Wellbore Storage Effects in Geothermal Wells
Abstract The early-time response in the well testing of a homogeneous reservoir customarily is expected to give a unit slope when the logarithm of pressure is plotted vs. the logarithm of time. It is shown that this response is a special case and that another nondimensional parameter must be defined to describe the set of curves that could take place for each value of the wellbore storage coefficient C . In addition, the effect of temperature changes along the bore is shown to increase the time when wellbore storage is important. Introduction The petroleum industry's technique of assessing oil and gas reservoirs by well testing has been extended to the geothermal field by a number of workers. However, at least two important differences between a geothermal field and an oil or gas field must be considered in analyzing geothermal well test data. First the kh/mu value of a geothermal field is usually much larger than that of an oil or gas field because the reservoir thickness h is greater in a geothermal field and the viscosity mu is smaller (k is the permeability). Second, heat loss in the wellbore, which can be ignored in oil and gas fields, is significant in geothermal bores.The concept of wellbore storage - which has been considered quite extensively and refined in such detailed studies as those of Agarwal et al., Wattenberger and Ramey, and Ramey - usually is treated as a boundary condition on the reservoir flow. The boundary condition used is (1) where dp w/dt is the flowing pressure change with time in the wellbore. However, dp w/dt is not necessarily independent of position in the well. When dp w/dt is dependent on the measurement point, a plot of log (p sf) vs. log (t) will not result in a unit slope at early times. This study will consider wellbore storage by looking at the flow in the well itself while treating the reservoir as simple homogeneous radial flow into the well.Heat loss from the well and temperature changes along the bore also have been ignored because oil and gas news can be treated as isothermal. Heat transfer from the well and heating of the fluid in the well is usually a very slow process. When very long times are considered, these temperature effects can become important. Once the early transient behavior is over and a semilog straight line of p sf vs. log(t) is expected in the pseudosteady region, temperature changes in the well can alter the slope of that line so that the slope would no longer be q mu/4 pi kh. The duration and importance of any temperature changes will be considered.A numerical model of transient two-phase flow in the wellbore with heat and mass transfer has been developed. It is used to investigate (1) the early-time interaction of the well flow with that of the reservoir and (2) the longer-time effect of temperature changes on the well test data. Concept of Wellbore Storage Wellbore storage is the capacity of the well to absorb or supply any part of a mass flow rate change out of a well/reservoir system. For a change in flow rate at the surface of the well, the sandface mass flow rate usually is expressed as (2) SPEJ P. 555＾
