flow-after-flow tests, Oil & Gas Glossary

What Is a Flow-After-Flow Test?

Flow-after-flow test (also called a backpressure test or four-point test) is a deliverability testing method for gas wells in which the well is produced at a series of increasing stabilized flow rates — typically four — with each rate held until pressure stabilizes before stepping to the next, without returning the well to shut-in between rates. The test produces an inflow performance relationship called the backpressure curve that quantifies how the well's production capacity varies with flowing wellbore pressure, enabling calculation of absolute open flow potential (AOF) and support for pipeline contract negotiations and regulatory reporting.

Key Takeaways

The test uses four sequential stabilized flow rates in ascending order, each held for 4-8 hours or until pressure change falls below 1% over one hour, without shut-in between rates.
A log-log plot of flow rate (qg) versus pressure-squared difference (p²r - p²wf) produces the backpressure curve, which is fit using the Rawlins-Schellhardt empirical equation.
Absolute open flow (AOF) is the theoretical maximum production rate at zero flowing wellbore pressure, read directly from the backpressure curve and used for pipeline sizing and regulatory permits.
Flow-after-flow tests are faster and cheaper than isochronal tests but are only reliable when each flow rate achieves true stabilization — a condition that may require days in low-permeability reservoirs.
Regulators in many jurisdictions require a witnessed deliverability test before issuing a gas well production permit; the flow-after-flow test is the most commonly accepted method.

How Flow-After-Flow Tests Work

Before the test begins, the well is shut in long enough to allow reservoir pressure to build to a stable value, which is recorded as the average reservoir pressure (p̄r) or static bottomhole pressure. The well is then opened and produced at the first (lowest) flow rate. Surface flow rate and bottomhole flowing pressure (BHFP) are recorded continuously. When pressure change at bottomhole falls below the stabilization criterion — typically less than 1% change over a one-hour interval — the rate is considered stabilized and the tester increases the choke to the next, higher flow rate. This sequence continues through all four rates without shutting the well in between.

At each stabilized rate, the pair of data points (qg, p²r - p²wf) is plotted on log-log paper or its digital equivalent. The four points define the backpressure curve, which under ideal conditions plots as a straight line with a slope of 1/n. The Rawlins-Schellhardt empirical equation describes this relationship: qg = C(p²r - p²wf)^n, where C is a performance coefficient and n is the backpressure curve slope exponent ranging from 0.5 (turbulence-dominated flow) to 1.0 (Darcy flow). Extrapolating the line to p²wf = 0 (or pwf = 0) gives the AOF.

Bottomhole pressure measurement is preferred but surface pressure can be used with a calculated pressure gradient correction if a bottomhole gauge is unavailable or cost-prohibitive. Modern electronic memory gauges and real-time downhole measurement tools have largely replaced mechanical gauges, providing continuous pressure-temperature records that make stabilization assessment more reliable and defensible to regulators.

Fast Facts: Flow-After-Flow Tests

Number of flow rates: Typically 4 (hence "four-point test")
Duration per rate: 4-8 hours for moderate-permeability wells; longer in tight reservoirs
Stabilization criterion: Pressure change <1% over 1 hour
Plot type: Log-log, qg vs. (p²r - p²wf)
Empirical equation: Rawlins-Schellhardt: qg = C(p² - p²wf)^n
n value range: 0.5 (turbulent) to 1.0 (Darcy/laminar flow)
Key output: Absolute open flow (AOF) in MMscf/d
Regulatory use: Required in many jurisdictions for well permit and pipeline contract baseline

Field Tip:

If the four points on the backpressure plot do not fall on a straight line — particularly if the points curve upward at high rates — the test was likely not stabilized and results will be unreliable. Turbulence effects (non-Darcy flow) at high rates cause the apparent n value to shift. Re-running the test with longer stabilization times or using a modified isochronal test in low-permeability wells is preferred over forcing a line through non-stabilized data.

Deliverability Plot Construction and AOF Determination

The backpressure curve is constructed by plotting the log of the flow rate on the x-axis against the log of the pressure-squared difference (p²r - p²wf) on the y-axis, or equivalently, plotting the log of (p²r - p²wf) on the x-axis and log of qg on the y-axis — both formats are used in the industry. The slope of the best-fit straight line through the four data points equals 1/n. The y-intercept (or its equivalent in the log form) gives the performance coefficient C.

