{
  "version": 1,
  "id": "po.wb.dca.decline-model-fitters",
  "name": "Decline Model Comparison — Arps, Duong, PLE",
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      "name": "Inputs",
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          "ref": "A1",
          "value": "Decline Model Comparison — Inputs"
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        {
          "ref": "A2",
          "value": "Three decline models compared: Arps (conventional), Duong (unconventional tight oil/gas), and PLE (Power Law Exponential). Each model predicts different late-time behavior — the EUR comparison shows how much this matters."
        },
        {
          "ref": "A4",
          "value": "Common Parameters"
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        {
          "ref": "A5",
          "value": "Initial Rate"
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        {
          "ref": "B5",
          "value": 800
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        {
          "ref": "C5",
          "value": "bbl/day"
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        {
          "ref": "A6",
          "value": "Economic Limit"
        },
        {
          "ref": "B6",
          "value": 10
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        {
          "ref": "C6",
          "value": "bbl/day"
        },
        {
          "ref": "A8",
          "value": "Arps Parameters"
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        {
          "ref": "A9",
          "value": "Di"
        },
        {
          "ref": "B9",
          "value": 0.08
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        {
          "ref": "C9",
          "value": "1/month"
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        {
          "ref": "A10",
          "value": "b-exponent"
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        {
          "ref": "B10",
          "value": 0.7
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        {
          "ref": "C10",
          "value": "dimensionless"
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        {
          "ref": "A12",
          "value": "Duong Parameters"
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        {
          "ref": "A13",
          "value": "a constant"
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        {
          "ref": "B13",
          "value": 1.3
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        {
          "ref": "C13",
          "value": "dimensionless"
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        {
          "ref": "A14",
          "value": "m exponent"
        },
        {
          "ref": "B14",
          "value": 1.15
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        {
          "ref": "C14",
          "value": "dimensionless"
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        {
          "ref": "A16",
          "value": "PLE Parameters"
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        {
          "ref": "A17",
          "value": "Di"
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        {
          "ref": "B17",
          "value": 0.1
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        {
          "ref": "C17",
          "value": "1/month"
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        {
          "ref": "A18",
          "value": "n exponent"
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        {
          "ref": "B18",
          "value": 0.4
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        {
          "ref": "C18",
          "value": "dimensionless"
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          "ref": "A19",
          "value": "Dinf"
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        {
          "ref": "B19",
          "value": 0.005
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          "ref": "C19",
          "value": "1/month"
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          "ref": "A21",
          "value": "EUR Comparison"
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          "ref": "A22",
          "value": "EUR (Arps)"
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          "ref": "C22",
          "value": "Mstb"
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          "ref": "A23",
          "value": "EUR (Duong)"
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          "ref": "C23",
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          "ref": "B24",
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          "ref": "C24",
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          "ref": "A2",
          "value": "Rate and cumulative forecasts out to 30 years. The spread % column shows model divergence — small at early time, growing dramatically at late time where EUR uncertainty is greatest."
