Type Curves

A type curve in petroleum engineering is a dimensionless reference plot of pressure change and its derivative (or production rate and its decline) versus time, derived from analytical solutions for idealized reservoir geometries, that a field engineer matches against actual well test data or production data to determine reservoir properties. In well testing, type curve analysis identifies the flow regime occurring at each time interval (wellbore storage, radial flow, boundary effects) by matching the shape of the measured pressure derivative curve to reference curves for known reservoir geometries. In production decline analysis, type curves (particularly those of Arps and the more recent modern decline curve analysis methods developed for unconventional wells) allow estimation of the estimated ultimate recovery (EUR) from a well by fitting the production history to a family of decline curves with defined initial rate, decline rate, and hyperbolic exponent parameters.

Key Takeaways

The Bourdet derivative (the derivative of the dimensionless pressure change with respect to the natural log of dimensionless time) is the most diagnostic element of a well test type curve. On a log-log plot, radial flow produces a flat horizontal derivative. Wellbore storage produces a unit slope (45-degree line) on both pressure and derivative. Dual-porosity behaviour (natural fractures) produces a distinctive valley in the derivative as the matrix feeds the fractures. Boundary effects cause the derivative to rise. These signatures are instantly recognizable to a trained well test analyst and allow identification of the flow regime without calculation.
Arps decline curves describe production decline in three forms defined by the hyperbolic exponent b. When b = 0, the decline is exponential (constant fractional decline rate per time unit, common in mature conventional wells). When b = 1, the decline is harmonic. When 0 < b < 1, the decline is hyperbolic, which is the most common form for primary production from conventional reservoirs. For unconventional wells (Montney, Duvernay, Bakken), b values above 1.0 are frequently observed in early transient flow, which led to significant EUR overestimates when analysts applied hyperbolic decline without a terminal exponential decline switch.
Modern unconventional decline analysis methods include the stretched exponential decline (SEPD), the Duong model (for transient-dominated shale wells), and rate transient analysis (RTA). These methods were developed in the 2010s specifically because Arps hyperbolic decline was calibrated on conventional wells and performed poorly for tight and shale wells where transient linear flow persists for years before boundary-dominated flow begins. RTA applies the same flow regime identification framework as pressure transient analysis (PTA) but works backward from production rates and flowing pressures to estimate permeability, fracture half-length, and drainage area.
In well testing, type curve matching is done by overlaying the field data pressure derivative curve on printed or digital reference type curves and sliding the field data curve horizontally and vertically until the shapes match. The horizontal shift gives the ratio of time to dimensionless time (which yields permeability-thickness product, kh, when combined with fluid properties). The vertical shift gives the ratio of pressure to dimensionless pressure (which yields kh independently). Agreement between the two kh estimates confirms the match is correct.
Normalized rate (rate divided by flowing pressure drawdown) and material balance time (cumulative production divided by current rate) are transformations applied to production data before type curve matching so that a variable-rate, variable-pressure well test can be analysed with the same type curves developed for constant-rate drawdown. These transformations, developed by Blasingame and McCray in the 1990s, are the foundation of modern rate transient analysis and are implemented in commercial software platforms including IHS Harmony, Kappa Topaze, and CMG FAST.

Well Test Type Curves: Reading the Derivative

A well test type curve is like a fingerprint library for reservoirs. Each reservoir geometry (infinite acting radial flow, dual porosity with fractures, finite conductivity vertical fracture, horizontal well with multiple transverse fractures) produces a characteristic pressure derivative pattern on a log-log plot. When a well is shut in after production, the pressure rises and its rise rate gives information about the reservoir.

The derivative is calculated as dP/d(ln t): the rate of pressure change per unit of log-time. On a log-log plot, flat derivative means radial flow from a homogeneous infinite reservoir, which is the most common analysis target. The permeability-thickness product kh comes directly from the level of the flat derivative: kh = 70.6 × q × B × mu / (derivative × h), where q is the rate, B is the formation volume factor, mu is viscosity, and h is net pay.

The skin factor comes from the vertical separation between the pressure change curve and the derivative at the time of the start of radial flow. A damaged well (positive skin) shows larger separation; a stimulated well (negative skin from hydraulic fracturing) shows the derivative rising after the flat section because the fracture boundaries are reached.

Fast Facts

The modern pressure derivative type curve was introduced by Bourdet and colleagues in 1983 in a Society of Petroleum Engineers paper that fundamentally changed well test analysis. Before Bourdet, analysts matched only the pressure change curve to type curves (the Ramey 1970 and McKinley 1974 type curves), which was ambiguous because different reservoir models could produce similar pressure shapes. The derivative uniquely identifies the flow regime: it is nearly impossible to match the derivative correctly with the wrong model. Arps (1945) published the original decline curve analysis framework based on exponential, hyperbolic, and harmonic decline. The Blasingame type curve (1991) extended this to modern rate transient analysis for variable-rate, variable-pressure data. These analytical foundations remain in daily use across the industry.

