Petroleum Pressure Derivative Calculator

Explicit three-point Bourdet derivative dP/dln(time) with opposite-side logarithmic interval weights on actual unequal sample times, not uniform finite differences or automatic well-test regime diagnosis. Caller independently verifies units, applicability and matching conditions; no operational recipe, safety certification, causal efficacy or legal/resource classification is inferred.

Description

Bourdet pressure derivatives summarize pressure change against natural log of elapsed time using neighboring intervals.

Bourdet pressure derivatives summarize pressure change against natural log of elapsed time using neighboring intervals.^[1]

This tool evaluates the three-point weighted derivative on unequal sample times and returns only interior observations.

When to use Petroleum Pressure Derivative Calculator

Use this tool when you need to calculate the stated measurement summary or conditional model from matched observations. Prepare completed matched measurements, SI or explicitly stated oilfield units, and independent evidence for the selected branch or calibration.

How to use Petroleum Pressure Derivative Calculator and understand its results

Prepare completed matched measurements, SI or explicitly stated oilfield units, and independent evidence for the selected branch or calibration.
Enter observedPressureDerivativeTimesSeconds, observedPressureChangePa, following the field table and calculation rules below, then run the tool.
Read interiorBourdetPressureDerivativePa, interiorDerivativeTimesSeconds. For result objects, inspect the nested output fields below, including any missing evidence or selected indices.
Correct any input issues and run again. Before using a successful result, review its units, signs, evidence coverage, and stated model or reference assumptions.

Input field	Meaning	Value type	Requirement
observedPressureDerivativeTimesSeconds	Observed pressure derivative times seconds	list of number	Required
observedPressureChangePa	Observed pressure change pa; pressure or stress in pascals, with the sign convention described above.	list of number	Required

Require at least three strictly increasing positive elapsed times and aligned finite signed pressure changes. Compute left and right ln-time intervals a and b, then combine the left pressure secant weighted by b with the right secant weighted by a, divided by a+b. Return n−2 values and their original interior times; no endpoint derivative or smoothing window is supplied.

derivative_i=((P_i−P_(i−1))/a×b+(P_(i+1)−P_i)/b×a)/(a+b)

Read these symbols with the field meanings and branch or reference rules above.

Output field	Meaning	Value type
interiorBourdetPressureDerivativePa	Interior bourdet pressure derivative pa; pressure or stress in pascals, with the sign convention described above.	list of number
interiorDerivativeTimesSeconds	Interior derivative times seconds	list of number

json

{
  "input": {
    "observedPressureDerivativeTimesSeconds": [
      1,
      2.718281828459045,
      7.3890560989306495
    ],
    "observedPressureChangePa": [
      0,
      1,
      2
    ]
  },
  "output": {
    "interiorBourdetPressureDerivativePa": [
      1
    ],
    "interiorDerivativeTimesSeconds": [
      2.718281828459045
    ]
  }
}

Limitations and assumptions

Measurements, unit conventions, branch identity, and model applicability must be independently established. The result does not infer a complete reservoir or flow model, operational settings, or a reserve classification.

Missing required fields, unknown fields, wrong types, and violated calculation rules return input issues. Numeric values must be finite; nonfinite numeric outputs are rejected. Arrays must be dense, with no missing cells. Numeric lists allow at most 10000 entries, subject to smaller tool-specific bounds above.

Alternative or Complementary methods

For a related task, use Petroleum Drawdown Pressure Analysis Calculator: Drawdown analysis can summarize a selected pressure branch by fitting pressure change against natural log of elapsed time. This tool retains the signed slope and its difference from an independently supplied reference rather than selecting a radial regime. For a complementary step, use Petroleum Well Test Skin Calculator: Transient well-test skin describes additional drawdown relative to a matched zero-skin reference under a radial-flow convention. This tool computes signed apparent skin from supplied traces and natural-log derivatives, without diagnosing formation damage.

References

Petroleum Pressure Derivative Calculator — tool.io

Similar or alternative tools

Petroleum Drawdown Pressure Analysis Calculator
Drawdown analysis can summarize a selected pressure branch by fitting pressure change against natural log of elapsed time. This tool retains the signed slope and its difference from an independently supplied reference rather than selecting a radial regime.
Petroleum Well Test Skin Calculator
Transient well-test skin describes additional drawdown relative to a matched zero-skin reference under a radial-flow convention. This tool computes signed apparent skin from supplied traces and natural-log derivatives, without diagnosing formation damage.