## Well Test Analysis in Naturally-Fractured Reservoirs

##### Following the article on Fracture Behaviour, this post looks at the types of transient responses and well tests that are expected in naturally-fractured reservoirs.

## Dual-porosity behaviour

##### A dual porosity behaviour may be visible with the presence of a porous medium of negligible permeability (matrix) and a high permeability medium (natural fractures). In this case, the parameter Kappa tends to 1.

##### A dual-porosity behaviour will be detected by a “U-shaped” derivative feature, as shown in the figure below.

##### After some wellbore storage and skin, a first derivative stabilization would represent the flow in the high permeability medium (natural fracture network) and be indicative of Kf.H, with Kf the fracture permeability. This stabilization may not be visible with a large wellbore storage and/or an induced fracture at the wellbore.

##### Then the U-shaped derivative feature represents the flow or recharge from the matrix into the fracture system. This transition, called interporosity flow from the matrix to the fracture, could occur under pseudo-steady flow (standard case) or under transient flow condition. In the latter case, the first derivative stabilization will no longer be visible and the U-shaped feature will develop right after the wellbore storage effect.

##### According to SPE 28917, an acid-frac stimulation in a dual-porosity reservoir would change the interporosity flow from pseudo-steady state to transient state. As the acid washes the fracture faces, the communication between the fractures and the matrix is improved, resulting in a transient state interporosity flow. We would no longer see the first derivative stabilization but directly the transition between the fracture and the matrix.

##### The derivative stabilization at late times would represent the contribution of the total system and be indicative of total KH. The total permeability-thickness is roughly the same as that of the high permeability medium, since the permeability in the matrix is negligible.

##### The dual-porosity is defined by 2 parameters: lambda and omega.

Lambda λ defines the communication between the matrix and the fracture network. The smaller the lambda, the more difficult the communication between the two media. The derivative transition would then be developed at a later times. λ usually varies between 10^{-10} and 10^{-4}.

^{-10}

^{-4}