AOF is determined by substituting p²wf = atmospheric pressure squared (essentially zero for high-pressure reservoirs) into the Rawlins-Schellhardt equation. Alternatively, the line on the log-log plot is extended to the pressure difference corresponding to flowing bottomhole pressure at atmospheric conditions, and the corresponding rate is read off the x-axis. AOF should be reported in MMscf/d (million standard cubic feet per day) with the reservoir pressure and test date stated, because AOF declines as reservoir pressure depletes over the producing life of the well.

Comparison to Isochronal and Modified Isochronal Tests

The isochronal test addresses the fundamental limitation of the flow-after-flow test: stabilization may take days or weeks in low-permeability reservoirs, making it impractical to hold each rate until true stabilization is achieved. In an isochronal test, the well is flowed for a fixed short time period at each rate, then shut in completely between rates to allow full pressure buildup. The short flow periods produce transient data points, and a single extended stabilized flow at one rate anchors the curve to stabilized conditions. The modified isochronal test simplifies further by using pressure buildups that do not fully recover to static reservoir pressure, using the pressure at the start of each flow period (rather than true static pressure) as the reference. Both isochronal variants require more rig time due to shut-in periods but are more accurate for tight or heterogeneous reservoirs.

The flow-after-flow test is also referred to as:

Four-point test — the most common alternative name, referring to the four stabilized flow rate data points used to construct the backpressure curve.
Backpressure test — emphasizes the methodology of varying backpressure (via choke adjustment) to achieve different flow rates.
Deliverability test — the broader category term encompassing all methods for measuring gas well production capacity, including isochronal and modified isochronal variants.
Open flow test — used informally when the test objective is specifically to determine AOF; technically refers to producing the well with minimal backpressure.

Frequently Asked Questions About Flow-After-Flow Tests

How long does a flow-after-flow test take in practice?

In moderate- to high-permeability gas reservoirs (above 1 millidarcy), each rate stabilizes within 4-8 hours, making the full four-point test completable in one to two days including initial shut-in. In tight gas formations (0.01-0.1 millidarcy), stabilization may require 24-72 hours per rate, making a true flow-after-flow test impractical. In tight reservoirs, the modified isochronal test is preferred because the isochronal periods are fixed at short durations (1-4 hours) regardless of stabilization, with only one extended stabilized flow point required.

Can flow-after-flow test results be used in pipeline contract negotiations?

Yes, and this is one of the primary commercial uses of the test. Gas purchase agreements and transportation contracts often specify a minimum deliverability obligation — the well must demonstrate it can sustain a minimum production rate at a specified flowing wellbore pressure. The AOF and backpressure curve from a witnessed deliverability test provide the documented basis for these commitments. Producers with higher AOF values can negotiate better contract terms, while low-AOF wells may require compression or wellbore cleanup before meeting contract minimums.

What is the difference between AOF and maximum allowable rate?

AOF is a theoretical maximum rate calculated by extrapolating the backpressure curve to zero flowing wellbore pressure. It is never actually achieved in practice because some flowing pressure must exist to move gas up the wellbore. Maximum allowable rate (MAR) or maximum efficient rate (MER) is a regulatory or engineering limit set below AOF to prevent reservoir damage, sand production, or excessive water coning. Regulatory agencies in Alberta, British Columbia, and several U.S. states set MERs as a fraction of AOF — typically 15-25% — to protect reservoir energy and prevent premature water or gas cap breakthrough.

Why Flow-After-Flow Tests Matter in Oil and Gas

Deliverability testing is foundational to gas field development economics. Without a reliable backpressure curve and AOF estimate, operators cannot confidently size gathering lines, compression facilities, or processing plants, nor can they commit to pipeline delivery contracts. Flow-after-flow tests provide this data at relatively low cost compared to isochronal tests, making them the default method in conventional gas reservoirs worldwide. As global gas demand grows and LNG export projects require firm supply commitments, the accuracy and regulatory defensibility of deliverability test results carry increasing financial significance.