Flow After Flow Test | Oil Authority

A flow after flow test (also called a back-pressure test or multi-rate deliverability test) is a well productivity evaluation procedure in which a gas or oil well is produced at a series of successively increasing or decreasing flow rates — each rate maintained until the wellbore pressure stabilizes or for a specified time period — and the stabilized flowing bottomhole pressure at each rate is recorded to construct a deliverability curve (backpressure curve) that relates the flow rate to the pressure drawdown, enabling calculation of the well's absolute open flow potential (AOF) and the inflow performance relationship (IPR) used for production engineering design, regulatory capacity certification, and reservoir characterization.

Key Takeaways

The flow after flow test protocol typically uses four flow rates in sequence (commonly denoted q₁, q₂, q₃, q₄) held for equal time periods (1 to 6 hours each for stabilized tests, or shorter periods for isochronal tests) followed by a final shut-in period for pressure buildup — the four-rate design provides sufficient data points to define the deliverability curve reliably, while the symmetry of equal test period durations allows comparison between rates without systematic bias from transient pressure effects that would distort tests with unequal period lengths.
The deliverability equation derived from flow after flow data takes one of two forms: the empirical backpressure equation of Rawlins and Schellhardt (q = C × (P²R − P²wf)ⁿ, where C and n are empirical constants, PR is static reservoir pressure, and Pwf is flowing wellbore pressure) or the theoretical Forchheimer equation (P²R − P²wf = Aq + Bq², where A represents Darcy (laminar) flow contribution and B represents non-Darcy (turbulent) flow contribution); the empirical equation is simpler and adequate for most deliverability certification purposes, while the Forchheimer equation is used when high-velocity non-Darcy flow in the near-wellbore region contributes significantly to the pressure drop at high flow rates (as in high-rate gas wells with tight completions).
Absolute open flow potential (AOF) is the hypothetical maximum flow rate the well could achieve if the flowing wellbore pressure were reduced to atmospheric pressure — calculated by extrapolating the deliverability curve to the point where Pwf = 0; AOF is not a realistically achievable operating condition but serves as a standardized comparison metric for well productivity across different reservoir pressures, used in regulatory filings (particularly in Canadian AER and US state agency capacity certifications), in production allocation calculations for commingled wells, and in economic assessments of well value.
Modified isochronal tests are a practical modification of the flow after flow procedure that addresses the difficulty of achieving true stabilized flow at each rate in low-permeability wells — instead of waiting for full pressure stabilization (which could require days or weeks in tight reservoirs), the modified isochronal test uses equal-duration flow and shut-in periods (typically 4 to 12 hours each), recording the transient flowing pressure at the end of each flow period and using the extended final shut-in for pressure buildup analysis; the resulting deliverability curve is a transient approximation of the true stabilized deliverability that is corrected to the stabilized condition using the final shut-in pressure recovery data.
The non-Darcy flow coefficient D (also called the turbulence factor) quantified from flow after flow data by fitting the Forchheimer equation represents the velocity-dependent pressure loss caused by inertial effects in the near-wellbore high-velocity flow zone — in high-rate gas wells, the non-Darcy contribution (B × q²) can exceed the Darcy contribution (A × q) at maximum production rates, causing well deliverability to fall significantly below the Darcy-only prediction; correctly quantifying D from multi-rate test data is critical for accurate production forecasting and for optimizing completions (perforation density, fracture conductivity) that reduce near-wellbore velocity and minimize the non-Darcy productivity penalty.

Fast Facts

The flow after flow test methodology was systematized by Rawlins and Schellhardt of the U.S. Bureau of Mines in a 1935 report titled "Back-Pressure Data on Natural Gas Wells and Their Application to Production Practices," which introduced the empirical deliverability equation and the log-log backpressure curve presentation that are still used in regulatory deliverability certification today. The Bureau of Mines back-pressure test procedure became the standard for US state regulatory agencies and was adopted with minor modifications by Canadian provincial regulators — its 80+ year longevity in regulatory practice reflects both its technical soundness and the institutional inertia of regulatory frameworks that have been continuously applied since the early period of organized gas production.

What Is a Flow After Flow Test?

Knowing how much gas or oil a well can produce is fundamental to every economic and operational decision about that well — but a well's productivity is not a single fixed number. It depends on the pressure drawdown applied (how far the wellbore pressure is reduced below the reservoir pressure), on the flow regime (laminar Darcy flow at low rates versus inertial non-Darcy flow at high rates), and on the reservoir pressure at the time of measurement (which declines with depletion). A flow after flow test determines the relationship between flow rate and pressure drawdown across a range of production conditions, providing the functional relationship needed for rigorous production engineering rather than a single point measurement that may not extrapolate reliably to other conditions.

The "flow after flow" name describes the procedure exactly — the well is produced at one rate, then at another rate, then another, creating a sequence of flow periods each at a different production level. By measuring the stabilized pressure at each rate, the engineer constructs a deliverability curve that spans the well's entire production range from minimum to maximum, and can read off the expected production rate at any desired wellbore pressure or read off the expected wellbore pressure at any desired production rate. This curve is the well's production engineering "fingerprint" — it defines what the well can and cannot do and sets the foundation for all subsequent production optimization decisions.

