Tarner’s Prediction Method

 Tarner (1944) suggested an iterative technique for predicting cumulative oil produc￾tion 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 simulta￾neously 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 conver￾gence 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:

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

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: