Browsing by Subject "transient flow"
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Item Implicit Runge-Kutta Methods to Simulate Unsteady Incompressible Flows(2009-05-15) Ijaz, MuhammadA numerical method (SIMPLE DIRK Method) for unsteady incompressible viscous flow simulation is presented. The proposed method can be used to achieve arbitrarily high order of accuracy in time-discretization which is otherwise limited to second order in majority of the currently used simulation techniques. A special class of implicit Runge-Kutta methods is used for time discretization in conjunction with finite volume based SIMPLE algorithm. The algorithm was tested by solving for velocity field in a lid-driven square cavity. In the test case calculations, power law scheme was used in spatial discretization and time discretization was performed using a second-order implicit Runge-Kutta method. Time evolution of velocity profile along the cavity centerline was obtained from the proposed method and compared with that obtained from a commercial computational fluid dynamics software program, FLUENT 6.2.16. Also, steady state solution from the present method was compared with the numerical solution of Ghia, Ghia, and Shin and that of Erturk, Corke, and Go?k??l. Good agreement of the solution of the proposed method with the solutions of FLUENT; Ghia, Ghia, and Shin; and Erturk, Corke, and Go?k??l establishes the feasibility of the proposed method.Item The Performance of Fractured Horizontal Well in Tight Gas Reservoir(2012-02-14) Lin, JiajingHorizontal wells have been used to increase reservoir recovery, especially in unconventional reservoirs, and hydraulic fracturing has been applied to further extend the contact with the reservoir to increase the efficiency of development. In the past, many models, analytical or numerical, were developed to describe the flow behavior in horizontal wells with fractures. Source solution is one of the analytical/semi-analytical approaches. To solve fractured well problems, source methods were advanced from point sources to volumetric source, and pressure change inside fractures was considered in the volumetric source method. This study aims at developing a method that can predict horizontal well performance and the model can also be applied to horizontal wells with multiple fractures in complex natural fracture networks. The method solves the problem by superposing a series of slab sources under transient or pseudosteady-state flow conditions. The principle of the method comprises the calculation of semi-analytical response of a rectilinear reservoir with closed outer boundaries. A statistically assigned fracture network is used in the study to represent natural fractures based on the spacing between fractures and fracture geometry. The multiple dominating hydraulic fractures are then added to the natural fracture system to build the physical model of the problem. Each of the hydraulic fractures is connected to the horizontal wellbore, and the natural fractures are connected to the hydraulic fractures through the network description. Each fracture, natural or hydraulically induced, is treated as a series of slab sources. The analytical solution of superposed slab sources provides the base of the approach, and the overall flow from each fracture and the effect between the fractures are modeled by applying superposition principle to all of the fractures. It is assumed that hydraulic fractures are the main fractures that connect with the wellbore and the natural fractures are branching fractures which only connect with the main fractures. The fluid inside of the branch fractures flows into the main fractures, and the fluid of the main fracture from both the reservoir and the branch fractures flows to the wellbore. Predicting well performance in a complex fracture network system is extremely challenged. The statistical nature of natural fracture networks changes the flow characteristic from that of a single linear fracture. Simply using the single fracture model for individual fracture, and then adding the flow from each fracture for the network could introduce significant error. This study provides a semi-analytical approach to estimate well performance in a complex fracture network system.