Introduction
Some of the roles of Reservoir Engineers are to estimate reserve, field development
planning which requires detailed understanding of the reservoir characteristics and
production operations optimization and more importantly; to develop a mathematical model that will adequately depict the physical processes occurring in the
reservoir such that the outcome of any action can be predicted within reasonable engineering tolerance of errors. Muskat (1945) stated that one of the functions
of reservoir engineers is to predict the past performance of a reservoir which is still in
the future. Therefore, whether the concept of the engineer is wrong or right, stupid
or clever, honest or dishonest, the reservoir is always right.
We have to bear in mind that reservoirs rarely perform as predicted and as such,
reservoir engineering model has to be updated in line with the production behaviour.
Thus, an accurate prediction of the future
production rates under various operating
conditions, apply the primary requirement for the oil and gas reservoirs feasibility
evaluation and performance optimization. The conventional method of utilizing
deliverability and material balance equations to predict the production performance
of these reservoirs cannot be utilized often when the complete reservoir data are
lacking.
Reservoir performance prediction is an iterative process. it requires that a convergence criterion must be met after a satisfactory history match is achieved, to be
executed in a short period of time, for a proper optimization of future reservoir
management planning of a field. There are basically four methods of reservoir
performance prediction applying material balance concept and not a numerical
approach where the reservoir is divided into grid blocks. These are:
• Tracy method
• Muskat method
• Tarner method
• Schilthuis method
All the techniques used to predict the future performance of a reservoir are based
on combination of appropriate MBE with the instantaneous GOR using the proper
saturation equation. The calculations are repeated at a series of assumed reservoir
pressure drops. These calculations are usually based on stock-tank barrel of oil-inplace at the bubble-point pressure. Above the bubble point pressure, the cumulative
oil produced is calculated directly from the material balance equations as presented
in Craft & Hawkins (1991), Dake (1978), Tarek (2010), Cole (1969), Cosse (1993),
Economides et al. (1994) & Hawkins (1955). The MBE for undersaturated reservoir
are expressed below.
11.1.1 For Undersaturated Reservoir (P > Pb) with No Water
Influx
That is above the bubble point; the assumptions made are:
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In applying the above methods of prediction for saturated reservoirs, we require
some additional information to match the previous field production data in order to
predict the future. Such relations are the instantaneous gas-oil ratio (GOR), equation
relating the cumulative GOR to the instantaneous GOR and the equation that relates
saturation to cumulative oil produced.
On the contrary, despite the fact that the material balance equation is a tool used
by the reservoir engineers, there are some aspects which were not put into consideration when performing prediction performance. These are:
• The contribution of the individual well’s production rate
• The actual number of wells producing from the reservoir
• The positions of these wells in the reservoir are not considered since it is assume
to be a tank model
• The time it will take to deplete the reservoir to an abandonment pressure
• Does not see faults in the reservoir if there is any and the variation in rock and
fluid properties.
Instantaneous Gas- Oil Ratio
Instantaneous gas-oil ratio at any time, R is defined as the ratio of the standard cubic
feet of gas produced to the stock tank barrel of oil produced at that same instant of
time and reservoir pressure. The gas production comes from solution gas and free
gas in the reservoir which has come out of the solution (Tarek, 2010).
Instantaneous producing GOR is given mathematically as
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Muskat’s Prediction Method
In 1945, Muskat developed a method for reservoir performance prediction at any
stage of pressure depletion by expressing the material balance equation for a
depletion-drive reservoir in differential form as derived below.
The oil pore volume (original volume of oil in the reservoir) is given as:
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Muskat’s Prediction Algorithm
At any given pressure, Craft et al. (1991) developed the following algorithm for
solving Muskat’s equation:
Step 1: Obtain relative permeability data at corresponding saturation values and then
make a plot of krg/kro versus saturation.
Step 2: Make a plot of fluid properties {Rs, Bo and (1/Bg)} versus pressure and
determine the slope of each plot at selected pressures, i.e., dBo/dp, dRs/dp, and d
(1/Bg)/dp.
Step 3: Calculate the pressure dependent terms X(p), Y(p), and Z(p) that correspond
to the selected pressures in Step 2.
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