Horner Time Calculator
Calculate Horner time ratios, Agarwal equivalent time, and superposition time for pressure buildup analysis. Generate tables at standard shut-in intervals.
Input Parameters
Horner Ratio = (tp + Δt) / Δt
Agarwal Equivalent Time = (tp × Δt) / (tp + Δt)
Superposition Time = log[(tp + Δt) / Δt]
Horner Time Ratio
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Agarwal Equivalent Time
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Superposition Time
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Additional Calculations
log(Horner Ratio)
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1/Horner Ratio
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tp / Δt Ratio
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Horner Ratio Table at Standard Shut-In Times
Using producing time tp = 720 hours
| Δt (hrs) | Horner Ratio | log(HR) | Agarwal te (hrs) | Superposition |
|---|
How this was calculated
Horner time ratio: HTR = (tp + dt) / dt. Used for Horner plot analysis where pressure is plotted against log(HTR). As dt approaches infinity, HTR approaches 1 (log HTR approaches 0), giving the extrapolated reservoir pressure p*.
Agarwal equivalent time: te = (tp * dt) / (tp + dt). Converts buildup data to equivalent drawdown time, allowing type-curve matching with drawdown solutions. Especially useful when tp >> dt.
Superposition time: Used in multirate testing to account for variable rate history. For a single rate change (buildup), it simplifies to log[(tp + dt) / dt].
When tp >> dt: Agarwal te approaches dt, and the buildup behaves like a drawdown test. When dt >> tp, the Horner analysis may be unreliable.
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Book a free strategy call →Understanding Horner Time in Pressure Buildup Analysis
The Horner plot is one of the most fundamental tools in well test analysis. Developed by D.R. Horner in 1951, it provides a method to determine reservoir pressure and permeability from pressure buildup data. The Horner time ratio (tp + dt) / dt is plotted on a logarithmic x-axis against shut-in pressure on a linear y-axis. When infinite-acting radial flow is established, the data falls on a straight line whose slope yields the formation permeability-thickness product (kh) and whose extrapolation to a Horner ratio of 1 gives the static reservoir pressure (p*).
The Agarwal equivalent time concept, introduced by Ram Agarwal, allows buildup data to be analyzed using drawdown type curves. By converting shut-in time to an equivalent drawdown time via te = (tp * dt) / (tp + dt), the buildup response can be matched against well-known drawdown solutions. This is particularly powerful for identifying flow regimes and estimating reservoir parameters when the traditional Horner analysis is inconclusive.
Production engineers use these calculations daily when planning and interpreting pressure surveys. Knowing the Horner ratio at various shut-in times helps determine how long a well needs to be shut in to get reliable reservoir pressure estimates, directly impacting revenue from lost production during the test.
All calculations run entirely in your browser. Built by Groundwork Analytics, an AI and engineering company building digital tools for the energy industry. Get in touch or email info@petropt.com.