bedblend 0.3.0

A bed-blending stockpile engine: repose-angle deposition, Gray-Thornton kinetic size segregation, a per-cell lot ledger with provenance, and the blending metrics (variance reduction, variograms, residence time).

bedblend

A bed-blending stockpile engine: repose-angle deposition, Gray-Thornton kinetic size segregation, a per-cell lot ledger with provenance, and the blending metrics.

pip install bedblend

The problem it answers

A blending bed is the cheapest variance reduction available in a mineral processing plant. Material is stacked in many thin layers and reclaimed across all of them at once, so the cut delivered to the mill is an average over the layers the reclaimer crosses rather than over whichever truck arrived last.

The question a planner actually has is how much variance a given pile removes, and the honest answer is often "less than you think". The layer count is the dominant term, and it is set by the reclaim geometry rather than by the stacking geometry: a bridge reclaimer rakes the whole cross-section and crosses every layer at a station, a front-end loader takes a shallow bite and crosses a handful. This engine computes that, on a real pile, with the provenance kept.

import bedblend as bb

pad = bb.PadSpec(nx=24, ny=16, cell_m=3.0)
dumps = bb.generate_stream(n_dumps=120, seed=7)          # a correlated grade stream, not white noise
cfg = bb.RunConfig(pad=pad, stacking="chevron", reclaim="fullface",
                   n_passes=12, sr=1.0, cut_tonnes=600.0)

result = bb.simulate(cfg, dumps)
m = result.metrics
print(f"{len(result.cuts)} cuts, VRR {m.vrr:.3f} against the 1/N ideal {m.vrr_ideal:.3f}")
print(f"{m.n_layers_mean:.1f} layers per cut")

43 cuts, VRR 0.093 against the 1/N ideal 0.046
21.9 layers per cut

The ratio is variance OUT over variance IN, on a tonnage base, so lower is better and 1.0 means the bed did nothing. It is reported next to the 1/N bound because the gap between them is the interesting quantity: it is what the pile fails to recover, and it is driven by the autocorrelation of the incoming stream. Layers only average if they are independent.

What is in it

Module	What it computes
heightfield	Mass-conserving relaxation to an imposed angle of repose. A priority cascade with a water-filling toppling rule; the ordered transfers ARE the avalanche path.
segregation	Gray-Thornton kinetic sieving in the flowing layer, dphi/dt + ... - Sr d/dz[phi(1-phi)] = 0, solved with a Godunov flux so the concentration shocks survive. Sr = 0 degenerates to a passive tracer, which is the negative control.
pile	The pad, the per-cell lot stacks, and four reclaim geometries (full face, bucket wheel, end, loader). Every reclaimed tonne carries provenance fractions back to the truck loads that made it.
stacking	Five build geometries: chevron, windrow, cone shell, chevcon, strata.
blending	Tonnage-weighted variance, VRR, the 1/N bound, mixing effect, experimental variograms with a spherical fit.
rtd	Residence-time distribution and its FIFO/LIFO character.
stream	A geostatistically correlated truck stream, generated exactly from a one-step recursion.

What it does NOT claim

• The angle of repose is imposed, not emergent. This is a continuum height-field model, not DEM. It reproduces the geometry a given repose angle produces; it does not predict that angle from particle properties.
• The segregation number Sr is a parameter, not a measurement. Gray and Thornton's non-dimensional group is supplied, and the honest use is to sweep it and report the sensitivity.
• It is not a blending optimizer. It evaluates a pile; it does not choose one.
• It is not plant metal accounting. It stops at the reclaimed stream.

Determinism

A run is a pure function of (parameters, seed). The stream generator is a 32-bit xorshift feeding Box-Muller, written out explicitly rather than using random or numpy, so the same stream can be reproduced bit for bit by an implementation in another language. That is what makes an in-browser mirror of this engine checkable against it.

References

The equations and their provenance:

• Gray, J.M.N.T. and Thornton, A.R. (2005), A theory for particle size segregation in shallow granular free-surface flows, Proc. R. Soc. A 461, 1447-1473. doi:10.1098/rspa.2004.1420
• Bak, P., Tang, C. and Wiesenfeld, K. (1987), Self-organized criticality: an explanation of 1/f noise, Phys. Rev. Lett. 59, 381. doi:10.1103/PhysRevLett.59.381
• Gerstner, W. and Schramm, G. — see docs/ for the blending-bed literature and the measured mixing effects the 1/N comparison is calibrated against.
• Kumral, M. (2006), Bed blending design incorporating multiple regression modelling and genetic algorithms, J. S. Afr. Inst. Min. Metall. 106, 229-236.

Licence

MIT. See LICENSE.