{
  "version": 1,
  "topic": "PR02",
  "title": "Productivity index versus production rate",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Fixed PI, changing drawdown",
    "premise": "Linear PI J = 2 STB/day/psi; pressures use one compatible datum and fluid-volume basis.",
    "formula": "q = J Δp",
    "variables": "This is an inflow relation. An operating point additionally requires an outflow model.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Drawdown (psi) = 500",
        "explanation": "Linear PI J = 2 STB/day/psi; pressures use one compatible datum and fluid-volume basis."
      },
      {
        "label": "Select the relation",
        "calculation": "q = J Δp",
        "explanation": "This is an inflow relation. An operating point additionally requires an outflow model."
      },
      {
        "label": "Substitute the values",
        "calculation": "2 STB/day/psi × 500 psi = 1,000 STB/day",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Oil rate (STB/day) = 1000; PI (STB/day/psi) = 2",
        "explanation": "PI is a coefficient, while rate depends on the selected drawdown."
      }
    ],
    "result": "Oil rate (STB/day) = 1000; PI (STB/day/psi) = 2",
    "interpretation": "PI is a coefficient, while rate depends on the selected drawdown.",
    "control": "Drawdown (psi)",
    "columns": [
      "Drawdown (psi)",
      "Oil rate (STB/day)",
      "PI (STB/day/psi)"
    ],
    "rows": [
      [
        100,
        200,
        2
      ],
      [
        250,
        500,
        2
      ],
      [
        500,
        1000,
        2
      ],
      [
        750,
        1500,
        2
      ],
      [
        1000,
        2000,
        2
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Drawdown (psi) = 100. Oil rate (STB/day): 200; PI (STB/day/psi): 2.",
      "Drawdown (psi) = 250. Oil rate (STB/day): 500; PI (STB/day/psi): 2.",
      "Drawdown (psi) = 500. Oil rate (STB/day): 1000; PI (STB/day/psi): 2.",
      "Drawdown (psi) = 750. Oil rate (STB/day): 1500; PI (STB/day/psi): 2.",
      "Drawdown (psi) = 1000. Oil rate (STB/day): 2000; PI (STB/day/psi): 2."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Oil rate (STB/day) without rounding intermediate values.",
        "answer": "2 STB/day/psi × 500 psi = 1,000 STB/day. Oil rate (STB/day) = 1000. PI is a coefficient, while rate depends on the selected drawdown."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Drawdown (psi) changes from 100 to 1000. Other controls remain as stated in the premise. Oil rate (STB/day) changes from 200 to 2000."
      },
      {
        "question": "What would be needed to apply this example to a different physical system?",
        "answer": "Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. This is an inflow relation. An operating point additionally requires an outflow model. PI is a coefficient, while rate depends on the selected drawdown."
      }
    ]
  },
  "recorded": null
}