Well Test Analysis of Multi-Layered Naturally Fractured Reservoirs
Authors: Aguilera R. 
Published: March 2010

Abstract
Permeabilities from layer to layer can vary significantly in naturally fractured reservoirs. This study makes a comparison of geometric mean fracture permeability with permeabilities from well testing data in a layered naturally fractured reservoir.
The research was conducted with a model that contains ten layers that are naturally fractured. The ten-layer model is validated by comparing its drawdown and buildup behavior against the behavior of a single-layer model.
It is shown that permeability of the 10-layered reservoir calculated using a single-layer method will be much larger than the geometric mean and even the arithmetic mean, and will reflect the two layers with the largest permeabilities. If this is used in reservoir studies together with the total net pay, it can lead to very optimistic forecasts.
The problem of multi-layered permeability behavior may be recognized by a pressure derivative indicating partial completion effects even if the well is perforated in all fractured layers. During a buildup this recognition is more difficult because the shape of the buildup curve is affected by the length of the flow period previous to shut-in and the length of the wellbore storage period.
Conclusions apply strictly only to the data set presented in this study. These conclusions, however, compare favorably with my observations in other naturally fractured reservoirs.

Introduction
Outcrop information, imaging logs, and production logs have shown that in some cases naturally fractured reservoirs are composed by many layers(1). The thinner the layer the smaller the fracture spacing (or distance between natural fractures).
Under these circumstances some of the fractures might be intersected by the wellbore and some might not as shown on Figure 1. A production log would show only the fluid entrance points into the wellbore.
It is important to emphasize that the production log would not give an indication of net pay in the naturally fractured reservoir, only an indication of where the wellbore intersects the most important fractures.
It is not unusual to see from a production log that out of 100 ft. perforated in a fractured reservoir only 5 to 10 ft. contribute production into the wellbore even if the 100 ft. are true net pay.
This is the result of a typical situation in most naturally fractured reservoirs I am familiar with, i.e., that the matrix has a very low permeability which does not permit efficient fluid flow into the wellbore. The same tight matrix, however, can flow very efficiently into the natural fractures(1).
FIGURE 1: Schematic of naturally fractured layered reservoir. Production log shows a couple of zones where fluids enter the wellbore. However, the whole section from top to bottom is net pay. (Available in full paper)
One of the first papers dealing with pressure behavior of layered reservoirs was published by Leftkovits et al.(2) There was no communication between layers except at the wellbore.
Later Russell and Prats(3) studied the practical aspects of interlayer crossflow, and concluded that the early time response would be similar to the response of a well draining a layered reservoir with no cross flow.