A Model to Estimate Heat Efficiency in Steam-Assisted Gravity

Dec 6, 2016 - On the basis of these studies, abundant analysis shows that the heat efficiency of SAGD can be improved by using moderate steam injectio...
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A Model to Estimate Heat Efficiency in Steam-Assisted Gravity Drainage by Condensate and Initial Water Flow in Oil Sands Dongqi Ji, He Zhong, Mingzhe Dong,* Zhangxin Chen, and Xinfeng Jia Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta T2N 1N4, Canada ABSTRACT: Steam-assisted gravity drainage (SAGD) is one of the most popular approaches for oil sands recovery. In this study, an accurate and simple heat efficiency calculation model is presented by modeling transient heat transfer involving the flow of both hot condensate and mobile initial water in oil sands. A 2-D numerical simulation procedure is proposed to calculate temperature distribution ahead of the steam chamber edge in SAGD. A new heat efficiency model is proposed to estimate heat efficiency in SAGD by using the temperature distribution obtained from the 2-D numerical simulation. Results indicate that convection dominates the heat transfer ahead of the steam chamber edge which is induced by condensate and initial water flow in oil sands. On the basis of these studies, abundant analysis shows that the heat efficiency of SAGD can be improved by using moderate steam injection pressures for the reservoir scenarios from 1 to 10 darcy permeability.

1. INTRODUCTION Over 50% of the global oil reserves are stored in the form of heavy oil and oil sands reservoirs, and Alberta (western Canada) and Eastern Venezuela have the top two largest heavy oil and oil sands deposits in the world.1 The high viscosity and low API of heavy oil and bitumen result in low oil recovery.2 To take advantage of high temperature and gravity drainage, SAGD was proposed as an in situ bitumen recovery method by Butler in 1982. Recently, SAGD has been employed extensively in commercial bitumen recovery operations.3 Typically, SAGD consists of a pair of horizontal wells drilled parallel into the base of a formation.4,5 Steam is introduced into the reservoir through the upper injection well, and a steam chamber is formed at the saturated steam temperature. The heat transfers to the surrounding formations and warms up the bitumen. Under the action of gravity, the heated oil and condensate flow downward to the lower horizontal production well.6 The main cost of SAGD is the extensive use of steam generation, which comes from natural gas combustion. In the total emissions from SAGD, natural gas emissions are the main contributors. 7 Comparison of greenshouse gas (GHG) emissions between SAGD and conventional crude oil recovery processes and surface mining showed that SAGD is a promising technology from both an environmental and economic point of view.8 The definition of heat efficiency is as proposed by Gates and Larter to evaluate the energy and emission intensity in SAGD. In this method, the ratio of the minimum required energy to the total injected energy into a reservoir is therefore used to calculate heat efficiency.9 Their calculation results show that many SAGD operations are not achieving thermally efficient conditions and that more work needs to be done to improve those SAGD operations. Calculations of energy consumption and GHG emissions showed, in consideration © 2016 American Chemical Society

of cogeneration technology and efficiency, the emissions from SAGD could be reduced by 33% to 48%.7 In SAGD, the propagation of condensate at the steam chamber edge usually separates the flow field into two regions: a region occupied by the injected steam (steam chamber), and a region occupied by mobile fluids, including oil, condensate, and initial connate water.10,11 To improve the heat efficiency of SAGD, particular interest is focused on heat transfer ahead of the steam chamber edge, since it directly affects the overall heat distribution by controlling the heat transferred across the edge and stored in the reservoir.10 In the majority of models proposed in the literature, conduction was assumed to be the only heat transfer mechanism to mobilize bitumen ahead of the steam chamber edge.4,12−14 However, a question was raised as to whether heat transfer by convection would be greater than that by conduction in SAGD.15 For most oil sands reservoirs, it is believed that there is a continuous water phase by virtue of the existence of water films surrounding sand grains at native conditions, which separate sand grains and bitumen.16−18 The continuous network of initial water permits water flow through oil sands reservoirs as shown in Figure 1. An experimental method was developed to demonstrate the continuous water phase in oil sands by measuring the effective permeability of initial water in a heavy oil−water−sand system, in which oil is static. Water movement was found to exist with water saturations as low as 0.17 within the pressure difference range of from 0.88 to 0.15 kPa between the inlet and outlet.19 Later, a novel method was proposed to determine effective permeability of initial water in oil sands by Received: Revised: Accepted: Published: 13147

September 14, 2016 December 2, 2016 December 6, 2016 December 6, 2016 DOI: 10.1021/acs.iecr.6b03550 Ind. Eng. Chem. Res. 2016, 55, 13147−13156

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Industrial & Engineering Chemistry Research

water movement on heat transfer and heat efficiency. The relative contributions of thermal convection and conduction to heat transfer are compared, and the impacts on heat efficiency are analyzed. On the basis of these analyses, the model developed herein has the potential to provide methods for significantly improving heat efficiency in SAGD.

