Fertigation Tank Dilution: Why Nutrient Concentration Changes During Injection

A flow-through fertigation tank becomes progressively diluted when incoming irrigation water replaces nutrient solution leaving the tank. A stable water flow through that tank therefore does not guarantee a stable nutrient injection rate. Identify whether water enters during injection, measure the relevant flows, and distinguish changing tank concentration from the concentration entering the irrigation mainline.

Solution storage tanks beside a fertigation injector. This arrangement differs from a flow-through pressure-differential fertilizer tank. Photo: IrriNex.

Identify which kind of tank your system uses

A differential-pressure tank forms a bypass between two points of different pressure. Water enters the vessel and carries solution back to the irrigation line. New Mexico State University's fertigation and injection guidance describes the progressive dilution of this batch-tank arrangement and its limitations when a constant concentration is required. The vessel must also be suitable for its actual pressurized service.

To avoid the declining concentration curve inherent in simple bypass tanks, commercial fertigation systems utilize differential pressure Venturi injectors connected to continuous stock solution supplies.

A stock tank supplying a metering injector behaves differently if no replacement water enters. Its liquid level falls as solution is withdrawn, while a uniformly mixed, fully dissolved stock can retain approximately the same concentration. A lid does not make a stock tank a pressure vessel. Conversely, a vessel staying full during a bypass run does not mean it still contains its initial nutrient mass.

Label the water inlet, solution outlet, injection point, and any automatic refill connection on a simple equipment map. Determine whether the tank loses volume, receives replacement water, or includes a separate dissolving chamber. The FAO handbook chapter on fertigation distinguishes closed bypass tanks from other injection arrangements. Do not choose a concentration formula from the word “tank” alone.

This guide examines a pre-dissolved nutrient in an ideal, continuously mixed flow-through tank. Its original numbers illustrate mass accounting, not a fertilizer recipe, pressure setting, crop recommendation, or measured performance of an IrriNex product.

Write the tank mass balance before using a dilution factor

Assume constant liquid volume V, equal inlet and outlet flow q, complete instantaneous mixing, and no further nutrient dissolution, precipitation, reaction, or leakage. Let C be the concentration of the tracked dissolved nutrient above a constant source-water background. Under these assumptions, the nutrient mass in the tank is V × C, and the excess nutrient leaves at the rate q × C.

With V in litres, q in litres per minute, C in grams per litre, and elapsed time t in minutes, the balance becomes V × dC/dt = −q × C. Its solution is C(t) = C0 × exp(−q × t ÷ V), where C0 is the initial excess concentration. The exponential argument is dimensionless. It describes continuous replacement, rather than a sequence of complete drain-and-refill batches.

For a constant nonzero background concentration Cb, the corresponding absolute concentration is Cb + (Cinitial − Cb) × exp(−q × t ÷ V). The example below uses the excess concentration to keep background nutrients separate from the added dose. Fertilizer-product mass, individual nutrient mass, and total dissolved salts are different quantities; the same concentration basis must be used throughout.

Real tanks can depart from this model because of incomplete mixing, flow paths that bypass part of the vessel, solids dissolving during injection, or changing flow. The exponential calculation is a stated ideal model to compare with measurements. It does not replace a tank-specific operating chart or prove the behavior of a device whose internal design is unknown.

Calculate an original dilution curve and mass ledger

Assume V = 100 L, q = 5 L/min, and C0 = 10 g/L of the tracked added nutrient. The initial nutrient mass is 1000 g. The turnover time V ÷ q is 20 min, and the concentration equation becomes C(t) = 10 × exp(−t ÷ 20). All displayed results are rounded from that equation.

High-precision greenhouse and field blocks maintain stable ppm targets throughout the irrigation cycle by operating closed-loop proportional fertigation machines with dynamic flow modulation.

After one turnover, 100 L has passed through a tank whose liquid volume remains 100 L. Approximately 632.12 g has left, while 367.88 g remains. Passing one tank volume does not completely exchange every molecule of a continuously mixed vessel. It also does not mean the tank concentration has fallen linearly to zero.

After 60 min, approximately 95.02% of the initial added nutrient has left the ideal tank, but approximately 49.79 g remains. The liquid level is still unchanged. Neither a full-looking vessel nor the passage of several turnover volumes establishes the residual mass without a concentration model or measurement.

The discharged mass is Mout(t) = V × C0 × [1 − exp(−q × t ÷ V)]. This is mass crossing the tank outlet. It is not automatically mass already delivered to every emitter, retained in the crop root zone, or taken up by plants. Those locations and processes require additional accounting.

Distinguish tank concentration, mainline concentration, and event average

Now assume the total irrigation flow downstream of the returning bypass is Q = 200 L/min, including the tank's 5 L/min return. The remaining 195 L/min takes the other path. Do not add the bypass return to Q again. With complete mixing at the return point, the added mainline concentration is q ÷ Q × C(t).

At the start, 5 ÷ 200 × 10 = 0.25 g/L, or 250 mg/L of the tracked added nutrient. At 20 min, it is approximately 91.97 mg/L. The tank's 3.679 g/L at that time must not be reported as the mainline concentration: the solution has been diluted by the combined water stream.

The interval average is higher than the ending concentration because the early discharge was more concentrated. Multiplying the final concentration by the whole interval would underestimate the mass delivered during this declining profile. Similarly, a start-of-event sample cannot represent every later minute.

Keep mass and concentration targets distinct when using the fertigation injection-rate calculation guide. A completed total dose can coexist with a changing concentration history. Whether that history suits a crop and network requires an agronomic and distribution assessment, not merely a correct total mass.

