Voidage replacement ratio (VRR)
Current voidage replacement at reservoir conditions: the injected water against the produced oil, water and free gas, and the injection needed for 100 % replacement.
VRR = q_i · B_w / (q_o · B_o + q_w · B_w + q_o · (R − R_s) · B_g)q_i(100 %) = (q_o · B_o + q_w · B_w + q_o · (R − R_s) · B_g) / B_wAll volumes are at reservoir conditions. Free gas counts only when R > R_s. Injection lost outside the pattern or to other zones and the influx of aquifer water are not included: with an active aquifer the pressure may hold at a replacement below 100 %.
Source: Reservoir withdrawal terms of the material balance equation: Dake, Fundamentals of Reservoir Engineering (1978)
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Daily for the development unit; cumulative volumes also work if every withdrawal is cumulative too.
Convert tonnes with the oil density.
All produced gas per m³ of oil.
At the current reservoir pressure; R − R_s is free gas from the reservoir. Above the bubble point R = R_s.
Usually 1.00–1.03.
B_g = z · T · P_sc / (P · T_sc): about 0.007 m³/Sm³ at 15 MPa and 70 °C.
Unit converter for this formulaLiquid rate · Gas-oil ratio · Oil formation volume factor · Gas formation volume factor · Fraction and percent
- m³/d1
- m³/h0.0416667
- L/s0.0115741
- L/min0.694444
- m³/min0.000694444
- bbl/d6.28981
- Mbbl/d0.00628981
- ft³/d35.3147
- US gpm0.183453
- bbl/min0.00436792
A day is 24 hours.
- V_res — Reservoir voidage rate–
- q_i(100 %) — Injection for 100 % replacement–
- V_g — Of which free gas (reservoir m³)–
More in Waterflooding and pressure maintenance
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.