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Research Papers: Heat and Mass Transfer

# Numerical Modeling of Heavy-Oil Recovery Using Electromagnetic Radiation/Hydraulic Fracturing Considering Thermal Expansion Effect

[+] Author and Article Information
A. Davletbaev, L. Kovaleva, A. Zainulin

Department of Applied Physics,
Bashkir State University,
Ufa 450074, Bashkortostan, Russia

Department of Civil
and Environmental Engineering,
School of Mining and Petroleum Engineering,
University of Alberta,

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 30, 2017; final manuscript received December 7, 2017; published online March 9, 2018. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 140(6), 062001 (Mar 09, 2018) (11 pages) Paper No: HT-17-1055; doi: 10.1115/1.4038853 History: Received January 30, 2017; Revised December 07, 2017

## Abstract

Production of heavy oil from deep/tight formation using traditional technologies (โcoldโ production, injection of hot steam, etc.) is ineffective or inapplicable. An alternative is electromagnetic (EM) heating after fracturing. This paper presents the results of a numerical study of heavy oil production from a well with hydraulic fracture under radiofrequency (RF) EM radiation. Two parameters ignored in our previous modeling studies, namely adiabatic effect and the thermal expansion of oil, are considered in the new formulation, while high gradients of pressure/temperature and high temperature occur around the well. The mathematical model calculates the distribution of pressure and temperature in the system of โwell-fracture-formation.โ The distribution of thermal heat source is given by the Abernetty expression. The mathematical model takes into account the adiabatic effect and the thermal expansion of heavy oil. The latter makes a significant contribution to heavy oil production. Multistage heavy production technology with heating is assumed and several stages are recognized: stage 1: โColdโ heavy oil production, stage 2: RF-EM heating, and stage 3: RF is turned off and โhotโ oil production continues until the flow rate reaches its initial (before heating) value. These stages are repeated starting from the second stage. Finally, RF-EM heating technology is compared to โcoldโ production in terms of additional oil production and economics. When producing with RF-EM heating with power 60โkW (50 days in the second stages), the oil rate increased several times. Repeated RF-EM heating (25 days in the fourth stage) doubled the production rate. Near-well region temperature increased by โผ82โยฐC in the second stage with RF-EM heating. Temperature increased by โผ87โยฐC in the fourth stage with repeated RF-EM heating and production cycles. Economic analysis and evaluation of energy balance showed that the multistage production technology is more efficient; i.e., the lower the payback period, the greater the energy balance. With the increase in pressure difference, the payback period and energy balance increased linearly.

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## Figures

Fig. 1

Model of the formation with fractured well

Fig. 2

Production oil rate flow in the well with fracture finite conductivity (Temperatureโ=โconst): 1โnumerical curve with 60โรโ30 cells, 2โnumerical curve with 80โรโ40 cells, 3โnumerical curve with 100โรโ50 cells, and 4โtheoretical curve with use Saphir module in the Ecrin software package (Kappa Eng.)

Fig. 3

Production oil rate flow (a) and temperature (b) in the well at ฮP=3โMPa, xfโ=50 m, kfโ=100โรโ10โ12 m2, ฮทOโ=0 K/Pa: 1โNgโ=โ0โkW, ฮดOโ=0 1/K; 2โNgโ=โ60โkW,ฮดOโ=โ0.5โรโ10โ4 1/K; 3โNgโ=โ60โkW, ฮดOโ=โ1.0โรโ10โ4 1/K; and 4โNgโ=โ60โkW, ฮดO =โ1.5โรโ10โ4 1/K

Fig. 4

Pressure (a) and temperature (b) distribution along the fracture at ฮPโ=3โMPa, xfโ=50 m, kfโ=100โรโ10โ12 m2, ฮทOโ=0 K/Pa, ฮt2=50 days: 1โNgโ=โ0โkW, ฮดOโ=โ0 1/K; 2โNg= 60โkW, ฮดOโ=0.5โรโ10โ4 1/K; and 3โNgโ=โ60โkW, ฮดOโ=โ1.5โรโ10โ4 1/K

Fig. 5

Pressure (a) and temperature (b) distribution across the fracture at ฮPโ=3โMPa, xfโ=50 m, kfโ=100โรโ10โ12 m2, ฮทOโ=0 K/Pa, ฮt2=50 days: 1โNgโ=โ0โkW, ฮดOโ=โ0 1/K; 2โNg= 60โkW, ฮดOโ=0.5โรโ10โ4 1/K; and 3โNgโ=โ60โkW, ฮดOโ=โ1.5โรโ10โ4 1/K