2. MODEL DESCRIPTION The numerical simulation model describes a 2-D homogeneous region ahead of the steam chamber edge of a SAGD process, in which heat is transferred laterally and vertically. Figure 2a illustrates a cross-section of SAGD, and Figure 2b illustrates a schematic of the region near the steam chamber edge. As the condensate propagates at the steam chamber edge, the lateral flow of condensate and initial water toward cold oil sands would be induced by the pressure gradient created by the steam pressure being greater than the initial reservoir value. In this model, the target region of thickness, h, is surrounded by permeable oil sands, above and below (which enables liquid flow by gravity drainage), initially saturated with oil (Soi) and water (Swi), and is at initial oil sands temperature (Tini) and pressure (Pini). In SAGD, as shown in Figure 2b, the region near the steam chamber edge is divided into three zones: the steam condensation zone, in which steam condenses upon contacting cold oil sands; the mobile oil zone, located in the vicinity and ahead of the steam chamber edge, containing mobilized oil and water; and the immobile oil zone, far from the chamber edge, which is at initial oil sands conditions.27 It is assumed that the steam chamber is equilibrated at saturation pressure (Pst) and temperature (Tst), and that the chamber edge (a condensation front) propagates toward the cold oil sands reservoir (downstream, at the right side of this region). Ahead of the steam chamber edge, a varying temperature zone is formed with hot liquids flowing in the lateral (x) direction. The mass conservation equation for each phase (oil and water) is provided by

Figure 1. Illustration of water film and continuous initial water in oil sands of bitumen, water, and sand matrix.

using wax in place of bitumen. The experimental analysis demonstrated the existence of mobile initial water when the water saturation is as low as 5%.20,21 This flow phenomenon has also been demonstrated by field data from the Underground Test Facility (UTF) SAGD pilot conducted in 1987.22,23 In this pilot, water was injected into the well pair before steam injection, and the movement of water was confirmed by examining the pressures of observation wells. In a SAGD process, water moves ahead of the steam chamber edge to places farther downstream once there is a pressure gradient. Although the bitumen is mobile at the high temperature in the area just ahead of the steam chamber edge, the bitumen only flows nearly parallel with the isothermals, rather than to cold oil sands,24 where bitumen has extremely low mobility due to its significantly high viscosity. Water flow in oil sands reservoirs is assumed to be a single phase flow through the matrix, composed of sand grains and solid-like bitumen.25 Thus, enhancing heat transfer ahead of the steam chamber edge to cold oil sands in SAGD by moving hot water (condensate and initial water), which is seldom studied, is a possible and viable way to optimize steam, and therefore energy, use. The effect of initial water movement on SAGD performance has been investigated before through the modeling of different initial water saturations by using a simulator, CMG.26 Closed boundaries that are popularly used in commercial simulators would stop the initial water movement in a reservoir, and a substantial reservoir extension will largely increase computation time because of the addition of more grids. In this study, a more accurate and simple numerical modeling is provided to simulate condensate and initial water movement in the vicinity of steam chamber edge in SAGD. In the numerical model, a moving steam chamber edge, timedependent heat transfer, and open reservoir boundaries are presented. A fine grid system is used to capture the effect of

−

∂ ∂ ∂ (ρ Vi , x) − (ρ Vi , z) = (ϕρi Si) ∂x i ∂z i ∂t

(1)

where ρi is the density of phase i, Vi,x and Vi,z are the flow velocities of phase i in the lateral (x) and vertical (z) directions, respectively, ϕ is the porosity, Si represents the saturation, and the subscript i refers to the two phases (oil and water). The energy balance equation involves conduction and convection in both the lateral (x) and vertical (z) directions, which can be expressed as

Figure 2. Illustration of SAGD steam chamber edge: (a) a cross-section of SAGD and location of the steam chamber edge, and (b) a schematic of a 2-D model of the steam condensation, mobile oil, and immobile oil zones in the vicinity of the steam chamber edge. 13148

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Industrial & Engineering Chemistry Research ⎛ ∂ 2T ⎞ ⎛ ∂ 2T ⎞ ∂ ∂ K⎜ 2 ⎟ + K⎜ 2 ⎟ − [∑ ρ Vi , xCiT ] − [∑ ρ Vi , zCiT ] ∂z i i ⎝ ∂x ⎠ ⎝ ∂z ⎠ ∂x i i ∂ = [∑ ϕρi SiCiT + (1 − ϕ)ρR CRT ] ∂t i

Vw, ξ = −

Vw, z =

(2)

where K is the thermal conductivity of the oil sands, T is the temperature, Ci is the heat capacity of each phase (oil and water), and ρR and CR are the density and heat capacity of the oil sands matrix, respectively. For the simulation of fluid flow and heat transfer ahead of the steam chamber edge in SAGD, the reference distance from the moving steam chamber edge ξ is used, rather than a fixed location. The chamber edge is assumed to progress at a constant velocity Ux.10 The new variable ξ is defined as4,10,25,28 ξ=x−

∫0

Vo, z =

According to eq 3, the first and second order derivatives, such as temperature, can be replaced with ξ, such that (4)

⎛ ∂ 2T ⎞ ⎛ ∂ 2T ⎞ ⎜ 2⎟ = ⎜ 2⎟ ⎝ ∂x ⎠ ⎝ ∂ξ ⎠

(5)

