Simulation of Downhole Heater Phenomena in the Production of Wellbore Fluids

Abstract

Summary A model is presented for predicting the pressure and temperature profiles for gas/liquid flow in wellbores stimulated with downhole heaters. The solution algorithm consists of coupling the momentum- and energy-balance equations for the wellbore fluids with the transient behavior in the surrounding rock. The heater is treated as a source term in the energy-balance equation. The model is capable of predicting wellbore thermal effects, such as reduction of fluid viscosity and increase of free gas. It can be used to simulate temperature maintenance during well shut-in periods to prevent pour-point problems and paraffin or hydrate formation. An existing well with production problems related to thermal effects was simulated by the model. Results indicate that wellbore temperatures can be controlled by downhole heaters. Also, under certain conditions, an increase in production was predicted with such an application. Introduction Many problems encountered in the production of oil and gas could be reduced by introduction of heat to increase the temperature of the fluids. A review of thermal stimulation methods was given by Farouq Ali, who included electrical or hot water heaters, gas bumers, limited in-situ combustion, and hot water or steam injection. Increasing the fluid temperature results in several advantages. Various reservoirs produce fluids that deposit semisolid asphaltic hydrocarbons. These solids can plug the flow path either in perforations or in the piping system. A similar phenomenon is the deposition of wax in tubing or flowlines, resulting in additional flow re-sistance. Thermal stimulation can reduce this deposition and increas well productivity. An increase in temperature will also result in a reduction in oil viscosity. This is important when highly viscous crudes are produced where frictional pressure losses can be large. Another positive result of beating is an increase in free gas, which in turn results in a lower pressure gradient in the system. Heating can also be used for temperature maintenance during well shut-in periods to prevent pour-point problems. Hydrate formation can also be prevented by thermal stimulation. Additional advantages are thermal fractures, clay dehydration, and removal of residual water. An investigation of the use of electrical heaters to assist in the production of viscous or waxy crudes has resulted in the development of a simulation model for well flow analysis. The model allows the simulation of the temperature profile in the flowing fluids, including the effect of the electric heater. Evaluation of the two-phase-flow pressure losses in the tubing and the effect of heating on the production rate are also considered. PVT properties of the fluids in the tubing were predicted with fluid property correlations, with emphasis on the variations in the liquid viscosity and the solution GOR with temperature. A significant reduction in the solution gas can occur with heating. This reduction will increase the free gas available, thereby making implementation of a gas-lift procedure possible. Mathematical Formulation Determination of the flowing pressure traverse in tubing for the simultaneous transport of liquid and gas phases requires a knowledge of the temperature variation with depth because the PVT properties depend strongly on pressure and temperature. When the temperature distribution is not known, coupling the heat-balance equation with the mechanical-energy equation to calculate the pressure and temperature changes simultaneously becomes necessary and requires a double iterative procedure. Brill and Beggs described the procedure. When the temperature distribution is known or can be determined explicitly, a single iterative procedure that involves a standard marching algorithm is used to evaluate the flowing pressure and temperature profiles. The following sections show the development of explicit equations for temperature prediction in the wellbore. Flowing-Temperature Determination. Two cases are analyzed in this study. The first case considers no heater in the wellbore. A solution for this configuration, developed by Ramey for injection wells, is modified here for producing wells. This solution is then extended in the second case for a wellbore with a heater. Without Heater. The wellbore heat-transmission process is governed by the following equation: (1) (2) The functionf(t) represents the resistance for radial conductive heat transfer in porous media. A discussion of f(t) is given in Appendix B. The boundary condition for a producing well can be written as (3) Note that D=O represents the bottom of the producing well in this equation. The geothermal temperature, represented as a linear function of depth, is given by (4) Solution of the partial-differential equation given by Eq. 1 with the boundary condition given by Eq. 3 yields (5) The solution assumes that the thermal properties of the earth and the wellbore fluids are independent of temperature. Also, heat transfer in the wellbore is assumed to be steady state, while heat flow to the surrounding rocks is described by the transient radial-heat-flow equation. The overall heat-transfer coefficient, Uo, incorporates the resistance to heat flow by the flowing fluids, tubing wall, fluid in the casing/tubing annulus, and casing wall. With Heater. A heat balance on an element of the two-phase flow mixture within the heater region yields (6) where S = rate of he-at supply per foot by the heater. The assumptions used in deriving Eq.1 were also applied in determining the heat balance represented by Eq. 6. The heater generally is not attached to the entire tubing string. Therefore, part of the tubing surface, usually near the bottom of the well, is always bare of the heater, while the remainder is always in contact with the heat source. Eq. 6 is valid only for fluid flow within the heated pipe section. An appropriate boundary condition for this situation is given by (7) In this case, D=O represents the location of the heater base. TFH(t), the temperature of the two-phase mixture at the entrance to the bottom section of the heater, is evaluated with Eq. 5. The geothermal temperature for this case is given by (8) SPEPE P. 309^

A fully-coupled thermal multiphase wellbore flow model for use in reservoir simulation

“…The energy conservation equation for the overall fluid can be written in a variety of forms (Ramey, 1962;Satter, 1965;Ishii and Mishima, 1984;Farouq Ali andAbou-Kassem, 1988, 1989;Sharma et al, 1989;Holmes et al, 1998;Hasan and Kabir, 2002;Stone et al, 2002;Hibiki and Ishii, 2003;Cheng and Mewes, 2006;Ishii and Hibiki, 2006). We express it as follows:…”

Two Issues in Wellbore Heat Flow Modelling Along With the Prediction of Casing Temperature in the Steam Injection Wells

“…In spite of these assumptions, which were necessary to obtain an analytical solution of the problem, this work was the basis of many wellbore flow models [see a detailed literature review on this topic by Bahonar et al (9) ]. Over the last few decades, different researchers [Satter (10) , Holst and Flock (11) , Willhite (12) , Pacheco and Ali (13) , Herrera et al (14) , Shiu and Beggs (15) , Ali (16) , Fontanilla and Aziz (17) , Yao (18) , Hong and Griston (19) , Griston and Willhite (20) , Sharma et al (21) , Stone et al (22) , Wu and Pruess (23) , Sagar et al (24) , Alves et al (25) and Hagoort (26) ] attempted to relax Ramey's assumptions, model more complex wells and find fast and stable solution methods for solving various wellbore models. Two of those researchers who have had great contributions in the fluid and heat flow modelling of wellbore are Hasan and Kabir, who started their major work by developing an analytical model of the flowing fluid temperature inside the well in 1994 (27) .…”

Two Issues in Wellbore Heat Flow Modeling along with the Prediction of Casing Temperature in the Steam Injection Wells

“…In spite of these assumptions that were necessary to obtain an analytical solution of the problem, this work was the basis of many wellbore flow models; see a detailed literature review on this topic by Bahonar et al (2009). Over the last few decades, different researchers (Satter 1965;Holst and Flock 1966;Willhite 1967;Pacheco and Farouq Ali 1972;Herrera et al 1978;Shiu and Beggs 1980;Farouq Ali 1981;Fontanilla and Aziz 1982;Yao 1985;Hong and Griston 1986;Griston and Willhite 1987;Sharma et al 1989;Wu and Pruess 1990;Sagar et al 1991;Alves et al 1992;Hagoort 2004) attempted to relax Ramey's assumptions, model more complex wells, and find fast and stable solution methods for solving various wellbore models. Two of those researchers who have had great contributions in the fluid and heat flow modeling of wellbore are Hasan and Kabir who started their major work by developing an analytical model of the flowing fluid temperature inside the well in 1994 (Hasan and Kabir 1994).…”