{
  "version": 1,
  "topic": "MB06",
  "title": "What water influx changes in a material balance interpretation",
  "createdAt": "2026-10-24",
  "case": {
    "title": "A family of closed simplified balances",
    "premise": "Fixed withdrawal F = 1,000,000 RB and oil expansion Eo = 0.1 RB/STB. Gas-cap and rock/water expansion terms are explicitly set to zero.",
    "formula": "F = N Eo + We; N = (F − We)/Eo",
    "variables": "We is assumed reservoir-barrel influx. This simplified balance illustrates ambiguity; the general calculator has additional terms.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Assumed influx (RB) = 200000",
        "explanation": "Fixed withdrawal F = 1,000,000 RB and oil expansion Eo = 0.1 RB/STB. Gas-cap and rock/water expansion terms are explicitly set to zero."
      },
      {
        "label": "Select the relation",
        "calculation": "F = N Eo + We; N = (F − We)/Eo",
        "explanation": "We is assumed reservoir-barrel influx. This simplified balance illustrates ambiguity; the general calculator has additional terms."
      },
      {
        "label": "Substitute the values",
        "calculation": "N = (1,000,000 − 200,000)/0.1 = 8,000,000 STB; 8,000,000 × 0.1 + 200,000 = 1,000,000 RB",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Inferred initial oil (STB) = 8000000; Reconstructed withdrawal (RB) = 1000000",
        "explanation": "Every row closes the balance; closure alone does not identify the true influx or inventory."
      }
    ],
    "result": "Inferred initial oil (STB) = 8000000; Reconstructed withdrawal (RB) = 1000000",
    "interpretation": "Every row closes the balance; closure alone does not identify the true influx or inventory.",
    "control": "Assumed influx (RB)",
    "columns": [
      "Assumed influx (RB)",
      "Inferred initial oil (STB)",
      "Reconstructed withdrawal (RB)"
    ],
    "rows": [
      [
        0,
        10000000,
        1000000
      ],
      [
        100000,
        9000000,
        1000000
      ],
      [
        200000,
        8000000,
        1000000
      ],
      [
        300000,
        7000000,
        1000000
      ],
      [
        400000,
        6000000,
        1000000
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Assumed influx (RB) = 0. Inferred initial oil (STB): 10000000; Reconstructed withdrawal (RB): 1000000.",
      "Assumed influx (RB) = 100000. Inferred initial oil (STB): 9000000; Reconstructed withdrawal (RB): 1000000.",
      "Assumed influx (RB) = 200000. Inferred initial oil (STB): 8000000; Reconstructed withdrawal (RB): 1000000.",
      "Assumed influx (RB) = 300000. Inferred initial oil (STB): 7000000; Reconstructed withdrawal (RB): 1000000.",
      "Assumed influx (RB) = 400000. Inferred initial oil (STB): 6000000; Reconstructed withdrawal (RB): 1000000."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Inferred initial oil (STB) without rounding intermediate values.",
        "answer": "N = (1,000,000 − 200,000)/0.1 = 8,000,000 STB; 8,000,000 × 0.1 + 200,000 = 1,000,000 RB. Inferred initial oil (STB) = 8000000. Every row closes the balance; closure alone does not identify the true influx or inventory."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Assumed influx (RB) changes from 0 to 400000. Other controls remain as stated in the premise. Inferred initial oil (STB) changes from 10000000 to 6000000."
      },
      {
        "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. We is assumed reservoir-barrel influx. This simplified balance illustrates ambiguity; the general calculator has additional terms. Every row closes the balance; closure alone does not identify the true influx or inventory."
      }
    ]
  },
  "recorded": null
}