Dye Recovery Percentage Calculator

Actual background-corrected dye concentration×matched discharge trapezoidal recovery integral/mass injected. Complete breakthrough collection, mixing and losses external; over100 percent retained as discrepancy, not forced to physical fraction.

Description

Tracer recovery integrates measured concentration times matched discharge over observation time.

Tracer recovery integrates measured concentration times matched discharge over observation time.^[1]

Comparing recovered mass with injected mass depends on background correction and sampling coverage.

When to use Dye Recovery Percentage Calculator

Use this tool to obtain observedIntegratedRecoveredTracerMass, conditionalObservedRecoveryPercent from the supplied records using the stated calculation. Establish the survey or observation scope, reference frame, units and independently applicable calibration or qualified plan.

How to use Dye Recovery Percentage Calculator and understand its results

Establish the survey or observation scope, reference frame, units and independently applicable calibration or qualified plan.
Enter actualObservedElapsedSeconds, actualBackgroundCorrectedConcentrationsMassPerVolume, actualMatchedDischargesVolumePerSecond, actualInjectedTracerMass, using the field meanings and rules below, then run the tool.
Read result.observedIntegratedRecoveredTracerMass, result.conditionalObservedRecoveryPercent. Use the units and sign conventions below, and review any unknown records separately.
Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.

Input field	Meaning	Value type	Requirement
actualObservedElapsedSeconds	Actual observed elapsed seconds	list of number	Required
actualBackgroundCorrectedConcentrationsMassPerVolume	Actual background corrected concentrations mass per volume	list of number	Required
actualMatchedDischargesVolumePerSecond	Actual matched discharges volume per second	list of number	Required
actualInjectedTracerMass	Actual injected tracer mass	number	Required

Supply at least two aligned strictly increasing finite times, nonnegative concentrations and nonnegative matched discharges, plus positive injected mass. Multiply concentration and discharge at each sample, then integrate that product by trapezoids. Return recovered mass and one hundred times recovered/injected mass. Values above one hundred percent are not clamped; this integrates sampled products rather than the exact product of two separately interpolated curves.

recoveredMass=Σ(deltaTime×(C_i×Q_i+C_(i+1)×Q_(i+1))/2); recoveryPercent=100×recoveredMass/injectedMass

Use the matching field units and the exact boundary, ordering and reference rules above.

Output field	Meaning	Value type
result	Qualified observed calculation or explicit reference	object
result.observedIntegratedRecoveredTracerMass	Observed Integrated Recovered Tracer Mass	number
result.conditionalObservedRecoveryPercent	Conditional Observed Recovery Percent	number

json

{
  "input": {
    "actualObservedElapsedSeconds": [
      0,
      1,
      2
    ],
    "actualBackgroundCorrectedConcentrationsMassPerVolume": [
      0,
      2,
      0
    ],
    "actualMatchedDischargesVolumePerSecond": [
      1,
      1,
      1
    ],
    "actualInjectedTracerMass": 4
  },
  "output": {
    "result": {
      "observedIntegratedRecoveredTracerMass": 2,
      "conditionalObservedRecoveryPercent": 50
    }
  }
}

Limitations and assumptions

The actual observation coverage, calibration and qualified plan determine applicability. A numerical result does not establish survey accuracy, route suitability, atmosphere conditions or equipment adequacy beyond the declared comparison.

Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Lists and matrices must be dense, without missing cells. Numeric lists allow at most 10000 entries, subject to the narrower lengths and code rules above. Extremely large composite outputs are rejected.

Alternative or Complementary methods

For a related step, use Karst Spring Discharge Dilution Gauging Calculator: Slug-dilution discharge relates injected tracer mass to the time integral of background-corrected concentration. For a complementary comparison, use Dye Trace Time of Travel Velocity Calculator: Tracer travel distance divided by observed travel time gives an apparent travel speed.

References

Dye Recovery Percentage Calculator — tool.io

Similar or alternative tools

Karst Spring Discharge Dilution Gauging Calculator
Slug-dilution discharge relates injected tracer mass to the time integral of background-corrected concentration.
Dye Trace Time of Travel Velocity Calculator
Tracer travel distance divided by observed travel time gives an apparent travel speed.