⎛ ∂T ⎞ ⎛ ∂T ⎞ dξ ⎛ ∂T ⎞ ⎛ ∂T ⎞ ⎛ ∂T ⎞ dt ⎜ ⎟ = ⎜ ⎟ +⎜ ⎟ = ⎜ ⎟ − Ux⎜ ⎟ ⎝ ∂t ⎠ξ ⎝ ∂t ⎠x ⎝ ∂t ⎠ξ dt ⎝ ∂ξ ⎠t ⎝ ∂ξ ⎠t dt

⎛∂ T ⎞ ⎛∂ T ⎞ ∂ ∂ K⎜ 2 ⎟ + K⎜ 2 ⎟ − [∑ ρi Vi , ξCiT ] − [∑ ρ Vi , zCiT ] ξ ∂ ∂ z i i ⎝ ∂ξ ⎠ ⎝ ∂z ⎠ i 2

(14)

ln[ln(μo )] = 22.8515 − 3.5784 ln(T + 273.15)

∂ = [∑ ϕρi SiCiT + (1 − ϕ)ρR C R T ] ∂t i

(15)

(16)

and: ⎛ 1 1 ⎞ ⎟ log(μw ) = 658.28⎜ − ⎝ T + 273.15 283.16 ⎠

(8)

(17)

The sensitivity of porosity to pore pressure is modeled by29,30

The fluid velocity in the mass and energy equations is calculated by Darcy’s law, which is expressed as kk ri (∇Pi − ρi g∇Zi) μi

(13)

where αi and βi are the corresponding thermal expansion coefficient and compressibility of each phase, respectively, with the reference density ρi,ref at the reference temperature (TR) and pressure (PR). Oil and water viscosity (cp) depend on temperature T(°C) by the correlations:4

(7)

Vi = −

kzk roz (ρo g ) μo

ρi = ρi ,ref [1 + αi(P − PR ) − βi (T − TR )]

∂ ∂ ∂ ∂ − (ρi Vi , ξ) − (ρi Vi , z) = (ϕρi Si) − Ux (ϕρi Si) ∂ξ ∂z ∂t ∂ξ

∂ [∑ ϕρi SiCiT + (1 − ϕ)ρR C R T ] ∂ξ i

(12)

The densities of oil and water rely on pressure and temperature:29,30

Since this is only for the lateral displacement, the vertical coordinate remains the same. New mass (eq 7) and energy (eq 8) equations can be pursued as below:

− Ux

(11)

Sw + So = 1

(6)

2

kzk rwz (ρw g ) μw

where Vw,ξ and Vw,z are the water flow velocities in the lateral and vertical directions, respectively, and Vo,ξ and Vo,z are the oil flow velocities in the lateral and vertical directions, respectively. kξ and kz are the oil sands absolute permeability in the lateral and vertical directions, respectively, krwξ and krwz are the water relative permeabilities in the lateral and vertical directions, respectively, and kroz is the oil relative permeability in the vertical direction. Since heat transfers far into the cold oil sands, which is assumed to be infinity. Applying this assumption, the average water phase permeability in the lateral direction can be estimated as the value of the water effective permeability in the cold oil sands.19,20 Auxiliary equations are added to decrease variables in eqs 7 and 8, and are summarized in eqs 14−21. The constraint of phase saturations is

(3)

⎛ ∂T ⎞ ⎛ ∂T ⎞ ⎜ ⎟ = ⎜ ⎟ ⎝ ∂x ⎠ ⎝ ∂ξ ⎠

(10)

Vo, ξ = 0

t

Ux dt = x − Uxt

kξk rwξ ⎛ ∂Pw ⎞ ⎜ ⎟ μw ⎝ ∂ξ ⎠

ϕ = ϕref [1 + c(P − PR )]

(18)

where c is the compressibility of oil sands, and ϕref is the reference porosity at the reference pressure (PR). For the two-phase flow by gravity drainage in the vertical direction, correlations of oil−water relative permeabilities at high temperatures are used:31

(9)

where k is the permeability, kri is the relative permeability of phase i, μi is the viscosity of phase i, Pi is pressure of phase i, g is the acceleration due to gravity, and Zi is the gravity drainage height. At initial oil sands reservoir conditions, effective permeability of water has been determined by experimental models.20,21 In this numerical model, oil and water flow can occur in the vertical direction, but only water can also flow laterally, as long as there is a pressure difference. Thus, eq 9 describing oil and water flow in both directions can be revised and expanded as follows:

k rwz = 0.055(1 − SN )2.5

(19)

k roz = (SN )3

(20)

SN =

0.85 − Sw 0.7

(21)

Due to the injection of steam into oil sands reservoirs, capillary pressure decreases with increasing temperature, as reported by 13149

