# Application of Temperature Fall-Off Interpretation Method in Superheavy Oil or Oil Sand SAGD Process

Authors: Guangyue Liang; Qian Xie; Shangqi Liu
Journal: Geofluids
 (2022)

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## Abstract

SAGD technology has been successfully and widely applied in the development of superheavy oil and oil sand projects. Before normal SAGD process, some preheating ways are often needed to realize interwell hydraulic connection, and this means that determining reasonable SAGD conversion timing from the preheating stage is an essential precondition for good performance. Previous numerical simulations or qualitative analysis of temperature fall-off data are often adopted in the industry, but they have deficiencies in terms of dependent on static geological model or insufficient data utilization. Therefore, on the basis of the temperature and pressure monitoring process comparison in China’s superheavy oil and Canada’s oil sand projects, this paper proposed a temperature fall-off interpretation model to obtain thermal diffusivity and preheating radius at different measurement points along the horizontal section by combining an unsteady thermal conduction model under constant heating power of wellbores in the radial coordinate system and approximately unsteady thermal conduction model with constant wellbore temperature and Fourier’s law of thermal conduction. Besides, the duration time, interpretation method, and application flow chart of temperature fall-off test were presented. Then, it was validated to successfully determine the timing of SAGD conversion from the preheating stage by an example combining with tracking numerical simulation, temperature inflection point analysis, and index analysis during the partial-SAGD and initial SAGD stages. The findings of this study can help determine the SAGD conversion timing from the preheating stage simpler and faster especially for the case of long horizontal well section deployed with more temperature measurement points.


