Radius Of Investigation For Well Tests In Dual Porosity Reserviors
Authors: Sobbi F.A. , Badakhshan A. 
Published: March 2010

Abstract
The reservoir parameters obtained from any transient pressure analysis reflect average values of the characteristics of the area around the well that has experienced a pressure disturbance due to the change of flow rate at the wellbore. This area is described by an associated radius called the radius of investigation. This paper describes a new equation for evaluation of the radius of investigation for well tests in reservoirs under pseudo-steady state interporosity flow regime.
The results have shown that the radius of investigation in such reservoirs starts increasing in the fracture network proportional to the square root of the fracture conductivity. When the matrix contribution to the flow of fluids starts, the rate of advance of the radius decreases until its magnitude reaches a maximum value and remains constant until the total system stabilizes. After this time, the radius increases again at a lower rate dependent now on the total system conductivity.

Introduction
The radius of investigation, also called the radius of influence or radius of drainage, is defined in many ways by several authors(l,2,3,4,5,6). In most definitions this radius defines a circular system with a pseudo-steady state pressure distribution around the wellbore, and takes the form as follows:
Equation 1 (available in full paper)
where A is a constant and rinv is the radius of investigation.
If the start of semi-steady state flow for a homogeneous and symmetrical bounded cylindrical reservoir at a time tDc of 0.3 is used, and the parameters are defined in oil field units where rinv is in feet, t is the duration of flow for a drawdown test or the duration of shut-in when Δt &lt;p for a buildup test in hr., k is the formation permeability in md, Φ is the reservoir porosity in fraction, and ct is the total system compressibility in psi 1, the constant A becomes 0.029.
Odeh and Nabor(7), by using an RC (Resistance/Capacitance) analyser, obtained A to be 0.0257, and Kazemi(8), from the numerical finite difference solution, obtained it to be 0.035.
Hurst et al.(3), Van Poolen(5) and Slider(9) separately used the concept of unsteady state radial flow to fmd out when to switch from infinite acting solution to finite solution of the homogeneous diffusivity equation. By taking the derivative of the difference between the above solutions with respect to time and putting it equal to zero, the following equation for radius of investigation is obtained:
Equation 2 (available in full paper)
Matthews and Russell(l0) picked a time tDe of 0.25 intermediate to the two times corresponding to the end of infinite acting and the start of semi-steady state, and obtained the same Equation (2).
Muskat(1), Chatas(11) and Craft and Hawkins(12), by equating the volume of fluid produced to the expansion of the fluid contained in the drainage area, and by considering steady state conditions, also obtained the same Equation (2) for rinv.
Craft and Hawkins also showed that if the semi-steady state radial flow equation is used to calculate the average reservoir pressure, the same Equation (2) is obtained except that the constant is 0.0459 instead of 0.0325.