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Multiple-Rate Tests

What Are Multiple-Rate Tests?

Multiple-rate tests (also called multi-rate deliverability tests or back-pressure tests) are a family of gas well evaluation procedures in which a well is produced at several different stabilized or transient flow rates to generate a matched set of flowing bottomhole pressure and production rate pairs. These data pairs define the inflow performance relationship (IPR) of the well and allow engineers to calculate the absolute open flow (AOF) potential, which is the theoretical maximum rate the well could produce if flowing against atmospheric pressure at the sandface.

Key Takeaways

  • Multiple-rate tests require measuring stabilized or transient flowing bottomhole pressure at a minimum of three to four different surface production rates to construct a deliverability curve.
  • The four main test types are: flow-after-flow, isochronal, modified isochronal, and single-point back-pressure tests, each suited to different reservoir permeability ranges.
  • The Rawlins-Schellhardt back-pressure equation uses empirical constants C and n to relate flow rate to the difference between average reservoir pressure squared and flowing wellbore pressure squared.
  • Laminar-inertial-turbulent (LIT) analysis separates Darcy (laminar) skin from non-Darcy (inertial) effects using the a and b coefficients, which is critical for high-rate gas wells where turbulence near the wellbore can account for 30-60% of total pressure drop.
  • Regulatory bodies in major gas-producing jurisdictions require AOF determination from multiple-rate tests before gas supply contracts can be executed and pipeline capacity allocated.

How Multiple-Rate Tests Work

In a flow-after-flow test, the well is opened to flow at a series of increasing rates, typically three to five, and held at each rate until bottomhole pressure stabilizes. Stabilization can require hours to days in low-permeability reservoirs, making this test practical primarily in high-permeability formations where pseudo-steady state is achieved quickly. Each stabilized rate-pressure pair is plotted on log-log paper as the difference in squared pressures (pR2 minus pwf2) against flow rate, and a straight line through these points defines the deliverability curve with slope n and intercept C from the Rawlins-Schellhardt equation: q = C(pR2 minus pwf2)n. The exponent n ranges from 0.5 for fully turbulent flow to 1.0 for pure Darcy flow, and values outside this range indicate data quality problems.

The isochronal test was developed for low-permeability wells where achieving stabilization at each rate would require days or weeks of production. In an isochronal test, the well flows at a selected rate for a fixed time period, typically four to eight hours, then is shut in until pressure fully recovers before the next flow period begins. Because each transient flow period starts from the same fully-recovered reservoir pressure, the transient data points trace a theoretical deliverability curve that is parallel to but displaced from the true stabilized deliverability curve. A single extended stabilization flow is then run to anchor the transient curve to the stabilized curve. The modified isochronal test relaxes the full-recovery shut-in requirement by using short equal-duration shut-in periods, making it more practical but introducing corrections for the incomplete pressure recovery.

LIT analysis, also called the Jones-Blount-Glaze method, plots pressure-squared drop divided by rate (delta p2/q) against rate on Cartesian coordinates. The y-intercept of the resulting straight line is the laminar flow coefficient a (containing Darcy skin and formation properties), and the slope is the inertial coefficient b (related to the non-Darcy flow coefficient D). Non-Darcy skin S' equals D times q, and the total skin is the sum of the mechanical skin from drilling and completion damage plus the rate-dependent inertial skin. This separation is critical because perforating, fracturing, and skin removal treatments reduce the laminar component, while the inertial component is largely fixed by near-wellbore geometry and cannot be eliminated by stimulation alone.

Fast Facts: Multiple-Rate Tests
  • Test types: Flow-after-flow, isochronal, modified isochronal, single-point
  • Rawlins-Schellhardt equation: q = C(pR2 - pwf2)n
  • n exponent range: 0.5 (turbulent) to 1.0 (Darcy)
  • LIT coefficients: a (laminar/Darcy), b (inertial/non-Darcy)
  • AOF definition: Rate at pwf = atmospheric pressure at sandface
  • Typical flow periods: 4-24 hours per rate point for isochronal tests
  • Pressure measurement: Downhole gauges at or near perforations preferred
  • Regulatory use: AOF required for gas supply contracts and pipeline allocation in Canada, US, and most international jurisdictions
Field Tip:

When running a modified isochronal test, keep each shut-in period equal in duration to the preceding flow period. If shut-in periods are too short relative to flow periods, the starting pressures for each successive flow sequence drift downward, which biases the deliverability curve and understates true AOF. Record the shut-in pressure at the end of each buildup, not the initial shut-in pressure, as your pseudo-static pressure for that sequence.

