncontrollable drilling variables. However, because a large number of drilling variables affect the drilling rate and there are some relationships between themselves, a model with 100% accuracy has not been proposed yet (1, 2). Perhaps the most complete drilling rate model, used for roller cone bits is Bourgoyne and Young's model (1). Eight functions are used in their equation to model the effect of most important drilling variables. In this model, there are some unknown coefficients that must be chosen based on local drilling conditions. In fact, the accuracy of this model is dependent to the constants quantities and therefore, applying a reliable mathematical technique to compute these coefficients is on the great importance. In this research, first, we will discuss in detail about Bourgoyne and Young drilling rate model. Then, the mathematical methods to find unknown coefficients of this model will be illustrated. Next, using the most reliable mathematical technique, unknowns of Khangiran gas field formations will be estimated.