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          "ref": "A4",
          "value": "Rate Comparison"
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          "ref": "A5",
          "value": "t (months)"
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          "ref": "B5",
          "value": "Arps (bbl/d)"
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          "ref": "D5",
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          "formula": "=IF(AVERAGE(B24:D24)>0,(MAX(B24:D24)-MIN(B24:D24))/AVERAGE(B24:D24)*100,0)",
          "cached": 149.33053704959173
        },
        {
          "ref": "A25",
          "value": 240
        },
        {
          "ref": "B25",
          "formula": "=PO.DCA.Arps.Rate(DMF_Qi,DMF_Arps_Di,DMF_Arps_b,A25)",
          "cached": 17.642715269499988
        },
        {
          "ref": "C25",
          "formula": "=PO.DCA.Duong.Rate(DMF_Qi,0,DMF_Duong_a,DMF_Duong_m,A25)",
          "cached": 188.56841537605303
        },
        {
          "ref": "D25",
          "formula": "=PO.DCA.PLE.Rate(DMF_Qi,DMF_PLE_Di,DMF_PLE_Dinf,DMF_PLE_n,A25)",
          "cached": 98.40314277119572
        },
        {
          "ref": "E25",
          "formula": "=IF(AVERAGE(B25:D25)>0,(MAX(B25:D25)-MIN(B25:D25))/AVERAGE(B25:D25)*100,0)",
          "cached": 168.33653084211153
        },
        {
          "ref": "A26",
          "value": 360
        },
        {
          "ref": "B26",
          "formula": "=PO.DCA.Arps.Rate(DMF_Qi,DMF_Arps_Di,DMF_Arps_b,A26)",
          "cached": 10.221065753869755
        },
        {
          "ref": "C26",
          "formula": "=PO.DCA.Duong.Rate(DMF_Qi,0,DMF_Duong_a,DMF_Duong_m,A26)",
          "cached": 148.10762893997398
        },
        {
          "ref": "D26",
          "formula": "=PO.DCA.PLE.Rate(DMF_Qi,DMF_PLE_Di,DMF_PLE_Dinf,DMF_PLE_n,A26)",
          "cached": 46.12647651898129
        },
        {
          "ref": "E26",
          "formula": "=IF(AVERAGE(B26:D26)>0,(MAX(B26:D26)-MIN(B26:D26))/AVERAGE(B26:D26)*100,0)",
          "cached": 202.32292834878643
        }
      ]
    }
  ],
  "namedRanges": [
    {
      "name": "DMF_Arps_Di",
      "refersTo": "Inputs!$B$9"
    },
    {
      "name": "DMF_Arps_b",
      "refersTo": "Inputs!$B$10"
    },
    {
      "name": "DMF_Duong_a",
      "refersTo": "Inputs!$B$13"
    },
    {
      "name": "DMF_Duong_m",
      "refersTo": "Inputs!$B$14"
    },
    {
      "name": "DMF_PLE_Di",
      "refersTo": "Inputs!$B$17"
    },
    {
      "name": "DMF_PLE_Dinf",
      "refersTo": "Inputs!$B$19"
    },
    {
      "name": "DMF_PLE_n",
      "refersTo": "Inputs!$B$18"
    },
    {
      "name": "DMF_Qecon",
      "refersTo": "Inputs!$B$6"
    },
    {
      "name": "DMF_Qi",
      "refersTo": "Inputs!$B$5"
    }
  ],
  "namedLambdas": [],
  "charts": [
    {
      "sheet": "Rate Comparison",
      "type": "XYScatterLines",
      "title": "Rate Comparison — Arps vs Duong vs PLE",
      "series": [
        {
          "name": "Arps",
          "values": "'Rate Comparison'!$B$6:$B$26",
          "categories": "'Rate Comparison'!$A$6:$A$26"
        },
        {
          "name": "Duong",
          "values": "'Rate Comparison'!$C$6:$C$26",
          "categories": "'Rate Comparison'!$A$6:$A$26"
        },
        {
          "name": "PLE",
          "values": "'Rate Comparison'!$D$6:$D$26",
          "categories": "'Rate Comparison'!$A$6:$A$26"
        }
      ],
      "anchor": "A28",
      "endAnchor": "F46",
      "xAxis": {
        "title": "Time (months)"
      },
      "yAxis": {
        "title": "Rate (bbl/day)"
      }
    }
  ],
  "shapes": [],
  "pictures": [],
  "connectors": [],
  "conditionalFormats": [],
  "sparklineGroups": [],
  "functions": [
    "PO.DCA.Arps.EUR",
    "PO.DCA.Arps.Rate",
    "PO.DCA.Duong.EUR",
    "PO.DCA.Duong.Rate",
    "PO.DCA.PLE.EUR",
    "PO.DCA.PLE.Rate"
  ]
}