Flow after flow tests are required by regulatory agencies in many petroleum-producing jurisdictions as the basis for official deliverability certification — the regulator needs to know the well's AOF (absolute open flow potential) to set production allowables, to allocate production from commingled multi-well test facilities, and to verify that the well's productive capacity justifies the development investment. Understanding the test procedure, the deliverability equation that fits the data, and the assumptions underlying the extrapolation to AOF is essential for engineers who design tests, interpret data, and submit deliverability reports to regulatory agencies.

Flow After Flow Test Design and Analysis

Test design begins with a rate sequence plan that covers the expected range of well productivity from a minimum rate (typically 20 to 30% of expected maximum) to the maximum safe operating rate (limited by equipment capacity, erosional velocity, or sand production threshold). Four rates are standard because fewer give insufficient definition of the deliverability curve shape (the exponent n in the Rawlins-Schellhardt equation cannot be reliably determined from fewer than three points, and four points provides a statistical quality check on the best-fit n value). The rates are traditionally set in increasing order for the conventional flow after flow test, though some variants use decreasing rates to assess rate-dependent skin effects more clearly.

Each flow period duration is chosen to achieve approximate stabilization of the bottomhole pressure at that rate — stabilization time depends on reservoir permeability, with high-permeability gas wells (greater than 50 mD) stabilizing in hours and low-permeability wells (less than 1 mD) potentially requiring days. For wells where full stabilization is not feasible within the allocated test time, the modified isochronal procedure (equal transient flow and shut-in periods) provides a practical approximation. The final extended shut-in for pressure buildup analysis confirms the static reservoir pressure (Pws) needed to calculate the total pressure drawdown (P²R − P²wf) for each flow rate.

Data analysis plots the log of the flow rate (q) versus the log of the pressure-squared drawdown (P²R − P²wf) for each stabilized rate on a log-log deliverability plot (Rawlins-Schellhardt plot). A straight line through the data points has slope 1/n (where n is the empirical deliverability exponent, with theoretical limits between 0.5 for fully turbulent flow and 1.0 for fully Darcy laminar flow) and intercept C. The AOF is extrapolated from the line to the point where Pwf = atmospheric pressure (or where P²wf = P²atm on the pressure-squared plot). The deliverability equation C(P²R − P²wf)ⁿ is then used to calculate the production rate expected at any wellbore pressure, enabling production optimization and facility design.

Flow After Flow Tests Across International Jurisdictions

Canada (AER / WCSB): The Alberta Energy Regulator requires deliverability tests on all WCSB gas wells as part of the licensing and production authorization process, with flow after flow (4-point backpressure test) being the standard test method specified in AER Directive 040 (Pressure and Deliverability Testing Oil and Gas Wells). The AER-required AOF calculation from flow after flow data is used to set the well's production allowable (the maximum permitted daily rate under the Gas Resources Conservation Regulation), with wells above a specified AOF threshold subject to MER (maximum efficient rate) restrictions designed to protect reservoir recovery efficiency. Major WCSB gas plays (Montney, Deep Basin, Horn River) require flow after flow tests on discovery and delineation wells as part of the development application package submitted to the AER.

United States (API / BSEE): US state regulatory agencies have varying requirements for deliverability testing — Texas Railroad Commission (RRC) requires deliverability tests for certain gas well classifications, Oklahoma Corporation Commission requires periodic deliverability testing for gas production reporting, and the Federal Energy Regulatory Commission (FERC) uses AOF data from flow after flow tests for interstate pipeline capacity calculations. API RP 14B (Design, Installation, Repair, and Operation of Subsurface Safety Valve Systems) references well deliverability as a factor in safety valve design, and industry standards for gas well reporting (API 14.1, API 14.3) include deliverability test data requirements for metering and allocation purposes.

Norway (Sodir / NORSOK): Sodir requires production test data — including multi-rate deliverability tests — on all NCS exploration and appraisal wells as part of the well testing program submitted with the development plan (Plan for Development and Operation, PDO). NCS gas field development applications include AOF and deliverability curve data from flow after flow tests conducted during the exploration and appraisal drilling program, providing the regulatory basis for the production plateau rate and facilities design commitments in the PDO. Norwegian gas fields with multiple reservoir layers (Åsgard B and C, Ormen Lange, Troll) require layer-specific deliverability tests to allocate production capacity between reservoir units and to ensure that commingled production profiles are consistent with reservoir engineering models.

Middle East (Saudi Aramco): Saudi Aramco conducts flow after flow deliverability tests on all Arab Formation gas cap wells and Khuff gas wells as part of the production allocation and reservoir management program for the world's largest oil field and its associated gas system. Aramco's deliverability testing protocol includes non-Darcy flow analysis for the high-rate Khuff gas wells where turbulent flow effects are significant, and the Forchheimer two-term analysis is standard for these high-velocity flow conditions. Aramco's data on Arab Formation oil well deliverability (using modified flow after flow procedures adapted for oil well inflow performance) contributes to the reservoir management models that have sustained Ghawar field production for over 70 years.