Simulator

One steam cycle, day by day

Set the steam and the pump, then follow the well through injection, soak and production. Every value comes from the physics model in the technical reference. Values marked Inferred cannot be read at the well; only the model gives them.

Operator inputs

Well

Unit type

Conventional beam unit or hydraulic long-stroke unit. Changes the well picture, the stroke range and the rod peak-speed factor in equation 5, so the safe pump speed moves too.

Pump setting depthD_pm

900Tier D1,140 m

Feeds equation 8, the wellhead temperature. It does not change the heated zone, the viscosity or the safe speed.

Stroke lengthSm

1.0Tier D3.0 m

Steam

Steam volumeV_sm³ CWE

500Tier B4,000 m³ CWE

Field practice: 1,040–1,560 m³ CWE. The tinted part of the track is outside it.

Steam qualityxfraction

0.60Tier B0.80 fraction

Field practice: 0.60–0.70 fraction. The tinted part of the track is outside it.

Soak timet_soakdays

3Tier B14 days

Steam temperature is fixed at 250 °C, the effective downhole value (tier D). Surface steam is 280–305 °C. The downhole value after wellbore losses is not reported.

Pump

Pump speed

The pump runs at one speed for the whole production phase.

Pump speedNSPM

0.9Tier D3.4 SPM

Cycle

Production length before re-steamingt_cutdays

60Tier D365 days

Oil rateMeasured

17.3bbl/d

Day 123.9 · production

Oil so far, this cycle

2,507bbl

Day 123.9 · production

Steam-oil ratio, so far

5.02

Day 123.9 · production

Floating risk

0.59

Day 123.9 · productionNormal

Pump fillage

31%

Day 123.9 · productionFluid pound

ProductionDay 123.9 · production day 90

Heated-zone temperature

50 °C250 °C

Estimated zone

Production, day 90. The pump runs at 2.0 SPM with a 2.5 m stroke. It is 31 % full and lifts 17.3 bbl/d. The barrel is part empty: fluid pound. The heated zone is 11.8 m and has cooled to 60 °C.

Steam heats the zone; production lets it cool

Eq 7 during injection and soak, Eq 2 during production

Reservoir temperature (°C)

Data table

The oil thickens steeply as the zone cools

Eq 3, ASTM D341 (Walther)

Oil viscosity (cP, log scale)

Data table

The safe pump speed falls as the oil thickens

Eq 5. Where the set speed is above the safe speed, the rods float.

Pump speed (SPM)

Safe speed
Set speed

Data table

The oil rate falls back towards the cold rate

Eq 4. The surface rate is the smaller of reservoir inflow and pump capacity.

Oil rate (bbl/d)

Surface rate
Reservoir inflow

Data table

Day 123.9 · production day 90

Injection
Soak
Production

With the day slider focused, press space to play or pause and the arrow keys to step one day. Click a chart to jump to a day.

What a sensor would read

These are measured values. A later stage uses them to infer the hidden state above. The well is shut in during injection and soak, so there is no reading then.

The oil cools on its way up, more so at a low rate

Eq 8, Ramey (1962)

Wellhead temperature (°C)

Data table

Thick oil drags on the rods and raises the load

Eq 8, peak polished-rod load

Peak polished-rod load (kN)

Data table

Measured

A sensor or the operator can read these at the well.

Wellhead temperatureMeasured

36.2°C

Eq 8

Peak polished-rod loadMeasured

50.1kN

Eq 8

Oil rate at the surfaceMeasured

17.3bbl/d

Eq 4

Days since steamingMeasured

97days

Eq 7

Set pump speedMeasured

2.00SPM

Operator setting

Stroke lengthMeasured

2.5m

Operator setting

Inferred

Only the model gives these. No sensor reads them. Risk above 1.0 means the rods float.

Reservoir temperatureInferred

60.0°C

Eq 2

Oil viscosityInferred

4,465cP

Eq 3

Heated zone volumeInferred

4,338m³

Eq 1

Heated zone radiusInferred

11.8m

Eq 1

Maximum safe pump speedInferred

3.40SPM

Eq 5

Floating riskInferred

0.59

Eq 5

Cycle summary

Cumulative oilN_pEq 4, trapezoid rule over the production days: 2,946 bbl
Steam–oil ratioSORSteam 12,579 bbl, cold-water equivalent: 4.27
Heated zone volumeV_hRadius 11.8 m, Eq 1: 4,338 m³
Cooling time constantτEq 2: 30.0 days
Injection lengtht_injEq 7, at the field steam rate: 26.9 days
The safe-speed limit starts to bindEq 5. The day the safe speed first falls below the mechanical ceiling. It does not depend on the set speed.: Production day 141.4, past the end of the cycle
The rods start to floatEq 5. The first whole day with floating risk above 1.: Not in this cycle

How the numbers connect

Each equation takes the values on the left of its arrow and produces the ones on the right. Hover a value, or a readout above, to see which equation made it. Values are for the day chosen on the day control.

