Downhole Ballistics Simulator

Performance modeling

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Proppant convection & flowback

§14 of the ResFrac formulation. Two coupled post-treatment phenomena: density-driven convection of the slurry inside the fracture (Rayleigh instability of dense over light layers), and the dynamic flowback of proppant once production resumes after shut-in. Use the calibration page to fit cell amplitude or RZ exponent against measured data.

Slickwater carrier, 40/70 sand at 0.15 vol, 8 bpm/cluster, 250k lb stage, 6,000 psi closure.

§14.1–14.3 Gravitational convection

§8.8 Gravitational convection (Ra = 394808652 / Ra* = 500)

Vigorous overturning
Δρ
2.07 ppg
u_cell
20.75 ft/min
Pe = U/u_cell
1.20
Cells over h
8000
max lateral drift
0.00 ft
mean residence τ_res
tracer mass (cum.)
0.0 lb
Rayleigh regime — Ra/Ra* = 789617.30(Ra=394808652, Ra*=500)
UNSTABLE — convection cells active
Stable
Ra/Ra* < 0.5
Marginal
0.5 ≤ Ra/Ra* < 1
Convecting
1 ≤ Ra/Ra* < 5
Vigorous
Ra/Ra* ≥ 5

Thresholds from ResFrac §8.8 calibration: Ra* = 500 (slot/Hele-Shaw critical). Horizontal advection damps cells when Pe = U/u_cell > 5 (current Pe = 1.20).

w/h aperture taper α0.00
near-wall friction f_wall1.00×
Regime map — Ra/Ra* vs Pe (log-log)
point: Ra/Ra*=789617.30, Pe=1.20
0.11101001000100001000001000000100000001e-20.1110100Ra / Ra*Pe = U / u_cellstablemarginalconvectingvigorous

Vertical bands use the active Ra/Ra* edges (0.50, 1.00, 5.00). Horizontal dashed line is the Pe demotion cutoff (5.00); the amber tint above it flags where strong horizontal advection knocks "convecting" / "vigorous" back to "marginal". Slide along the dotted guides to see how shifting Ra alone (vertical) or Pe alone (horizontal) flips the regime.

intensity
83%

Δρ = (ρ_s − ρ_f)·c drives buoyancy in a slot of width w. Cell velocity = min(√(g·Δρ·w/ρ_f), g·Δρ·w²/12μ). Strong horizontal advection (Pe ≫ 1) suppresses cells; vigorous regimes redistribute proppant and degrade the bed-slumping equilibrium predicted above.

Evolving cells (t = 0 s · 20 cells · mean intensity 0%)

↘ 2 merges · ↗ 0 splits
ρ=1247ρ=1234ρ=1221ρ=1208ρ=1195ρ=1182ρ=1169ρ=1156ρ=1143ρ=1130ρ=1117ρ=1104ρ=1091ρ=1078ρ=1065ρ=1051ρ=1038ρ=1025ρ=1012ρ=999h (ft) ↑ — warm = rising, cool = sinking, blue bar = horizontal drift
frame1/24
window120s

§14.4–14.6 Post-shut-in flowback

§8.13 Post-Job Proppant Flowback
production startssolid: proppant rate (lb/hr) · mobile (lb) · dashed: trapped (lb)
Total recovered
250000 lb
Recovered fraction
100.00 %
Final trapped
0 lb
Final mobile
0 lb
k_trap @ prod start
3.31e-2
k_trap final
6.24e-2
Peak rate
592261.9 lb/hr
Peak time
12.2 hr
  • Shut-in hardened k_trap by 65% before production began.
  • Significant flowback: 100.0% of placed mass returned despite consolidation.
§8.13 Flowback calibration — fit τ_c, p, k_remob, initial mobile fraction to measured returns

Paste measured surface returns since start of production. The fitter searches all four free parameters (256-sample Halton scan + per-axis golden-section refinement) and returns the parameter set that minimizes RMSE against your data. Use the resulting values in the live flowback panel above.

CSV columns: t_prod_hr, value