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Industrial & Engineering Chemistry Research experiments conducted at temperatures ranging from 120 to 180 °C.24 For the practical simulation of SAGD, it is acceptable to neglect capillary pressure, especially for high flow rate conditions induced by gravity drainage.32−35 Thus, the pressure of the water phase (Pw) is equal to the pressure of the oil phase (Po) in this model. Furthermore, constant thermal conductivity of the oil sands is assumed, since the amount of convective heat flow is significantly greater than the conductive heat flow for a forced convection dominant heat transfer process.14,36 In Table 1, the characteristics of the modeled oil sands reservoir are summarized, representing Phase B at the Underground Test Facility (UTF).23,37 Table 1. Characteristics of the Modelled Oil Sands Reservoir, (Including Initial and Boundary Conditions) (Phase B at the UTF) items mobile oil zone length, Lm, m mobile oil zone thickness, h, m initial temperature, Ti, °C initial pressure, Pi, Pa steam temperature at steam chamber edge, Tst, °C steam pressure at steam chamber edge, Pst, Pa initial water saturation, Swi, fraction water saturation at steam chamber edge, Swst, fraction vertical permeability, kz, md horizontal absolute permeability, kξ, darcy horizontal water relative permeability, krwξ water heat capacity, Cw, kJ/(kg·°C) oil heat capacity, Co, kJ/(kg·°C) sand matrix heat capacity, CR, kJ/(kg·°C) oil sands thermal conductivity, K, W/(m·°C) sand density, ρR, kg/m3 reference water density, ρw,ref, kg/m3 reference oil density, ρo,ref, kg/m3 reference porosity, ϕref, fraction reference temperature, TR, °C reference pressure, PR, Pa water thermal expansion coefficient, βw, 1/°C oil thermal expansion coefficient, βo, 1/°C water compressibility, αw, 1/Pa oil compressibility, αw, 1/Pa oil sands compressibility, c, 1/Pa gravitational acceleration, g, m/s2 steam chamber moving velocity, Ux, m/s

Figure 3. Neighbors of grid (i,j).

4,20,23,24,38

value

40 1 10 1470 × 103 205 1740 × 103 0.2 0.5 2.4 × 103 6 0.0022 4.2 1.8 0.8 1.45 2400 1000 1050 0.33 1 0.1 × 10−5 0.207 × 10−3 0.72 × 10−3 4.58 × 10−10 1.5 × 10−10 1.0 × 10−9 9.8 1.70 cm/day

f in++1,1j − f in−+1,1j ∂f ≈ ∂ξ 2Δξ

(22)

f in, j++11 − f in, j+−11 ∂f ≈ ∂z 2Δz

(23)

∂ ⎛ ∂f ⎞ ⎜Ts ⎟ ∂ξ ⎝ ∂ξ ⎠ ≈

1 n+1 n+1 n+1 n+1 Tin++1/2, − f in−+1,1j ) j(f i + 1, j − f i , j ) − Ti − 1/2, j(f i , j

Δξ 2 (24)

The upstream principal is applied to the approximated transmissibility Tn+1 i ± 1/2,j in eq 24. The discretization in time is approximated as f in, j+ 1 − f in, j ∂f ≈ ∂t Δt

(25)

The Newton−Raphson iteration is implemented to solve the nonlinear equations. All properties are initialized at reservoir conditions of the oil sands: pressure (Pini), temperature (Tini), and water saturation (Swi).To represent the mobile water in an oil sands reservoir, open boundaries are used in this 2-D model to allow fluid to leave the domain and ensure global mass conservation.39 Thus, at the external boundaries, a Neumann condition is imposed, which implies that pressure on the boundary remains constant for liquid inflow and outflow. At the steam chamber edge, the pressure is consistent with the injected steam pressure (Pst), temperature (Tst), and water saturation (Swst), while the pressure at the far side of the oil sands reservoir remains at the initial reservoir pressure (Pini), temperature (Tini), and water saturation (Swi).40 The process is simulated step by step (v) with Newton− Raphson iterations, which are terminated when the changes between two continuous iteration steps are less than the given limitations of pressure, temperature, and water saturation: TOLP, TOLT, and TOLSw, respectively:

After obtaining the main governing and auxiliary equations, the following three principal unknowns are selected: pressure (P), temperature (T), and water saturation (Sw). The heat transfer ahead of the steam chamber edge, and its effect on heat efficiency in SAGD, can be simulated fully implicit by solving the discretized linear system using a finite difference method.

3. SOLUTION METHOD The fully implicit method is used as an approach to deal with the transient discretization, as it is more stable than explicit methods.29 The region is divided into a sample grid, with a single grid size being Δx × Δz. Figure 3 demonstrates the connectivity of the grid (i, j). The first and second order spatial derivatives are approximated by a central differential: 13150

max|Piv, j+ 1 − Piv, j| ≤ TOLP

(26)

max|Tiv, j+ 1 − Tiv, j| ≤ TOLT

(27)

