Separate dissolved concentration from total nutrient removal

Connect the Earth-system mechanism

Phosphorus can occur in dissolved forms and associated with particles. Weathering supplies mineral phosphorus, biological uptake transfers it to organic material, and adsorption or precipitation can change its distribution. Erosion transports particle-associated material; settling and resuspension move it across water-column boundaries. Unlike nitrogen, its major environmental cycle lacks a comparable dominant atmospheric gas reservoir.

Build the declared budget

The supplied model is deliberately narrower: a reversible linear partition between water and suspended solids at fixed chemistry. Particle concentration Cs in mg P/kg solids equals Kd in L/kg times dissolved Cd in mg P/L. With solids S in kg/L, total phosphorus per litre is Cd+S Cs. Solving gives Cd=total/(1+Kd S). The unit conversion from mg solids/L to kg/L is essential.

Separate the competing quantities

Increasing solids or the assigned coefficient can lower dissolved concentration while conserving the total in the suspension. The particle-associated concentration per litre and concentration per kilogram of solids are different quantities. Removing settled particles from the water column would change its total, but that additional transport process is not automatically represented by repartitioning.

Challenge the inference

A constant Kd is not a universal phosphorus property. Surface chemistry, pH, competing ions, redox state, saturation and kinetics can matter. Biological accessibility also depends on processes beyond a dissolved/particle split. Treat the ledger as a transparent conditional model, not a calibrated remediation prediction or a chemical-addition recommendation.

Worked original packet

At solids 400 mg/L, S=0.0004 kg/L; Kd 700 gives KdS 0.28. From total 1 mg P/L, dissolved concentration is 1/1.28=0.78125 and particle-associated concentration 0.21875 mg P/L. The particles carry 546.875 mg P/kg solids, not 0.21875 mg/kg.

Investigation

Compare solids 100 and 1000 mg/L at Kd 1000. Reconcile both mass currencies, then explain how actually exporting settled solids would add a new boundary flux.

Changed-case transfer

At solids 1000 mg/L and Kd 1000 L/kg, calculate dissolved, particle-associated-per-litre and particle-mass-basis concentrations.

Feedback

S 0.001 kg/L and KdS 1; dissolved 0.5 mg/L, particle-associated 0.5 mg/L, particle concentration 500 mg/kg. Total remains 1 mg P/L in the stipulated suspension.

Sources and evidence boundary

Original prose, numerical packets and exercises. Mechanism/method context checked 30 October 2026: primary source. These are conditional computational models, not measured field records, carbon credits, safe yields, treatment standards or independent mastery. No physical extraction, chemical addition or environmental release is requested.