Numerous full field water-flooding projects are currently under way throughout the world to improve recovery. In many large oil fields water injection is initiated during the early stages of reservoir development. Exploratory wells are tested for injectivity, and injectors are tested during the field operation. As in production tests, it is quite difficult, if not impossible, to maintain a constant rate during an injection test. Any small variation in the injection rate, if not accounted for, may lead to considerable error in the calculated results. In some falloff tests, the pressure at the wellhead drops below the atmospheric pressure. When this occurs, the tubing becomes partially empty, leading to a change in the wellbore storage coefficient. A falloff of long duration is not suitable because the injection is stopped which is uneconomic.
In 1963, the two-rate flow test method was introduced. This was designed to eliminate the disadvantages of buildups and drawdowns. The disadvantage of the two-rate flow test is that the flow rate during the second flow period must be constant which leads to considerable errors in the results. To eliminate some of these difficulties, it was proposed a modification consisting of following the second rate with a rate increase. However it still required constant-rate flow. Another technique using a plot of Pwf vs log ([t+∆t)/∆t]+q2/q1log∆t to relate to system transmissibility was also introduced. This had a lacking on accuracy which was corrected later on by other study. Another researcher removed the constant rate requirement during the second flow period. Thus the test is easier to run and any fluctuation in rate is accounted for in the calculations. To overcome the problems encountered when using drawdown type curves to analyze buildup test, a technique was developed to account for the dependence of the producing time especially when the producing period is short or the flow rate is variating. This method was extended to include analysis of data from two-rate tests and multiple rate tests.
Multi-rate injection pressure test should be designed to avoid most of the above problems. In this paper, new relationships for a multi-rate injection pressure test in a non-unit mobility ratio system were developed. The pressure derivative was introduced to analyze such a pressure transient tests. Estimation of reservoir parameters was performed by the application of the Tiab’s Direct Synthesis Technique, which uses exact analytical solutions to obtain reservoir parameters, was applied to solve different possible cases.
The proposed interpretation technique was tested during simulated examples and comparing the results to those obtained from conventional techniques. A comparison between the use of equivalent time (the rigorous method) and real time to analyze a multi-rate injection test was made.