Computed Tomography for the Quantitative Characterization of Flow Through a Porous Medium

Abstract

ABSTRACT X-ray computed tomography (CT) has become an increasingly popular research tool in petroleum engineering for characterizing porous media. Its highly detailed images have been used to construct maps of porosity, saturation and atomic composition, and to visualize the displacement of fluids. However, extracting data necessary to characterize flow through porous media is both time consuming and dependent on the availability of extensive computational resources - - a consequence of the large size of the image files. We have applied a known technique, based upon the ability to recognize regions with similar features, which avoids these difficulties. It allows us to substitute for the image, the pixel location of the boundaries of the recognized regions, reducing considerably the computer storage requirements. We have used this technique to study the dynamics of two miscible liquids of different densities flowing through a porous medium where buoyancy plays an important role. Our specific concern is the movement of mud filtrate as it penetrates a permeable formation in the vicinity of a recently drilled wellbore. We quantify the manner in which impermeable horizontal barriers influence the movement of the filtrate. Using the CT scanner, we image and then recognize the shape and progression of the advancing front of filtrate as a function of time. The profile of the front is also mathematically modeled, and the solution for the movement of the filtrate is obtained. We find quite good agreement between the recognized shape of the front and the predictions of the time dependent solution. This enables us to quantitatively assess the roles of the various parameters in the system, such as the horizontal permeability. It also establishes the robustness of the image analysis technique to the X-ray computed tomography (CT) scanner. Although the CT scanner was first developed in 1972 by Hounsfield1 for medical purposes, the technique has now been applied in material science and engineering2,3 to observe density variations in a sensitive and nondestructive manner. The X-ray scanner has also proved to be a useful tool in studies of fluid flow through porous media, especially in laboratory core flood experiments where two- and three-phase saturations were obtained with suitable dopants. These studies relied on suitable calibrations relating X-ray attenuations to the different saturations of each phase.4 In addition to determining the physical properties of materials such as bulk density and effective atomic number,5 computed tomography can precisely reconstruct geometric features contained in a cross-sectional slice of a scanned object. Extracting these features may be necessary to characterize flow in porous media. Unfortunately, this can consume extensive computational resources. To avoid these difficulties, we have developed a procedure to systematically recognize geometric features in images, referred to as pattern recognition; we illustrate its utility in a study of the dynamic evolution of moving fronts in porous media between two fluids. Special attention is given to the motion of an invading fluid ( mud filtrate for instance) injected at constant flow rate into a permeable formation through a point on its lower horizontal impermeable boundary, the formation being initially saturated with fresh water (formation fluid). This arises from a desire to understand the influence of horizontal impermeable barriers on the motion of mud filtrate entering a formation at the well-bore. Due to buoyancy (i.e., the difference in density between the filtrate and the formation fluid), it is often observed that the filtrate either rises or falls as it enters a formation.6 The objective of the study is to understand the dynamics of the filtrate as it spreads across the horizontal barrier. An important aspect of this study is being able to compare the shape of the filtrate/formation fluid interface obtained by pattern recognition with those generated by the theoretical analysis.