Two-Rate Testing: An Alternative to Build-Ups and Drawdowns

By Mike Redman | Mon, 10 Nov 2008

Pressure-transient testing is a valuable tool for a reservoir engineer. A properly executed test will enable the engineer to evaluate one or more of the following well properties: Skin, Permeability, Reservoir Pressure, Boundaries and Reserves. Typically these properties are acquired by either conducting a build-up or a drawdown test. However, circumstances may prevent the well from being shut-in, negating the possibility of performing either test. In this situation, the solution is to perform a two-rate test. A two-rate test is advantageous whenever any of the following is a concern:

• Loss of Production (Cash Flow)
• Wellbore Liquid Accumulation
• Difficulty Returning a Well to Production

By performing a two-rate test, the operator avoids the loss of cash flow associated with the shut-in time necessary for either a build-up or drawdown. A well that is shut in generates no income. Wellbore liquid accumulation is a concern for wells that would develop a standing liquid column upon shut-in. If this occurs, reservoir response is masked until the liquids re-inject. Depending upon the volume of liquid and the kh of the reservoir, this could take a significant amount of time, making the build-up test an unreasonable option. During a two-rate test where both rates are above the critical unloading velocity, this liquid column does not accumulate; the reservoir response is valid during the entire test. The potential difficulty of returning a well to production is the final concern. In some instances, after a well has been shut in for a test, it is difficult or impossible to return the well to pre-test flow rates. There is little point in running a test if it results in a permanent reduction of well productivity. Running a two-rate test eliminates this potential risk.

Analysis of a two-rate test is relatively straightforward. Build-ups and drawdowns are essentially special cases of a two-rate test, with one of the rates equal to zero! The permeability equation is the same equation associated with conventional build-ups and drawdowns:

In this formulation of the permeability equation, the flow rate is employed in the calculation is the first rate of the two-rate test. The skin equation is somewhat different due to the fact that it incorporates both rates:

Finally, the initial reservoir pressure, Pi can be obtained by the following equation:

With these equations, a properly executed two rate test can provide the same information that a build-up or drawdown can, without the loss of cash flow or other associated concerns. The graphs below are Cartesian and Semi-log Plots from a two-rate test in which the second rate is approximately 33% larger than the first.

Figure 1 – Cartesian Plot

Figure 2 – Semilog Plot with Radial Flow Identified