max|Swiv +, j1 − Swiv , j| ≤ TOLSw

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the locations ahead of the steam chamber edge. The outstanding performance of the numerical model used in this research demonstrates its successful application for heat transfer approximation in SAGD. Since the assumptions included in this numerical model simplify reality, more confirmations are necessary to validate the assembled simulation model. This validation process includes a sensitivity analysis with respect to grid refinement (closely related to the effect of numerical diffusion) and moving velocity of the steam chamber edge (may significantly affect temperature profiles ahead of the steam chamber edge). To achieve a sufficiently accurate grid refinement to be used in heat transfer modeling, the curves of temperature distributions, at the same time (3.05 days), are plotted in Figure 5a, with varying grid sizes of 0.03, 0.04, 0.05, and 0.10 m. The simulated temperature curves ahead of the steam chamber edge converge as the grid size is reduced, especially for the nearly zero difference between the curves of 0.03 and 0.04 m. Thus, the effect of numerical diffusion on heat transfer with grid sizes below 0.04 m can be neglected. That is, the extreme similarity in temperature profiles confirms the validation of 0.04 m grid size (Δx × Δz = 0.04 × 0.04) as sufficiently refined for simulating the forced convective heat transfer process in SAGD. Due to possible changes in the moving velocity of the steam chamber edge, under various oil sands reservoir properties and operating parameters, the effect of steam chamber edge velocity on heat transfer is evaluated through modifying the reference velocity (1.70 cm/d)24,27,35 by 1.2 times (2.04 cm/d) and 1/1.2 times (1.42 cm/d). Since the steam chamber moving velocity is assumed to be essentially constant or very slowly varying,10 this range of velocity modification is reasonably large in terms of representing the velocity change in SAGD. Figure 5b plots the temperature profile of these three steam chamber edge moving velocities at the time of 3.05 days. Although some difference is seen among the temperature profiles of these three cases, the difference is deemed to be too small to adversely impact the accuracy of the heat transfer modeling in this study. Thus, the real value of 1.70 cm/d is used reliably in this study. In addition, the effect of water and mobile oil vertical flow (along the steam chamber edge) on lateral heat transfer is analyzed by changing the vertical permeability. It was found that the results are consistent with the report by Irani and Gates of little effect on lateral heat transfer,28 so this impact can also be neglected. 4.2. Mechanism of Heat Transfer ahead of a Steam Chamber Edge. The heat transfer model coupling thermal conduction and convection in this study is compared to the

Tolerances of TOLSw = 0.005, TOLP = 500 Pa and TOLT = 0.5 °C were applied, resulting in an accurate and fast calculation.30

4. RESULTS AND DISCUSSION In this part, the assembled simulation model is first validated by comparing the temperature profile with the field data obtained by Birrell from an observation well,41 and then the heat transfer mechanisms and potentials for heat efficiency improvements, based on heat efficiency calculations, are discussed. 4.1. Model Validation. The temperature profile in the lateral direction as shown in Figure 4 obtained from this

Figure 4. Comparisons between field data from UTF and simulation results of temperature (lateral direction) versus distance from steam chamber edge at 3.05 days.

numerical model has been compared with field data25,41 to verify the accuracy of our simulation model, before using it to predict heat transfer ahead of a steam chamber edge in SAGD. The referenced Dover Phase B SAGD pilot operated at the UTF operated by Devon Canada is the longest running and best documented SAGD pattern.41 In this pilot, thermocouples were installed in 29 observation wells to measure the temperature along the direction in which the steam chamber progressed. The temperature in the lateral direction of the 2-D numerical model in this study is obtained, as plotted in Figure 4, to map the time-dependent heat transfer, with the characteristics of the numerical model, as previously noted representing Phase B at the UTF, summarized in Table 1. By varying the simulation time, the temperature profile at the time of 3.05 days is found to be in excellent agreement with the data from the field along

Figure 5. Model validation with variations in grid size and chamber edge moving velocity: (a) Temperature (lateral direction) profiles at time of 3.05 days. Grid sizes studied include 0.03, 0.04, 0.05, and 0.10 m. (b) Temperature (lateral direction) profiles of three different steam chamber edge moving velocities studied at the time of 3.05 days. The reference steam chamber moving velocity is 1.7 cm/d.25,28 13151

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Figure 6. Analysis of heat transfer ahead of the steam chamber edge (lateral direction) at 3.05 days: (a) temperature versus distance ahead of the steam chamber edge of this numerical model and Butler’s conduction model; (b) pressure versus distance ahead of the steam chamber edge of this numerical model; (c) water flow velocity versus distance ahead of the steam chamber edge of this numerical model; (d) convective and conductive heat flux versus distance ahead of the steam chamber edge of this numerical model.

much closer to the steam chamber edge, at around 11 m. This deviation is caused by continuous movement of cooled down water further into the oil sands, from 11 to 21 m, without transferring apparent heat or increasing the temperature. The relative roles of convective and conductive heat transfer ahead of the steam chamber edge are compared in Figure 6d, by heat flux calculations, as expressed in eqs 31 and 32, respectively:24,28

analytical model with the assumption of only conduction as proposed by Butler.4 The fluids and reservoir properties remain the same in the representation of Phase B at the UTF (Table 1). The two curves of temperature versus distance for the two models are shown in Figure 6a. The apparently higher temperature of the forced convection process (simulation results in this study) than that of the conductive only process (Butler’s model) reveals that significantly more heat can be transferred to cold oil sands through thermal convection for the entire region ahead of the steam chamber edge, which is, unfortunately, omitted by improper assumptions in most previous studies. By confirming that 80 °C is sufficient for oil mobilization,42 the mobile oil zone in the range from the steam chamber edge to the location of 80 °C is significantly enlarged from 2.3 m (Butler’s model) to 4.3 m (simulation results in this study), demonstrating the significant contribution of heat convection. Correspondingly, the oil flow rate to the production well is also greatly enhanced. The profiles of the corresponding pressure and water flow velocity from the steam chamber edge to the cold oil sands are plotted in Figure 6 panels b and c, respectively. The pressure decreases rapidly in the first 21 m ahead of the steam chamber edge, which creates the high potential for propagated hot condensate and initial water to flow toward the cold oil sands, in the lateral direction. The pressure gradient becomes zero by pressure relief to the oil sands, until an equilibrium condition is reached where water is static. As the high pressure steam touches the cold oil sands, the condensate is pushed ahead of the steam chamber edge and moves with the initial water to deliver heat to the cold oil sands. The water flow velocity is fast in the vicinity of the steam chamber edge, and slows down gradually in the direction of the cold reservoir. Water flow can be found far from the steam chamber edge, at around 21 m, whereas the elevated temperature compared to initial reservoir temperature is

