{
  "version": 1,
  "id": "po.wb.dca.decline-functions",
  "name": "Decline Curve Analysis — Arps with EUR",
  "sheets": [
    {
      "name": "Inputs",
      "cells": [
        {
          "ref": "A1",
          "value": "Decline Curve Analysis — Inputs"
        },
        {
          "ref": "A2",
          "value": "Arps decline model: q(t) = qi / (1 + b·Di·t)^(1/b). The b-exponent controls the decline shape — 0 = exponential (steepest), 1 = harmonic (most optimistic). EUR is the cumulative production when rate drops below the economic limit."
        },
        {
          "ref": "A4",
          "value": "Well Parameters"
        },
        {
          "ref": "A5",
          "value": "Initial Rate (qi)"
        },
        {
          "ref": "B5",
          "value": 1000
        },
        {
          "ref": "C5",
          "value": "bbl/day"
        },
        {
          "ref": "A6",
          "value": "Initial Decline Rate (Di)"
        },
        {
          "ref": "B6",
          "value": 0.05
        },
        {
          "ref": "C6",
          "value": "1/month"
        },
        {
          "ref": "A7",
          "value": "b-Exponent"
        },
        {
          "ref": "B7",
          "value": 0.5
        },
        {
          "ref": "C7",
          "value": "(0=exp, 1=harmonic)"
        },
        {
          "ref": "A9",
          "value": "Economic Parameters"
        },
        {
          "ref": "A10",
          "value": "Economic Limit Rate"
        },
        {
          "ref": "B10",
          "value": 10
        },
        {
          "ref": "C10",
          "value": "bbl/day"
        },
        {
          "ref": "A12",
          "value": "Calculated EUR"
        },
        {
          "ref": "A13",
          "value": "EUR"
        },
        {
          "ref": "B13",
          "formula": "=PO.DCA.Arps.EUR(DCA_Qi,DCA_Di,DCA_b,DCA_Qecon)/1000",
          "cached": 36
        },
        {
          "ref": "C13",
          "value": "Mstb"
        },
        {
          "ref": "A14",
          "value": "Time to Economic Limit"
        },
        {
          "ref": "B14",
          "formula": "=PO.DCA.Arps.Time(DCA_Qi,DCA_Di,DCA_b,DCA_Qecon)",
          "cached": 360
        },
        {
          "ref": "C14",
          "value": "months"
        }
      ]
    },
    {
      "name": "Forecast",
      "cells": [
        {
          "ref": "A1",
          "value": "Production Forecast"
        },
        {
          "ref": "A2",
          "value": "Rate and cumulative production over 20 years. The decline % column shows how much rate has dropped from the initial. Cumulative is in Mstb (thousands of stock-tank barrels)."
        },
        {
          "ref": "A4",
          "value": "Rate & Cumulative Forecast"
        },
        {
          "ref": "A5",
          "value": "t (months)"
        },
        {
          "ref": "B5",
          "value": "q (bbl/d)"
        },
        {
          "ref": "C5",
          "value": "Np (Mstb)"
        },
        {
          "ref": "D5",
          "value": "Decline %"
        },
        {
          "ref": "E5",
          "value": "D(t) (1/mo)"
        },
        {
          "ref": "A6",
          "value": 0
        },
        {
          "ref": "B6",
          "formula": "=PO.DCA.Arps.Rate(DCA_Qi,DCA_Di,DCA_b,A6)",
          "cached": 1000
        },
        {
          "ref": "C6",
          "formula": "=PO.DCA.Arps.Prod(DCA_Qi,DCA_Di,DCA_b,A6)/1000",
          "cached": 0
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        {
          "ref": "A7",
          "value": 3
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          "formula": "=PO.DCA.Arps.Rate(DCA_Qi,DCA_Di,DCA_b,A7)",
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          "formula": "=PO.DCA.Arps.Prod(DCA_Qi,DCA_Di,DCA_b,A7)/1000",
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        {
          "ref": "D7",
          "formula": "=1-B7/DCA_Qi",
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          "ref": "E7",
          "formula": "=PO.DCA.Arps.D(DCA_Qi,DCA_Di,DCA_b,A7)",
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          "formula": "=1-B8/DCA_Qi",
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        {
          "ref": "D12",
          "formula": "=1-B12/DCA_Qi",
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          "ref": "A13",
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          "formula": "=1-B13/DCA_Qi",
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          "formula": "=PO.DCA.Arps.D(DCA_Qi,DCA_Di,DCA_b,A16)",
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          "formula": "=1-B18/DCA_Qi",
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          "formula": "=PO.DCA.Arps.D(DCA_Qi,DCA_Di,DCA_b,A18)",
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          "formula": "=1-B19/DCA_Qi",
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          "formula": "=PO.DCA.Arps.D(DCA_Qi,DCA_Di,DCA_b,A19)",
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          "ref": "D20",
          "formula": "=1-B20/DCA_Qi",
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          "formula": "=PO.DCA.Arps.D(DCA_Qi,DCA_Di,DCA_b,A20)",
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          "formula": "=1-B24/DCA_Qi",
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          "formula": "=PO.DCA.Arps.D(DCA_Qi,DCA_Di,DCA_b,A24)",
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          "formula": "=1-B25/DCA_Qi",
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          "formula": "=PO.DCA.Arps.D(DCA_Qi,DCA_Di,DCA_b,A25)",
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    },
    {
      "name": "b-Exponent Sensitivity",
      "cells": [
        {
          "ref": "A1",
          "value": "b-Exponent Sensitivity"
        },
        {
          "ref": "A2",
          "value": "Compare three b-exponent values: 0 (exponential), 0.5 (hyperbolic), and 1.0 (harmonic). Higher b gives slower decline and higher EUR — but b>1 is physically unrealistic."
        },
        {
          "ref": "A4",
          "value": "EUR Comparison"
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        {
          "ref": "A5",
          "value": "EUR (b=0, Exponential)"
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        {
          "ref": "C5",
          "value": "Mstb"
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          "value": "EUR (b=0.5, Hyperbolic)"
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          "formula": "=PO.DCA.Arps.EUR(DCA_Qi,DCA_Di,0.5,DCA_Qecon)/1000",
          "cached": 36
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        {
          "ref": "C6",
          "value": "Mstb"
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          "ref": "A7",
          "value": "EUR (b=1.0, Harmonic)"
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          "formula": "=PO.DCA.Arps.EUR(DCA_Qi,DCA_Di,1.0,DCA_Qecon)/1000",
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        {
          "ref": "C7",
          "value": "Mstb"
        },
        {
          "ref": "A9",
          "value": "Rate Forecast Comparison"
        },
        {
          "ref": "A10",
          "value": "t (months)"
        },
        {
          "ref": "B10",
          "value": "b=0 (Exp)"
        },
        {
          "ref": "C10",
          "value": "b=0.5 (Hyp)"
        },
        {
          "ref": "D10",
          "value": "b=1.0 (Harm)"
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          "value": 0
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          "ref": "A12",
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