menu_book Chapters 12–13IPR / VLPVogelWell performance

Nodal Analysis → Operating Point

Find the rate a well will actually flow — where reservoir inflow meets tubing outflow — the most intuitive result in production engineering.

What it does

Builds an inflow (IPR) curve with Vogel's equation and a tubing outflow (VLP) curve, then finds their intersection — the well's operating rate and flowing bottomhole pressure — and shows how tubing size, water cut and reservoir pressure move it.

How it works

1Build the IPR (inflow) from reservoir pressure and Vogel's equation.
2Build the VLP (outflow) from hydrostatic head plus tubing friction.
3Find where the two curves cross — that is the operating point.
4Read off the operating rate, flowing BHP and drawdown.
5Change tubing size, water cut or reservoir pressure and watch the point move.

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Run it live

Runs entirely in your browser — no install. Edit any value and press Run to see the result change. This is the whole project; read it top to bottom.

nodal-operating-point.pystarting Python…

import numpy as np
import matplotlib.pyplot as plt

# ── Well & reservoir inputs — tweak these and re-run ────────────────────
Pr    = 3000.0     # average reservoir pressure, psia
qmax  = 1500.0     # absolute open-flow potential (Vogel), bopd
depth = 6000.0     # tubing length, ft
Pwh   = 150.0      # wellhead (surface) pressure, psia
tub_id = 2.992     # tubing inside diameter, in
water_cut = 0.30   # fraction
SG_o, SG_w = 0.85, 1.05

# ── IPR (Vogel): flowing BHP the reservoir supports at rate q ───────────
def pwf_ipr(q):
    x = (-0.2 + np.sqrt(0.04 + 3.2*(1 - np.clip(q/qmax, 0, 1)))) / 1.6
    return x*Pr

# ── VLP (tubing outflow): BHP required to lift rate q to surface ────────
SG_mix = SG_o*(1 - water_cut) + SG_w*water_cut
grad   = 0.433*SG_mix                              # hydrostatic gradient, psi/ft
def pwf_vlp(q):
    hydrostatic = Pwh + grad*depth
    friction    = 3.0e-4 * q**2 * (2.992/tub_id)**5    # rises with rate, falls with ID
    return hydrostatic + friction

# ── Operating point = where inflow meets outflow ────────────────────────
q = np.linspace(1, qmax, 500)
diff = pwf_ipr(q) - pwf_vlp(q)
cross = np.where(np.diff(np.sign(diff)))[0]
if len(cross):
    i = cross[0]
    q_op = np.interp(0, [diff[i], diff[i+1]], [q[i], q[i+1]])
    p_op = float(pwf_vlp(q_op))
    print(f"Operating rate : {q_op:6.0f} bopd")
    print(f"Flowing BHP    : {p_op:6.0f} psia")
    print(f"Drawdown       : {Pr - p_op:6.0f} psi")
else:
    q_op = None
    print("Well will not flow: the tubing outflow is above inflow at every rate.")
    print("Try lowering the wellhead pressure, water cut, or depth.")

# ── Plot IPR and VLP ────────────────────────────────────────────────────
plt.figure(figsize=(8, 5))
plt.plot(q, pwf_ipr(q), color="navy", lw=2, label="IPR  (inflow, Vogel)")
plt.plot(q, pwf_vlp(q), color="firebrick", lw=2, label="VLP  (tubing outflow)")
if q_op is not None:
    plt.scatter([q_op], [p_op], s=90, color="gold", edgecolor="k", zorder=5,
                label=f"Operating point ({q_op:.0f} bopd)")
plt.xlabel("Oil rate (bopd)"); plt.ylabel("Flowing bottomhole pressure (psia)")
plt.title("Nodal Analysis - inflow vs. outflow", fontweight="bold")
plt.legend(); plt.grid(alpha=0.3); plt.ylim(0, None); plt.tight_layout(); plt.show()

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Want the full theory and the real-data version? Read the chapter this project is built from.

Read the chapter Companion repo