Rate–Time Forecast Calculator

Selecting a decline model for your system

Exponential decline suits processes with near-constant percentage loss per period. Hyperbolic decline captures fast early drops that flatten over time, which is common in field performance data. Harmonic is the slowest late-time decline and can be optimistic for long horizons. Use the same time unit for rate, decline, horizon, and step before comparing models. Check fit by overlaying historical rates and minimizing residuals. A semilog plot tends to look linear for exponential behavior, while hyperbolic commonly bends. If you are unsure, start with hyperbolic and test exponential as a conservative alternative.

Interpreting nominal decline and the b-factor

The input Di is a nominal decline per chosen time unit. In exponential form, a 25% nominal decline per year gives q(1)=qi·e^−0.25≈0.779qi, not 0.75qi. For hyperbolic decline, b controls curvature: values around 0.3–0.8 often indicate moderate flattening, while b above 1.0 shifts more volume to later time. Keep b within a defensible range and calibrate against measured data.

Choosing horizon and time step for stable forecasts

Time step is a resolution setting: smaller steps create smoother curves but larger tables. A practical rule is monthly steps for monthly bases and quarterly steps for annual bases. Very large steps can hide changes and distort step-decline percentages. Set horizon to match the decision window, such as 1–3 years for budgeting and 5–15 years for life-cycle planning. If the table grows too large, increase step or reduce horizon slightly.

Using an abandonment rate as an operating limit

Abandonment rate qAb defines a technical or economic cutoff. Choose it from minimum stable operation, contract thresholds, or a cost break-even estimate. The calculator solves the time when q(t)=qAb and reports cumulative at that point. If qAb is set unrealistically low, long-tail forecasts may exceed practical constraints, so revisit qAb as conditions change.

Turning results into actionable engineering decisions

The rate curve supports capacity, maintenance, and staffing plans, while cumulative Np estimates total throughput. For scenario work, vary Di and b, export CSV, and compute deltas or sensitivity bands. When reporting, document model, time unit, rounding, and any cutoff assumptions alongside the exported table to keep reviews consistent.

FAQs

What does nominal decline (Di) represent?

Di is the decline parameter per selected time unit, entered as a percentage and converted to a decimal internally. It controls how quickly the modeled rate decreases with time in the chosen decline equation.

Why does 25% decline not always mean 75% after one unit?

In exponential decline, Di is nominal and the model uses an exponential term. With Di=0.25 per year, q(1)=qi·e^−0.25≈0.779qi. Other models apply Di differently, so the one-step drop can vary.

When should I use hyperbolic instead of exponential?

Use hyperbolic when observed data shows steep early decline that gradually flattens. Exponential is better when the percentage decline appears roughly constant over time. Always check fit against historical rates before committing.

What is the b-factor and why is it constrained?

The b-factor shapes the curvature of hyperbolic decline. Higher b values produce a longer tail and more late-time volume. Constraining b helps prevent unrealistic long-term forecasts and encourages calibration within ranges supported by measured performance.

What does cumulative Np mean here?

Np is the time-integral of rate from t=0 to the selected time. It represents total produced or processed quantity over the period, in “rate-units × time” that aligns with your chosen basis.

How do I export or share the forecast?

After calculating, use Download CSV to get the table for spreadsheets, or Download PDF for a ready-to-share report. Printing from the browser can also capture the summary, charts, and the results table.