Real Gas Transient Analysis of Three-Rate Flow Tests
Authors: Doyle R.E. , Sayegh E.F. 
Published: December 2007

With this gas well testing method the effective permeability, reservoir pressure, formation damage, and non-Darcy flow coefficient can be pressure, formation damage, and non-Darcy flow coefficient can be calculated from the flowing bottom-hole pressure of a three-rate production survey. Unique to the method is that it is possible to compare the theoretical and observed values of the pressure-time slope ratios to obtain an estimate of the reliability of the calculated reservoir parameters.

Introduction
Multiple-rate flow testing has gained widespread application as a means of determining effective permeability, reservoir pressure, and formation damage from permeability, reservoir pressure, and formation damage from transient bottom-hole pressure behavior following changes in stabilized rates. When required supporting data are available, it is also possible to estimate reservoir heterogeneities and distance to a linear barrier. One reason for the popularity of this testing technique is that a shut-down in production and prolonged use of bottom-hole pressure equipment are not required. (Elimination of shut-down production prevents the loss in current income that may occur with conventional pressure buildup surveys. Also, a shut-in of gas wells producing significant quantities of water may cause permanent formation damage.) In addition, the effects of after-production and wellbore phase separation are eliminated, thereby avoiding the possibility of running useless or questionable surveys. Although data from multiple-rate testing are now often used to determine oil reservoir characteristics, the technique was earlier modified and used to approximate gas reservoir properties. The latter customarily includes both two-rate and four-rate open-flow potential surveys. Russell provided a technique for determining permeability, reservoir pressure, and formation damage permeability, reservoir pressure, and formation damage from two-rate flow tests. Although his method is designed primarily for oil well testing, it may, with approximations, be applied also to gas well surveys. Gas properties are estimated from an average of flowing properties are estimated from an average of flowing and shut-in pressures to assess formation damage and calculate reservoir pressure. If the reservoir pressure gradients are relatively low, this will yield acceptable results. However, where high withdrawal rates or low permeability are involved the method may yield less permeability are involved the method may yield less accurate results. In addition, high production rates may cause turbulent flow around the wellbore, which will result in a deviation from Darcy flow. Part of this difficulty may be overcome with the Odeh-Jones approach to variable-rate gas well testing. Although the non-Darcy coefficient is included in the flow equations, their approach involves modifying the point source solution of a slightly compressible fluid to point source solution of a slightly compressible fluid to approximate real gas behavior. If pressure gradients are sufficiently low, reservoir parameters may be calculated with satisfactory accuracy. Selim proposed an extension of the two-rate technique to include an additional rate level. The third rate is generally about equal to the first and hence involves returning to the initial stabilized conditions. This method not only has the same advantages as the two-rate technique but also makes possible a comparison of pressure-time slopes of the two transient pressure periods, thus providing a check on the pressure periods, thus providing a check on the calculation of permeability. An accurate determination of the slope is required in multiple-rate testing since the values of permeability and reservoir pressure are sensitive to small changes in slope. Selim's testing method is adaptable primarily to reservoirs containing fluid of small and constant compressibility.
JPT
P. 1347