Well production profile
A model of one oil well from start-up to the economic limit: inflow to a vertical, deviated, horizontal or hydraulically fractured well, transient and pseudo-steady flow, the bubble point, a liquid-rate plateau, water cut and a material balance with depletion or pressure support. Monthly rate and pressure charts, a yearly table and CSV export.
J = 2π·k_h·h / (μ_o·B_o·(½·ln(4A / (γ·C_A·r_w²)) + s_eq)), γ = 1.781q_L = min(max(q_tr, q_pss), q_L,max), q_o = q_L·(1 − f_w), q_w = q_L·f_w, ΔV = q·U·ΔtΔp̄ = −(1 − VRR)·(q_o·B_o + q_w·B_w)·U·Δt / (V_p·c), V_p = A·h·φ, N = V_p·(1 − S_w) / B_o, B_w = 1All formulas and assumptions of the model
s_eq = 2π·k_h·h / (μ_o·B_o·J) − ½·ln(4A / (γ·C_A·r_w²))s_θ = −(θ'/41)^2.06 − (θ'/56)^1.865 · log(h_D/100), θ' = atan(√(k_v/k_h) · tan θ), h_D = (h/r_w) · √(k_h/k_v)J_h = 2π·k_h·h / (μ_o·B_o·(ln((a + √(a² − (L/2)²)) / (L/2)) + (β·h/L)·(ln(β·h / (r_w·(β + 1))) + s)))a = (L/2)·√(0.5 + √(0.25 + (2·r_eh / L)⁴)), β = √(k_h/k_v), r_eh = √(A/π)s_f = f(F_CD) − ln(x_f / r_w), f = (1.65 − 0.328·u + 0.116·u²) / (1 + 0.18·u + 0.064·u² + 0.005·u³), u = ln F_CDq_tr = 2π·k_h·h·(p_i − p_wf) / (μ_o·B_o·p_D), p_D = ½·(ln t_D + 0.80907) + s_eq, t_D = k_h·t / (φ·μ_o·c_t·r_w²) ≥ 100q_pss = J·(p̄ − p_wf); p_wf < p_b ≤ p̄: J·(p̄ − p_b) + (J·p_b / 1.8)·(1 − 0.2·x − 0.8·x²), x = p_wf / p_b; p̄ < p_b: J → J·p̄/p_bc = c_t; p̄ < p_b: c = c_t + S_o·(B_g / B_o)·(R_s / p_b), B_g = (p_sc / p̄)·(T / T_sc)·Z, Z = 0.9, S_o = (1 − S_w)·(1 − N_p / N)p_wf,min = p_wh + ρ_mix·g·H (TVD); f_w = f_w0 + (0.98 − f_w0)·(RF / RF_ult)^n; t_pss ≈ 0.1·φ·μ_o·c_t·A / k_hAssumptions: one well at the centre of a closed drainage area, a homogeneous reservoir. J refers to the average reservoir pressure (pseudo-steady state); a horizontal well takes Joshi's J (derived for a constant pressure at the boundary, so it errs on the low side), a fractured well takes its skin from the fracture alone (the fracture bypasses the mechanical skin), a deviated well Cinco-Ley's slant skin up to 75°. Transient flow is radial to the effective radius r_w·e^(−s_eq), from t_D = 100 (for s_eq < 0, relative to the effective radius); linear flow to a fracture or a lateral is not modelled. It applies until it meets the pseudo-steady rate, at t_pss at the latest. Below the bubble point the drawdown follows Vogel and J falls as J·p̄/p_b (Fetkovich), in both regimes. J applies to the whole liquid (oil and water taken as equally mobile); under depletion the water cut stays constant, under pressure support it rises with the recovery and the well is shut in at 98 %. The material balance is a tank: water replaces the VRR share of the voidage, and the pressure never rises above the initial one. Below the bubble point the liberated gas adds to the compressibility (Z = 0.9), but free-gas production is ignored, so solution-gas-drive recovery can be overstated. For natural flow p_wf,min = p_wh + ρ_mix·g·H with the true vertical depth, not the measured depth: the hydrostatic head depends only on the height of the column; tubing friction is neglected, so the real p_wf,min is higher. Rates are per producing day, volumes include the uptime; the oil rate is compared with the economic limit.