Q convection = Vw, ξCwρw (T − Ti ) Q conduction = −K

∂T ∂ξ

(29)

(30)

From these results, it is clearly found that convective heat transfer, which is several tens of times greater than that of conductive heat transfer, is the dominant heat transfer mechanism through the region ahead of the steam chamber edge in SAGD. In the lateral direction, toward the cold oil sands, convective heat flux decreases as the liquid flow velocity gradually slows down. Referring again to the temperature profile of this model in Figure 6a, at around 11 m, this flux approaches zero. For capturing the heat transfer enhancement observed in Phase B at the UTF, the convective process must be utilized in any reasonable simulation, since the convective process provides the possibility of improving heat transfer by stimulating water flow capacity and enlarging the pressure gradient. Conversely, it is impossible to largely increase the effectiveness of a conductive process by somehow (and unreasonably) increasing the temperature gradient, changing the thermal conductivity of the oil sands, or enlarging the steam chamber surface area.25 Another light shed on the understanding of heat transfer ahead of the moving steam chamber edge is the timedependent prediction method used in this study. In most 13152

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Figure 7. Effect of initial water saturation on heat transfer, oil mobility, and heat efficiency: (a) temperature (lateral direction) versus distance ahead of the steam chamber edge of the cases with initial water saturations from 0.10 to 0.30; (b) oil mobility (vertical direction by gravity drainage) versus distance ahead of the steam chamber edge with initial water saturations from 0.10 to 0.30; (c) heat efficiency of the cases with initial water saturations from 0.10 to 0.30.

chamber, and energy returned as sensible heat within the produced bitumen and water.42 In this study, we use only the returned energy to approximate the total energy injected. The returned energy (Qreturned) can be estimated by the sensible heat stored within the mobile oil and water in the mobile oil zone, which are flowing downward to the production well. Thus, the returned energy can be estimated by the heat summation of oil and water flowing in the mobile oil zone:

analyses of heat transfer, a steady state solution is assumed to be accurate enough to represent the temperature profile. Unfortunately, with the moving steam chamber edge and varying properties of the fluid and matrix, the heat flow predicted by a steady state solution cannot be transferred as far as the conditions assumed at time infinity. The finding of timedependent heat transfer across a moving steam chamber edge would be a more accurate tool to calculate energy distribution in SAGD, whose cost is strongly dependent on heat efficiency performance. 4.3. Heat Efficiency Calculation. In this section, the heat efficiency, which is the ratio of the theoretical minimum amount of energy required to the total energy injected into the reservoir,11 is calculated. The minimum amount of energy is the heat required to raise the temperature of bitumen from the initial reservoir temperature (Tini) to the ideal temperature (Tideal), which is defined as the lowest temperature required to mobilize bitumen. In the process of heating oil in the reservoir, not only is the oil heated up, but also the existing water and solid matrix. In SAGD, the energy is transferred ahead of the steam chamber edge to the mobile oil zone. In this zone, the energy used to raise reservoir temperature from the initial temperature (Tini) to the ideal temperature (Tideal), such as 80 °C,42 can be estimated as the minimum required energy (Qmin) by the following expression:9

Q returned = [ϕSoρo Co + ϕSwρw Cw ](T − Tini)BV

On the basis of the heat distribution in Phase B at the UTF, which is a five-year SAGD operation, about one-third of the injected heat returned as sensible heat in the produced oil and water.43 The total amount of energy injected (Qtotal) can be estimated by the division of returned energy to the fraction of returned energy in the total injected energy:

Q total =

Q returned ηchamber

(33)

where ηchamber is the fraction of heat returned in the total heat injected. The fraction of returned energy (ηchamber) is estimated at 0.331 of the total energy injected into the reservoir, calculated based on the SAGD energy distribution of Phase B at the UTF.43 The definition of the calculation of SAGD heat efficiency (ηheat), used by Gates and Larter,9 is the ratio of minimum required energy to make oil flow to the total energy injected into the reservoir, and is also used here to represent heat efficiency:

Q min = [ϕ(1 − Swc)ρo Co + ϕSwcρw Cw + (1 − ϕ)ρR C R ] (Tideal − Tini)BV

(32)

(31)

where BV is the bulk volume of the mobile oil zone ahead of the steam chamber edge. The total amount of energy injected (Qtotal) into the oil sands includes the energy remaining within the steam chamber, energy dissipated into the reservoir surrounding the steam

ηheat = 13153

Q min Q total

(34) DOI: 10.1021/acs.iecr.6b03550 Ind. Eng. Chem. Res. 2016, 55, 13147−13156

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Industrial & Engineering Chemistry Research

Figure 8. Heat efficiency analysis by changing absolute permeability: (a) temperature (lateral direction) versus distance ahead of the steam chamber edge of the cases with absolute permeability ranging from 1 to 10 darcy; (b) heat efficiency of the cases with absolute permeability ranging from 1 to 10 darcy.

