Tarner (1944) suggested an iterative technique for predicting cumulative oil production Np and cumulative gas production Gp as a function of reservoir pressure. The
method is based on solving the MBE and the instantaneous GOR equation simultaneously for a given reservoir pressure drop from a known pressure Pi 1 to an
assumed (new) pressure Pi. It is accordingly assumed that the cumulative oil and gas
production has increased from known values of (Np)i 1 and (Gp)i 1at reservoir
pressure Pi 1 to future values of (Np)i and (Gp)i at the assumed pressure Pi. To
simplify the description of the proposed iterative procedure, the stepwise calculation
is illustrated for a volumetric saturated oil reservoir; however, this method can be
used to predict the volumetric behavior of reservoirs under different driving
mechanisms.
Tarner’s method was preferred to Tracy and Muskat because of the differential
form of expressing each parameter of the material balance equation by Tracy. Also,
Tarner and Muskat method use iterative approach in the prediction until a convergence is reached.
Furthermore, a first approach of the Cumulative Oil Production is needed before
the calculation is performed; a second value of this variable is calculated through the
equation that defines the Cumulative Gas Production, as an average of two different
moments in the production life of the reservoir; this expression, as we will see, is a
function of the Instantaneous Gas Oil Rate, then we need also to calculate this value
in advance from an equation derived from Darcy’s law, this is a very important
relationship since it is strongly affected by the relative permeability ratio between oil
and gas. Finally, both values are compared, if the difference is within certain
predefined tolerance, our first estimate of the Cumulative Oil Production will be
considered essentially right, otherwise the entire process is repeated until the desire
level of accuracy is reached (Tarner 1944).
Tarner’s Prediction Algorithm
Step 1: Select a future reservoir pressure Pi below the initial (current) reservoir
pressure Pi 1 and obtain the necessary PVT data. Assume that the cumulative oil
production has increased from (Np)i 1 to (Np)i. It should be pointed out
that (Np)i 1 and (Gp)i 1 are set equal to zero at the bubble-point pressure
(initial reservoir pressure).
Step 2: Estimate or guess the cumulative oil production (Np)i at Pi.
Step 3: Calculate the cumulative gas production (Gp)i by rearranging the MBE to
give:
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Tracy Prediction Method
Tracy (1955) developed a model for reservoir performance prediction that did not
consider oil reservoirs above bubble-point pressure (undersaturated reservoir) but
the computation starts at pressures below or at the bubble-point pressure. To use this
method for predicting future performance, it is pertinent therefore to select future
pressures at desired performance. This means that we need to select the pressure step
to be used. Hence, Tracy’s calculations are performed in series of pressure drops that
proceed from a known reservoir condition at the previous reservoir pressure (Pi 1)
to the new assumed lower pressure (Pi). The calculated results at the new reservoir
pressure becomes “known” at the next assumed lower pressure. The cumulative gas,
oil, and producing gas-oil ratio are calculated at each selected pressure, so the goal is
to determine a table of Np, Gp, and Rp versus future reservoir static pressure.
Tracy’s Prediction Algorithm
Step 1: Select an average reservoir pressure (Pi) of interest
Step 2: Calculate the values of the PVT functions ɸo, ɸg & ɸw where
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Schilthuis Prediction Method
Schilthuis develop a method of reservoir performance prediction using the total
produced or instantaneous gas-oil ratio which was defined mathematical as:
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