Production Decline Type Curves and EUR Estimation

When a well is put on production, its rate declines over time as reservoir pressure drops and the near-wellbore drainage area depletes. The shape of that decline carries information about the reservoir. Arps decline curve analysis fits a mathematical model to the observed decline to extrapolate future production.

The Arps equation is q = qi / (1 + b × Di × t)^(1/b), where qi is initial rate, Di is initial decline rate, b is the hyperbolic exponent, and t is time. At b = 0 (exponential), the equation simplifies to q = qi × exp(-Di × t). The EUR is found by integrating the rate curve from the start of production to abandonment rate.

For a Cardium sandstone vertical well in the Pembina area of Alberta, b typically falls between 0.5 and 0.8, reflecting a transition from transient radial flow to boundary-dominated flow within the first year. Fitting the first 24 months of production to an Arps curve with b = 0.7 and Di = 0.18 per month gives a reasonable EUR estimate that will be within 15 to 25 percent of the actual 10-year recovery.

For Montney horizontal wells, the story is more complex. Transient linear flow (where the drainage front is still moving away from the fractures) can persist for 3 to 5 years. During transient linear flow, the rate decline follows a half-slope on a log-log plot of rate versus time, not the Arps pattern. Fitting Arps to the first year of Montney production and extrapolating gives EURs that are 2 to 4 times too high because the analyst is fitting transient data with a boundary-dominated model. Modern Montney type curves are specific to the play, built from the production histories of thousands of wells, and calibrated to observed long-term performance rather than early-time transient behaviour.

Type curves are also called type-curve families, decline curve templates, or analytical type curves (in the context of well test analysis). Related terms include pressure transient analysis (PTA, the interpretation of wellbore pressure changes over time to determine reservoir properties including permeability, skin, and boundary distances; type curves are the matching templates used in PTA), decline curve analysis (DCA, the fitting of a mathematical decline model to production history to extrapolate future production and estimate EUR; Arps type curves are the classical DCA framework), rate transient analysis (RTA, modern extension of PTA applied to production rate and flowing pressure data rather than shut-in pressure data; uses the same dimensionless type curves as PTA after transforming rate data to equivalent pressure), estimated ultimate recovery (EUR, the total production expected from a well over its producing life; determined by integrating the fitted type curve from initial production to abandonment rate; the key metric for well economics and reserves booking), and flow regime (a distinct period during a well test or production history with a characteristic flow geometry: wellbore storage, radial flow, linear flow, pseudosteady state, boundary-dominated flow; each flow regime has a distinctive signature on the pressure derivative type curve).

How Type Curve Misapplication Overvalued a Duvernay Package by CAD 180 Million

A private equity group was evaluating an acquisition of 40 Duvernay horizontal wells in the Fox Creek area of west-central Alberta. The vendor's engineering report estimated total proved and probable EUR of 32 million barrels of oil equivalent across the package, valued at CAD 320 million at the time of the proposed transaction.

The vendor's decline analysis had fitted Arps hyperbolic curves to the first 18 months of production history from each well. Because Duvernay wells exhibit strong transient linear flow during the first 2 to 3 years, the early-time rate versus time data shows a very gradual decline, which the Arps model interpreted as a high b value (averaging 1.4 across the wells). Integrating these high-b Arps curves to abandonment rate gave the large EUR estimates in the vendor report.

The buyer's independent engineering firm re-analysed the same 40 wells using rate transient analysis, plotting the normalized rate against material balance time on a log-log plot and identifying the flow regime. All 40 wells showed clean half-slope linear flow, consistent with drainage from hydraulic fractures in a tight matrix. The analyst applied Duvernay analogue type curves built from 200 wells with more than 5 years of production history, which showed that linear flow typically transitions to boundary-dominated flow at 3 to 4 years and that the appropriate long-term b value after the transition is 0.3 to 0.5, not 1.4.

Re-forecasting the 40 wells with the calibrated type curves cut the total EUR to 14 million barrels of oil equivalent, a reduction of 56 percent. At the same oil price and discount rate, the package value fell to CAD 140 million. The buyer presented the independent analysis to the vendor, negotiations reset around the revised value, and the package transacted at CAD 152 million, saving the buyer CAD 168 million relative to the vendor's original ask. The Arps b-value above 1.0, applied to transient-dominated wells without an analogue-calibrated terminal decline, is one of the most common and consequential errors in unconventional reserves estimation.