body {
font-family: -apple-system, BlinkMacSystemFont, “Segoe UI”, Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
max-width: 1200px;
margin: 0 auto;
padding: 20px;
background-color: #f4f7f6;
}
.calculator-container {
background: #ffffff;
padding: 30px;
border-radius: 12px;
box-shadow: 0 4px 15px rgba(0,0,0,0.1);
margin-bottom: 40px;
border-left: 5px solid #0056b3;
}
.calculator-title {
color: #0056b3;
margin-top: 0;
margin-bottom: 25px;
font-size: 24px;
border-bottom: 1px solid #eee;
padding-bottom: 15px;
}
.form-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 20px;
}
@media (max-width: 768px) {
.form-grid {
grid-template-columns: 1fr;
}
}
.input-group {
margin-bottom: 15px;
}
.input-group label {
display: block;
margin-bottom: 8px;
font-weight: 600;
color: #444;
}
.input-group input {
width: 100%;
padding: 12px;
border: 1px solid #ddd;
border-radius: 6px;
font-size: 16px;
box-sizing: border-box;
transition: border-color 0.3s;
}
.input-group input:focus {
border-color: #0056b3;
outline: none;
}
.input-hint {
font-size: 12px;
color: #666;
margin-top: 4px;
}
.calc-btn {
background-color: #0056b3;
color: white;
border: none;
padding: 15px 30px;
font-size: 18px;
border-radius: 6px;
cursor: pointer;
width: 100%;
margin-top: 20px;
font-weight: bold;
transition: background-color 0.2s;
}
.calc-btn:hover {
background-color: #004494;
}
.result-box {
margin-top: 25px;
padding: 20px;
background-color: #eef7ff;
border-radius: 8px;
display: none;
border: 1px solid #b8daff;
}
.result-value {
font-size: 32px;
font-weight: bold;
color: #0056b3;
text-align: center;
margin: 10px 0;
}
.result-label {
text-align: center;
font-size: 16px;
color: #555;
}
.article-content {
background: white;
padding: 40px;
border-radius: 12px;
box-shadow: 0 2px 10px rgba(0,0,0,0.05);
}
h2 {
color: #2c3e50;
border-bottom: 2px solid #ecf0f1;
padding-bottom: 10px;
margin-top: 30px;
}
p {
margin-bottom: 15px;
}
.formula-box {
background-color: #f8f9fa;
padding: 15px;
border-left: 4px solid #28a745;
font-family: monospace;
font-size: 1.1em;
margin: 20px 0;
overflow-x: auto;
}
Solids Capture Rate Calculator (Van Kleeck Formula)
Understanding Solids Capture Rate
The solids capture rate (often referred to as recovery) is a critical performance metric in wastewater treatment, specifically within sludge dewatering processes such as centrifuges, belt filter presses, and screw presses. It represents the percentage of dry solids from the feed sludge that remains in the dewatered “cake” rather than returning to the head of the plant via the centrate or filtrate.
High capture rates indicate efficient separation, meaning cleaner centrate is being returned to the treatment process. Low capture rates imply that a significant amount of solids is recirculating, which can increase the biological load on the plant, increase polymer consumption, and reduce overall treatment capacity.
The Calculation Logic
This calculator utilizes the standard Van Kleeck formula, which allows operators to calculate efficiency using concentration percentages without needing total mass flow rates. This is widely used because sampling concentrations is easier than measuring the mass flow of the cake.
Where:
- Cs: Cake Solids concentration (%)
- Cf: Feed Solids concentration (%)
- Ce: Centrate/Effluent concentration (converted to %)
Note: Because centrate is usually measured in mg/L (ppm) while feed and cake are in %, our calculator automatically converts the Centrate input from mg/L to percent by dividing by 10,000 before applying the formula.
Typical Performance Values
Benchmarks vary by equipment type and sludge characteristics, but general guidelines include:
- Excellent: > 95% capture rate
- Acceptable: 90% – 95% capture rate
- Poor: < 90% capture rate (Requires optimization)
Factors Affecting Solids Capture
If your calculation shows a low recovery rate, consider investigating the following parameters:
- Polymer Dosage: Insufficient polymer dosing is the most common cause of poor capture.
- Hydraulic Loading: Exceeding the design flow rate of the machine reduces residence time and separation efficiency.
- Differential Speed (Torque): In decanter centrifuges, a lower differential speed increases retention time, potentially improving cake dryness but sometimes impacting capture if not balanced.
- Feed Characteristics: Changes in the sludge volume index (SVI) or ratio of primary to secondary sludge can impact dewaterability.
function calculateCaptureRate() {
// 1. Get input values
var feedVal = document.getElementById(‘feedSolids’).value;
var cakeVal = document.getElementById(‘cakeSolids’).value;
var centrateVal = document.getElementById(‘centrateSolids’).value;
// 2. Validate inputs exist
if (feedVal === “” || cakeVal === “” || centrateVal === “”) {
alert(“Please fill in all fields (Feed, Cake, and Centrate).”);
return;
}
// 3. Parse numbers
var cf = parseFloat(feedVal); // Feed %
var cs = parseFloat(cakeVal); // Cake %
var ce_mgl = parseFloat(centrateVal); // Centrate mg/L
// 4. Validate numbers are positive
if (cf <= 0 || cs <= 0 || ce_mgl Centrate, Cake must be > Feed
if (ce >= cf) {
alert(“Error: Centrate concentration cannot be higher than Feed concentration.”);
return;
}
if (cf >= cs) {
alert(“Error: Feed concentration cannot be higher than Cake concentration.”);
return;
}
// 7. Calculate Capture Rate using Van Kleeck Formula
// Formula: (Cs * (Cf – Ce)) / (Cf * (Cs – Ce)) * 100
var numerator = cs * (cf – ce);
var denominator = cf * (cs – ce);
var captureRate = (numerator / denominator) * 100;
// 8. Display Results
var resultBox = document.getElementById(‘resultBox’);
var resultText = document.getElementById(‘captureResult’);
var feedbackText = document.getElementById(‘resultFeedback’);
resultBox.style.display = “block”;
resultText.innerHTML = captureRate.toFixed(2) + “%”;
// Provide feedback based on the result
if (captureRate >= 95) {
feedbackText.innerHTML = “Status: Excellent Performance“;
} else if (captureRate >= 90) {
feedbackText.innerHTML = “Status: Acceptable Performance“;
} else {
feedbackText.innerHTML = “Status: Optimization Required (Low Capture)“;
}
}