Paper ID 119 ABSTRACT Development of Thermal Recovery Simulator for Hot Water Flooding Shotaro Nihei, Masanori Kurihara Department of Resources and Environmental Engneering, Waseda University, Japan Author to correspondence should be addressed via e-mail: n_shotaro.in1989@moegi.waseda.jp In this study, a numerical simulator that enables the prediction of reservoir behaviors for hot water flooding was developed and tested. This study is composed of two parts: 1) development of the numerical simulator and 2) case studies investigating the effects of some parameters on heavy oil recovery. In the first part, a 1-dimensional and 2-phase (oil-water) black oil type simulator was developed. This simulator was then expanded so that it could deal with hot water, by adding the energy conservation equation as a governing equation. In the second part, using the simulator thus developed, effects of some parameters such as oil viscosity, hot water temperature and well spacing on the heavy oil recovery were examined. Through these case studies, it was envisaged that this simulator worked properly and that the energy efficiency could be optimized by appropriately determining the values of these parameters. KEY WORDS: Hot water / Thermal / EOR / numerical simulator / Petroleum 1. INTRODUCTION 1.1 Background In these days, energy demands have been drastically increased all over the world, especially in developing regions. International Monetary Fund reported that the crude oil price will continue to increase year by year. For this reasons, the studies on Enhanced Oil Recovery (EOR) techniques and on the development of unconventional resources become more and more important. Considering an oil field development, it is said that only 2-3% of oil can be recovered from oil reservoirs by primary recovery methods. Therefore, a variety of EORs, which are techniques for improving the oil recovery factor, are developed and applied in the world. In some cases, EOR makes it possible to improve the recovery factor up to around 5%. USA, UK, and USSR have been studying EOR since 197s. However, EOR needs extra energy for producing hydrocarbon resources in comparison with the primary recovery method. EOR was not widely prevalent at that time. At present, however, we are faced with the serious energy shortage problem. The EOR techniques are attracting attentions of the world even if the cost of EOR is taken into consideration. Furthermore, EOR is applied not only to conventional oil and gas fields, but also unconventional oil and gas fields. In this study, we focused on the development of heavy oil fields, which are difficult to develop with ordinary methods because the viscosity of heavy oil is much higher than that of conventional oil. 1.2 Heavy oil It is reported that heavy oil can be discovered under the ground of Canada, Venezuela and China in recent years. The original in place of heavy oil is Environmental Concerns 57
estimated to be several times greater than that of conventional oil. The recovery factor of heavy oil is intensely related to the parameter called Mobility, λ. The mobility to the phase-α is ordinarily expressed as λ = kk μ, (1) where k denotes absolute permeability, k stands for relative permeability to the phase-α and μ is viscosity of the phase-α. EOR techniques for heavy oil fields focus on increasing the mobility of oil phase. In other words, it is a point in heavy oil fields to decrease the viscosity of oil phase by EOR techniques. In this study, we focused on the hot water flooding technique, which is one of popular EORs for heavy oil fields. In this EOR, hot water is injected into a reservoir and its temperature is increased. Along with the increase in the temperature, the viscosity of oil phase is decreased. In order to numerically simulate these phenomena, we developed a Thermal Recovery Simulator with a great attention to the change in oil-phase viscosity. 2. BLACK OIL RESERVOIR SIMULATOR 2.1 Development of black oil reservoir simulator First of all, we developed a one-dimensional black oil reservoir simulator, which can predict the fluid flow behavior of oil and water phases under constant temperature condition. The governing equations of this numerical simulator is the mass conservation equations for oil and water phases, as expressed by the following partial differential equations. B : formation volume factor of phase-α D : depth k : absolute permeability k : relative permeability to phase-α p : phase pressure Q, : injection rate of phase-α per unit reservoir bulk volume t : time S : saturation of phase-α γ : gravity potential of phase-α μ : viscosity of phase-αφ : porosity These governing equations are discretized by the finite difference method and then solved numerically for the primary unknowns of oil phase pressure and water saturation. The pressure and water saturation are set as main variables and their distributions can be obtained as the simulation results. Hence, the distributions of reservoir pressure and fluid saturations are predicted as a result of numerical simulation. 2.2 Verification of 1-D and 2-Phase black oil simulator In order to verify the simulator developed in Section 3.1, a classic Buckley Leverett problem [1] was solved by the simulator. Fig.1 shows the simulated results in comparison with the analytical solutions. The simulation results are plotted by marker symbols while the analytical solutions are signified by lines. This figure suggests that the simulator developed in section 3.1 worked properly as the results were close to the analytical solution. kk μ B (p γ D) + Q, B, (2) = t φs B, α = o, w where Environmental Concerns 58
