Well Test Analysis of Multi-Layered Naturally Fractured Reservoirs with Variable Thickness and Variable Fracture Spacing
Authors: Aguilera R. , Aguilera M.S. 
Published: July 2010

Introduction
This technical note is a synopsis of paper 2001–091. The readers are referred to the full-length paper for additional details, nomenclature and illustrations. Outcrop information, cores, images, and well logs have shown that in some cases, naturally fractured reservoirs are composed of many layers(1). The thinner the layer, the smaller the fracture spacing (or distance between natural fractures). This is illustrated in Figure 1, which is a photo of the Cardium sandstone outcrop at Seebe Dam near Calgary, Alberta.
For this type of reservoir, some fractures may be intersected by the wellbore and others may not, as is shown in the schematic of Figure 2. A production log would show only the fluid entrance points into the wellbore.
The production log would not give an indication of net pay in this 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 30 m perforated in a fractured reservoir, only 2 to 3 m contribute production into the wellbore, even if the 30 m are true net pay. This is the result of a typical situation that occurs in most naturally fractured reservoirs we are familiar with; i.e., the matrix has a very low permeability, which does not permit efficient fluid flow into the wellbore. This same tight matrix, however, can flow very efficiently into the natural fractures(1). Various papers have contributed to our understanding of transient behaviour in multi-layered reservoirs(2–6).
Aguilera et al.(7) evaluated data from the naturally fractured Palm Valley gas field using analytical and numerical simulation techniques. Both approaches provided approximately the same results. In a subsequent paper, Aguilera(8) used a numerical simulator to examine the behaviour of a naturally fractured reservoir with ten layers and with fracture permeabilities ranging between 6.91 and 1,232.41 mD. The geometric mean permeability was 40 mD. The thickness of each layer (1.6 m) and the fracture spacing (3.35 m) were constant. From this analysis, it was concludedthat multi-layered behaviour could be recognized by a pressure derivative indicating partial penetration effects, even if the well was perforated in all layers. The partial penetration effects correspond to a derivative with a slope equal to about - 0.5. This was followed by an indication of linear flow; i.e., aslope of the pressure derivative equal to approximately +0.5. This technical note is a continuation of the research published by Aguilera(8). In the present paper, we are using the same numerical model, but in addition to variations in fracture permeability, we include variations in layer thickness, fracture spacing, and fracture porosity(9).
FIGURE 1: Outcrop of the Cardium sandstone showing variations in layer thickness and fracture spacing (Seebe Dam, Alberta, Canada). Width of shown outcrop is approximately 25 m.

Results
Most reservoir parameters have been kept as in the previous study(8). Pay thickness for the reservoir is 16 m. Matrix porosity is 4.8% Matrix permeability is 0.023 mD. Gas saturation in the matrix is 42%, and gas saturation in the fractures is 99%.