In this paper, a novel model was proposed for pressure transient analysis in multiple fractured horizontal wells (MFHW) with consideration of pressure loss within the wellbore. To facilitate solution of this problem, the whole system was divided into (1) reservoir subsystem, (2) fracture subsystem, and (3) wellbore subsystem. Incorporating with frictional and acceleration pressure drops, a mathematical model with finite horizontal well conductivity (HWC) was established. Employing Laplace transform, the mathematical model was solved. Transient pressure solutions of MFHW were acquired using Stehfest numerical inversion. Model validation was carried out by comparing with simplified cases in literatures. Case study and sensitivity analysis were conducted based on a real case from the Ordos Basin. The case study strongly shows that when ignoring the wellbore hydraulics, errors could be caused during the performance forecast. Results of sensitivity analysis show that, the dimensionless wellbore pressure of MFHW increases with the increase of Reynolds number; it decreases with the increase of reservoir-wellbore constant. The effect of pressure loss on pressure performance of MFHW will be exaggerated by increasing Reynolds number, or decreasing reservoir-wellbore constant.

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Flapwise flexural vibration of rotating beams has been extensively studied since the 1970s. Existing methods for solving the aforementioned vibration problem range from the conventional finite element method to variable-order finite element method, Frobenius method, differential transformation method and dynamic stiffness method (DSM). Although various approximation methods are available, most of these methods are based on perturbation or discretization of the governing equation, often leading to tedious calculations. This paper re-examines flapwise flexural vibration of rotating beams using the method of variational iteration, which is relatively new and capable of providing accurate solutions for eigenvalue problems. The extracted natural frequencies and mode shapes for sample rotating beams with various rotational speeds and hub radii are compared with existing results that were published in the open literature.

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