Introduction
The material balance equation is a complex equation for calculating the original oil
in place, cumulative water influx and the original size of the gas cap as compared to
the oil zone size. This complexity prompted Havlena and Odeh to express the MBE
in a straight line form. This involves rearranging the MBE into a linear equation. The
straight lines method requires the plotting of a variable group against another
variable group selected, depending on the reservoir drive mechanism and if linear
relationship does not exist, then this deviation suggests that reservoir is not
performing as anticipated and other mechanisms are involved, which were not
accounted for; but once linearity has been achieved, based on matching pressure
and production data, then a mathematical model has been achieved. This technique
of trying to match historic pressure and production rate is referred to as history
matching. Thus, the application of the model to the future enables predictions of the
future reservoir performance. To successfully develop this chapter, several textbooks
and materials such Craft & Hawkins (1991), Dake (1994), Donnez (2010), Havlena
& Odeh AS (1964), Numbere (1998), Pletcher (2002) and Steffensen (1992) were
consulted.
The straight line method was first recognized by Van Everdigen et al. (2013) but
with some reasons, it was never exploited. The straight line method considered the
underground recoverable F, gas cap expansion function Eg, dissolved gas-oil expansion function Eo, connate water and rock contraction function Ef,w as the variable for
plotting by considering the cumulative production at each pressure.
Havlena and Odeh presented the material balance equation in a straight line form.
These are presented below:
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Diagnostic Plot
In evaluating the performance of a reservoir, there is need to adequately identify the
type of reservoir in question based on the signature of pressure history or behaviour
and the production trend. Campbell and Dake plots are the vital diagnostic tools
employed to identify the reservoir type. The plots are established based on the
assumption of a volumetric reservoir, and deviation from this behaviour is used to
indicate the reservoir type.
For volumetric reservoirs whose production is mainly by oil and connate water/
rock expansion, the value of STOIIP, N can be calculated at every pressure where
production data is given. Rearranging the material balance equation as shown below.
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If a plot of cumulative oil production versus net withdrawal over the fluid
expansions is created with a volumetric reservoir data, then the calculated values
of STOIIP, N on the horizontal axis should be constant at all pressure points. In
practice, this is often not the case either because there is water influx or because there
may be faulty pressure or production readings.
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If a gas cap is present, there will be a gas expansion component in the reservoir’s
production. As production continues and the reservoir pressure decreased, the gas
expansion term increases with an increase in the gas formation volume factor. To
balance this, the withdrawal over oil/water/formation expansion term must also
continue to increase. Thus, in the case of gas cap drive, the Dake plot will show a
continual increasing trend.
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expansion term must increase to balance the water influx. With a very strong aquifer,
the water influx may continue to increase with time, while a limited or small aquifer
may have an initial increase in water influx to the extent that it eventually decreases.
The Campbell plot is very similar to Dake’s diagnostic tool, with an exception
that it incorporates a gas cap if required. In the Campbell plot, the withdrawal is
plotted against withdrawal over total expansion, while the water influx term is
neglected. If there is no water influx, the data will plot as a horizontal line. If there
is water influx into the reservoir, the withdrawal over total expansion term will
increase proportionally to the water influx over total expansion. The Campbell plot
can be more sensitive to the strength of the aquifer. In this version of the material
balance, using only ET neglects the water and formation compressibility (compaction) term. The Campbell plot is shown below.
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The Linear Form of the Material Balance Equation
According to Tarek (2010), the linear form of MBE is presented in six scenarios to
determine either m, N, G or We as follow:
• Undersaturated reservoir without water influx
• Undersaturated reservoir with water influx
• Saturated reservoir without water drive
• Saturated reservoir with water drive
• Gas cap drive reservoir
• Combination drive reservoir
Scenario 1: Undersaturated Reservoir Without Water
Influx
Applying the above assumption, the equation reduces to
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Applying the above assumption, the equation reduces to
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Scenario 3: Saturated Reservoir Without Water Influx
Applying the above assumption, the equation reduces to
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Scenario 4: Saturated Reservoir with Water Influx
Applying the above assumption, the equation reduces to
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Scenario 5: Gas Cap Drive Reservoir
• Finding the STOIIP, N when the gas cap size, m is known
• Finding the gas cap size, m the STOIIP, N and the GIIP, G
Finding the STOIIP, N when the gas cap size, m is known
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Linear Form of Gas Material Balance Equation
Havlena and Odeh also expressed the material balance equation in terms of gas
production, fluid expansion and water influx as
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