{"uid":"cap_w_WiGTvgrnJcT-3urSgi1","slug":"fixed-bed-axial-dispersion-kinetic-langmuir-breakthrough-inventory-7d641ef4","name":"Fixed-Bed Axial Dispersion Kinetic Langmuir Breakthrough & Inventory Transcript","description":"Recover a complete coupled transport-and-uptake column artifact and its breakthrough/inventory ledger.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B011/fixed-bed-axial-dispersion-kinetic-langmuir-breakthrough-inventory-transcript?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["chromatography"],"properties":{"chromatography":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["initial_mobile_concentrations","initial_bound_concentrations","porosity","velocity","dispersion","adsorption_rate","desorption_rate","capacity","cell_spacing","timestep","inlet_per_step","sample_steps"],"properties":{"capacity":{"type":"number","maximum":10,"minimum":0.01},"porosity":{"type":"number","maximum":0.9,"minimum":0.1},"timestep":{"type":"number","maximum":0.1,"minimum":0.0001},"velocity":{"type":"number","maximum":10,"minimum":0.001},"dispersion":{"type":"number","maximum":1,"minimum":0},"cell_spacing":{"type":"number","maximum":10,"minimum":0.1},"sample_steps":{"type":"array","items":{"type":"integer","maximum":128,"minimum":0},"maxItems":4,"minItems":1},"inlet_per_step":{"type":"array","items":{"type":"number","maximum":10,"minimum":0},"maxItems":128,"minItems":1},"adsorption_rate":{"type":"number","maximum":10,"minimum":0.001},"desorption_rate":{"type":"number","maximum":10,"minimum":0.001},"initial_bound_concentrations":{"type":"array","items":{"type":"number","maximum":10,"minimum":0},"maxItems":16,"minItems":3},"initial_mobile_concentrations":{"type":"array","items":{"type":"number","maximum":10,"minimum":0},"maxItems":16,"minItems":3}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_W3VG9dd9NaZh3VuHcnCdh","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Simulates a fixed-bed chromatography column using axial dispersion and Langmuir kinetics, returning breakthrough curves and inventory ledger data for specified time steps.","exampleAgentPrompt":"Simulate a fixed-bed chromatography column with porosity 0.4, interstitial velocity 0.5, dispersion 0.01, adsorption rate 1.2, desorption rate 0.3, Langmuir capacity 5.0, cell spacing 0.5, and a timestep of 0.001; use initial mobile concentrations [0,0,0] and bound concentrations [0,0,0], step the inlet concentration to 2.0 for 100 steps, and sample the breakthrough and inventory at steps 25, 50, 75, and 100.","exampleUseCases":[{"title":"Column loading optimization for bioprocessing","prompt":"Model a packed-bed adsorber with porosity 0.35, velocity 0.8, dispersion 0.005, adsorption rate 2.0, desorption rate 0.5, Langmuir capacity 8.0, and cell spacing 1.0 — start everything at zero concentration, run inlet at 3.0 for 128 steps with timestep 0.001, and give me the breakthrough curve and inventory at steps 32, 64, 96, and 128."},{"title":"Validating claimed column kinetics against measurements","prompt":"I have a claimed chromatography column artifact — porosity 0.45, velocity 0.3, dispersion 0.02, adsorption rate 0.8, desorption rate 0.2, capacity 4.5, cell spacing 0.5, timestep 0.005, all starting concentrations zero — run the inlet at 1.5 for 60 steps and recover the full transport-uptake transcript sampled at steps 15, 30, 45, and 60 so I can compare against my measured breakthrough data."},{"title":"Process design for pharmaceutical adsorption step","prompt":"Simulate a Langmuir fixed-bed column for a pharmaceutical purification step: porosity 0.38, velocity 1.2, dispersion 0.008, adsorption rate 3.5, desorption rate 0.9, capacity 6.0, cell spacing 0.8, timestep 0.002, initial concentrations all zero, inlet concentration 5.0 for 80 steps — sample the breakthrough transcript and inventory ledger at steps 20, 40, 60, and 80."}],"resultDescription":"Returns the complete reconstructed coupled transport-and-uptake column artifact — including breakthrough concentration profiles at the column outlet and an inventory ledger recording total solute masses in mobile and bound phases — evaluated at the requested sample time steps.","failureModes":["Invalid porosity outside [0.1, 0.9] returns validation error","Timestep outside [0.0001, 0.1] rejected with schema error","sample_steps array exceeds 4 entries returns bad request","inlet_per_step length mismatched to step count causes processing error","Langmuir capacity or rate constants at boundary extremes may cause numerical instability","Missing required fields in chromatography.data returns 400 schema validation error","Claim field mismatch against computed simulation may return reconciliation failure"],"whenToPreferThis":"Choose this endpoint when you need to simulate or verify fixed-bed chromatography column behavior using the axial dispersion model with Langmuir adsorption kinetics — specifically when you need breakthrough curves and column inventory at discrete time points. Prefer this over generic ODE solvers when you need the coupled transport-uptake formulation with built-in kinetic Langmuir isotherm and axial dispersion, or when you need to reconcile a claimed column artifact against simulation results.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:41:19.946Z","isFirstParty":false,"canonicalSlug":"fixed-bed-axial-dispersion-kinetic-langmuir-breakthrough-inventory-7d641ef4"}