How to define the hydrocarbon reserves with a well test ?
The well test objectives in general include the determination of the well and reservoir performance: KH, skin S, turbulence (non-Darcy skin), hydrocarbon reserves, etc… The latter can be formulated in terms of minimum connected volume or minimum drainage area.
The conventional method to define the well reserves V is to produce a volume of hydrocarbon ∆V and measure the resulting decrease in average reservoir pressure ∆P. As per the material balance equation, we have:
∆V = V x Ct x ∆P
With Ct: the total compressibility, V: the proven volume, ∆V: the cumulative production (flared) volume and ∆P: the change in reservoir pressure.
This technique implies that we measure the average reservoir pressure both before and after production of the ∆V volume. This is not a simple task in practice and may result in some errors in extrapolating to reservoir pressure. Given that a test design may assume a certain depletion (a ∆P of 10-20 psi should be enough), this approach may imply some large flared volume and long shut-ins to minimize errors.
Modern well test analysis techniques can be used instead to reduce flaring and optimize the shut-in duration while reducing the uncertainty on the connected volume. Please contact us for more info.
Considerations when designing the PBU Duration
When the well test shows a homogeneous reservoir of infinite acting, the connected reservoir volume depends on the following radius of investigation:
With ∆t: the shut-in duration and ƞ the diffusivity coefficient in oilfield unit (ft2/hr)
With K: reservoir permeability in mD, Φ: porosity (fraction), Ct: total compressibility in 1/psi, : gas viscosity in centipoise cp.
Cr is a constant. According to Muskat (1937) and Lee (1982), Cr = 2 and we have:
The hydrocarbon volume that is investigated by the test is then:
With h: the net reservoir thickness (ft), Φ: porosity (fraction), Sw: initial water saturation (fraction).
This volume can be divided by the formation volume factor to obtain the volume at surface conditions.
As shown in the equations above, the radius of investigation and the connected volume increase with the test duration ∆t so doubling the test duration will double the volume.
In addition the connected volume does not depend on the production rate. So the flow rate could be lowered to reduce flaring while still acquiring some detectable pressure changes at the gauge.
The radius of investigation and connected volume are proportional to the permeability-thickness KH. It is for example more difficult to prove a larger volume for a test in a lower permeability reservoir.
These equations are derived assuming a homogeneous reservoir of infinite extent but could still be useful and provide some guidance on flow and shut-in duration. For our VIP members, an excel file is attached to help you.
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With the presence of boundaries in the reservoir, the volume investigated by a well test may be different. Then a full design study is needed.
Design a test for a large connected volume while reducing hydrocarbon flaring and rig cost.
For a well test design study, it is recommended to work with a range of parameters and several cases. The pressure response can be simulated for each well and reservoir scenario and converted into “actual data”. These data can then be analyzed to calculate the minimum connected volume. Then sensitivities are performed while reducing the flaring volume and optimizing the shut-in periods.
Modern well test analysis tools and techniques can be used to further reduce flaring and increase connected volume. For example, if a reliable deconvolution can be derived then the entire test sequence could be used to provide evidence for larger reserves. However, the PBU durations need to be long enough to provide enough information and derive a reliable deconvolution.
Calculate the minimum connected volume with the test data
Two main methodologies are used :
Some fictitious boundaries can be added to close the interpretation model. Then reduce the distances to these fictitious boundaries until a discrepancy is noted between the actual and simulated derivatives at late times (SPE 102483). If the deconvolved derivative is used, a larger connected volume should be derived.
If a reliable deconvolution is derived (and this needs a bit of expertise), then place the unit-slope straight line indicative of pseudo-steady state on the final point of the deconvolved derivative (SPE 116575). The resulting minimum connected volume will be conservative.
Beware of the gauge noise and resolution
The test duration is not the only factor that should be considered when designing a test. After a long shut-in period, the pressure change in a PBU test can become so small that it may not be detectable by the gauge. Then there is no point in leaving the well shut-in any longer, no more useful information can be extracted. When designing a well test, the user should make sure that the pressure change can be detectable at the end of the planned PBU. Nowadays, this is less of an issue due to the high quality modern quartz gauges.
For more information or for a discussion, please don’t hesitate to contact us.
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