Pressure Transient Analysis of Partially Penetrating Wells in a Naturally Fractured Reservoir
Authors: Slimani K. , Tiab D. , Moncada K. 
Published: December 2007

Abstract
Often and for many reasons the wellbore does not completely penetrate the entire formation, yielding a unique early-time pressure behavior. Some of the main reasons for partial penetration, in both fractured and unfractured formations, are to prevent or delay the intrusion of unwanted fluids into the wellbore, i.e. water coning. A similar early-time pressure behavior may be due to the presence of plugged perforations. Drilling problems associated with high mud losses when the well encounters fractures, often prevent well penetration of the total formation thickness. Penetration in naturally fractured reservoirs is usually minimal (10 to 20%), but with the right mud, it can reach 50% and in some cases 100%. Such well completions are referred to as limited-entry, restricted-entry or partially penetrating wells. The transient flow behavior in these types of completions is different and more complex compared to that of a fully penetrating well.
This paper proposes a method for identifying, on the pressure and pressure derivative curves, the unique characteristics of the different flow regimes resulting from these types of completions and to obtain various reservoir parameters, such as vertical and horizontal permeability, fracture properties, and various skin factors. Both naturally fractured and unfractured (homogeneous) reservoirs have been investigated.
For unfractured and homogeneous formations, a spherical or hemispherical flow regime occurs prior to the radial flow regime whenever the penetration ratio is twenty percent or less. A half-slope line on the pressure derivative is the unique characteristic identifying the presence of the spherical flow. This straight line can be used to calculate spherical permeability and spherical skin values. These parameters are then used to estimate vertical permeability, anisotropy index and skin.
For a naturally fractured formation, the type curves of the pressure and pressure derivative reveal that the combination of partial penetration and dual-porosity effects yields unique finger prints at early and transition periods. These unique characteristics are used to calculate several reservoir parameters, including the storage capacity ratio, interporosity flow coefficient, permeability and pseudo-skin. Equations have been developed for calculating the skin for three partial completion cases: top, center and bottom. The analytical solution was obtained by combining the partially penetrating well model in a homogeneous reservoir with the pseudo-steady model for a naturally fractured reservoir.
The interpretation of pressure tests in both systems, i.e. fractured and unfractured reservoirs, is performed using Tiab's Direct Synthesis (TDS) technique for analyzing log-log pressure and pressure derivative plots. TDS uses analytical equations to determine reservoir and well characteristics without using type-curve matching. These characteristics are obtained from unique fingerprints, such as flow regime lines and points of intersection of these lines, that are found on the log-log plot of pressure and pressure derivative. It is applied to both drawdown and buildup tests. Several numerical examples are included to illustrate the step-by-step application of the proposed technique.