Chapter 3 Material Balance Applied to Oil Reservoirs § 3.1 Introduction -The Schilthuis material balance equation - Basic tools of reservoir engineering => Interpreting and predicting reservoir performance. -Material balance 1. zero dimension – this chapter 2. multi-dimension (multi-phase) – reservoir simulation

§ 3.2 General form of the material balance equation for a hydrocarbon reservoir Underground withdrawal (RB) = Expansion of oil and original dissolved gas (RB)………(A) + Expansion of gascap gas (RB) ……………… ………(B) + Reduction in HCPV due to connate water expansion and decrease in the pore volume (RB)……………………… …….……(C)

Expansion of oil & originally dissolved gas

Expansion of the gascap gas Expansion of the gascap gas =gascap gas (at p) –gascap (at pi)

Change in the HCPV due to the connate water expansion & pore volume reduction

Underground withdrawal

The general expression for the material balance as

where

No initial gascap, negligible water influx With water influx eq(3.12) becomes Eq.(3.12) having a combination drive-all possible sources of energy.

§ 3.4 Reservoir Drive Mechanisms - Solution gas drive - Gascap drive Natural water drive - Compaction drive In terms of reducing the M.B to a compact form to quantify reservoir performance determining the main producing characteristics, for example, GOR; water cut determining the pressure decline in the reservoir - estimating the primary recovery factor

§ 3.5 Solution gas drive (a) above the B.P. pressure (b) below the B.P. pressure

Above the B.P. pressure - no initial gascap, m=0 - no water flux, We=0 ; no water production, Wp=0 - Rs=Rsi=Rp from eq.(3.7)

Exercise3.1 Solution gas drive, undersaturated oil reservoir Determine R.F. FromTable2.4(p.65) Eq(3.18)

Table 2.4 Field PVT P(psia) Bo (Rb/STB) Rs(SCF/STB) Bg( Rb/SCF) 4000 (pi) 1.2417 510 3500 1.2480 510 3300 (pb) 1.2511 510 0.00087 3000 1.2222 450 0.00096 1.2022 401 0.00107 1.1822 352 0.00119 1.1633 304 0.00137 1800 1.1450 257 0.00161 1.1287 214 0.00196 1200 1.1115 167 0.00249 1.0940 122 0.00339 1.0763 78 0.00519 300 1.0583 35 0.01066

Bo as Function of Pressure

Rs as Function of Pressure

Bg and E as Function of Pressure

Producing Gas-oil Ratio (R) as Function of Pressure

Below B.P. pressure (Saturation oil) P<Pb =>gas liberated from saturated oil

Exercise3.2 Solution gas drive; below bubble point pressure Reservoir-described in exercise 3.1 Pabandon = 900psia (1) R.F = f(Rp)? Conclusion? (2) Sg(free gas) = F(Pabandon)? Solution: (1) From eq(3.7)

Eq(3.7) becomes Conclusion:

(2) the overall gas balance liberated gas in the reservoir total amount of gas gas produced at surface gas still dissolved in the oil = − −