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## Body

## 1. Introduction

Steam-assisted gravity drainage (SAGD) technology has been commonly applied in developing superheavy oil or oil sand projects. It usually drills dual horizontal wells near the bottom of the reservoir, with vertical well spacing of 5 to 10 meters between the injector and the producer. The basic principle of this technology is that steam injects into the upper horizontal well and moves upward and laterally to heat the reservoir by combination of thermal conduction and thermal convection, and then, the heated oil drainages to the lower producer under the gravity [1].For superheavy oil or oil sand SAGD projects, the preheating stage is usually indispensable to form interwell hydraulic connection or mobile oil before conversion to the normal SAGD process [2]. The preheating ways usually include steam circulation, steam bullheading, and steam stimulation [3–5]. Affected by strong reservoir heterogeneity, shale interlayers or laminae, thief zones (e.g., bottom water, top water, and gas cap), and undulating well trajectory, there are great differences in both preheating time (usually 3-6 months) and steam consumption (usually 25,000-50,000 m3) among different well pairs [6]. If the well pair transfers to the normal SAGD process too late, it will cause more steam waste. Otherwise, it even needs retransfer to preheating stage after SAGD conversion due to poor steam conformance [7]. Therefore, it is of great significance to ensure good SAGD performance by accurately judging the SAGD conversion timing.Many scholars conducted a numerical simulation study on accelerating steam circulation preheating process through electric heating, discretized wellbore, or flexible wellbore models, and the related strategy or parameters include reasonable steam injection rate allocation, timing and size of enforcing pressure difference, and duration time [8–13]. Especially, two researchers conducted history matching of the steam circulation stage [8, 13]. Parmar et al. [8] carried out history matching of steam circulation preheating and subsequent sensitivity analysis of its influencing parameters in MacKay River project by combing CMG and QFlow software. Similarly, Ayala and Gates [13] conducted history matching of the steam circulation stage in Lindberg SAGD project by using a discretized wellbore model in Exotherm software, and the data includes steam injection pressure and rates for the long tubing and return pressure and rates for the short tubing. Accordingly, one condition for SAGD conversion from preheating stage was judged by whether the simulated interwell temperature along 80% of horizontal section length reaches the temperature condition of mobile oil. However, the numerical simulation prediction critically depends on the accuracy of the specific geological model and thermodynamic parameters.When steam circulation for a certain time or thermal connectivity is reached and judged by tracking numerical simulation, it can further determine if the injector and producer bottom pressures track each other closely when enforcing a certain interwell pressure difference. If so, it is regarded as established hydraulic or pressure connection. Then, a brief period of partial-SAGD can be conducted when the injector only injects steam but stops returning liquid, and the producer continues to circulate and return liquid. At this time, if the ratio of liquid production to steam injection increases significantly, which can be regarded as established good interwell connectivity [8, 14, 15]. Besides, Ai [16] presented a comprehensive method to judge thermal connection point by point, that is, analyzing the temperature change trend when the injector continues steam circulation but shut-in the producer for 24 h or normal SAGD conversion trial for 2 h. These methods work well in temperature measurements deployed with fewer thermocouples, but there are limitations in DTS temperature measurements with more points and dense data. Furthermore, in terms of utilization of temperature fall-off data derived by shut-in the producer, many operators try to qualitatively analyze the preheating effect to assist in judging SAGD conversion timing [17–19]. Particularly, Stone et al. [19] presented a qualitative evaluation method of the preheating effect along the horizontal section by calculating the second derivative of temperature with respect to time. However, for these studies, it is still unable to quantitatively judge connectivity or connectivity ratio.Besides, many researchers attempted to establish an analytical model to quickly estimate the preheating effect. Wei et al. [20] established a dual horizontal well SAGD electrical preheating model with constant electric power. Liu et al. [21] created a mathematical model for constant temperature electrical heating of dual horizontal well SAGD start-up which was presented. Irani and Ghannadi [22] presented an analytical model to predict the temperature-falloff trend with shut-in time under the condition of constant wellbore temperature heating. Similar to a numerical simulation strategy of dual horizontal well preheating based on the heat conduction theory in CMG software, Duong et al. [14] established an analytical model to calculate interwell temperature under the condition of the constant wellbore heating rate by using the superposition principle. Wu et al. [23] proposed a mathematical model for SAGD preheating of dual horizontal wells under the condition of constant wellbore temperature. Similarly, Xu et al. [24] presented a calculation model of temperature field in the SAGD preheating stage of dual horizontal wells in an isotropic reservoir. However, the above research mainly focuses on studying the preheating effect through forward modeling analysis or prediction based on known static reservoir and thermodynamic parameters, but the difference of these properties along the horizontal section is rarely considered and these methods are not convenient for direct field application.In order to deal with the drawbacks of the existing methods related to numerical simulation, analysis of temperature and pressure data, and analytical model, this paper focuses on establishing a quantitative interpretation model and application method of temperature fall-off data to conveniently judge the SAGD conversion timing from the preheating stage. In this study, the pressure and temperature monitoring process was first compared between superheavy oil sand projects in China and oil sand projects in Canada. Second, an unsteady thermal conduction model was obtained under constant heating power of wellbores in the radial coordinate system, and then, the subsequent unsteady thermal conduction model with constant wellbore temperature can be approximately obtained. Third, the temperature fall-off interpretation model were derived by further combining with Fourier’s law of thermal conduction, and then, the application flow chart of temperature fall-off interpretation method was presented to calculate the preheating radius and thermal diffusivity. Finally, the application method of temperature fall-off interpretation in SAGD conversion judgment was successfully validated by an example combining with tracking numerical simulation, inflection point analysis of temperature during post fall-off period, and index analysis during the partial-SAGD and initial SAGD stages. Figure1 presents the flow chart of the research.Figure 1
The flowchart of the problem under study.


## 2. Downhole Temperature and Pressure Monitoring Technology of Dual Horizontal SAGD Process

Dual horizontal wells with parallel tubing are mostly adopted in Canadian oil sand SAGD projects. As shown in Figure2, the short tubing outlet of the upper steam injection well is 100-300 m away from the heel while long tubing outlet is at the toe. For monitoring process, bottom-hole pressure of the steam injection well is calculated by insulation gas pressure monitoring in casing annulus to keep below the maximum operating pressure. The temperature and pressure sensor above the pump is bound to the heel of the short tubing of producer. The coiled tubing inside is preset with a temperature fiber. The preheating process can be monitored and optimized through real-time temperature and pressure measurement.Figure 2
Completion and temperature and pressure monitoring process of dual horizontal wells.In contrast, the length of horizontal well section is only 350-500 m in Xinjiang and Liaohe superheavy oil SAGD projects in China. The pressure monitoring method is similar to Canadian oil sand projects, but the temperature monitoring is usually by thermocouples with less points, i.e., 4 temperature measurement points at an average interval of about 100 m are placed near the pump, heel, 1/3 from the heel and toe of the producer in Xinjiang and Liaohe superheavy oil SAGD projects [16, 25]. The length of the horizontal section is mostly 700-1200 m in Canadian oil sands SAGD projects. DTS or FBG temperature fiber is often adopted with 40-100 points at an average interval of 10 m. The densely distributed real-time temperature measurement points do not only provide richer temperature data for dynamic monitoring but also bring greater challenges to make full use of data information for rapid and accurate quantitative analysis.


