Abstract: We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.
Abstract: Relative permeabilities are practical factors that are used to correct the single phase Darcy’s law for application to multiphase flow. For effective characterisation of large-scale multiphase flow in hydrocarbon recovery, relative permeability and capillary pressures are used. These parameters are acquired via special core flooding experiments. Special core analysis (SCAL) module of reservoir simulation is applied by engineers for the evaluation of these parameters. But, core flooding experiments in shale core sample are expensive and time consuming before various flow assumptions are achieved for instance Darcy’s law. This makes it imperative for the application of coreflooding simulations in which various analysis of relative permeabilities and capillary pressures of multiphase flow can be carried out efficiently and effectively at a relative pace. This paper presents a Sendra software simulation of core flooding to achieve to relative permeabilities and capillary pressures using different correlations. The approach used in this study was three steps. The first step, the basic petrophysical parameters of Marcellus shale sample such as porosity was determined using laboratory techniques. Secondly, core flooding was simulated for particular scenario of injection using different correlations. And thirdly the best fit correlations for the estimation of relative permeability and capillary pressure was obtained. This research approach saves cost and time and very reliable in the computation of relative permeability and capillary pressures at steady or unsteady state, drainage or imbibition processes in oil and gas industry when compared to other methods.
Abstract: The results reported in this paper are the part of an extensive laboratory investigation undertaken to study the effects of fibre parameters on the permeability and strength characteristics of steel fibre reinforced concrete (SFRC). The effect of varying fibre content and curing age on the water permeability, compressive and split tensile strengths of SFRC was investigated using straight steel fibres having an aspect ratio of 65. Samples containing three different weight fractions of 1.0%, 2.0% and 4.0% were cast and tested for permeability and strength after 7, 14, 28 and 60 days of curing. Plain concrete samples were also cast and tested for reference purposes.
Permeability was observed to decrease significantly with the addition of steel fibres and continued to decrease with increasing fibre content and increasing curing age. An exponential relationship was observed between permeability and compressive and split tensile strengths for SFRC as well as PCC. To evaluate the effect of fibre content on the permeability and strength characteristics, the Analysis of Variance (ANOVA) statistical method was used. An a level (probability of error) of 0.05 was used for ANOVA test. Regression analysis was carried out to develop relationship between permeability, compressive strength and curing age.
Abstract: Darcy’s Law is a well-known constitutive equation describing the flow of a fluid through a porous medium. The equation shows a relationship between the superficial or Darcy velocity and the pressure gradient which was first experimentally observed by Henry Darcy in 1855-1856. In this study, we apply homogenization method to Stokes equation in order to derive Darcy’s Law. The process of deriving the equation is complicated, especially in multidimensional domain. Thus, for the sake of simplicity, we use the indicial notation as well as the homogenization. This combination provides a smooth, simple and easy technique to derive Darcy’s Law.