| Popis: |
In low permeability reservoirs, the pressure transient response of the build-up takes a long time to stabilize. During the history matching process, the observed non-stabilized build-up pressure cannot be compared to simulated well block pressure (WBP). This challenge arises because most reservoir simulators convert the WBP of flowing wells to wellbore pressure using Peaceman’s equation, but do not perform this conversion for build-up pressure data. Such conversion is particularly important for low permeability reservoirs. This paper discusses a new method to calculate the wellbore pressure of shut-in wells and highlights its benefits. A full superposition equation for analytical wellbore-pressure, without the usual logarithmic approximation of Ei function, is the basis of the mathematical formulation proposed here. A modified equivalent radius concept together with the superposition principle are used to arrive at an expression to calculate numerical wellbore pressure from simulated WBP. To verify the validity of the approach, the calculated numerical wellbore pressure data is compared with analytical wellbore pressure build-up data described by the Horner function. The results show that numerical wellbore pressure is in better agreement with the non-stabilized observed pressure data than WBP. This is because WBP is an average pressure over a spatial distance in which theoretical pressure varies as a logarithmic function of distance. Therefore, when the grid size is large and spatial pressure gradient is significant (as the case in low permeability reservoirs), simulated shut-in WBP may be very different from observed shut-in wellbore pressure measured by a downhole gauge. Our results demonstrate that this difference increases with increasing grid size. If, during numerical well testing, numerical wellbore pressure is used for the log-log pressure derivative plot instead of WBP, the early distortions of infinite acting radial flow (IARF) stabilization, which has been observed by some investigators is eliminated. In summary, the presented methodology to calculate shut-in wellbore pressure is practically attractive to complement existing simulator capabilities for relating wellbore pressure to well block pressure. The use of numerical wellbore pressure instead of WBP, which is currently used, eliminates the need to apply the time-shift proposed by some investigators to correct IARF signature deviation, and observe the true flow regime. |
