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Proppant physicsMethod

Phase 13 of the 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.

Single-fracture proppant transport physics.
w = 0.039 in(PKN)h = 400 ftq/cluster = 80.0 bpm
Proppant

Effective d_p = 0.0139 in (from mesh)

typical 0–0.06 in

Set to 0 to use the mesh table value.

typical 150–200 lb/ft³

Sand≈165, ceramic≈173, RCS≈156.

typical 0.02–0.3 v/v

≈ 0.10 v/v ≈ 2 PPA in slickwater.

typical 2.4–4.65 –

4.65 (Stokes) → 2.4 (Newton).

Carrier fluid

typical 8–10.5 ppg

Slickwater ≈ 8.34, linear gel ≈ 8.7.

typical 1–50 cP

At slot temperature.

typical 100–300 °F

Slot geometry & rate(live — read-only)

typical 0.05–0.5 in

PKN/KGD avg width (PKN) from BC bundle + depletion run · w/d_p = 12.95

typical 50–400 ft

2 × bubble radius (200 ft) from depletion run

typical 1–20 bpm

|BHP rate| (80.0 bpm) / 1 cluster

Single-particle settling
Terminal velocity v_t0.1191 ft/stransition
Reynolds Re_p6.406
Drag C_D5.759
Hindered settling
Hindered v_h0.0730 ft/s(1−C)^n = 0.613
Concentration C0.100
Exponent n4.65
Slot convection
Mean v_slot0.780 ft/s
Slot area1.80 ft²
Flow per cluster1.404 ft³/s
Residence time153.88 s
Bridging
w / d_p12.95clear
Slot bridgingno
Max safe C45.0 %
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

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

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sweep — concentration × slot width

Concentration C (–)

Fracture width w (in)

72 grid points
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