Modelling facility for field-average formation pressure at any time moment as response to production flowrates history, which in case of MBO fluid takes form:
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where
Cumulative oil production by the time moment | |||
initial open pore volume of the main pay (excluding the aquifer and gas cap) | Cumulative gas production by the time moment | ||
Cumulative water production by the time moment | |||
pore compressibility | Cumulative water injection by the time moment | ||
initial water saturation | Cumulative gas injection by the time moment | ||
initial gas saturation | Cumulative water influx from Aquifer Expansion by the time moment | ||
initial oil saturation: | Cumulative gas influx from Gas Cap expansion by the time moment | ||
Oil formation volume factor as functions of reservoir pressure | Solution GOR as functions of reservoir pressure | ||
Gas formation volume factor as functions of reservoir pressure | Vaporized Oil Ratio as functions of reservoir pressure | ||
Water formation volume factor as functions of reservoir pressure |
The MatBal equation can be re-written in the following popular form:
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where
Cumulative Voidage Replacement Balance (CVRB) |
The MatBal equation can be complemented by constant PI model of Bottom-Hole Pressure ( for producers and for injectors):
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where | where | ||||
cumulative offtakes from -th producer by the time moment | cumulative intakes to -th injector by the time moment | ||||
productivity index of -th producer | injectivity Index of -th injector |
In practice there is no way to measure the external influx and so that one need to model them and calibrate model parameters to fit available data on production flowrates history and formation pressure data records.
There is a list of various analytical Aquifer Drive and Gas Cap Drive models which are normally related to pressure dynamics :
Gas Cap Drive @model | Aquifer Drive @model | ||
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which closes equation for the pressure .
In some specific cases equation can be explicitly integrated with the accuracy sufficient for practical applications:
Low pressure dry gas | ||||
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where
Cumulative Voidage Replacement Balance (CVRB) |
The above approximations sometime allow using simple graphical methods for rough estimation of drainage volume and associated Hydrocarbon Reserves.
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Material Balance Analysis (MatBal)
[ Material Balance Pressure Plot ][ FMB Pressure @model]
[ Derivation of Material Balance Pressure @model ]
[ Modified Black Oil fluid @model (MBO) ]