{
  "version": 1,
  "topic": "PR09",
  "title": "What an inflow curve cannot tell you about a producing system",
  "createdAt": "2026-10-24",
  "case": {
    "title": "A transparent synthetic inflow–outflow intersection",
    "premise": "Inflow q = 2(3,000 − pwf) STB/day. Teaching outflow pwf = pbase + 0.5q psi; pbase varies.",
    "formula": "q = (6,000 − 2pbase)/2; pwf = 3,000 − q/2",
    "variables": "The outflow is an explicitly invented linear teaching relation, not a tubing correlation.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Outflow base pressure (psi) = 1500",
        "explanation": "Inflow q = 2(3,000 − pwf) STB/day. Teaching outflow pwf = pbase + 0.5q psi; pbase varies."
      },
      {
        "label": "Select the relation",
        "calculation": "q = (6,000 − 2pbase)/2; pwf = 3,000 − q/2",
        "explanation": "The outflow is an explicitly invented linear teaching relation, not a tubing correlation."
      },
      {
        "label": "Substitute the values",
        "calculation": "At pbase = 1,500: q = 2[3,000 − (1,500 + 0.5q)]; 2q = 3,000; q = 1,500 STB/day and pwf = 2,250 psi",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Intersection rate (STB/day) = 1500; Matched bottom pressure (psi) = 2250",
        "explanation": "Only a compatible intersection supplies the synthetic operating point."
      }
    ],
    "result": "Intersection rate (STB/day) = 1500; Matched bottom pressure (psi) = 2250",
    "interpretation": "Only a compatible intersection supplies the synthetic operating point.",
    "control": "Outflow base pressure (psi)",
    "columns": [
      "Outflow base pressure (psi)",
      "Intersection rate (STB/day)",
      "Matched bottom pressure (psi)"
    ],
    "rows": [
      [
        500,
        2500,
        1750
      ],
      [
        1000,
        2000,
        2000
      ],
      [
        1500,
        1500,
        2250
      ],
      [
        2000,
        1000,
        2500
      ],
      [
        2500,
        500,
        2750
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Outflow base pressure (psi) = 500. Intersection rate (STB/day): 2500; Matched bottom pressure (psi): 1750.",
      "Outflow base pressure (psi) = 1000. Intersection rate (STB/day): 2000; Matched bottom pressure (psi): 2000.",
      "Outflow base pressure (psi) = 1500. Intersection rate (STB/day): 1500; Matched bottom pressure (psi): 2250.",
      "Outflow base pressure (psi) = 2000. Intersection rate (STB/day): 1000; Matched bottom pressure (psi): 2500.",
      "Outflow base pressure (psi) = 2500. Intersection rate (STB/day): 500; Matched bottom pressure (psi): 2750."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Intersection rate (STB/day) without rounding intermediate values.",
        "answer": "At pbase = 1,500: q = 2[3,000 − (1,500 + 0.5q)]; 2q = 3,000; q = 1,500 STB/day and pwf = 2,250 psi. Intersection rate (STB/day) = 1500. Only a compatible intersection supplies the synthetic operating point."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Outflow base pressure (psi) changes from 500 to 2500. Other controls remain as stated in the premise. Intersection rate (STB/day) changes from 2500 to 500."
      },
      {
        "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. The outflow is an explicitly invented linear teaching relation, not a tubing correlation. Only a compatible intersection supplies the synthetic operating point."
      }
    ]
  },
  "recorded": null
}