Deliverability Curve Construction and AOF Calculation

Once rate-pressure pairs are collected, engineers construct the deliverability curve by plotting flow rate on the x-axis against the pressure-squared difference on the y-axis using log-log scales. The best-fit line through the data points, constrained to an n value between 0.5 and 1.0, is extrapolated to the abandonment pressure condition. AOF is read at the point where pwf equals atmospheric pressure (approximately 14.7 psia at sea level) or, in some regulatory jurisdictions, at the minimum line pressure of the gathering system. The AOF is a theoretical maximum and not a sustained operating rate; actual field deliverability is limited by wellhead pressure, gathering line pressure, compressor suction requirements, and sand or water production constraints.

For high-pressure deep gas wells, the pressure-squared approach (p2 method) is replaced by the real-gas pseudo-pressure function m(p), also called the Al-Hussainy-Ramey-Crawford function, which accounts for the pressure-dependent variation of gas viscosity and compressibility factor (z). The pseudo-pressure approach linearizes the diffusivity equation over the full pressure range and produces more accurate deliverability estimates for wells producing above 2,000 to 3,000 psia where the p2 approximation breaks down.

  • back-pressure test: the original term introduced by Rawlins and Schellhardt in 1936, referring to testing the well against various back-pressures at the wellhead
  • deliverability test: a general synonym emphasizing the purpose of the test: to determine what the well can deliver to the pipeline at various operating pressures
  • open-flow test: informal term for a single-point test at maximum rate, often used loosely to refer to the overall AOF determination process
  • four-point test: common field shorthand for a flow-after-flow test conducted at exactly four successive rates, which is the minimum recommended for a reliable Rawlins-Schellhardt fit

Related terms: absolute open flow, inflow performance relationship, isochronal test, pressure buildup test, skin factor

Frequently Asked Questions About Multiple-Rate Tests

Why is the isochronal test preferred over flow-after-flow in tight gas reservoirs?

In low-permeability reservoirs (below 1 millidarcy), achieving stabilized flow at each rate may require days or weeks of continuous production before bottomhole pressure stops declining. Running flow-after-flow would deplete a significant portion of the near-wellbore pressure support between rate steps, violating the assumption that all rate-pressure pairs are measured against the same average reservoir pressure. The isochronal test avoids this by allowing full pressure recovery between rates, ensuring each flow period begins from the same initial condition. The modified isochronal test is a further compromise that accepts partial pressure recovery to reduce total test time while applying correction factors to account for the residual pressure depletion.

What causes the n exponent to fall outside the 0.5 to 1.0 range?

An n value greater than 1.0 usually indicates that the well did not reach stabilized flow at the higher rates, that there is a measurement error in the flow rate or pressure, or that liquid loading is affecting the lower rate points. An n value below 0.5 is theoretically impossible under the Rawlins-Schellhardt model and typically signals rate measurement errors (often due to liquid carryover in the separator), wellbore storage effects masking true formation response, or non-unique flow regimes at different rates such as crossflow between layers. Engineers should investigate the data quality before reporting an AOF based on an out-of-range n value.

How does non-Darcy flow affect the AOF estimate?

Non-Darcy or turbulent flow near the wellbore creates an additional pressure drop proportional to the square of the flow rate, meaning that each incremental unit of rate requires a disproportionately larger drawdown at high rates. This inertial effect, captured by the b coefficient in LIT analysis, causes the deliverability curve to curve downward at high rates relative to a pure Darcy extrapolation, resulting in a lower true AOF than would be predicted from low-rate data alone. In high-permeability, high-rate gas wells, failing to account for non-Darcy effects can overestimate AOF by 20-50%, leading to pipeline capacity commitments the well cannot sustain.

Why Multiple-Rate Tests Matter in Oil and Gas

Multiple-rate tests are the industry-standard method for determining how much gas a well can deliver to market under varying pipeline pressure conditions, making them foundational to field development economics, gas sales contracts, and reservoir management decisions. Regulatory agencies in Alberta (AER), British Columbia (BCOGC), and US states with significant gas production routinely require AOF documentation before approving gas well completion reports and before gas supply contracts can be registered. For operators, an accurate AOF established early in a well's life provides the baseline against which future production decline is measured, enabling early detection of formation damage, liquid loading, or depletion effects. For gas purchasers and pipeline companies, the AOF and deliverability curve confirm that the well can meet contractual minimum supply rates across the range of expected operating pressures throughout the contract term.

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