fluid_properties · black oil
Oil Viscosity (Dead / Saturated / Undersaturated)
μod = 10^x − 1 (Beggs-Robinson dead) → μob = A·μod^B (saturated) → μo = μob(P/Pb)^m (undersaturated, Vasquez-Beggs)
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Inputs
°F
°API
scf/STB
psi
psi
Description
Computes oil viscosity through the standard three-stage black-oil chain: dead (gas-free) viscosity from API and temperature (Beggs-Robinson 1975), then gas-saturated (live) viscosity from the solution GOR (Beggs-Robinson 1975), then the undersaturated pressure correction above the bubble point (Vasquez-Beggs 1980). Oil viscosity controls IPR, fractional flow, and lift design.
Variables
| Symbol | Unit | Description |
|---|---|---|
| μod | cP | Dead Oil Viscosity (μod) |
| μob | cP | Saturated Oil Viscosity (μob) |
| μo | cP | Oil Viscosity at P (μo) |
| T | °F | Reservoir temperature. The Beggs-Robinson dead-oil correlation was fit to 70–295°F (21–146°C); accuracy degrades outside that window. |
| °API | °API | Oil API gravity. Beggs-Robinson was regressed over 16–58°API; heavy oils below ~16°API are outside the fit and viscosity is increasingly underpredicted. |
| Rs | scf/STB | Solution gas-oil ratio at the pressure of interest (or Rsb at the bubble point), from black_oil_pvt or a PVT report. More dissolved gas lowers live-oil viscosity. |
| P | psi | Pressure at which viscosity is evaluated. Above the bubble point the undersaturated Vasquez-Beggs pressure correction is applied; at or below Pb the saturated viscosity is returned. |
| Pb | psi | Bubble point pressure, from bubble_point_pressure or a PVT report. Sets the saturated/undersaturated boundary; the Rs supplied should be the value appropriate to that state. |
Assumptions
- Black oil (not a volatile oil or gas condensate) — the correlations were fit to conventional crude systems
- Dead-oil inputs (API, T) are inside the Beggs-Robinson fitted ranges (16–58°API, 70–295°F) for best accuracy
- The supplied Rs corresponds to the pressure state being evaluated (Rs at P below Pb, or Rsb at and above Pb)
Limitations
- Below the bubble point this calculator returns the gas-saturated viscosity at the supplied Rs — it does not itself track how Rs declines as pressure drops; recompute Rs (black_oil_pvt) at each pressure for a depletion profile
- Chew-Connally (1959) is the classic alternative for the saturated stage; it is not implemented here because its A(Rs)/b(Rs) coefficients are a later chart digitization rather than equations printed in the 1959 paper — Beggs-Robinson's saturated correlation comes from the same paper as the dead-oil stage and needs no digitization
- Very heavy or waxy crudes (API < 16, or non-Newtonian behavior) are outside the fit and viscosity can be underpredicted by a wide margin — use measured PVT viscosity where available
Use Cases
- → IPR and productivity: Provide μo to Darcy/PI and Vogel IPR calculations — inflow rate scales inversely with oil viscosity, so an accurate μo is essential to deliverability estimates.
- → Depletion viscosity profile: Pair with black_oil_pvt to evaluate how μo rises as reservoir pressure falls toward and below the bubble point (gas coming out of solution thickens the oil).
- → Artificial lift design: Supply live-oil viscosity to lift and multiphase-flow calculations, where viscosity drives frictional pressure loss and pump sizing.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Bone Spring light oils (35–48°API, ~180–240°F) typically give dead-oil viscosity ~0.5–2 cP and live-oil viscosity ~0.3–0.8 cP — well inside the Beggs-Robinson fit. Reliable here.
Middle East Carbonates
Medium crudes (25–35°API) at 180–250°F: μob commonly 0.5–3 cP. Beggs-Robinson performs adequately; validate against PVT for heavier (< 25°API) carbonate crudes where the correlation begins to underpredict.
Global
For heavy oil (< 16°API — e.g. Orinoco, Lloydminster) neither Beggs-Robinson nor the Vasquez-Beggs correction is reliable; dedicated heavy-oil viscosity correlations or lab measurement are required.
References
Primary source
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