The Hurst and van Everdingen model is used to solve for height and cumulative water influx of a partially radial reservoir and aquifer.
An aquifer provides water drive to an oil reservoir. The shape of the reservoir is such that it does not form the full radial shape but a 60 degree wege. The supporting aquifer is considered infinite. The reservoir radius is 27,000ft.
First calculate height of reservoir if after two years 150,000 bbls of water were found to have influxed from the aquifer.
Second, calculate cumulative water influx at the end of each period. Pressure data is given below.
I have attached photographs below of the worked solutions. Just some notes when calculating height. Because the water influx is given for the second year we need to be aware that both year 1 and year two are included in calculations. We calculate dimensionless time for each year, note that these values are applied retrospectively, or in reverse chronological order. Dimensionless time for year two applies to the first year pressure drop because the pressure drop at this moment has been acting for two years. Dimensionless time for year one applies to the second year pressure drop because this has been acting for one year. The value we get for the reservoir is unrealistically thin – I just chose arbitrary numbers for the purpose of calculations.
When calculating the cumulative water influx for each period it is critical to think how long the pressure drop has been acting for rather than at what point in time it occurred. So if we have a pressure drop that occurred in year three, and we are calculating cumulative water influx at year four, we know the pressure drop has been acting for one year and so we use the dimensionless water influx value Q(t) for one year (retrieved from tables using dimensionless time for one year). It can be a trap to write down the pressure drop and dimensionless water influx product in a table, this is why I crossed the section out. Values need to be updated depending on at what point in time a water influx must be calculated.
If there’s any mistakes or suggestions please let me know 🙂
For more information about the Hurst and van Everdingen model and water influx theory go to – http://petrowiki.org/Water_influx_models