## 3. Temperature Fall-Off Interpretation Model

### 3.1. Assumptions

The simulated interwell temperature field under the preheating method of dual horizontal wells is shown in Figure3. The following assumptions in the preheating stage are considered:
(a)
Circular heating range or heating rings form near each temperature measurement point, and the reservoir properties or thermal diffusivity are homogeneous in each heating range, but they may not be similar at different temperature measuring points(b)
Thermal conduction is considered but relatively weak thermal convection can be ignored, this is because many studies believe that the range and size of thermal convection are relatively limited even close to the edge of steam chamber under the condition of high oil saturation [2, 26, 27](c)
No evident steam chamber forms near the injector and the producer(d)
Both the interwell interference and the interference between different sections of the same horizontal well are ignored(e)
Thermal conductivity and specific heat capacity of reservoir do not change with time(f)
Heating power is assumed to be uniform in each heating range, but it may not be equal at different temperature measuring points(g)
The wellbore cooling power of temperature fall-off test at the shut-in stage is approximately equal to the heating power at shut-in timeFigure 3
Simulated temperature field during preheating period of dual horizontal wells.


### 3.2. Unsteady Thermal Conduction Model under Constant Heating Power of Wellbores

For a specific horizontal well section controlled by each temperature measurement point, it can be regarded as being in homogeneous infinite formation during the preheating stage. It should be noted that the following studies are aimed at the horizontal well section or heating area controlled by a certain temperature measurement point. The heat transfer process from the wellbore to the surrounding formation is shown in Figure4.Figure 4
Sketch map of thermal conduction at cross-section of the horizontal well section.In the radial coordinate system, thermal conduction equation can be expressed as(1)∂2T∂r2+1r∂T∂r=1α∂T∂t,(2)α=λκρCp.The formation temperature everywhere is equal under the initial condition. The initial condition is(3)Tr,tt=0=Ti.Assuming the wellbore transfers heat with constant heating power, the internal boundary condition is(4)2πκrdTdrr=rw=q.For the infinite formation, the external boundary condition is(5)Tr,tr⟶∞=Ti.By analogy with the derivation process of elastic unsteady seepage flow equation in infinite formation, the line-source solution of temperature relation to time near wellbore is obtained:(6)T=Ti‐q4πκEi−r24αt,where the exponential integral function is Ei−r2/4αt=−∫r2/4αt+∞e−x/xdx.For the expansion equation of exponential integral function, assumingγ=r2/4α, when r2/4αt≤0.01, equation (6) can be simplified to
(7)T=Ti+0.183qκlgt1.781γ.Assumingmq=0.183q/κ, equation (7) can be simplified as
(8)T=Ti+mqlgt1.781γ.Note that the conditionr2/4αt≤0.01 is easily met in the preheating stage before SAGD conversion. For example, assuming the well radius is 0.11 m and the thermal diffusivity is 0.135 m2/d, it can meet the requirement γ/t≤0.01 for 2.24 days of heating.


### 3.3. Unsteady Thermal Conduction Model at Constant Wellbore Temperature

In the preheating stage, the upper and lower horizontal wells are mostly at constant wellbore temperature (corresponding to basically unchanged steam injection pressure), whereas the unit heating power is not constant but decreases with time, which is similar to the unsteady seepage law under the condition of constant bottom hole pressure. By learning from the derivation process of thermal transient analysis applied to horizontal wells [28] and analogy with the thermal conduction theory established by Smith [29], Jacob and Lohman [30] demonstrated that formation pressure solution with a constant flow rate could be approximately written as the solution with constant bottom hole pressure, when the flow time is long enough, under unsteady seepage in infinite formation. Similarly, the solution with constant heating power can be approximately written into the solution with constant wellbore temperature, when the heating time is long enough, and the unsteady thermal conduction model with constant wellbore temperature can be approximately obtained by equation (8):
(9)1q=mT⋅lgt1.781γ,where
(10)mT=0.183κTs−Ti.