Water saturation 1..8.6.4.2. Fig. 1 Water saturation versus distance 3. DEVELOPMENT OF THERMAL RECOVERY SIMULATOR 3.1 Expansion of black oil simulator The black oil simulator developed in the previous chapter cannot be applied to the hot water flooding, since it cannot deal with the changes in reservoir temperature. In order to deal with the hot water flooding, the simulator was expanded by incorporating an energy conservation equation into the governing equations. It enables to simulate the energy transport phenomena. The equation is expressed as below. (λ T) +, + Q, ρ H, = [(1 ϕ) ρ U +ϕ, S ρ U where Q loss : heat loss ρ H u - Q loss ], α = o, w H : phase enthalpy of phase-α T: temperature 5 days days 15 days 2 days 25 days 5 days (analytical) days (analytical) 15 days (analytical) 2 days (analytical) 25 days (analytical) 2 3 u : Darcy velocity of phase-α U : unit internal energy of phase-α λ: total thermal conductivity ρ : density of phase-α Distance (m), (3) The term (λ T) represents a conductive heat transfer, where T stand for a reservoir temperature and is the total thermal conductivity of the reservoir rock/fluid. The term [ρ H u ], represent a heat transfer associated with a convection of fluids in the porous media. The term Q, ρ H represents a sink/source term associated with injection and/or production of fluids. The injected or produced heat rate is related to both the injection/production rate and the enthalpy of the fluid under the reservoir conditions. The term Q loss denotes the heat loss to the overburden and under burden. In the thermal recovery process, the heat injected into a reservoir by a hot fluid is lost successively from the boundaries. The heat loss has a far greater influence on the simulation results than one might imagine. The major heat loss takes place across cap rocks, whereas heat loss through the lateral reservoir boundaries is usually ignored. In this study, the heat loss is evaluated based on the theory proposed by [3]. Finally, the term in the right hand side expresses an accumulation, and this term means the time derivative of the internal energy of the rock and total fluid. The governing equations, composed of the mass conservation equations for oil and water phases and the energy balance equation, are also discretized by the finite difference method and numerically solved for the primary unknowns of oil phase pressure, water saturation and temperature. Thereby, the reservoir pressure, saturation and temperature distributions can be predicted when the hot water flooding is conducted. 3.2 Constitutive equation for viscosity In addition to the governing equations, constitutive equations are specified to calculate the rock and fluid properties. In this section, the constitutive equation in my simulator is explained because one of the major mechanisms of the thermal recovery process is to reduce the oil viscosity. In the simulator, the viscosities of oil and water phases are calculated based on the Environmental Concerns 59
following equation, which is proposed by R.C. Reid (1977). μ = a, ex p b, T, (4),wherea a, and b vis,α denote first and second empirical parameters. These empirical parameters depend on the type of fluid. For example, the value of these parameters for the water phase is consistent with a, = 5.48 1.47352 (cp) and b, = 1515.7 (K).. The change in viscosity with the temperature variation can be simulated using this equation. Tab. 2 Reservoir oil properties Temp. ( ) Viscosity (cp) Oil C Oil B Oil A 15 35.14 2 15.41 15 351.42 2 154.5 1 15 3.51 2 1.54 4. CASE STUDIES OF THE THERMAL RECOVERY SIMULATOR In order to validate the thermal simulator thus developed, some case studies were conducted. In these case studies, the simple reservoir model with the conditions and properties listed in Table 1 were constructed. Furthermore, three types of oil with different viscosities (Table 2), three different temperatures of injection water and three different well spacing were assumed in these case studies. Tab. 1 Reservoir conditions/properties depth 3 (m) temperature ( ) permeability 3 (md) irreducible water saturation.3 ( - ) density (oil) 966 (kg/m 3 ) density (water) 998 (kg/m 3 ) viscosity (oil) Tab 2. viscosity (water).27 (cp) 4.1 Basic case study The reservoir performances were simulated assuming that the hot