{
  "version": 1,
  "topic": "PR03",
  "title": "Gas deliverability pressure squared versus pseudopressure",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Rawlins-Schellhardt Gas Deliverability Rate",
    "premise": "Fixed controls: C_rs = 0.0003 MSCF/day/psi^(2n); P_r = 3000 psia; n_rs = 0.8 dimensionless. P_wf is varied as shown.",
    "formula": "q_g = C_{RS}(P_r^2 - P_{wf}^2)^{n_{RS}}",
    "variables": "C_rs: Rawlins-Schellhardt Deliverability Coefficient (MSCF/day/psi^(2n)). P_r: Average Reservoir Pressure (psia). P_wf: Flowing Bottom-Hole Pressure (psia). n_rs: Rawlins-Schellhardt Deliverability Exponent (dimensionless).",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Flowing Bottom-Hole Pressure (psia) = 1500",
        "explanation": "Fixed controls: C_rs = 0.0003 MSCF/day/psi^(2n); P_r = 3000 psia; n_rs = 0.8 dimensionless. P_wf is varied as shown."
      },
      {
        "label": "Select the relation",
        "calculation": "q_g = C_{RS}(P_r^2 - P_{wf}^2)^{n_{RS}}",
        "explanation": "C_rs: Rawlins-Schellhardt Deliverability Coefficient (MSCF/day/psi^(2n)). P_r: Average Reservoir Pressure (psia). P_wf: Flowing Bottom-Hole Pressure (psia). n_rs: Rawlins-Schellhardt Deliverability Exponent (dimensionless)."
      },
      {
        "label": "Substitute the values",
        "calculation": "C_rs = 0.0003; P_r = 3000; P_wf = 1500; n_rs = 0.8 → q_g = 87.2095957 MSCF/day",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "q_g (MSCF/day) = 87.2095957",
        "explanation": "The pressure-squared relation uses absolute pressures and its own fitted coefficient; no pseudopressure property integral is supplied."
      }
    ],
    "result": "q_g (MSCF/day) = 87.2095957",
    "interpretation": "The pressure-squared relation uses absolute pressures and its own fitted coefficient; no pseudopressure property integral is supplied.",
    "control": "Flowing Bottom-Hole Pressure (psia)",
    "columns": [
      "Flowing Bottom-Hole Pressure (psia)",
      "q_g (MSCF/day)"
    ],
    "rows": [
      [
        0,
        109.77798685202418
      ],
      [
        750,
        104.25389353325083
      ],
      [
        1500,
        87.2095956720053
      ],
      [
        2250,
        56.66275782163529
      ],
      [
        3000,
        0
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Flowing Bottom-Hole Pressure (psia) = 0. q_g (MSCF/day): 109.777987.",
      "Flowing Bottom-Hole Pressure (psia) = 750. q_g (MSCF/day): 104.253894.",
      "Flowing Bottom-Hole Pressure (psia) = 1500. q_g (MSCF/day): 87.2095957.",
      "Flowing Bottom-Hole Pressure (psia) = 2250. q_g (MSCF/day): 56.6627578.",
      "Flowing Bottom-Hole Pressure (psia) = 3000. q_g (MSCF/day): 0."
    ],
    "provenance": "Replayed with the same equation record and calculation engine as /calculators/rawlins-schellhardt-gas-deliverability-rate. Original synthetic inputs; engine outputs are saved in the downloadable record.",
    "questions": [
      {
        "question": "Reproduce the baseline q_g (MSCF/day) without rounding intermediate values.",
        "answer": "C_rs = 0.0003; P_r = 3000; P_wf = 1500; n_rs = 0.8 → q_g = 87.2095957 MSCF/day. q_g (MSCF/day) = 87.2095957. The pressure-squared relation uses absolute pressures and its own fitted coefficient; no pseudopressure property integral is supplied."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Flowing Bottom-Hole Pressure (psia) changes from 0 to 3000. Other controls remain as stated in the premise. q_g (MSCF/day) changes from 109.777987 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. C_rs: Rawlins-Schellhardt Deliverability Coefficient (MSCF/day/psi^(2n)). P_r: Average Reservoir Pressure (psia). P_wf: Flowing Bottom-Hole Pressure (psia). n_rs: Rawlins-Schellhardt Deliverability Exponent (dimensionless). The pressure-squared relation uses absolute pressures and its own fitted coefficient; no pseudopressure property integral is supplied."
      }
    ]
  },
  "recorded": {
    "kind": "scalar",
    "equation": "rawlins-schellhardt-gas-deliverability-rate",
    "parameter": "P_wf",
    "inputs": {
      "C_rs": "0.0003",
      "P_r": "3000",
      "P_wf": "1500",
      "n_rs": "0.8"
    },
    "values": [
      0,
      750,
      1500,
      2250,
      3000
    ],
    "outputs": [
      {
        "expression": "C_rs * (P_r^2 - P_wf^2)^n_rs",
        "intermediates": {},
        "inputs": {
          "C_rs": 0.0003,
          "P_r": 3000,
          "P_wf": 0,
          "n_rs": 0.8
        },
        "target": "q_g",
        "unit": "MSCF/day",
        "value": 109.77798685202418
      },
      {
        "expression": "C_rs * (P_r^2 - P_wf^2)^n_rs",
        "intermediates": {},
        "inputs": {
          "C_rs": 0.0003,
          "P_r": 3000,
          "P_wf": 750,
          "n_rs": 0.8
        },
        "target": "q_g",
        "unit": "MSCF/day",
        "value": 104.25389353325083
      },
      {
        "expression": "C_rs * (P_r^2 - P_wf^2)^n_rs",
        "intermediates": {},
        "inputs": {
          "C_rs": 0.0003,
          "P_r": 3000,
          "P_wf": 1500,
          "n_rs": 0.8
        },
        "target": "q_g",
        "unit": "MSCF/day",
        "value": 87.2095956720053
      },
      {
        "expression": "C_rs * (P_r^2 - P_wf^2)^n_rs",
        "intermediates": {},
        "inputs": {
          "C_rs": 0.0003,
          "P_r": 3000,
          "P_wf": 2250,
          "n_rs": 0.8
        },
        "target": "q_g",
        "unit": "MSCF/day",
        "value": 56.66275782163529
      },
      {
        "expression": "C_rs * (P_r^2 - P_wf^2)^n_rs",
        "intermediates": {},
        "inputs": {
          "C_rs": 0.0003,
          "P_r": 3000,
          "P_wf": 3000,
          "n_rs": 0.8
        },
        "target": "q_g",
        "unit": "MSCF/day",
        "value": 0
      }
    ]
  }
}