In this paper, we present a new method for analyzing a multi-layered, commingled reservoir with unequal initial layer pressures. The main objective is to provide techniques and methodology to determine the individual layer permeabilities, porosities and skin factors from the pre-production well test data. The layer information obtained early in the life of the reservoir is very important for planing production schedule and economic decisions concerning the future of the wells. This pre-production well test is carried early in the life of the reservoir, during the period after perforation but before any surface production and is caused by crossflow in the wellbore only.
The results of this study provide a useful foundation for the design of a new pre-production well test procedure that ensures that the individual layer properties are measured adequately and early in the life of the reservoir when they are most needed.
The pre-production well test requires no production on surface. Thus, the environmental impact caused by flaring oil or gas during a conventional well test is alleviated.
Most reservoirs are stratified and consist of layers with different porosities and permeabilities. In many cases, wells are perforated simultaneously in two or more layers. The major drawback of the multiple-layer completions is that the origin of the produced fluid is generally unknown. As a result, it is difficult to predict recovery and future performance under primary and enhanced recovery operations from each of the layers. Normally, it is necessary to determine the properties of the individual layers to improve the prediction of reservoir behavior.
Interest in the behavior of multi-layered reservoir systems has prompted numerous studies in the last 25 years. In the last 5 years testing methods have begun to provide quantitative grasp of reservoir descriptions. The earliest studies modeled commingled reservoirs with equal initial pressures in layers. The second phase included the effect of unequal initial layer pressures which Papadupolos studied first for layered aquifers. Larsen presented a method for analyzing wellbore pressures prior to the start of production for a two-layer reservoir, provided such data are available from the infinite-acting period. The method had the disadvantage that it requires estimates of the average permeability, porosity and compressibility for each individual layer. Also, this method can yield only an estimate of the ratios of reservoir properties and it does not work for reservoirs with negative skin. Kuchuk et al. presented generalized analytical solutions for commingled reservoirs in which each reservoir or layer can be at a different initial pressure or can have different initial pressure distribution. Agarwal et al. presented a study of pre-production time period. The study showed that much information that has a bearing on production performance can be discerned by the observation of the pressure behavior during the preproduction time period. Agarwal et al. presented a number of approximate solutions for analyzing well responses. Aly presented a complete study of the performance of commingled reservoirs with unequal initial pressures.
In this paper, we present a new solution technique, the "Derivative Extreme Method" (DEM), to analyze pre-production wellbore pressures in a two-layer reservoir. It is based on the analysis of the early and late transient (i.e., including initial boundary effects) wellbore pressure data measured during the pre-production well test. The solution technique was developed from the approximate solutions that Agarwal et al. presented for analyzing well response. The (DEM) concept is based on solving four equations containing four unknowns. The four equations are solved at the extreme critical point of the pre-production pressure and pressure derivative curves. We can determine individual layer skin, diffusivity, porosity and permeability for a two-layer system with the DEM. The advantage of the proposed method is that it does not require direct knowledge of the average layer properties to determine the individual layer properties. Also, the DEM has the advantage of determining individual layer properties from transient and late-transient region data.
This work examines the effect of unequal initial layer pressures on the wellbore pressure and sandface rate responses of wells producing from commingled reservoirs. The results of this study provide a useful foundation for the design of well test procedures to ensure that layer properties are adequately measured. The new well test enables us to determine the individual layer properties early in the life of the reservoir when they are most needed, while minimizing cost, reducing testing time and alleviating the environmental impact of conventional well-testing.