How to Perform a Mill Circulating Load Calculation
A mill circulating load calculation shows how much material returns from a classifier, hydrocyclone, or screen to the grinding mill compared with the fresh feed entering the circuit. This value is essential for evaluating grinding efficiency, sizing equipment, checking operating stability, and identifying restrictions in classification.
The circulating load is commonly expressed as a ratio or percentage. A result of 2.5, for example, means that the internal stream returning to the mill is 2.5 times the fresh feed. Expressed as a percentage, the same result is 250%.
Accurate calculation depends on a clear definition of the circuit boundary and reliable measurements of dry solids flow, particle size, density, or assay. The calculation should describe a steady operating period rather than a short interval affected by startup, shutdown, feed changes, or unstable cyclone operation.
Define The Grinding Circuit Boundary
Start by identifying the fresh feed, mill discharge, classifier feed, classifier overflow, and classifier underflow. In a closed-circuit grinding operation, fresh ore enters the circuit and combines with classifier underflow before returning to the mill. The classifier overflow leaves the circuit as the final product or proceeds to downstream processing.
Use consistent symbols throughout the calculation:
- (F) = fresh dry solids feed
- (U) = classifier underflow or recycled dry solids
- (P) = classifier overflow or circuit product
- (T) = total dry solids entering the classifier
The classifier feed is therefore:
[ T = F + U ]
At steady state, the dry solids entering the circuit equal the dry solids leaving it. If the overflow is the only product stream, then:
[ F = P ]
This relationship makes it possible to calculate the circulating load even when the internal mill feed is much larger than the fresh ore feed.
Use The Basic Circulating Load Formula
The dry-solids circulating load ratio is calculated as:
[ CL = \frac{U}{F} ]
The circulating load percentage is:
[ CL% = \frac{U}{F} \times 100 ]
For example, if a grinding circuit receives 100 t/h of fresh ore and sends 250 t/h of dry solids in classifier underflow back to the mill, then:
[ CL = \frac{250}{100} = 2.5 ]
[ CL% = 2.5 \times 100 = 250% ]
The total dry solids passing through the mill feed stream are:
[ T = F + U = 100 + 250 = 350\text{ t/h} ]
A circulating load of 250% does not mean that 250% of the ore is lost or produced as an additional product. It represents repeated internal passage through the grinding and classification circuit. The same particles may circulate several times before reaching the required product size.
Calculate From Particle Size Data
When reliable dry-tonnage measurements are unavailable, circulating load can be estimated using a size fraction measured in the classifier feed, overflow, and underflow. Select a size at or near the circuit product specification, such as 75 microns, and determine the mass fraction passing that size in each stream.
Let:
- (x_f) = fraction passing the selected size in classifier feed
- (x_o) = fraction passing the selected size in overflow
- (x_u) = fraction passing the selected size in underflow
The underflow-to-overflow ratio is:
[ \frac{U}{P} = \frac{x_f - x_o}{x_u - x_f} ]
At steady state, (P=F), so:
[ CL = \frac{U}{F} = \frac{x_f - x_o}{x_u - x_f} ]
Suppose the classifier feed contains 45% passing 75 microns, the overflow contains 80%, and the underflow contains 20%. The result is:
[ CL = \frac{0.45-0.80}{0.20-0.45} = \frac{-0.35}{-0.25} = 1.4 ]
The circulating load is therefore 140%. The result is meaningful only if the samples represent the same operating period and the particle-size analyses are performed consistently.
Calculate From Density Or Water Balance
Density measurements are often useful when the circuit has stable slurry conditions but limited belt-scale or flowmeter data. First convert each stream’s percent solids into a water-to-solids ratio:
[ D = \frac{1-S}{S} ]
where (S) is the solids fraction expressed as a decimal. For example, 65% solids becomes (S=0.65), giving:
[ D = \frac{1-0.65}{0.65}=0.538 ]
Use (D_f), (D_o), and (D_u) for the classifier feed, overflow, and underflow. A water balance gives:
[ CL = \frac{U}{P} = \frac{D_o-D_f}{D_f-D_u} ]
If classifier feed, overflow, and underflow contain 50%, 20%, and 70% solids respectively, their water-to-solids ratios are 1.00, 4.00, and 0.429. The calculation becomes:
[ CL = \frac{4.00-1.00}{1.00-0.429}=5.25 ]
That result indicates a 525% circulating load. Such a high value should prompt a review of sampling, density measurement, water additions, and classifier operation before it is accepted as a plant performance result.
