Radius and Linear Distance of Investigation and Interconnected Pore Volume in Naturally Fractured Reservoirs
Authors: Aguilera R. 
Published: March 2010

Abstract
The radius of investigation (ri) in a naturally fractured reservoir is dependent on flow time, the relative storativity of matrix and fractures and the size and shape of the matrix blocks. Not taking this into account while using the conventional radius of investigation equation developed for single porosity isotropic reservoirs can lead to significant errors. This paper presents an equation that can be used for the case of pseudo steady state (restricted) or transient (unrestricted) interporosity flow when radial flow is dominant during the test. A straightforward approach using a function Ya) permits calculating interconnected pore volume and hydrocarbons investigated during the test in the fractured and composite systems.
In addition, an equation is presented for calculating the distance of investigation in those cases where linear flow (as opposed to radial) is dominant. This occurs, for example, in paleo channels of continental origin. The radius of investigation is strictly a flow equation (not a build-up equation).

Introduction
The radius of investigation (ri)) has been shown throughout the years to be a very useful concept for designing tests and for estimating the influenced pore volume and the hydrocarbons investigated during the test. The concept assumes radial flow into a common source or sink in a homogeneous, isotropic reservoir where permeability, porosity, thickness and saturation are constant. The fluid is only slightly compressible. The compressibility is constant and small. The effects of gravity and inertial forces in fluid flow are ignored.
Radius of investigation, as used in this paper, is the distance that a pressure disturbance (transient) moves into a reservoir at a certain time as a result of changing the flow rate in a well. On the other hand, the radius of drainage of a well is the distance reached at a stabilization time (ts)), i.e., the time at which pseudo steady state begins.
Different authors have used different concepts for estimating the radius of investigation (and radius of drainage) and for defining the stabilization time. For example, Muskat(1). assumed a constant flow rate and a succession of disturbances (transients) going from unsteady to steady state. Miller et al.(2) and Brownscombe and Kern(3) estimated a stabilization time (ts)) that occurs when the reservoir is within 2% of equilibrium. Chatas(4) used the same basic assumptions as Muskat(1) to develop equations for stabilization time, radius of drainage and linear distance of investigation. Tek et al(5) defined the drainage radius at that point where the fluid flowing is 1% of the fluid flowing into the wellbore. Jones(6) assumed that the drainage radius is that distance at which the pressure changes only by 1%. These assumptions with respect to 1 or 2% of the pressure (or sometimes the flow rate) are arbitrary and because of that, the equations have to be used with care.
H.K. van Poollen(7) used a different approach that allows calculating radius of investigation, radius of drainage or stabilization time depending on the type of data available. He used Jones(6) Y functions for finite and infinite reservoirs.