Naturally fractured reservoirs have two distinct porosities, one in the matrix and one in the fractures. Although naturally fractured reservoirs consist of irregular fractures, they can be represented by equivalent homogeneous dual porosity systems (Warren and Root (1963)).

Quite often, the volume of hydrocarbon stored within the natural fractures is much lower than is stored in the matrix. In dual porosity systems, the natural fractures have much higher permeability than the matrix. When the well begins to flow, fluid travels from the high permeability natural fractures to the wellbore and is rapidly produced. Once the natural fractures have been drained, the large volume of hydrocarbons contained within the bulk of the reservoir (matrix) begins to flow. These hydrocarbons flow to nearby natural fractures and virtually all of the fluid is transported to the wellbore via these fractures.

The signature of dual porosity systems on a semi-log plot is two parallel lines as shown below.

The first semi-log straight line is observed at early time and represents radial flow as the fluid, initially in the fractures, travels to the wellbore. The second semi-log straight line occurs when the fractures deliver fluid from the matrix to the wellbore. The transition period between the two semi-log straight lines occurs when fluid begins to flow from the matrix to the fractures but has not yet reached a state of equilibrium.

Be aware that dual porosity, especially the first semi-log straight line, may not be noticeable even if the reservoir is naturally fractured because wellbore storage effects could affect the data.

Naturally fractured reservoirs are characterized by two parameters, the interporosity flow coefficient (l) and the storativity ratio (w).

As shown in the plot below, as the interporosity flow coefficient decreases, the transition between the two semi-log straight lines is delayed. That is, the larger the fracture permeability is in comparison to that of the matrix, the more time the fractures will have to drain before the contribution from the matrix becomes significant.

Note that there are two types of interporosity flow which are used to model dual porosity systems:

The second parameter, storativity ratio
(*w*),
essentially represents the time separation in log cycles between the two
semi-log straight lines as shown below.

A storativity ratio of 1 is a single porosity system with all of the reserves inside the fractures, and a storativity ratio approaching 0 is a single porosity reservoir with all the reserves inside the matrix. Therefore, as the storativity ratio is decreased, a greater portion of the reserves are contained in the matrix and the longer it takes for the matrix and fracture system to reach a state of equilibrium. This is shown in the following plot:

The signature of dual porosity on a derivative plot shows up as two
regions of radial flow with the same conductivity,
*kh*, separated by a transition
period. This is often referred to as the dual porosity dip.

As in the case for the semi-log plot, the shape and location of this
transition period or dual porosity signature are defined by the interporosity
flow coefficient (*l*)
and the storativity ratio (*w*)
as shown in the plots below.

It is important to note that when analyzing dual porosity data that
the value of apparent or total skin (*s'*)
should always be taken from the second semi-log straight line or the second
radial flow region on the derivative plot.

"Gas Reservoir Engineering", J. Lee and R. Wattenbarger, Society of Petroleum Engineers Inc. (1996) Volume 5, 73 - 74, 173 - 181.

"The Behavior of Naturally Fractured Reservoirs", J.E. Warren and P.J. Root, Society of Petroleum Engineers Inc. (1963) SPEJ 426.