Proppant physics

§13.1–§13.5 of the ResFrac formulation. The single-fracture transport physics that govern whether a grain reaches the tip: settling regime, hindered correction, slot convection, bridging, and equilibrium dune height. Multi-cluster allocation and washout risk live in the existing transport panel.

ResFrac §13 — single-fracture proppant transport physics.

Live link to §12 BC / §11 run

w = 0.039 in(PKN)h = 400 ftq/cluster = 80.0 bpm

Clusters

Pump time (min)

Proppant

Mesh

Effective d_p = 0.0139 in (from mesh)

Grain diameter override (in)

typical 0–0.06 in

Set to 0 to use the mesh table value.

Particle density (lb/ft³)

typical 150–200 lb/ft³

Sand≈165, ceramic≈173, RCS≈156.

Bulk concentration (v/v)

typical 0.02–0.3 v/v

≈ 0.10 v/v ≈ 2 PPA in slickwater.

Richardson–Zaki exponent n (–)

typical 2.4–4.65 –

4.65 (Stokes) → 2.4 (Newton).

Carrier fluid

Carrier density (ppg)

typical 8–10.5 ppg

Slickwater ≈ 8.34, linear gel ≈ 8.7.

Carrier viscosity (cP)

typical 1–50 cP

At slot temperature.

Slot temperature (°F)

typical 100–300 °F

Slot geometry & rate(live — read-only)

Fracture width (in)

typical 0.05–0.5 in

PKN/KGD avg width (PKN) from §12 BC + §11 run · w/d_p = 12.95

Fracture height (ft)

typical 50–400 ft

2 × bubble radius (200 ft) from depletion run

Rate per cluster (bpm)

typical 1–20 bpm

|BHP rate| (80.0 bpm) / 1 cluster

§13.1 Single-particle settling

Terminal velocity v_t0.1191 ft/stransition

Reynolds Re_p6.406

Drag C_D5.759

§13.2 Hindered settling

Hindered v_h0.0730 ft/s(1−C)^n = 0.613

Concentration C0.100

Exponent n4.65

§13.3 Slot convection

Mean v_slot0.780 ft/s

Slot area1.80 ft²

Flow per cluster1.404 ft³/s

Residence time153.88 s

§13.4 Bridging

w / d_p12.95clear

Slot bridgingno

Max safe C45.0 %

§13.5 Bed deposition / dune

Settling number N_s = v_h / v_slot0.0936bed load

Equilibrium dune fraction46.6 %

Dune height55.89 ft

v above dune1.460 ft/s

Dune fill (% of fracture height)

Daneshy-style equilibrium: dune fills until v_above can re-suspend the proppant (N_crit ≈ 0.05).

v_t vs grain diameter (§13.1)

Current d_p = 0.0139 in → v_t = 0.1191 ft/s (transition).

v_h vs concentration (§13.2)

Current C = 0.100 (RZ n = 4.65).

Dune fraction vs N_s (§13.5)

Current N_s = 0.0936 → f = 46.6 % (bed load).

§13 sweep — concentration × slot width

Concentration C (–)

C min

C max

Steps

Fracture width w (in)

w min (in)

w max (in)

Steps

72 grid points

§13.2 calibration — fit Richardson–Zaki n from measured dune data

Enter (C, w, q, measured dune fraction) rows from a tracer survey, post-job tag, or under-tandem placement reading. Width and rate overrides are optional — leave blank to use the live slot inputs (0.180 in, 15.0 bpm). The fit minimizes RMSE on dune fraction f against the §13 forward model.

C (–)	w (in, opt.)	q (bpm, opt.)	Measured f	Predicted f	Residual
				0.637	+0.457
				0.547	+0.097
				0.418	-0.262

n̂ = 2.000RMSE(f) = 30.94 %N = 3

RMSE(f) vs Richardson–Zaki n — minimum at n̂ = 2.000

Current live n = 4.65. Click "Apply" to push n̂ into the proppant inputs and refresh every readout / plot / sweep on this page.