Theoretical Studies of Flowrates from Slimholes and Production - Size Geothermal Wells

The relationship between production rates of large diameter geothermal production wells, and slimholes, is studied. The analysis is based on wells completed in liquid-dominated geothermal fields, where flashing occurs either in the wellbore or at the surface. Effects of drawdown in the reservoir, and pressure drop in the wellbore, are included; heat losses from the wellbore to the formation are not presently included in our analysis. The study concentrates on the influence of well diameter on production rate. For situations where the pressure drop is dominated by the reservoir, it is found that the mass flowrate varies with diameter according to W Da, where the exponent a is a function of reservoir outer radius, well diameter and skin factor. Similarly, when pressure drop in the wellbore is dominant, the scaling exponent was found to be a function of well diameter and pipe roughness factor. Although these scaling laws were derived for single-phase flow, numerical simulations showed them to be reasonably accurate even for cases where flashing occurs in the wellbore. INTRODUCTION Drilling of slimholes instead of large diameter productionsized wells may be economically beneficial during the exploration phase of a geothermal prospect or during exploration of an undeveloped part of a producing reservoir. It has been reported that slimholes with diameters less than or equal to 4" could reduce the cost and time of drilling significantly (see for example, Entingh and Petty, 1992). Slimholes can also provide continuous cores which would help identify geological features more clearly. This report concentrates on the effect of wellbore diameter on production characteristics. Cost analysis, drilling practices and other relevant topics concerning slimholes are not discussed. As fluid flows from the reservoir to the surface through the wellbore, pressure drawdown occurs both in the reservoir and in the wellbore. As pointed out by Pritchett (1993), it would be helpful to have a scaling law that allows the flowrate of a slimhole to be predicted from the flowrate of a normal-diameter hole under the same conditions. Following Pritchett, we will attempt to develop power-law scaling relationships to describe the effect of wellbore diameter on well output. We first carry out an analysis for single-phase flow, for which it is possible to derive some analytical expressions. We then discuss the case where flashing occurs at some point in the wellbore. PRESSURE DRAWDOWN IN THE RESERVOIR Fluid flow from the reservoir into the wellbore has been studied by many investigators over the last half century or so, including processes such as the nature and direction of flow, transient or steady-state, single or two-phase, laminar or turbulent flow, and permeability reduction (well damage) or enhancement due to drilling and productiodinjection activities. In these studies, reasonable simplifications have been suggested. For instance, the flow from the reservoir into the wellbore is sometimes assumed to be steady or quasisteady, because flow equilibrates faster near the wellbore than in the reservoir as a whole (Pritchett and Garg, 1980). One could consider the direction of flow into the wellbore as spherical. However, with time it is assumed to approach horizontal radial flow. Other assumptions can also be made based on estimates of the amount and type of fluid, and the near-well reservoir behavior. Consider the pressure drop that occurs in the reservoir as the fluid flows toward the wellbore. Imagine a bounded, circular reservoir, whose outer boundary r = ro is maintained at some pressure po (see Fig. 1). If the wellbore has radius rw, and the downhole wellbore pressure is maintained at Pwb, the steady-state flowrate under Darcy-flow conditions will be given by (Matthews and Russell, 1967, p. 21) 2npkh (Po-Pwb) p ln(ro/rw) +s W = 4