reservoir · material balance
Material Balance — Havlena-Odeh Straight Line
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Inputs
—
Paste one row per line — separate columns with a comma or tab: Underground Withdrawal (bbl), Total Oil+Gas Expansion (RB/STB), Gas Cap Expansion (RB/STB)
⚠ Needs at least 3 valid rows to calculate — 0 so far.
Description
Back-solves original oil in place (N) from production and PVT history using the Havlena-Odeh straight-line rearrangement of the general material balance equation: plotting underground withdrawal (F) against total expansion (Et, optionally plus a gas-cap term m·Efg) gives a line through the origin whose slope is N. This is the multi-point extension material_balance_undersaturated's own limitations already point to — it uses ALL available historical (F, Et, Efg) triples in one regression instead of solving N from a single pressure/production pair.
Variables
| Symbol | Unit | Description |
|---|---|---|
| N | STB | OOIP (from Havlena-Odeh) |
| m | — | Ratio of initial gas-cap reservoir volume to initial oil-zone reservoir volume — a single reservoir-wide constant, the same value at every row, so it is a scalar sibling input rather than a per-row array column. Set to 0 for a reservoir with no initial gas cap. |
| F, Et, Efg | — | One row per historical reporting date: underground withdrawal (F, from production data) and the two expansion terms Et (Oil & Solution Gas Expansion calculator's Eo, generalized to include water/formation compressibility) and Efg (Gas Cap Expansion calculator's Eg) at that same date. Et and Efg are kept as separate columns rather than pre-combined by the user, since m is a single reservoir-wide constant applied uniformly — the calculator computes x = Et + m·Efg internally so the same m entered once above is used consistently across every row, rather than requiring the user to hand-multiply m·Efg per row. |
Assumptions
- The reservoir has no significant water influx (We=0) over the history being analyzed — an actively water-driven reservoir requires the general Havlena-Odeh form with We as an additional term, not implemented here
- Et and Efg at each row are computed consistently (e.g. from the Oil & Solution Gas Expansion and Gas Cap Expansion calculators) at the SAME reporting date as that row's F
- m (gas cap ratio) is constant over the production history analyzed — a materially changing m over time would require a more general treatment
Limitations
- Excludes water influx entirely — applying this to a reservoir with real aquifer support will produce a systematically biased (usually inflated) N, visible as a curving or non-origin-passing trend in the underlying data
- A single m value is applied to every row — if the true gas cap size is uncertain, running the regression at a few candidate m values and comparing R² is the standard practice for sensitivity-testing m, not automated here
- Requires several (F, Et, Efg) triples spanning a meaningful range of expansion values for a well-constrained fit; early-life data with little pressure depletion carries high leverage and low information content
Use Cases
- → Multi-point dynamic OOIP: Replace material_balance_undersaturated's single-point N estimate with a regression across the reservoir's full production history once multiple (P, Np) data points are available, reducing sensitivity to any one point's measurement error.
- → Gas cap size sensitivity check: Re-run the regression at several candidate m values; the m that produces the highest R² (straightest line) is the standard Havlena-Odeh diagnostic for confirming or refining an assumed gas cap size.
- → Reservoir connectivity / water-drive screening: A poor fit (low R²) after excluding water influx by assumption is itself diagnostic — it suggests either compartmentalization or that the reservoir has more aquifer support than assumed, both actionable findings for reservoir management.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Spraberry unconventional reservoirs are almost always closed, depletion-drive systems (We≈0), making the no-water-influx form used here directly applicable without the general Havlena-Odeh extension.
Gulf of Mexico
GOM sandstone reservoirs with a known or suspected gas cap commonly use m in the 0.1-0.5 range; always cross-check the fitted N against a volumetric OOIP estimate.
North Sea
Brent Group reservoirs with a gas cap benefit from the m-sensitivity check (useCases above) since gas cap size is often one of the more uncertain volumetric parameters in these fields.
Global
If the fitted N drifts significantly as more historical points are added over time (rather than converging to a stable value), that is the classic Havlena-Odeh signature of unaccounted water influx — revisit the We=0 assumption.
References
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