The following methods can be compared when selecting a calculation basis:
| Calculation basis | Required measurements | Main equation | Best application | Main limitation |
|---|---|---|---|---|
| Dry mass balance | Fresh feed and underflow tonnage | (CL=U/F) | Circuits with reliable flowmeters or belt scales | Requires accurate dry solids flow |
| Particle size balance | Size fraction in feed, overflow, and underflow | (CL=(x_f-x_o)/(x_u-x_f)) | Sampling campaigns and circuit surveys | Sensitive to sampling and laboratory error |
| Water balance | Percent solids in three classifier streams | (CL=(D_o-D_f)/(D_f-D_u)) | Circuits with dependable density data | Water additions and leaks can distort results |
| Tracer or assay balance | Assay or tracer concentration in streams | (CL=(f-p)/(u-f)) | Metallurgical surveys and selected mineral tracers | Requires a representative conserved component |
| Combined reconciliation | Two or more independent data sets | Mass-balance reconciliation | Audits, design validation, and troubleshooting | Needs more time and carefully coordinated sampling |
Check Sampling And Mass Balance Quality
Sampling is often the largest source of error. Collect samples from streams that are fully mixed and accessible across the complete cross-section. Avoid sampling only the top of a slurry pipe, the edge of a launder, or a briefly changing discharge. For a cyclone cluster, sample the combined overflow and underflow when the objective is to evaluate the full circuit.
Record sampling time, feed rate, mill power, cyclone pressure, slurry density, water additions, and operating conditions. A sample set collected while cyclone pressure is fluctuating may produce incompatible results because the three streams do not represent the same separation state.
Every calculation should also pass a simple plausibility check. The feed size fraction should normally lie between the overflow and underflow values for the selected cut size. If it does not, investigate incorrect labels, laboratory errors, poor sampling, or a changing circuit. Compare the calculated product tonnage with the fresh feed rate and inspect whether the implied water balance is physically reasonable.
For a plant survey, calculate the result using at least two independent methods where possible. Agreement between dry mass, size-fraction, and density-based estimates increases confidence. A large difference usually identifies a measurement problem rather than an unusual grinding phenomenon.
Interpret The Result For Plant Decisions
A high circulating load can indicate a coarse classifier cut, excessive mill discharge density, inadequate cyclone pressure, worn liners, insufficient grinding energy, or overloading of the classification stage. It may also reflect a deliberate operating choice when the circuit requires a finer product and accepts more internal recycling.
A low circulating load is not automatically desirable. If classification is too coarse or the mill is underfed, the circuit may have a low recycle rate while producing an unacceptable coarse overflow. The correct target depends on ore competency, liberation requirements, mill design, classifier performance, and downstream recovery needs.
For projects involving equipment selection or an expansion study, the calculation should be connected to the full process design. Providers of EPC delivery services can use the expected circulating load to assess mill capacity, cyclone duty, pump sizing, instrumentation, and commissioning requirements. It is also important to test representative ore because laboratory grindability and classification results can differ significantly from design assumptions.
Apply A Consistent Calculation Procedure
Use the following practices when preparing a plant survey or daily operating calculation:
- Define the circuit boundary and identify every fresh, recycled, and product stream.
- Convert all flow measurements to dry solids tonnes per hour before calculating the ratio.
- Collect synchronized samples and record density, water addition, cyclone pressure, and operating conditions.
- Use particle-size or density balances as independent checks on measured tonnage.
- Trend circulating load with product size, mill power, feed rate, and recovery rather than interpreting one result alone.
A repeatable worksheet should show the raw measurements, unit conversions, selected size fraction, calculation method, and balance error. Store the assumptions with the result so that operators and engineers can distinguish a measured circulating load from an estimate based on density or laboratory data.
For practical process development, mineral processing solutions can support the wider evaluation of crushing, grinding, classification, separation, and plant performance. A well-defined circulating load calculation gives that evaluation a sound operating baseline and helps connect laboratory findings with actual plant capacity.
Use the calculated value to set a stable operating reference, then verify it after any change in ore type, feed rate, cyclone configuration, mill speed, grinding media, or product-size target. Regularly repeated measurements turn a one-time calculation into a useful control tool for improving throughput, energy use, and final recovery.