The default values are an illustrative example, not data from a real field. The model is simplified: one well in a homogeneous reservoir, a tank material balance, no free-gas production and no tubing friction (see the model's assumptions above).
Source: Dake, Fundamentals of Reservoir Engineering (1978); Earlougher, SPE Monograph 5 (1977); Cinco-Ley, Ramey & Miller, SPE 5589 (1975); Joshi, JPT (1988); Cinco-Ley & Samaniego, JPT (1981); Vogel, JPT (1968); Fetkovich, SPE 4529 (1973); Economides et al., Petroleum Production Systems
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Vertical, not measured depth: in natural flow the tubing column's weight depends on its height, not on the hole length.
In a normally pressured reservoir ≈ (0.0100–0.0105 MPa/m) · H (0.44–0.46 psi/ft): 24–25 MPa at 2 400 m.
Used for the volume factor of the gas liberated below the bubble point.
Total thickness of the oil-bearing layers in the drainage area.
Usually the connate water, 0.15–0.35.
Area per well: 36 ha for a 600 × 600 m pattern (about 89 acres).
Oil, water and rock together; usually (1–2)·10⁻³ MPa⁻¹ (7–14·10⁻⁶ psi⁻¹) for undersaturated oil.
From the PVT analysis of a bottomhole sample. If p_b is not below the initial pressure, the reservoir is saturated and p_b = p_i is used.
At the bubble point; below it the gas comes out of solution in proportion to the pressure drop.
To convert the production into tonnes.
The well geometry sets J and the equivalent skin s_eq.
From the bit: 0.108 m for 8½″ (215.9 mm), 0.078 m for 6⅛″ (155.6 mm).
From a build-up: above 0 means damage. For a horizontal well it refers to the lateral, as in Joshi's formula.
Sets the lowest bottomhole pressure the well can produce at.
Set by the pump submergence below the fluid level and the gas the pump can take; usually 3–8 MPa for ESPs and rod pumps.
Pump capacity or the development plan's limit; while the well could give more, it produces on a plateau.
Share of calendar time on production, usually 90–97 %. Rates are per producing day, volumes include the downtime.
The rate at which the revenue equals the well's operating costs, taxes included.
Up to 50 years.
Under depletion the pressure falls with production; under pressure support water replaces part of the voidage.
Share of the reservoir voidage replaced by water: 100 % holds the pressure, less lets it fall; it never rises above the initial pressure.
Constant under depletion; under pressure support it rises with the recovery.
Usually 30–50 % for waterflooded sandstones; from analogues or a simulation model. When the recovery reaches it, the water cut is 98 % and the well is shut in.
f_w = f_w0 + (0.98 − f_w0)·(RF/RF_ult)^n: n = 1 means an immediate rise, 2–3 a late breakthrough; fit it to analogues.
Unit converter for this formulaLength · Pressure · Temperature · Permeability · Area · Viscosity · Oil formation volume factor · Compressibility · Gas-oil ratio · Density and °API · Liquid rate · Time · Liquid volume · Mass · Productivity index · Fraction and percent
- m1
- cm100
- mm1,000
- km0.001
- ft3.28084
- in39.3701
- 1/32 in1,259.84
- 1/64 in2,519.69
- mile0.000621371
- N_p·ρ_o — The same in tonnes156.1
- q_o,i — Initial oil rate (first-month average)95.0
- t_pl — Plateau length (liquid at its cap)12.6
- t_life — Well life14.4
- RF — Recovery factor of the drainage area34.9
- N — Oil initially in place in the drainage area525.9
- J — Productivity index for liquid (vs the average pressure)10.09
- t_pss — Time to pseudo-steady state6.8
- s_eq — Equivalent skin of the well geometry1.00
- p_wf,min — Minimum bottomhole pressure used7.00
More in Production forecast
The rate after a given time and the cumulative production for exponential, hyperbolic or harmonic decline — from the initial rate, the first-year decline and the exponent b.
The time for the rate to fall to the economic limit and the production until then — the well's remaining recoverable reserves from the decline curve.
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.