TX 75083-3836, U.S.A., fax 01-972-952-9435.
AbstractDarcy's law can not describe fluid flow accurately when the flow rate is high. In most cases in the recovery process, fluid flow is governed by Darcy's law. But when the flow rate is very high, for an instance, near the wellbore, Darcy's law is inadequate to describe fluid flow.In 1901, Forchheimer put forward a classical equation, known as the Forchheimer equation, to make up the deficiency encountered by Darcy's law at high flow rates. He added a non-Darcy term into the Darcy flow equation. The non-Darcy term is the multiplication of the non-Darcy coefficient, fluid density, and the second power of velocity. One of the most important aspects in determining the non-Darcy effect is to estimate the non-Darcy coefficient as accurately as possible.In this paper, theoretical and empirical correlations of the non-Darcy coefficient in one-phase and multi-phase cases in the literature are reviewed. Most researchers have agreed that the non-Darcy effect is not due to turbulence but to inertial effect. The non-Darcy coefficient in wells is usually determined by analysis of multi-rate pressure test results, but such data are not available in many cases. So, people have to use correlations obtained from the literature. This paper summarizes many correlations in the literature, and will provide a good reference for those who are interested in the investigation of the non-Darcy effect in the recovery process.
TX 75083-3836, U.S.A., fax 01-972-952-9435.
AbstractDarcy's law governs most flow patterns in petroleum recovery processes. However, when fluid flow velocity is very high, for example, near the wellbore, Darcy's law may be inadequate to simulate the fluid flow.The non-Darcy effect has been incorporated into the Department of Energy (DOE) reservoir simulator MASTER (Miscible Applied Simulation Techniques for Energy Recovery). Based on the simulator BOAST (Black-Oil Applied Simulation Tool), MASTER was developed by DOE mainly to solve gas injection problems. However, only Darcy's flow was considered in these simulators. In this study, Forchheimer's non-Darcy flow equation has been incorporated into the simulator code and an iterative method has been used to solve for pressures.The modeling of non-Darcy flow proved successful and enabled the simulator to match high-velocity gas flow more accurately. Based on a number of non-Darcy flow coefficient equations found in the literature, a general correlation was proposed. The appropriate constants in the proposed correlation were found by running simulations with the modified simulator for the non-Darcy flow experiments.The model has been verified using laboratory high flow data obtained using single-phase nitrogen gas. The data comprised a wide range of flow rates collected using a heterogeneous Berea sandstone wafer. The gas flowed into and out of a hockey puck-shaped wafer via 0.125-in. diameter ports. Thus the flow rate varied within the wafer, simulating near-wellbore flow conditions. It was found that, the differential pressures from simulations were in good agreements with their counterparts from experiments.
Additive manufacturing (AM) is an advanced manufacturing process that provides the opportunity to build geometrically complex and highly individualized lightweight structures. Despite its many advantages, additively manufactured components suffer from poor surface quality. To locally improve the surface quality and homogenize the microstructure, friction stir processing (FSP) technique was applied on Al-Si12 components produced by selective laser melting (SLM) using two different working media. The effect of FSP on the microstructural evolution, mechanical properties, and corrosion resistance of SLM samples was investigated. Microstructural investigation showed a considerable grain refinement in the friction stirred area, which is due to the severe plastic deformation and dynamic recrystallization of the material in the stir zone. Micro-hardness measurements revealed that the micro-hardness values of samples treated using FSP are much lower compared to SLM components in the as-built condition. This reduction of hardness values in samples treated with FSP can be explained by the dissolution of the very fine Si-phase network, being characteristic for SLM samples, during FSP. Surface topography also demonstrated that the FSP results in the reduction of surface roughness and increases the homogeneity of the SLM microstructure. Decreased surface roughness and grain size refinement in combination with the dissolved Si-phase network of the FSP treated material result in considerable changes in corrosion behavior. This work addresses the corrosion properties of surface treated additive manufactured Al-Si12 by establishing adequate microstructure-property relationships. The corrosion behavior of SLM-manufactured Al-Si12 alloys is shown to be improved by FSP-modification of the surfaces.
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