A new physical modeling for two-phase wellbore storage due to phase redistribution

Abstract Pressure transient analysis is one of the main dynamic sources for reservoir characterization. The main task in well test interpretation is to understand the reservoir properties using the bottom-hole pressure behavior. Unfortunately, one of the main factors that can affect this task is wellbore storage effects, especially in cases that we have a non-ideal one. In pressure build-up test if pressure is below the bubble point or if gas enters into the wellbore, the phase redistribution can happen during the shut-in period. This phenomenon causes pressure anomalies. Besides, due to pressure increase or existence of under-saturated liquid in the wellbore, the gas starts to dissolve, and it is led to pressure decrease. So the pressure build-up test is dominated by three main factors: firstly, the pressure increase resulted from build-up test. Secondly, the pressure increase due to phase redistribution. Finally, the pressure decrease due to gas dissolution. These effects are known as non-ideal wellbore storage. Most of the studies focused on non-ideal wellbore storage try to propose an empirical equation to simulate the pressure curve more accurately instead of proposing an analytical model, because of the large number of effective parameters in an actual case. This paper is proposing a new analytical model for changing wellbore storage and analysis of gas phase segregation during the pressure build-up test in the existence of the under-saturated liquid. This model is further modified for two-phase flow when pressure falls below the bubble point in the wellhead. When the well is shut in at the start of build-up test, gas bubbles travel upward because of the buoyancy force. This model is presented for the case of dissolving gas pockets while rising in the wellbore. The novelty of this paper in comparison to previous researches is in developing a new physical model for two-phase wellbore storage done by modeling pressure increase due to gas bubbles rise while modeling gas dissolution against time. In this study, first, the basic assumptions for simplifying the model are described and the basic theory behind the proposed model is explained. Then a simple model without gas dissolution, using Laplace transformation, is introduced. Next, the modified model considering gas dissolution effect is proposed. A synthetic case is considered and the corresponding well test type curves are generated using the proposed method. Finally, the comparison between the proposed model and a real build-up case is made. The result is consistent with the typical non-ideal wellbore storage that is seen in the literature.