ResvEngine

Material balance · energy plot

Havlena–Odeh plot

The 0D tank material balance can be written so that underground withdrawal F is linear in expansion Etot. On that plane the slope is original oil in place N (Sm³). The same axes are live in the material balance calculator; this page is the plot, the members, and the literature.

PVT that feeds Bo, Bg, Rs is already live: black-oil calculator.

Why a straight line

Havlena and Odeh recast the tank balance as an equation of a straight line (energy plot). FieldFlow’s canonical oil form is:

F=N⋅Etot+We,resF = N \cdot E_{\mathrm{tot}} + W_{e,\mathrm{res}}

With no aquifer, F vs Etot goes through the origin; the slope is N in Sm³. Units: F and We,res in Rm³, Etot in Rm³/Sm³. Do not divide Eo by Boi in this writing — that would make the slope N Boi (initial oil volume in the reservoir), not N.

Havlena–Odeh energy plot schematicStraight line through the origin on F versus E tot axes. Slope is N. A dashed curve bending above the line marks water influx or gas-cap effects.E tot (Rm³/Sm³)F (Rm³)slope ≈ NWe or gas cap — leaves the line0
Schematic only — not calculated from field data. A live plot will sit on the future tank calculator, same axes.

What leaves the line

  • Water influx — We > 0 shifts points above the closed-tank line (same idea as a Cole p/Z bend on gas).
  • Gas cap — parameter m adds Eg; a wrong m looks like a curve or a wrong intercept.
  • Bad PVT — inconsistent B or Rs scatters the plot even when the tank is closed.

Free ResvEngine material balance is sliders for N and m, not an autofit of N. The plot is for reading energy, not for claiming a unique OOIP from one click.

Underground withdrawal F

Black-oil voidage (surface cumulatives × formation volume factors at current p). Rs here is the current solution GOR, not Rsi:

F=Np(Bo+(Rp−Rs)Bg)+WpBw−WiBw,inj−Gi,injBg,injF = N_p \bigl( B_o + (R_p - R_s) B_g \bigr) + W_p B_w - W_i B_{w,\mathrm{inj}} - G_{i,\mathrm{inj}} B_{g,\mathrm{inj}}

Rp = Gp/Np (cumulative). Injection terms are zero in the first public tank.

Expansion members

Two-phase oil FVF Bt = Bo + (Rsi − Rs) Bg, with Bti = Boi:

Eo=Bt−BtiE_o = B_t - B_{ti}
Eg=m Boi(BgBgi−1)E_g = m\, B_{oi}\left(\frac{B_g}{B_{gi}} - 1\right)
Ef,w=(1+m) Boi cwSwc+cf1−Swc (pi−p)E_{f,w} = (1+m)\, B_{oi}\,\frac{c_w S_{wc} + c_f}{1-S_{wc}}\,(p_i - p)
Etot=Eo+Eg+Ef,wE_{\mathrm{tot}} = E_o + E_g + E_{f,w}

Dry-gas tanks use a separate F = G Eg + We and a p/Z Cole plot — not this oil H–O plane.

Applicability

  • Single 0D tank — not a 3D grid or well drainage model.
  • Same METRIC standard conditions as the PVT pack: 1.01325 bar, 15.5 °C.
  • Live history match is on the material balance calculator, not this theory page.

What you can do now

The tank calculator is live. Build the PVT table the match will use, or open material balance.

Open PVT calculatorOpen material balance

References

  • D. Havlena, A.S. Odeh, The Material Balance as an Equation of a Straight Line, J. Pet. Technol., SPE-559-PA, 1963. Read SPE-559-PA
  • L.P. Dake, Fundamentals of Reservoir Engineering.
  • B.C. Craft, M.F. Hawkins, Applied Petroleum Reservoir Engineering.