Hydraulic Fracture Carter Leakoff Guide
A hydraulic-fracturing leakoff guide for Carter square-root-time fluid loss, spurt loss, exposed area, time basis, fluid balance, fracture efficiency, and model limitations.
By PetroCalcHub Editorial Team | Updated 2026-07-31
linked formula references
verified source links
Engineering context
Fracturing-fluid material balance divides injected volume among wellbore volume, created fracture volume, leakoff to the formation, and any unaccounted or compressibility terms in the chosen model. Carter leakoff approximates time-dependent fluid loss with a coefficient multiplied by square root of exposure time and adds an instantaneous spurt-loss thickness.
The equation is compact, but area and time definitions are easy to mishandle. Every newly created piece of fracture surface has a different exposure age, and publications may report geometry for one wing, both wings, one face, or both faces. A useful hand calculation states those conventions before entering numbers and treats the result as a fluid-balance screen rather than a coupled fracture simulation.
Practical workflow
- 1
Define whether area and injected volume represent one wing or both wings and one or both fracture faces.
- 2
Enter a leakoff coefficient, exposure time, and spurt-loss thickness on one consistent unit basis.
- 3
Calculate leakoff volume and reconcile it with injected volume and estimated fracture volume.
- 4
Test sensitivity to coefficient, time, and area, then use calibrated treatment data for design-critical decisions.
Define the area convention first
Leakoff area is the formation-contact area across which fluid is lost. A bi-wing fracture has two wings, and each wing can have two faces. Whether a length-times-height expression already includes these factors depends on the source and implementation. Integer-factor errors occur when the convention is left implicit.
Injected volume and fracture volume must use a compatible basis. If a model reports one-wing volume but field injection is total-well volume, the comparison needs the correct symmetry factor. The University of Texas source linked below explicitly discusses one-wing and bi-wing volume treatment in its hydraulic-fracturing chapter.
Separate spurt loss and Carter leakoff
Spurt loss represents an initial fluid volume per area before an effective filter cake or leakoff regime develops. In the simplified expression it is a thickness added inside the area multiplier. Carter leakoff then grows with square root of exposure time, so doubling time does not double the time-dependent volume.
Coefficient units must match the time unit under the square root. A coefficient stated per square-root minute cannot be combined with seconds without conversion. The same numerical time entered on the wrong basis can change leakoff by the square root of 60.
Recognize the effective-time approximation
A real propagating fracture continuously creates surface. Early area has been exposed longer than area near the current tip. Applying one total area and one time assumes an effective exposure history. More complete models integrate leakoff over surface creation time and couple it to changing pressure and geometry.
The coefficient can also vary with permeability, compressibility, viscosity, pressure differential, filter cake, saturation, natural fractures, and fluid chemistry. A single fitted value can be useful over one treatment window without being transferable to another stage or formation.
Use fluid balance as a diagnostic
Fracture efficiency is commonly expressed as fracture volume divided by injected volume after accounting for leakoff on a consistent basis. An impossible negative fracture volume or efficiency above one is a signal to review wellbore storage, area factors, time basis, coefficient, spurt loss, compressibility, and measured rate integration.
Treatment pressure matching, mini-frac or DFIT interpretation, tracer response, proppant placement, production history, and post-job diagnostics provide constraints that a hand calculation cannot. Use the simple model to reveal assumptions and sensitivities before moving to a calibrated design tool.
Worked Carter leakoff balance
Use effective leakoff area = 20,000 ft2, Carter coefficient = 0.003 ft/min^0.5, exposure time = 60 min, and spurt-loss thickness = 0.02 ft.
- 1. Square-root timesqrt(60) = 7.746 min^0.5
Exposure time is placed on the same minute basis used by the coefficient.
- 2. Carter thickness2 x 0.003 x 7.746 = 0.04648 ft
This is the time-dependent leakoff thickness in the implemented form.
- 3. Total fluid-loss thickness0.04648 + 0.02000 = 0.06648 ft
Spurt-loss thickness is added separately from the time-dependent term.
- 4. Leakoff volume20,000 x 0.06648 = 1,329.52 ft3 = 236.78 bbl
The stated effective area converts loss thickness into total volume.
Result
The simplified Carter equation returns 1,329.52 ft3 of leakoff, equal to about 236.78 bbl.
Interpretation
Time-dependent Carter loss contributes about 929.5 ft3 and spurt loss contributes 400 ft3, for a total of 1,329.5 ft3. If the 20,000 ft2 area omits a required face or wing factor, the total changes in direct proportion, so geometry convention is the first review item.
Method selection guide
Match the calculation method to the physical question and the evidence available.
| Condition | Use | Why |
|---|---|---|
| Transparent first-pass fluid balance | Carter square-root-time leakoff | The relationship separates leakoff area, coefficient, exposure time, and spurt loss in an auditable estimate. |
| Mini-frac or DFIT pressure data available | Pressure-transient leakoff interpretation | Observed pressure behavior can constrain leakoff and closure behavior more directly than an assumed coefficient. |
| Treatment design depends on propagation and proppant placement | Calibrated coupled fracture simulator | Growing geometry, pressure-dependent leakoff, rheology, proppant transport, and stress interaction are coupled. |
Before using the result
- State whether area represents one face, two faces, one wing, or both wings.
- Keep coefficient and exposure-time units consistent before taking the square root.
- Separate spurt-loss thickness from time-dependent leakoff.
- Do not assign one exposure time to all fracture area without labelling the approximation.
- Reconcile leakoff plus fracture volume with injected volume on the same wing basis.
- Calibrate against mini-frac, DFIT, treatment pressure, and post-job evidence when available.
Start with these calculators
These links keep the guide close to the working calculator flow.