4.4. Effect of Initial Water Saturation on Heat Transfer, Oil Mobility, and Heat Efficiency. The mobile water can strongly affect SAGD performance, such as cumulative oil production. In oil sands, the increase of effective water permeability in oil sands with an increase of the initial water saturation has been observed and confirmed by experiments. Under high initial water saturation, a thick continuous water film can be established with a large amount of water, and this film enables the fast flow of water through the oil sands. On the contrary, low initial water saturation attenuates the water film formed in the pore/throat margins and decreases effective water permeability.20,21 This relationship of water effective permeability and initial water saturation is established in the following equation: k w, ξ

⎛ Sw − Swir ⎞1.950 = [kξk rwξ(Sw = 0.4)]·⎜ ⎟ ⎝ 0.400 − Swir ⎠

water saturation resulting from much steam condensation at the steam chamber edge). In the downstream region ahead of the steam chamber edge, the oil mobility increases gradually, first as a result of increased oil phase relative permeability (decrease in water saturation). However, because of the decrease in temperature ahead of the steam chamber edge, which results in an increase in oil viscosity, there is a peak of oil phase mobility. With the increase of initial water saturation from 0.10 to 0.30, the value of oil mobility peak lessens and the peak points move farther downstream from the steam chamber edge. Although high initial water saturation enables a large amount of heat to be transferred to the cold oil sands, it also impairs oil flow velocity in the reservoir as a result of reduced oil saturation in the oil sands. The curve in Figure 7c is used to evaluate the effect of initial water saturation on SAGD heat efficiency. The plot shows that the efficiency increases almost linearly with an increase in initial water saturation from 0.115 to 0.148, with a tapering off of efficiency to a plateau as water saturation increases to 0.30. The thickness of the mobile oil zone is enlarged (from 3.00 to 5.60 m) together with an increased amount of mobilized oil. On the basis of the simulation results, a balance of the oil flow velocity and the heat efficiency needs to be achieved in SAGD applications. 4.5. Effect of Oil Sands Absolute Permeability on Heat Transfer and Heat Efficiency. To investigate the impacts of oil sands absolute permeability on SAGD performance, more heat efficiency calculations are required. According to the findings from experiments conducted by Zhou et al.,21 effective water permeability increases with an increase in the absolute permeability of oil sands, at the same initial water saturation.20,21 The generally high absolute permeability of oil sands implies a large average pore throat radius, and results in a highly permeable water network within the oil sands. Figure 8a depicts the temperature profiles ahead of the steam chamber edge for cases with absolute permeability ranging from 1 to 10 darcy, which has been regressed and extended from experimental results.20,21 For this analysis, the injected steam pressure and temperature are kept consistent with the values in Table 1. It is noted that, by increasing absolute permeability from 1 to 10 darcy, heat is delivered further ahead of the steam chamber as a result of the elevated temperature profiles, in which the mobile oil zone is enlarged from 3.15 to 4.75 m. However, the magnitude of increase in temperature profile is not as significant as might be expected considering the several times change in absolute

(35)

where krwξ(Sw = 0.4) is the water relative permeability at a water saturation of 0.4. The effect of initial water saturation on heat transfer and heat efficiency is also analyzed. The reservoir properties, as well as injected steam pressure and temperature are kept consistent with the values in Tables 1. On the basis of the simulation results, the temperature versus distance profiles ahead of a steam chamber edge, with varying initial water saturations in the range of from 0.10 to 0.30, are plotted in Figure 7a. Heat transfer analysis reveals that the initial water saturation has the dominant effect on the temperature profile, in which the temperature level rises with an increase in initial water saturation. With a high initial water saturation, the increased water effective permeability results in a large amount of water flow in the oil sands, resulting in much heat being transferred to cold oil sands and an improved heat efficiency. In SAGD, the flowing of heated oil to the lower production well is driven by gravity drainage. The effect of initial water saturation is critical to oil mobility because the water saturation would largely change oil phase relative permeability (a function of oil saturation) and oil viscosity (a function of temperature). In Figure 7b, the curves of oil phase mobility flowing by gravity drainage versus the distance from the steam chamber edge are plotted. Five reservoir scenarios of initial water saturations, including 0.10, 0.15, 0.20, 0.25, and 0.30, are compared. For example, in the reservoir with initial water saturation of 0.20, the oil phase mobility is relatively low at the steam chamber edge due to the relatively low oil saturation (because of high 13154

