Calculations

How to Calculate Precursor Yield, Metal Sulfate Usage, and Calcination Energy for Cathode Active Material

Worked formulas for cathode active material and precursor production, from metal sulfate stoichiometry through co-precipitation efficiency, lithium charge sizing, calcination energy, and PSD yield, with real units and numbers.

Cathode active material plants live and die on mass balance. Every kilogram of NMC811 that ships started as nickel, cobalt, and manganese sulfate solution, passed through a co-precipitation reactor, a filter press, a dryer, and a calcination kiln, and lost mass at every step. The five calculations that matter most are metal sulfate usage, co-precipitation efficiency, precursor yield, lithium charge sizing, and calcination energy. Each is a short formula with inputs you already log in your DCS or LIMS. This guide works every formula with real units and worked numbers so you can reproduce them on your own line before your next mass balance review.

Start with stoichiometry. NMC811 hydroxide precursor, Ni0.8Mn0.1Co0.1(OH)2, has a molar mass of 92.3 g/mol. One metric ton contains 10,830 mol of transition metal, split 8,664 mol Ni, 1,083 mol Mn, and 1,083 mol Co. Convert each to sulfate feedstock: nickel sulfate hexahydrate at 262.85 g/mol means 8,664 mol times 262.85 g/mol, about 2,277 kg per ton of precursor. Manganese sulfate monohydrate at 169.02 g/mol adds 183 kg, and cobalt sulfate heptahydrate at 281.10 g/mol adds 304 kg. The Metal Sulfate Usage calculator runs this conversion for any Ni:Mn:Co ratio and hydrate form, which matters because a crystal water error shifts the charge by 20 to 40 percent.

Co-precipitation efficiency is the fraction of fed metal that ends up in solid precursor rather than staying dissolved in mother liquor. The formula is efficiency = 1 - (filtrate metal mass / fed metal mass). Feed 10 m3 of 2.0 mol/L mixed sulfate, which is 20,000 mol of metal, roughly 1,180 kg. If ICP shows the filtrate carries 120 mg/L nickel plus 40 mg/L combined cobalt and manganese across 12 m3 of liquor, dissolved losses total about 1.9 kg, so efficiency is 99.84 percent. Run the Co-Precipitation Efficiency calculator on every batch; a drop below 99.5 percent usually means pH drifted under 10.8 or ammonia climbed past 12 g/L.

Precursor yield tracks solid mass through filtration, washing, and drying. Yield equals dry precursor out divided by theoretical precursor from metal fed. Using the batch above, 20,000 mol of metal should give 20,000 times 92.3 g/mol, about 1,846 kg of hydroxide. If the dryer discharges 1,762 kg at 0.4 percent moisture, dry basis output is 1,755 kg and yield is 95.1 percent. The gap splits between dissolved metal, fines lost through the filter cloth, and handling losses. The Precursor Yield calculator does the dry basis correction automatically, and the Wash Water Load calculator tells you whether a 6 to 10 L per kg wash ratio actually strips sulfate below a 2,000 ppm spec.

Lithium charge sizing sets the lithium to transition metal molar ratio, typically 1.02 to 1.05 for high nickel CAM fired under oxygen. Target one ton of NMC811, formula LiNi0.8Mn0.1Co0.1O2 at 97.3 g/mol: that is 10,280 mol of formula units. At a 1.03 ratio you need 10,588 mol of lithium, which is 10,588 times 41.96 g/mol of LiOH·H2O, about 444 kg, blended with 949 kg of precursor. The excess offsets lithium volatilization above 700 C and feeds the residual lithium washing step. The Lithium Excess Cost calculator sizes the charge and shows what each 0.01 of ratio does to consumption; the money side lives in our cost guide.

Calcination mass yield surprises new engineers. The 949 kg of precursor plus 444 kg of LiOH·H2O above weighs 1,393 kg going into the kiln, but only about 1,000 kg of CAM comes out, a 72 percent mass yield, because crystal water, hydroxide water, and volatilized lithium leave as vapor. Energy follows sensible heat: Q = m times cp times delta T. Heating 1,000 kg of blend, cp near 0.85 kJ/kg·K, from 25 to 780 C takes 642 MJ, or 178 kWh, before you add saggars weighing twice the powder, process air, and wall losses. The Calcination Energy calculator stacks those terms; expect the real number at 4 to 8 times the powder-only figure.

Two more calculations close the loop. Particle size distribution yield is the mass fraction inside your D50 window after crushing and classification. With a D50 spec of 12 µm plus or minus 2 µm and a span of (D90 - D10)/D50 near 1.1, a well tuned classifier passes 92 to 96 percent, and the Particle Size Distribution Yield calculator converts a laser diffraction report into salable mass. Drying capacity is an evaporation balance: removing 8 percent moisture from 2,000 kg/h of wet cake means evaporating 174 kg/h of water, which at 2,260 kJ/kg latent heat plus 30 percent losses demands about 142 kW. The Drying Capacity calculator flags when the dryer is the bottleneck.

Finally, budget the measurement itself. A batch released on ICP metals, PSD, tap density, moisture, sulfate, and magnetic impurities consumes 6 to 10 lab tests, and a 5 t/day line running 2 t batches generates 15 to 25 tests daily. The Quality Sampling Load calculator converts batch size, sampling plan, and test menu into instrument hours so you can see when the lab, not the kiln, caps release rate. Keep every input in SI units, carry molar masses to two decimals, and reconcile the full balance weekly; a 1 percent unexplained loss on a 10 kt per year plant is 100 tons of nickel bearing material.

Published 2026-07-02.