Steam and pump settings

Equation 7

CSS phases: injection and soak

Assumption, tier D

t_inj = ρ_w · V_s / (ṁ_s · 24)

T(t) = T_i + (T_s − T_i)(1 − e^−t/τ_inj)

V(t) = f_inj · V_h · t / t_inj, f_inj = [c_p(T_s − T_i) + f_c·x·L] / H

Injection heats the rock and grows the zone; soak holds it at steam temperature while the rest of the steam condenses. Both end in the state production starts from.

Steam volume V_s2,000m³ CWE

Steam quality x0.70fraction

Soak time t_soak7days

Out

Constants: ṁ_s · τ_inj · f_c

Equation 1

Steam → heated zone

Assumption: reduced-order energy balance

V_h = η · m_s · [x·L + c_p(T_s − T_i)] / [M_R(T_s − T_i)]

r_h = √(V_h / πh)

The heat the steam carries, divided by the heat each cubic metre of rock needs to reach steam temperature, gives the heated rock volume.

Steam volume V_s2,000m³ CWE

Steam quality x0.70fraction

Out

Constants: ρ_w · L · c_p · M_R · η · T_i · T_s · h · Feeds Eq 2, Eq 4, Eq 7

Equation 2

Heated zone and time → temperature

Physics; the cooling law is an assumption (tier D)

T(t) = T_i + (T_s − T_i) · e^−t/τ

τ = τ_∞ · r_h / (r_h + h), τ_∞ = τ_ref · (r_h,ref + h) / r_h,ref

After soak the zone cools towards the native temperature. A larger zone has less surface for its volume, so it cools more slowly.

Heated zone radius r_h11.8m

Day in the production phase t90days

Out

Constants: τ_ref · h · T_i · T_s · Feeds Eq 3, Eq 8

Equation 3

Temperature → viscosity

Physics: ASTM D341 / Walther, one constant calibrated

log₁₀(log₁₀(ν + 0.7)) = A − B · log₁₀(T)

μ = ν · SG, T in kelvin

Heavy oil thins steeply as it heats. The double-logarithm form holds from 50 °C to 250 °C, where one exponential cannot.

Reservoir temperature T60.0°C

Out

Constants: ρ_o · ρ_w · μ_anchor · T_anchor · B · Feeds Eq 4, Eq 5, Eq 8

Equation 4

Viscosity → production

Physics; the rate law and pump constants are assumptions (tier D)

q_in = q_cold · ln(r_e/r_w) / [(μ_h/μ_c)·ln(r_h/r_w) + ln(r_e/r_h)]

Q_pump = A_p · S · N · 1440 · η_v

q = min(q_in, Q_pump)

The heated zone and the cold rock beyond it resist flow in series. The surface rate is the smaller of what the reservoir gives and what the pump can lift.

Oil viscosity μ4,465cP

Heated zone radius r_h11.8m

Stroke length S2.5m

Set pump speed N2.00SPM

Out

Constants: q_cold · r_w · r_e · d_p · η_v · T_i · Feeds Eq 8

Equation 5

Viscosity → safe pump speed

Assumption: static force balance, needs calibration

v_f = (ρ_s − ρ_o) · g · d_r² · ln(d_t/d_r) / (8μ)

N_max = min(30 · v_f / (f · S), N_mech)

risk = N / N_max

The rods must fall one stroke in half a pump cycle. Thick oil slows their fall, so the safe speed drops. Above a risk of 1 the rods float.

Oil viscosity μ4,465cP

Stroke length S2.5m

Set pump speed N2.00SPM

Out

Constants: ρ_s · ρ_o · g · d_r · d_t · N_mech · f

Equation 8

Measured signals

Assumption, tier D

T_wh = T_g,0 + g_G·A − (T_g,0 + g_G·D + g_G·A − T_r) · e^−D/A, A = a·q

PPRL = W_rb(1 + S·N²/1790) + ρ_o·g·D_p·A_p + 2π·μ·v·D_p / ln(d_t/d_r)

What a sensor would read: the oil cools as it rises, so a low rate arrives cooler; thick oil drags on the rods and raises the load.

Oil rate at the surface q17.3bbl/d

Reservoir temperature T60.0°C

Oil viscosity μ4,465cP

Stroke length S2.5m

Set pump speed N2.00SPM

Out

Constants: T_g,0 · D · a · D_p · 1790 · ρ_s · ρ_o · d_r

Cumulative oil and steam–oil ratio are totals for the whole cycle, not values for one day. Equation 6 (rod dynamics) is not computed in v1.