MBE of an under-saturated reservoir with pressure falling below the bubble point pressure

Havlena and Odeh (1963) provides the best explanation of the material balance of a reservoir. It

considers most reservoir conditions including the produced fluid, expansion of oil and its originally

dissolved gas, the gas cap expansion and the initial water expansion and pore volume reduction.

The formula derived by Havlena and Odeh is described below:

ewfg WEmEENF ][ ,0 ……… eqn (1)

Where:

Underground Withdrawal, wpgspop BWBRRBNF ])([

Expansion of oil and its originally dissolved gas, gssioioo BRRBBE )()(

Expansion of the gas cap,

1

gi

g

oigB

BBE

Expansion of initial water and the reduction of pore volume, pS

cScBmE

wi

fwiw

oiwf

1)1(,

When the reservoir pressure falls below the bubble point pressure:

From equation (1) When the pressure of the reservoir is equal to the bubble point pressure

of the reservoir )( bPP , the gas dissolved in the oil begins to be liberated. Because of this, the

initial volume of the gas cap is zero. Hence, the ratio of the initial gas cap to the initial oil volume in

the reservoir is, 0m . This results in the term for the expansion of the gas cap gE to be neglected

from the equation.

From the bubble point pressure and below )( bPP , the expansion of the solution gas far

outweighs the expansion of the initial reservoir water and formation rock expansion. This allows us

to neglect the term, wfE ,

For the sake of simplicity, we will assume that water is not encroached or produced from the

reservoir. 0pW and 0eW

][ 0ENF

By completing the terms:

])()[(])([ gssioiogspop BRRBBNBRRBN

This equation clarifies that the produced fluids on the LHS of the equation contains both oil and gas.

The RHS provides a difference between the oil and gas liberated from the initial conditions to the

current conditions below the bubble point pressure which is equal to the LHS. (The difference

between the initial and current conditions gives us the produced fluids)

When below the bubble point pressure, the values of Rs and Rp cannot be neglected as the oil in the

reservoir and the produced oil is no longer the same value of Rsi as when the reservoir pressure was

above the bubble point pressure.

By expanding the equation:

gsgsioiogspgppop BNRBNRNBNBBRNBRNBN

Terms Explanation

opBN The volume of oil produced in res.bbl

gpp BRN The volume of gas liberated from the produced oil in res.bbl

gsp BRN The volume of gas dissolved in the produced oil in res.bbl

oNB The volume of oil remaining in the reservoir in res.bbl

oiNB The initial volume of oil in the reservoir at the initial reservoir pressure in res.bbl

gsiBNR The initial volume of gas dissolved in the oil in the reservoir at the initial reservoir pressure in

res.bbl

gsBNR The current volume of gas dissolved in the oil in the reservoir at the current pressure res.bbl