A Simple Method for Determination of Radius of Investigation for Non-Newtonian Fluids and Other Non-Ideal Systems

Abstract

Abstract Transient pressure testing is an important tool in obtaining reservoir information. Information derived from transient tests is useful only to those portions of the reservoir in which flow has occurred during the test. Thus, determination of radius of investigation (ROI) is essential. The most commonly used ROI equations were derived for Newtonian fluids Darcy flow in a homogeneous formation. Limited information of ROI is available for systems involved with non-Newtonian fluids or non-Darcy flow which could be important in polymer flooding or production of gas wells. ROI was determined in this paper by combining material balance equation and pressure distribution at any given testing time. This method of determining ROI was applied to non-Newtonian power-law fluids Darcy flow and Newtonian fluids non-Darcy flow in both homogeneous and composite formations. Main observations from this study included that for non-Newtonian power-law fluids:ROI was compared with a literature ROI model which is applicable in the range of 0<n<1. Within {0,1}, the two models give consistent results with the difference being zero at about n=0.6. The applicable range for the new model however is n 0 9.When n<1, ROI increases with flow rate, q, while n>1, ROI decreases with increase in q. At n=1, ROI is independent on q.Difference between original formation permeability, k, and the permeability around wellbore, kA, has a significant effect on ROI if kA/k<1. The effect of kA /k on ROI increases with n, kA/k has minor effect on ROI if kA/k>1. For Newtonian fluids non-Darcy flow,ROI is dependent on flow rate,ROI is less than that for Darcy flow, andROI decreases with increase in turbulent factor. Introduction Radius of investigation (ROI) is used to estimate the time required to test the desired area in a formation. The most commonly used radius of investigation, ri, was obtained by van Poollen,1 ri,P, by assuming that a Newtonian fluid flows in a uniform, homogeneous, and isotropic formation under the conditions of Darcy flow. (This is referred as ideal systems.) Equation 1 where k is the formation permeability, f porosity, µ Newtonian fluid viscosity, Ct total compressibility, t testing time, and E1 is a unit conversion factor. A detailed review and discussion of Eq. 1 was given by Johnson.2 Consistent units should be used in Eq. 1 and all the following equations in this study. However, direct application of these equations could be difficult. Therefore a unit conversion factor, E, is included for the more convenient field units. If the parameters in Eq. 1 have the units as shown in Table 1, E1 is equal to 0.016238. Numerous pressure transient studies for non-Newtonian fluids3–6 and high flow rate non-Darcy flow7–9 have been reported. However, limited information on ROI was available for systems involved with (1) non-Newtonian fluids, (2) non-Darcy flow, and (3) non-homogeneous porous media.