### 3.4. Temperature Fall-Off Interpretation Model

After heating stops, the relationship between wellbore temperature and time can be solved, that is, the temperature fall-off model.Considering that the heating powerqh in the preheating stage is unknown and decreases with time, the unit heating power before shut-in can be obtained by constant wellbore temperature solution and substituting into equation (9):
(11)1qh=0.183κTs−Tilgth1.781γ,where Ts is the wellbore temperature at initial shut-in time and −qh can be approximately considered as the unit heating power. Apply equation (7) to obtain wellbore temperature versus shut-in time:
(12)T=Ts−0.183qhκlgΔt1.781γrw.Combining equations (11) and (12), there is
(13)T∗=lgΔt/1.781γrwlgth/1.781γrw,where T∗ is the dimensionless temperature, T∗=Ts−T/Ts−Ti.Particularly, several points about equation (13) need to be explained:
(a)
T∗~lgΔt/1.781γrw/lgth/1.781γrw shows a liner relation with a slope of 1 passing through the origin, and it can be used as a validation plot(b)
WhenΔt<<th, the correlation between T∗ and Δt is a straight line on semi-log coordinate with a slope of 1/lgth/1.781γrw(c)
WhenT∗=0, the intercept Δt∗ on the timeline can be used to calculate γrw=Δt∗/1.781, then thermal diffusivity is(14)α=1.781rw24λΔt∗(d)
WhenT∗=1, the theoretical time of the wellbore cooling to initial temperature after well shut-in can be calculated:(15)t∗=Δt⋅101/mAssuming thatTm is mobile oil temperature, we introduce the concept of preheating radius, which is the heating radius ro corresponding to the oil reaching the target temperature Tm in the preheating stage, and the theoretical time tm∗ corresponding to the wellbore cooling to the temperature Tm is
(16)tm∗=Δt⋅10101/2m⋅Ts−Tm/Ts−Ti.Besides, based on Fourier’s law of thermal conduction, the equation of the heating rate under steady thermal conduction is(17)q=2πκlgro/rwTs−Ti.The equation of preheating radius can be obtained by combining equations (9) and (17):
(18)ro=rw⋅tm∗Δt=rw⋅101/2m⋅Ts−Tm/Ts−Ti.Particularly, Bird et al. [31] proposed the concept and calculation equation of thermal conduction penetration thickness δT, and it can assist in determining the reasonable shut-in time Δt required for temperature fall-off test. The equation is as follows:
(19)δT=4λκρCp⋅Δt=4α⋅Δt.For Athabasca oil sands in Canada, when thermal conduction penetration thickness is 1 m, corresponding shut-in time for temperature fall-off test is about 2 days, which can accurately reflect the temperature decline of the reservoir near the wellbore without seriously damaging the preheating process.


### 3.5. Application Conditions

In order to obtain reasonable results by applying the temperature fall-off interpretation model, there are several application conditions that need to be emphasized:(a)
At the time of temperature fall-off test, the preheating time should not be too long to avoid the possible errors caused by strong thermal convection or the formation of local steam chamber(b)
The difference of reservoir and fluid properties near the horizontal section of the producer should not be too large, especially the difference of water saturation which may cause great difference in thermal diffusivity(c)
The preheating process should be relatively steady, or at least the effective preheating time should be adopted


## 3.1. Assumptions

The simulated interwell temperature field under the preheating method of dual horizontal wells is shown in Figure3. The following assumptions in the preheating stage are considered:
(a)
Circular heating range or heating rings form near each temperature measurement point, and the reservoir properties or thermal diffusivity are homogeneous in each heating range, but they may not be similar at different temperature measuring points(b)
Thermal conduction is considered but relatively weak thermal convection can be ignored, this is because many studies believe that the range and size of thermal convection are relatively limited even close to the edge of steam chamber under the condition of high oil saturation [2, 26, 27](c)
No evident steam chamber forms near the injector and the producer(d)
Both the interwell interference and the interference between different sections of the same horizontal well are ignored(e)
Thermal conductivity and specific heat capacity of reservoir do not change with time(f)
Heating power is assumed to be uniform in each heating range, but it may not be equal at different temperature measuring points(g)
The wellbore cooling power of temperature fall-off test at the shut-in stage is approximately equal to the heating power at shut-in timeFigure 3
Simulated temperature field during preheating period of dual horizontal wells.


