{
  "version": 1,
  "topic": "PR10",
  "title": "Three synthetic IPR curves from one test point",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Three shapes matched to one test point",
    "premise": "pr = 3,000 psia, test q = 700 STB/day at pwf = 1,500 psia. Models: line, Vogel, and explicitly synthetic q = A(1 − pwf/pr)².",
    "formula": "qline = 1,400(1 − r); qVogel = 1,000(1 − 0.2r − 0.8r²); qsynthetic = 2,800(1 − r)²",
    "variables": "r = pwf/pr. The third function is a teaching alternative, not a validated named inflow correlation.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Pressure ratio pwf/pr = 0.5",
        "explanation": "pr = 3,000 psia, test q = 700 STB/day at pwf = 1,500 psia. Models: line, Vogel, and explicitly synthetic q = A(1 − pwf/pr)²."
      },
      {
        "label": "Select the relation",
        "calculation": "qline = 1,400(1 − r); qVogel = 1,000(1 − 0.2r − 0.8r²); qsynthetic = 2,800(1 − r)²",
        "explanation": "r = pwf/pr. The third function is a teaching alternative, not a validated named inflow correlation."
      },
      {
        "label": "Substitute the values",
        "calculation": "At r = 0.5: 1,400 × 0.5 = 700; 1,000 × 0.7 = 700; 2,800 × 0.25 = 700 STB/day",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Straight-line rate (STB/day) = 700; Vogel rate (STB/day) = 700; Synthetic quadratic rate (STB/day) = 700",
        "explanation": "The matched test does not constrain the extrapolated intercept or the rest of the curve."
      }
    ],
    "result": "Straight-line rate (STB/day) = 700; Vogel rate (STB/day) = 700; Synthetic quadratic rate (STB/day) = 700",
    "interpretation": "The matched test does not constrain the extrapolated intercept or the rest of the curve.",
    "control": "Pressure ratio pwf/pr",
    "columns": [
      "Pressure ratio pwf/pr",
      "Straight-line rate (STB/day)",
      "Vogel rate (STB/day)",
      "Synthetic quadratic rate (STB/day)"
    ],
    "rows": [
      [
        0,
        1400,
        1000,
        2800
      ],
      [
        0.25,
        1050,
        899.9999999999999,
        1575
      ],
      [
        0.5,
        700,
        700,
        700
      ],
      [
        0.75,
        350,
        399.9999999999999,
        175
      ],
      [
        1,
        0,
        0,
        0
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Pressure ratio pwf/pr = 0. Straight-line rate (STB/day): 1400; Vogel rate (STB/day): 1000; Synthetic quadratic rate (STB/day): 2800.",
      "Pressure ratio pwf/pr = 0.25. Straight-line rate (STB/day): 1050; Vogel rate (STB/day): 900; Synthetic quadratic rate (STB/day): 1575.",
      "Pressure ratio pwf/pr = 0.5. Straight-line rate (STB/day): 700; Vogel rate (STB/day): 700; Synthetic quadratic rate (STB/day): 700.",
      "Pressure ratio pwf/pr = 0.75. Straight-line rate (STB/day): 350; Vogel rate (STB/day): 400; Synthetic quadratic rate (STB/day): 175.",
      "Pressure ratio pwf/pr = 1. Straight-line rate (STB/day): 0; Vogel rate (STB/day): 0; Synthetic quadratic rate (STB/day): 0."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Straight-line rate (STB/day) without rounding intermediate values.",
        "answer": "At r = 0.5: 1,400 × 0.5 = 700; 1,000 × 0.7 = 700; 2,800 × 0.25 = 700 STB/day. Straight-line rate (STB/day) = 700. The matched test does not constrain the extrapolated intercept or the rest of the curve."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Pressure ratio pwf/pr changes from 0 to 1. Other controls remain as stated in the premise. Straight-line rate (STB/day) changes from 1400 to 0."
      },
      {
        "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. r = pwf/pr. The third function is a teaching alternative, not a validated named inflow correlation. The matched test does not constrain the extrapolated intercept or the rest of the curve."
      }
    ]
  },
  "recorded": null
}