The wellbore storage effect is defined immediately after a production start-up or shut-in, when the pressure behaviour at early times is dominated by the compressibility and volume of the wellbore fluid.
At the start of a flow period, production at surface is due to the expansion of the fluid in the wellbore, and not the reservoir. There is a time lag when the surface production rate becomes consistent with the sandface rate and this defines the wellbore storage period. At shut-in, the fluid gets compressed in the wellbore and the rate at sandface gradually goes to 0.
Wellbore storage is a function of the wellbore fluid and the completion size. The wellbore storage coefficient is defined as: C = Cf Vf with Cf the fluid compressibility and Vf the fluid volume. It is measured in units of bbl/psi.
All types of wells, including fractured wells, may experiment wellbore storage at the start of a drawdown period or a PBU test.
Log-log derivative shape
During wellbore storage, the pressure changes linearly with time:
As a result, wellbore storage is identified by a unit-slope straight line on a log-log plot, as shown below:
A typical wellbore storage coefficient for a vertical well is C= 0.01 bbl/psi and it could be reduced to 0.001 bbl/psi with a downhole shut-in. Horizontal and fractured wells will have larger wellbore storage effects with C ≥ 0.1 bbl/psi with a surface shut-in, as they connect to larger fluid volumes.
A higher compressibility or fluid volume will increase the wellbore storage coefficient and shift the unit-slope straight line towards later times, as shown below.
Usually a parasitic effect
During wellbore storage, the rate measured at surface is not equivalent to the rate at sandface.
The rate at the perforations is related to the surface measured rate as follows:
With C the wellbore storage coefficient, B the formation volume factor and Pwf the well flowing pressure.
Let’s assume an oil production well with the following rate and BHP history:
As the well starts to produce, we can notice some large pressure drop, with a well flowing pressure that decreases to 1,000 psi. This could be explained by some large wellbore damage or some small permeability value. We need to have a look at the derivative plot for more information.
As seen in the above log-log plot, only the wellbore storage effects are visible and the PBU tests are too short. Looking at the short flow periods in the production history plot, the flow behaviour and the entire pressure data are in fact controlled by the wellbore unloading process. As a result, we cannot extract any information about the well and the reservoir.
For this particular case, there may be some additional problems related to wellbore phase redistribution. The fluid weight below the gauge may change over time and the measured pressure data may not be representative of the pressure at the perforations.
Since the data are dominated by wellbore storage, the surface rate is not related to the downhole rate and we cannot rely on the rate measurement to perform a well test interpretation.
The figure below shows a comparison between the measured surface rate and the downhole rate.
While the two rates are different, the cumulative production using the rate at sandface should follow the cumulative production from the surface rate.
During shut-in, wellbore storage effects could mask some critical flow regimes
Wellbore storage effects could mask some characteristic reservoir responses and should be minimized as a result. This can be achieved by using a downhole shut-in tool and reducing the volume between the tool and the perforations.
The plot below shows a comparison between a PBU test acquired at surface and one with a downhole shut-in tool.
In this example, the radial flow regime is masked by the wellbore storage effects from the surface shut-in. Without a downhole shut-in, the derivative stabilization (red horizontal line) would be misinterpreted as radial flow regime, leading to a wrong skin and permeability (under-estimated by a factor of 2 here). In reality, this red stabilization is due to the presence of a fault and the “true” radial flow regime (blue horizontal line) is visible when a downhole shut-in is performed. For this particular case, minimizing the wellbore storage effects with a downhole shut-in helped to identify the radial flow regime and obtain KH and skin.
A downhole shut-in valve will also help minimize wellbore phase redistribution, resulting in a more representative well and reservoir response.
Changing wellbore storage during the same PBU test
During a PBU test, the wellbore storage may change over time with some phase redistribution in the wellbore. This is often the case with a shallow pressure gauge and a surface shut-in.
If the fluid compressibility is reduced during the shut-in period (liquid falling at the bottom of the well), the derivative will show this typical behaviour:
If the fluid compressibility is getting increased during the shut-in period (gas accumulation, condensate getting re-vaporized, liquid re-injection in the reservoir), the derivative could have the following shape:
A changing wellbore storage would increase the duration of the wellbore storage effects and could mask flow regimes and a larger part of the reservoir response.
Worse, it could create some derivative features that could be misinterpreted as flow regimes. For example, changing wellbore storage could be misinterpreted as limited perforations, damage, sand fill, multilayer effect, dual porosity behaviour, reservoir heterogeneities, etc… On some occasions, the entire PBU test may become useless due to changing wellbore storage.
When the build-up pressure stabilizes or even decreases due to the accumulation of an heavier fluid at the bottom of the well, some discontinuity and “break” in the derivative will be visible, as shown below.
Applications with multiple PBUs
There are some cases when the pressure behaviour associated with wellbore storage may contain some useful information.
Comparing wellbore storage coefficients from several PBUs could help to detect some changes in fluid properties or connected volume.
For example, a gas condensate well may see a decrease in wellbore storage, as the condensate drops out in the reservoir and reduce the total compressibility. This is illustrated below with the PBU test in blue, showing a decrease in storage. Between the two PBU tests, the well would have produced below the dew point pressure and some condensate would have dropped out.
For an oil well, an increase in wellbore storage may indicate an increase in compressibility due to a gas breakout.
An increase in wellbore storage could indicate a connection to some larger fluid volume. For a water injector, this could be created by a thermal fracture.
For a fractured well, an increase in wellbore storage tends to indicate an increase in fracture volume. The fracture dimension could be approximately calculated from the storage coefficient (the fracture storage would be equal to the fluid volume inside the fracture, extracting a fracture length based on a frac width and height).
The wellbore storage coefficient could be tracked over time, via opportunistic PBUs, to monitor the fracture dimension and ensure no excessive frac growth (fluid containment and cap rock integrity).
Wellbore storage is an important flow regime in well test interpretation