water of 2 C was injected into the reservoir containing the Oil A with the constant injection pressure of 45.5 MPa. On the other hand, the fluid production was constrained by the constant flowing pressure of 15.2 MPa. Fig. 2 shows the simulated distributions of temperature and water saturation for different times. Fig. 3 shows the changes in the temperature and oil viscosity predicted for the grid block where the production well is located. The reservoir temperature increases smoothly as times goes while the regional decrease in water saturation (i.e. regional increase in oil saturation) was simulated at the regions around the boundaries between the location where the reservoir temperature is high enough for the oil to move and the locations where the reservoir temperature is still too low for the oil to move. At these regions, the oil saturation becomes higher than the other locations due to the generation of so-called oil bank (i.e. accumulation of movable oil). Fig. 3 indicates the successful transfer of the injected water toward the Environmental Concerns 6
production well and hence the increases in temperature around the production well. The above results seem to suggest that the simulator can appropriately predict the increase in the reservoir temperature and hence the reduction of the oil viscosity along with the hot water injection. Waster saturation.6 25.55 2.5.45 15.4.35.3 5.25.2 5 15 2 25 3 Distance (m) Fig. 2 Sw vs. distance Sw(2days) Sw(4days) Sw(6days) Sw(8days) Sw(days) Temperature(2days) Temperature (4days) Temperature (6days) Temperature (8days) Temperature (days) Temperature ( ) Case 3: well spacing (.5, 1. and 1.5 times longer than that of the base case) Following Figs. 4 through 6 depict the predicted oil production for Cases 1 through 3, respectively. These case studies revealed that oil production increases 1) with increase in the temperature of the injection water, 2) with decrease in original oil viscosity and that the effect of hot water injection is observed earlier as the well distance becomes shorter. Production oil rate (m 3 /d) 2 25 2 15 5 5 15 2 Fig. 4 Oil production rate vs. time in Case 1 Oil A Oil B Oil C Temperature ( ) 2 14 18 12 16 8 14 Reservoir temperature 6 12 Oil Viscosity 4 2 8 5 15 2 Fig. 3 Temperature and oil visicosity at grid#1 4.2 Case studies The following three cases of simulation were performed to investigate the effects of oil properties and the operating conditions on the heavy oil recovery. Case 1: temperature of injection water (, 15, 2 and 25 C) Case 2: reservoir oil (Oil A, B and C) Viscosity (cp) Production oil rate (m 3/ d) 35 3 25 2 15 5 5 15 2 Fig. 5 Oil production rate vs. time in Case 2 Production oil rate (m3/d).5 1 1.5 18 16 14 12 8 6 4 2 2 3 4 Fig. 6 Oil production rate vs. time in Case 3 5. CONCLUSION AND FUTURE WORK Environmental Concerns 61
In this study, a 1-D and 2-phase black oil type simulator was first developed, which was validated through the simulation of the Buckley-Leverett problem. This simulator was then expanded to the thermal simulator incorporating an energy conservation equation as a governing equation. Using this simulator, some case studies were conducted assuming a simple hot water injection into a heavy and viscous oil reservoir, which revealed that 1) oil viscosity decreases and oil bank is generated along with the advancement of hot water. 2) oil production rate and hence oil recovery increase with increase in the temperature of injection water and with decrease in the original oil viscosity. 3) shorter well spacing hasten the effect of hot water injection. The simulator developed in this study can deal with only one-dimensional problem and two-phases of oil and water. We are planning to further improve this simulator so that it can be applied to 2D- and 3Dproblems and can deal with gaseous phase including steam. [4] Usman, Morio Arihara (26), Streamline Simulation of Hot Water Flooding Processes in Heavy Oil Reservoirs: Journal of the Japan Petroleum Institute. [5] Vinit Hansamuit, Jamal H. About-Kassem, S.M.Farouq Ali (199), Heat Loss Calculation in Thermal Simulation: Transport in Porous Media 8: 149-166,1992. [6] Vinsome, P. and Westerveld, J. (198), A Simple Method for Predicting Cap and Base Rock Heat Losses in Thermal Reservoir Simulators. Journal of Canadian Petroleum Technology 19 (3). [7] Zhangxin Chen, Guanren Huan, Yuanle Ma (26), Computational Methods for Multiphase Flows in Porous Media: SIAM Computational Science & Engineering. ACKNOWLEDGMENT The authors would like to express sincere gratitude to the colleague, Mr. Kaito, for his helpful guidance and advice. REFERENCE [1] Computer Modeling Group Ltd., STARS Version 211 User s Guide (211) [2] Craft, B.C., Hawkins, M.F. and Terry (1959), Applied Petroleum Reservoir Engineering: Old Tappan, NJ (USA); Prentice Hall Inc. [3] Prausnitz, J.M. and Poling (1987), The Properties of Gases and Liquids: McGraw Hill Book Co., New York, NY. Environmental Concerns 62