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.
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.
Omega ω defines the storativity contrast between the fracture network and the total system. As omega decreases, the transition will start at an earlier time and last longer.
The dual-porosity behaviour is not very common in practice. Other possible solutions could also explain the transient response in naturally-fractured reservoirs.
Linear composite behaviour
In naturally-fractured reservoirs, the derivative tends to show several stabilizations at different levels. Depending on the selection of the radial flow regime, different well and reservoir models may be possible.
In most cases, the data would indicate the presence of reservoir heterogeneities (changes in mobility and storativity further away from the well) and the possible presence of boundaries. Most likely, those heterogeneities would represent some changes in fracture density (SPE 24678).
A network of faults and fractures can be modelled as a linear composite system. As it is often the case with complex systems, the results will be non-unique and several possible combinations of heterogeneities and boundaries could match the data. An effort should be made to show the different possible solutions.
Exploration and Appraisal Well Testing
Usually a stimulation (acidification, acid frac or hydraulic frac) is performed during Exploration and Appraisal well testing operations. A pre-stimulation PBU may also be available to help understand the reservoir characterization, the pre-stim productivity index and the matrix permeability.
Two post-stimulation PBU tests are recommended after the stimulation and clean-up phases. This will help understand the fracture behaviour, the natural fracture network and the well productivity. It will also help obtain some information on connectivity over large volume.
While the stimulation operations should be optimized, sometimes the operator tries to maximize the fracture length and the production rate. Achieving the highest rate possible in Exploration and Appraisal may be counter-productive and could mask some important characteristics of the naturally fractured reservoir. The example below shows that a large fracture in a dual-porosity reservoir will mask the properties of the natural fracture network and lead to an over-estimation of permeability, in this case by 50%.
The post-stimulation PTA response will depend on the type of stimulation.
An acidification is quite common for wells in carbonate reservoirs. The improvement in reservoir mobility and storativity near the wellbore will result in a response similar to a radial composite behaviour.
We should expect a small radius (1-10s of feet) for the acidized zone around the wellbore. Sometimes the first derivative stabilization may not even be visible and the response may look like a hydraulic fracture response.
With an acid frac in a carbonate reservoir, the transient response should be similar to that of an infinite conductivity fracture that connects to a fracture network, as shown below.
The derivative stabilization at late times should represent the permeability of the nearby fracture network. A change in derivative stabilization may develop at later times due to a change in fracture density.
well test analysis in naturally fractured reservoirs such as carbonate, dolomite, chalk reservoirs