DOI: 10.1021/acs.iecr.6b03550 Ind. Eng. Chem. Res. 2016, 55, 13147−13156

Article

Industrial & Engineering Chemistry Research

transferred because of weak convection, resulting in a small mobile oil zone for oil flow and in much of the heat contained in condensate being recycled to the surface without being used for heating bitumen. These effects greatly impair heat efficiency. On the other hand, relatively high values of steam pressure and temperature also impair the heat efficiency (ηheat), as there is an excess of heat being used to raise the temperature of the oil sands above the minimum requirement. In addition, with a high steam temperature, heat loss increases considerably, which is driven by the temperature difference between the steam and the surrounding formations.10 For the reservoir scenario of 1 darcy and 0.10 initial water saturation, the maximum heat efficiency achieved is about 0.100 at a steam pressure of around 2300 kPa, and the scenario of 10 darcy and 0.30 initial water saturation raises the maximum heat efficiency to the highest value simulated of about 0.160 at a steam pressure of around 1600 kPa. Thus, high reservoir permeability and high initial water saturation can enable increased heat efficiencies with lowered steam pressure requirements.

permeability. The derived analytical solution of pressure gradient distribution in forced convective flow (eq 36) describes single phase flow in oil sands, and can be used to explain this phenomenon:23 ⎛ ϕμ c ⎞ ϕμ cUx(Pst − Pini) ∂P =− w exp⎜ − w Uxξ⎟ + Pini ∂ξ k w, ̅ ξ ⎝ kk rw ⎠

(36)

Since the pressure gradient ahead of the steam chamber edge is inversely proportional to the absolute permeability, the increase in permeability adversely decreases the pressure gradient, and decreases the potential for water flow to transfer heat. In addition, as shown in Figure 8b, the heat efficiency is estimated and compared. The large heat efficiency (ηheat) jump (from 0.037 to 0.065) from a conduction only model without mobile water to the model described herein of 1 darcy, with mobile water, confirms the capability of mobile water to enhance heat efficiency. With the increase in permeability (from 1 to 10 darcy), the additional energy that is delivered to heat up the cold oil sands is associated with the improvement in heat efficiency from 0.065 to 0.153. Thus, with generally high permeability oil sands, SAGD heat efficiency can be improved through the mechanism of more heat being transferred ahead of the steam chamber without being drained and produced directly with liquids through the production well or losses to the overburden and underburden. 4.6. Effect of Steam Pressure on Heat Efficiency. Since steam injection pressure is a critical operating parameter in the process of SAGD, the effect of pressure on the heat efficiency performance is analyzed, and the heat efficiency comparisons are shown in Figure 9. In this analysis, reservoir scenarios are

5. CONCLUSIONS A heat efficiency calculation model of SAGD process has been proposed by the consideration of mobile initial water in oil sands. First, a new 2-D numerical simulation procedure is proposed to investigate heat transfer ahead of the steam chamber edge in SAGD. Because of the mobile initial water in oil sands, hot condensate can be forced, together with the initial water, to penetrate into the cold oil sands beyond the SAGD chamber. Second, the heat efficiency of SAGD is calculated according to the temperature distribution in oil sands, which is from the 2-D numerical simulation procedure. Finally, the impacts of reservoir properties and operation parameters on heat efficiency in SAGD are analyzed by using the proposed heat efficiency model. Heat efficiencies of the SAGD process are analyzed by varying initial water saturation, absolute permeability, and steam pressure. The results show that heat transfer in SAGD is significantly enhanced by the convective water flow ahead of steam chamber edge. Heat efficiency of SAGD can be improved by generally high permeabilities and initial water saturations. There exists an optimal steam pressure for having the highest heat efficiency of a SAGD process. The proposed heat efficiency calculation model can be used to screen field operation parameters for reducing the cost of SAGD operations.

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Figure 9. Heat efficiency analyses by changing steam injection pressure from 1500 to 5000 kPa, with four reservoir scenarios included: 1 darcy absolute permeability with 0.10 initial water saturation, 5 darcy absolute permeability with 0.15 initial water saturation, 6 darcy absolute permeability with 0.20 initial water saturation, and 10 darcy absolute permeability with 0.30 initial water saturation.

AUTHOR INFORMATION

Corresponding Author

*Tel: +1 403 210 7642. Fax: +1 403 284 4852. E-mail: [email protected]. ORCID

Dongqi Ji: 0000-0002-5288-9695 Notes

The authors declare no competing financial interest.

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studied of laterally absolute permeability ranging from 1 to 10 darcy together with initial water saturation ranging from 0.10 to 0.30. Other reservoir properties are consistent with the values in Table 1. The heat efficiency calculated is an indicator of achieving a preferred steam injection pressure, since this efficiency would not necessarily be consistent with an increase in pressure. For example, the reservoir scenario with absolute permeability of 6 darcy and initial water saturation of 0.20 shown in Figure 9 results in relatively low injection pressures. This results in a relatively small amount of heat being

ACKNOWLEDGMENTS The support of the Department of Chemical and Petroleum Engineering, University of Calgary, and the Reservoir Simulation Research Group are gratefully acknowledged. The research is partly supported by NSERC/AIEES/Foundation CMG, AITF iCore, IBM Thomas J. Watson Research Center, and the Frank and Sarah Meyer FCMG Collaboration Centre for Visualization and Simulation. The research is also enabled in 13155

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part by support provided by WestGrid (www.westgrid.ca) and Compute Canada (www.computecanada.ca).

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DOI: 10.1021/acs.iecr.6b03550 Ind. Eng. Chem. Res. 2016, 55, 13147−13156