Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

Permeability Estimation From Well Log Responses

Permeability is one of the most important characteristics of hydrocarbon bearing formations. Formation permeability is often measured in the laboratory from reservoir core samples or evaluated from well test data. However, core analysis and well test data are usually only available from a few wells in a field. On the other hand, almost all wells are logged. This paper presents a non-parametric model to predict reservoir permeability from conventional well log data using an artificial neural network (ANN). The ANN technique is demonstrated by applying it to one of Saudi Arabia’s oil fields. The field is the largest offshore oil field in the world and was deposited in a fluvial dominated deltaic environment. The use of conventional regression methods to predict permeability in this case was not successful. The ANN permeability prediction model was developed using some of the core permeability and well log data from three early development wells. The ANN model was built and trained from the well log data and their corresponding core measurements by using a back propagation neural network (BPNN). The resulting model was blind tested using data which was taken from the modelling process. The results of this study show that the ANN model permeability predictions are consistent with actual core data. It could be concluded that the ANN model is a powerful tool for permeability prediction from well log data

A New Optimization Model for 3d Well Design

This paper introduces a software package that uses a genetic algorithm to find the optimum drilling depth of directional and horizontal wells in 3D. A special penalty function, mutation, crossover probabilities, and stopping criterion were used to obtain the global minimum of drilling depth. This minimum was achieved at the minimum values for kickoff point, inclination angle, build-up and drop-off rates. The minimum values of these parameters reduce the dogleg severity, which in turn reduce the drilling operation problems. The optimized design was compared to the conventional design (based on a trial and error method) and the WELLDES program (based on sequential unconstrained minimization technique) for two wells. The optimized design reduced the total drilling length of the two wells, while all other operational parameters were kept within the limiting constraints. The conventional design and WELLDES program have some variables out of their constraint limit

Developing novel correlations for calculating natural gas thermodynamic properties

Natural gas is a mixture of 21 components and it is widely used in industries and homes. Knowledge of its thermodynamic properties is essential for designing appropriate processes and equipment. This paper presents simple but precise correlations of how to compute important thermodynamic properties of natural gas. As measuring natural gas composition is costly and may not be effective for real time process, the correlations are developed based on measurable real time properties. The real time properties are temperature, pressure and specific gravity of the natural gas. Calculations with these correlations are compared with measured values. The validations show that the average absolute percent deviation (AAPD) for compressibility factor calculations is 0.674%, for density is 2.55%, for Joule-Thomson coefficient is 4.16%. Furthermore, in this work, new correlations are presented for computing thermal properties of natural gas such as enthalpy, internal energy and entropy. Due to the lack of experimental data for these properties, the validation is done for pure methane. The validation shows that AAPD is 1.31%, 1.56% and 0.4% for enthalpy, internal energy and entropy respectively. The comparisons show that the correlations could predict natural gas properties with an error that is acceptable for most engineering applications