## 3.2. Unsteady Thermal Conduction Model under Constant Heating Power of Wellbores

For a specific horizontal well section controlled by each temperature measurement point, it can be regarded as being in homogeneous infinite formation during the preheating stage. It should be noted that the following studies are aimed at the horizontal well section or heating area controlled by a certain temperature measurement point. The heat transfer process from the wellbore to the surrounding formation is shown in Figure4.Figure 4
Sketch map of thermal conduction at cross-section of the horizontal well section.In the radial coordinate system, thermal conduction equation can be expressed as(1)∂2T∂r2+1r∂T∂r=1α∂T∂t,(2)α=λκρCp.The formation temperature everywhere is equal under the initial condition. The initial condition is(3)Tr,tt=0=Ti.Assuming the wellbore transfers heat with constant heating power, the internal boundary condition is(4)2πκrdTdrr=rw=q.For the infinite formation, the external boundary condition is(5)Tr,tr⟶∞=Ti.By analogy with the derivation process of elastic unsteady seepage flow equation in infinite formation, the line-source solution of temperature relation to time near wellbore is obtained:(6)T=Ti‐q4πκEi−r24αt,where the exponential integral function is Ei−r2/4αt=−∫r2/4αt+∞e−x/xdx.For the expansion equation of exponential integral function, assumingγ=r2/4α, when r2/4αt≤0.01, equation (6) can be simplified to
(7)T=Ti+0.183qκlgt1.781γ.Assumingmq=0.183q/κ, equation (7) can be simplified as
(8)T=Ti+mqlgt1.781γ.Note that the conditionr2/4αt≤0.01 is easily met in the preheating stage before SAGD conversion. For example, assuming the well radius is 0.11 m and the thermal diffusivity is 0.135 m2/d, it can meet the requirement γ/t≤0.01 for 2.24 days of heating.


## 3.3. Unsteady Thermal Conduction Model at Constant Wellbore Temperature

In the preheating stage, the upper and lower horizontal wells are mostly at constant wellbore temperature (corresponding to basically unchanged steam injection pressure), whereas the unit heating power is not constant but decreases with time, which is similar to the unsteady seepage law under the condition of constant bottom hole pressure. By learning from the derivation process of thermal transient analysis applied to horizontal wells [28] and analogy with the thermal conduction theory established by Smith [29], Jacob and Lohman [30] demonstrated that formation pressure solution with a constant flow rate could be approximately written as the solution with constant bottom hole pressure, when the flow time is long enough, under unsteady seepage in infinite formation. Similarly, the solution with constant heating power can be approximately written into the solution with constant wellbore temperature, when the heating time is long enough, and the unsteady thermal conduction model with constant wellbore temperature can be approximately obtained by equation (8):
(9)1q=mT⋅lgt1.781γ,where
(10)mT=0.183κTs−Ti.


