In this paper we present a new theoretical model for three-layer reservoirs with unequal initial pressures. We developed a semianalytical simulator based on the developed model. The computational model proved to be much faster than a three-dimensional, finite-difference commercial simulator used to validate the analytical model. Also, the amount of information (spatial gridding) needed to run the model is much reduced. The analytical model allows each layer to have different layer properties, different boundary conditions, and different initial pressures.
We used the semi-analytical simulator to perform a detailed study of the behavior of three-layered reservoirs during the "pre-production period." The pre-production period occurs early in the life of the reservoir, after perforation but before any surface production and is caused by crossflow in the wellbore. The layer information obtained is very important for scheduling production and making economic decisions concerning the future of the wells. The pre-production well test requires no production on the surface during the test; thus the impact on the environment is negligible.
The main objective of this work is to develop a qualitative approach to extract more information about the reservoir from preproduction wellbore pressure, dimensionless pressure and dimensionless pressure derivative curves. More specifically, we studied the preproduction behavior of three-layered reservoirs. Effects of the ratio of flow capacity and storage in different layers were investigated. We found that the layers with highest and lowest permeabilities can be characterized with the logarithmic time derivative of pre-production pressures. A positive derivative indicates high permeability in the layer with the highest initial pressure, and a negative derivative indicates high permeability in the layer with low initial pressure. Also, the layer with the highest initial pressure will always flow into the wellbore whereas flow will always be from the wellbore into the layer with minimum initial pressure. As the sandface rates reach steady state, the three-layer system behaves like an equivalent single layer system. Thus, we can apply a single-layer model to analyze the late transient in high permeability reservoirs.
Most multi-layered reservoir models reported in the literature includes only two layers with equal initial pressures. In this paper, we extend modeling first to three-layer reservoirs and provide the basis for n-layer reservoirs. This work addresses the need for a practical and easily applied method to determine the individual layer properties.
The first phase in layered reservoir studies dealt with the problem of commingled reservoirs with equal initial pressures1–11. The second phase included the effect of unequal initial layer pressures which Papadupolos12 studied first for layered aquifers. Larsen13 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 has 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 average reservoir properties and not individual layer properties. Kuchuk et a1.14 presented generalized analytical solutions for commingled reservoirs in which each reservoir or layer can be at a different initial pressure or may have a different initial pressure distribution. Agarwal et a1.15 presented a detailed study of preproduction time period. The study showed that much information that has bearing on production performance can be discerned by the observation of the pressure behavior during the pre-production time period. A number of approximate solutions are presented for analyzing well responses. Aly16 and Aly et al.17 presented a complete study of the performance of commingled reservoirs with unequal initial pressures. Aly and Lee18 presented a comprehensive semi-analytical simulator and verified it against cases from the literature. They also introduced the pre-production well test, PPWT. They presented a detailed procedure to show how to implement this test in the field and introduced analysis methods to determine the individual layer properties from the pre-production wellbore pressure.