Fig. 6

Rate of fluid flow (a) and fluid mobility (b) distribution along the fracture at ฮPโ=3โMPa, xfโ=50 m, kfโ=100โรโ10โ12 m2, ฮทOโ=0 K/Pa, ฮt2=50 days: 1โNgโ=โ0โkW, ฮดOโ=โ0 1/K; 2โNg= 60โkW, ฮดOโ=0.5โรโ10โ4 1/K; and 3โNgโ=โ60โkW, ฮดOโ=โ1.5โรโ10โ4 1/K

Fig. 7

Rate of fluid flow (a) and fluid mobility (b) distribution across the fracture at ฮPโ=3โMPa, xfโ=50 m, kfโ=100โรโ10โ12 m2, ฮทOโ=0 K/Pa, ฮt2=50 days: 1โNgโ=โ0โkW, ฮดOโ=โ0 1/K; 2โNg= 60โkW, ฮดOโ=0.5โรโ10โ4 1/K; and 3โNgโ=โ60โkW, ฮดOโ=โ1.5โรโ10โ4 1/K

Fig. 8

Production oil rate flow (a) and temperature (b) in thewell at ฮPโ=โ3โMPa, xfโ=โ50 m, kfโ=โ100โรโ10โ12 m2, ฮดOโ=โ1.0โรโ10โ4 1/K: 1โNgโ=โ0โkW, ฮทOโ=โ0 K/Pa; 2โNgโ=โ60โkW, ฮทOโ=โ0 K/Pa; and 3โNgโ=โ60โkW, ฮทOโ=โ3200โรโ10โ10 K/Pa

Fig. 9

Pressure (a) and temperature (b) distribution along the fracture at ฮPโ=โ3โMPa, xfโ=โ50 m, kfโ=โ100โรโ10โ12 m2, ฮt2โ=โ50 days, ฮดOโ=โ1.0โรโ10โ4 1/K: 1โNgโ=โ0โkW, ฮทOโ=โ0 K/Pa; 2โNgโ=โ60โkW, ฮทOโ=โ0 K/Pa; and 3โNgโ=โ60โkW, ฮทOโ=โ3200โรโ10โ10 K/Pa

Fig. 10

Pressure (a) and temperature (b) distribution across the fracture at ฮPโ=โ3โMPa, xfโ=โ50 m, kfโ=โ100โรโ10โ12 m2, ฮt2โ=โ50 days, ฮดOโ=โ1.0โรโ10โ4 1/K: 1โNgโ=โ0โkW, ฮทOโ=โ0 K/Pa; 2โNgโ=โ60โkW, ฮทOโ=โ0 K/Pa; and 3โNgโ=โ60โkW, ฮทOโ=โ3200โรโ10โ10 K/Pa

Fig. 11

Rate of fluid flow (a) and fluid mobility (b) distribution along the fracture at ฮPโ=โ3โMPa, xfโ=โ50 m, kfโ=โ100โรโ10โ12 m2, ฮt2โ=โ50 days, ฮดOโ=โ1.0โรโ10โ4 1/K: 1โNgโ=โ0โkW, ฮทOโ=โ0 K/Pa; 2โNgโ=โ60โkW, ฮทOโ=โ0 K/Pa; and 3โNgโ=โ60โkW, ฮทOโ=โ3200 รโ10โ10 K/Pa

Fig. 12

Rate of fluid flow (a) and fluid mobility (b) distribution across the fracture at ฮPโ=โ3โMPa, xfโ=โ50 m, kfโ=โ100โรโ10โ12 m2, ฮt2โ=โ50 days, ฮดOโ=โ1.0โรโ10โ4 1/K: 1โNgโ=โ0โkW, ฮทOโ=โ0 K/Pa; 2โNgโ=โ60โkW, ฮทOโ=โ0 K/Pa; and 3โNgโ=โ60โkW, ฮทOโ=โ3200โรโ10โ10 K/Pa

Fig. 13

Payback times as a function of oil price for different values of thermal expansion coefficient of oil: 1โฮดOโ=โ0.5โรโ10โ4 1/K, 2โฮดOโ=โ1.0โรโ10โ4 1/K, and 3โฮดOโ=โ1.5โรโ10โ4 1/K

Fig. 14

The dynamics of the contribution of thermal expansion of oil fP(2) (a) and the contribution of the adiabatic effect fT(2), (b) in the oil production with EM heating: ฮPโ=โ3โMPa, xfโ=โ50 m, kfโ=โ100โรโ10โ12 m2, ฮt2โ=โ50 days, Ngโ=โ60โkW, ฮดOโ=โ1.0โรโ10โ4 1/K: 1, 2โฮทOโ=โ1600โรโ10โ10 K/Pa and 3, 4 โฮทO=3200ยท10โ10 K/Pa

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