Single phase flow in porous media Darcy’s law.ppt

Single phase flow in porous media: Darcy’s law Porosity Rock Matrix and Pore Space Pore Structure Porosity in Sandstone Porosity of common rock types Permeability Permeability (Darcy’s Law) Darcy’s experiment was performed to design a filter large enough to ensure the daily requirement of water for the city of Dijon (1856). Permeability (Darcy’s Law) In Petroleum Engineering we use phase potentials Darcy’s Law and dip angle Definition of parameters Definition of parameters Bundle of capillary tubes Many pore space models are based on capillary tube bundle Restrictions and assumptions ofDarcy’s law Permeability Permeability is influenced by: Pore size and pore-size distribution Grain size Grain-distribution Compaction (which is function of pressure) Grain shape Permeability measurement methods core scale Inject a fluid with defined properties Use Darcy’s law to calculate permeability Well test Measure flow and pressure Calculate permeability Representative Elementary Volume (REV) Limitations of applicability of Darcy’s law Forchheimer equation Forchheimer equation Forchheimer equation Permeability-porosity correlations General form of correlations: k = Shape factor * Porosity factor * square of grain size diameter Other Data Used in Well Testing Formation Volume Factor Viscosity Fluid Compressibility Pore Compressibility Net Pay Thickness h = h1 + h2 + h3 Net Pay Thickness Wellbore Radius Total Compressibility Skin Geometric Skin Flow in parallel Flow in series Permeability averaging Another type of skin is the “geometric skin”, caused by the way we perforate the well. In our simplified model, we assume that the well is perforated from the top of the reservoir to the bottom so that the we have horizontal, radial flow all the way to the well bore. Sometimes we will not complete the entire productive interval - either on purpose or by accident. Sometimes we will not complete all the way to the top or to the bottom of the well bore to avoid gas or water conin