Decline Curves of a Vertical Well in Stress-Sensitive Reservoir

Abstract

Stress-sensitivity effects have been recognized to have impact on the pressure/rate transient behavior of wells in several reservoirs. Although the effects of stress-sensitivity have been considered in well testing theory in the past thirty years, little has been done to determine their influence on rate decline behavior. This paper presents a single phase flow model considering stress-sensitive formation permeability to investigate the characteristic of production rate decline of a vertical well. The stress-sensitive permeability is considered as an exponential form. The permeability changes with pressure drop are described by a permeability modulus. By introducing two pseudo functions, the equations of the mathematical model are linearized and approximate semi-analytical solutions are obtained. The analytical solutions are carefully verified through numerical simulation. Two sets of new decline type curves are diagramed on a log-log plot for constant rate case and constant bottomhole pressure case respectively. The influence of stress-sensitive permeability on decline curves are analyzed and compared. From this work, we recognized that the rate decline characteristics of stress-sensitive reservoir under constant rate and constant bottomhole producing condition are different. New analysis method should be developed to analyze field variable rate/variable pressure drop data.

Productivity Evaluation of Vertical Wells Incorporating Fracture Closure and Reservoir Pressure Drop in Fractured Reservoirs

“…Here, we applied the exponential stress sensitivity relation to describe stress sensitivity in this fractured reservoir. e permeability expression of the outer and inner zones can be presented as follows [26]:…”

“…Combining equations (19) and (26), the relationship between closed radius and bottom-hole pressure can be obtained:…”

“…, and r f � r w , equation (26) can be reduced to the case without fracture closure (equation (17)). Furthermore, in the early-time production, due to minor reservoir pressure changes, equation (26) can also be simplified to…”

“…When reservoir pressure drops over a period of time, it is more accurate to use equation (26) to calculate the productivity than to use equation (28). erefore, equation (26) can be regarded as a general equation, and Mathematical Problems in Engineering equations (17) and (28) are two degradation forms of this equation.…”