Modeling coupled transient transport of mass, momentum and energy in wellbore/reservoir systems

The total reserve of a hydrocarbon bearing formation and its ability to economically produce the fluids determine a reservoir's development potential. Oil companies in the United States and abroad spend millions of dollars a year in well testing to estimate parameters related to these factors. A large fraction of these tests are surface "buildup" tests in which a producing well in the reservoir is "shut-in" either at the wellhead or at the bottom, or "drawdown" tests in which a well initially closed, is suddenly opened at the wellhead. The transient response of the pressure to these changes at the well bottom provides valuable information about formation properties. Shut-in at the bottom is usually very difficult and expensive, especially in the hostile environment of a high temperature/high pressure reservoir.; Fluid flow in the wellbore is complicated by heat transfer between the fluid and the surrounding earth. Earth temperature generally increases with depth. Thus, as the hot fluid from the bottom flows upward, its temperature becomes higher than its surrounding causing heat loss from the wellbore. Conversely, when a well is shut-in at the wellhead, the warm fluid losses heat to the surrounding colder formation more rapidly than it gains it from the decreasing mass influx. Since fluid properties are temperature sensitive, pressure profile computation, which depends on fluid properties, is influenced by the fluid temperature profile in the wellbore. Thus, the transport processes in the wellbore are coupled.; In this work we presented a transient wellbore/reservoir model for testing wells. We used a hybrid approach to couple the wellbore with the reservoir. The reservoir flow was modeled using the standard analytic approach, including superposition effects. The wellbore model, requiring simultaneous solution of the mass, momentum, and energy balance equations, used a finite difference numerical approach. Two simulators based on our model were developed: the forward simulator allowed us to simulate wellbore fluid temperature, pressure, and other variables at any depth and time for given reservoir parameters and well completion details; the reverse simulator allowed us to convert measured wellhead pressure and temperature to bottomhole pressure for subsequent analysis.; Three field examples were used to demonstrate various applications of these two simulators. The good agreement between field data and predictions showed the quality of our simulators. We also identified the phenomenon of wellbore thermal storage. Wellbore thermal storage is the energy absorbed or released by the tubulars and cement sheaths, which is a significant fraction of the energy exchange between the wellbore and the formation at early time.; A sensitivity study gave us further insights into the effect of various process variables on wellbore pressure and temperature. Thus, our simulators can be very useful in designing well tests as well as to augment conventional well test analysis.