Nodal Analysis Calculator

Overview

Nodal analysis (systems analysis) is a method for optimizing well performance by dividing the production system into inflow (reservoir to node) and outflow (node to surface) components and finding the intersection point — the operating point. Developed by Gilbert (1954) and systematized by Brown (1977), it is the foundation of production optimization, artificial lift selection, and completion design.

Theory

The production system from reservoir to separator can be analyzed at any "node" (typically the bottomhole). At the node:

• Inflow: Reservoir delivers fluid to the node (IPR curve)
• Outflow: Tubing/flowline moves fluid from the node to surface (VLP/TPC curve)

The operating point is where inflow = outflow (supply = demand). Changing any component (tubing size, choke, reservoir pressure, artificial lift) shifts the curves and changes the operating point.

Formulas

Inflow Performance (IPR)

Vogel (below Pb):

q/qmax = 1 - 0.2*(Pwf/Pr) - 0.8*(Pwf/Pr)^2

Darcy (above Pb):

q = J * (Pr - Pwf)

Outflow Performance (VLP — Vertical Lift Performance)

The VLP curve is calculated using multiphase flow correlations (Beggs-Brill, Hagedorn-Brown, or Gray) from wellhead to bottomhole:

Pwf_required = WHP + ΔP_gravity + ΔP_friction - ΔP_acceleration

For single-phase liquid (simplified):

Pwf = WHP + 0.433 * SG * L + f * ρ * v^2 * L / (2 * D)

Operating Point

Solve simultaneously:

q_IPR(Pwf) = q_VLP(Pwf)

Graphically: intersection of IPR and VLP curves.

System Sensitivity Analysis

Common nodal analysis sensitivities:

1. Tubing size: Larger tubing → lower friction → shifts VLP left → higher rate (up to a point where slip increases)
2. WHP: Higher backpressure → shifts VLP up → lower rate
3. Reservoir depletion: Lower Pr → shifts IPR down → lower rate
4. GLR: Gas lift changes VLP shape — optimum GLR minimizes VLP
5. Water cut: Increases hydrostatic head → shifts VLP up

Critical Velocity (Turner Equation for Gas Wells)

v_critical = 1.593 * σ^0.25 * ρL^0.25 / ρG^0.5  (ft/s)

Below critical velocity, liquid loading occurs and well may die.

Worked Example

Given: Pr = 3,500 psi, Pb = 2,800 psi, J = 2.0 STB/d/psi (above Pb), WHP = 200 psi, 2-7/8" tubing, depth = 7,000 ft, SG = 0.85, GLR = 500 scf/STB.

Inflow (Composite IPR):

At Pwf = 2,800 psi: q = 2.0 * (3,500 - 2,800) = 1,400 STB/d
qmax_vogel = 1,400 + J*Pb/1.8 = 1,400 + 3,111 = 4,511 STB/d

At Pwf = 2,000 psi:

q_vogel_below = 3,111 * (1 - 0.2*(2000/2800) - 0.8*(2000/2800)^2)
              = 3,111 * (1 - 0.143 - 0.408) = 3,111 * 0.449 = 1,397
q_total = 1,400 + 1,397 = 2,797 STB/d

Outflow (VLP): Calculated using Beggs-Brill or correlation — produces a curve of Pwf_required vs q.

Operating point: Where IPR crosses VLP, e.g., q ≈ 2,200 STB/d at Pwf ≈ 2,200 psi.

Key Design Variables

Component	Effect on Operating Point
Tubing ID increase	Lowers VLP → higher rate (to a limit)
WHP increase	Raises VLP → lower rate
Gas lift	Lowers VLP (lighter column) → higher rate
ESP	Adds ΔP to IPR side → dramatically higher rate
Reservoir depletion	Lowers IPR → lower rate over time
Skin damage	Shifts IPR left → lower rate

References

1. Brown, K.E. & Beggs, H.D. (1977). The Technology of Artificial Lift Methods, Vol. 1. PennWell.
2. Gilbert, W.E. (1954). "Flowing and Gas-Lift Well Performance." Drilling and Production Practice, API.
3. Golan, M. & Whitson, C.H. (1991). Well Performance, 2nd ed. Prentice Hall.
4. PetroWiki — Nodal analysis: https://petrowiki.spe.org/Nodal_analysis