Check what changes when bypass flow or tank size changes

In the ideal equation, the ratio q ÷ V controls how quickly concentration declines. A larger liquid volume at the same q and C0 produces a slower decline and also starts with more nutrient mass. If the intended total nutrient mass must stay fixed, increasing V requires changing C0 instead. Specify which quantity stays constant before comparing tanks.

Doubling q from 5 to 10 L/min in the same 100 L ideal tank halves its turnover time from 20 to 10 min. If the assumed total downstream Q remains 200 L/min and C0 remains 10 g/L, the initial added mainline concentration doubles from 250 to 500 mg/L. Faster tank depletion does not mean the concentration profile has become flat.

This is a mathematical comparison, not an instruction to throttle a mainline or adjust a pressure differential. Real bypass flow depends on the tank, valves, connecting lines, and operating pressures. A change that increases bypass flow can also change conditions elsewhere. Verify the actual q and Q after any approved equipment adjustment.

For a variable measured q with constant V, the ideal exponential depends on cumulative bypass volume divided by V. Clock time alone is then an incomplete predictor. Use suitable flow measurement and correctly interpreted pulse totals, as discussed in the irrigation flow-meter pulse conversion guide. A controller being on does not establish a constant bypass flow.

Compare flow-through dilution with withdrawal from prepared stock

For a uniformly mixed stock tank with no water refill, withdrawing solution reduces both dissolved mass and liquid volume together. If no other process changes the solution, concentration remains approximately constant until the usable stock is depleted. In a flow-through tank, incoming water replaces the withdrawn volume and changes that concentration. These arrangements need different monitoring records.

UMass Extension explains stock concentration and injector ratios, including why a ratio setting is not itself a nutrient concentration. Constant stock concentration still does not guarantee constant mainline concentration if the stock injection rate, irrigation flow, or ratio changes. Verify what the injector's ratio denominator represents and measure actual delivery.

Before treating stock as constant, check that it was fully dissolved and compatible under actual conditions. The stock-solution solubility and compatibility guide covers that separate preparation decision. Settling, precipitation, evaporation, accidental refill, or ongoing dissolution can invalidate a constant-concentration assumption.

Do not transfer the 100 L flow-through example to a suction tank and run its injector until the vessel is physically empty. Usable stock volume depends on the equipment's minimum level and suction requirements. Stop and refill according to its approved procedure; a mathematical depletion time does not override those operating limits.

Test the concentration history and locate the measurement boundary

Use an approved sampling arrangement to collect time-stamped samples at defined locations: source water, tank outlet or representative mixed stock, the mixed mainline, and selected downstream delivery points as needed. A tank sample and an emitter sample taken simultaneously do not necessarily represent the same parcel of solution because the network introduces travel time and mixing.

EC can help follow a known solution under a suitable calibrated procedure, but it does not uniquely identify every nutrient concentration. Record background water, temperature treatment, fertilizer formulation, and the applicable concentration relationship. Solution color and a generic EC-to-nutrient multiplier are inadequate substitutes for that relationship.

Do not open a pressurized vessel to obtain a sample or judge remaining fertilizer. Use the installed sampling procedure and appropriate isolation or depressurization arrangements. Preserve the protection against backflow and unintended injection while carrying out the test. The pump and irrigation-permission interlock guide addresses a related control boundary. Its pump example does not specify a complete fertigation protection system.

Close the event with a residual-mass and water-budget record

An ideal mixed-tank exponential approaches zero concentration gradually; it does not reach exactly zero in a finite time. For the example, reaching 99% discharge of the initial added nutrient would require approximately 92.10 min and 18.42 m³ of mainline water at the assumed constant flows. That is a calculated model point, not a recommended flushing target or permission to apply that volume to the crop.

Continuing irrigation solely to chase a tiny tank residue may exceed the field's water allowance. Establish the event's acceptable dose, concentration history, residual handling, and line-clearing procedure together with the relevant crop and equipment requirements. Water and nutrient permissions must remain valid throughout the operation.

Retain the actual liquid volume, initial concentration basis, bypass and mainline flow records, sample times, discharged mass estimate, residual estimate, and any deviations from the assumed model. Separate the mass still in the tank from solution still travelling through the network. That distinction makes the next event's starting inventory and the completed event's dose understandable and reproducible.

Frequently Asked Questions on Fertigation Tank Exponential Dilution Decay

What is the mathematical equation governing the decline of nutrient concentration in a passive bypass pressure tank?

$$C(t) = C_0 \times e^{-\left(\frac{q}{V}\right) t}$$ where $C_0$ is initial stock concentration, $q$ is bypass flow rate through the tank, $V$ is total tank volume, and $t$ is elapsed injection time.

How many tank volume turnovers ($q \times t / V$) are required to displace 95% of the total fertilizer mass from a batch tank?

Exactly 3.0 volume turnovers: $e^{-3.0} \approx 0.0498$ (meaning only $5.0\%$ of original fertilizer remains in the tank, meaning $95\%$ has been delivered to the field).

Why can an exponential dilution curve create agronomic problems in sensitive crops?

During the first 15 minutes, electrical conductivity (EC) spikes dangerously high, risking salt burn on young root hairs. In the second half of the cycle, EC drops to near zero, causing non-uniform nutrient placement along the crop root profile.

When is an automated electric metering pump or multi-channel fertigation machine superior to a passive bypass tank?

When exact, continuous EC/pH targets are mandated (such as closed-loop hydroponics, rockwool, or fertigation of high-value fruit trees), a smart metering unit (e.g. IrriNex CHKN3-ZDB) maintains flat, constant nutrient concentration from start to finish.