## 3.4. Temperature Fall-Off Interpretation Model

After heating stops, the relationship between wellbore temperature and time can be solved, that is, the temperature fall-off model.Considering that the heating powerqh in the preheating stage is unknown and decreases with time, the unit heating power before shut-in can be obtained by constant wellbore temperature solution and substituting into equation (9):
(11)1qh=0.183κTs−Tilgth1.781γ,where Ts is the wellbore temperature at initial shut-in time and −qh can be approximately considered as the unit heating power. Apply equation (7) to obtain wellbore temperature versus shut-in time:
(12)T=Ts−0.183qhκlgΔt1.781γrw.Combining equations (11) and (12), there is
(13)T∗=lgΔt/1.781γrwlgth/1.781γrw,where T∗ is the dimensionless temperature, T∗=Ts−T/Ts−Ti.Particularly, several points about equation (13) need to be explained:
(a)
T∗~lgΔt/1.781γrw/lgth/1.781γrw shows a liner relation with a slope of 1 passing through the origin, and it can be used as a validation plot(b)
WhenΔt<<th, the correlation between T∗ and Δt is a straight line on semi-log coordinate with a slope of 1/lgth/1.781γrw(c)
WhenT∗=0, the intercept Δt∗ on the timeline can be used to calculate γrw=Δt∗/1.781, then thermal diffusivity is(14)α=1.781rw24λΔt∗(d)
WhenT∗=1, the theoretical time of the wellbore cooling to initial temperature after well shut-in can be calculated:(15)t∗=Δt⋅101/mAssuming thatTm is mobile oil temperature, we introduce the concept of preheating radius, which is the heating radius ro corresponding to the oil reaching the target temperature Tm in the preheating stage, and the theoretical time tm∗ corresponding to the wellbore cooling to the temperature Tm is
(16)tm∗=Δt⋅10101/2m⋅Ts−Tm/Ts−Ti.Besides, based on Fourier’s law of thermal conduction, the equation of the heating rate under steady thermal conduction is(17)q=2πκlgro/rwTs−Ti.The equation of preheating radius can be obtained by combining equations (9) and (17):
(18)ro=rw⋅tm∗Δt=rw⋅101/2m⋅Ts−Tm/Ts−Ti.Particularly, Bird et al. [31] proposed the concept and calculation equation of thermal conduction penetration thickness δT, and it can assist in determining the reasonable shut-in time Δt required for temperature fall-off test. The equation is as follows:
(19)δT=4λκρCp⋅Δt=4α⋅Δt.For Athabasca oil sands in Canada, when thermal conduction penetration thickness is 1 m, corresponding shut-in time for temperature fall-off test is about 2 days, which can accurately reflect the temperature decline of the reservoir near the wellbore without seriously damaging the preheating process.


## 3.5. Application Conditions

In order to obtain reasonable results by applying the temperature fall-off interpretation model, there are several application conditions that need to be emphasized:(a)
At the time of temperature fall-off test, the preheating time should not be too long to avoid the possible errors caused by strong thermal convection or the formation of local steam chamber(b)
The difference of reservoir and fluid properties near the horizontal section of the producer should not be too large, especially the difference of water saturation which may cause great difference in thermal diffusivity(c)
The preheating process should be relatively steady, or at least the effective preheating time should be adopted


## 4. Application Method of Temperature Fall-Off Interpretation Model

Based on the above temperature fall-off interpretation model, as shown in Figure5, the application flow chart of temperature fall-off interpretation method was constructed and it can aid in developing the interpretation template or software.Figure 5
Flow chart of temperature fall-off interpretation method.At a certain time in preheating stage, the upper and lower horizontal wells are shut-in simultaneously to measure the temperature fall-off data, and a certain time interval, usually 0.5-2 h, is set to evenly dilute the data. Then, the relationship betweenT∗ and shut-in time Δt can be calculated and drawn on a semilog plot. Next, data points in the mid to later stage will be selected to automatically calculate the slope, intercept, and correlation coefficient of the regression straight line. If the correlation coefficient is greater than 0.9 (changeable), the regression result is considered to have high confidence. Otherwise, if the correlation coefficient of some temperature points is less than 0.9, the corresponding data should be checked or revised by setting another time interval to filter the data again. Eventually, the thermal diffusivity α can be calculated by equation (14) at different temperature sensing points along the horizontal section, and the preheating radius along the horizontal section can be calculated based on equation (18). The thermal connectivity can be determined by comparing the preheating radius and half the interwell spacing, and then, the thermal connectivity ratio can be further obtained by dividing the total number of temperature sensing points by the point number of thermal connectivity. If thermal connectivity ratio reaches 80% (changeable), it can be regarded as established thermal connectivity.


## 5. Results and Discussions

### 5.1. Interpretation and Analysis of Temperature Fall-Off Data

The target oil sands SAGD project is in Athabasca, Canada. The reservoir property of a well pair is relatively good, and the thickness of the bottom transition zone is 0-1 m with little adverse effect. 70 optical fiber temperature measurement points evenly distribute along 850 m long horizontal section of the producer.On January 12, 2017, steam circulation started. After 103 days, the upper and lower horizontal wells were shut-in at the same time to conduct temperature fall-off test for 48 h, which is consistent with the previous analysis. The data of each temperature measuring point along the producer was real-time recorded, and the corresponding temperature fall-off curves of partial measuring points are shown in Figure6.Figure 6
Temperature fall-off curves of partial measuring points along horizontal section.First, the temperature data of 70 measurement points along the horizontal section were diluted at 2-hour intervals. Then, the curve of dimensionless temperature versus shut-in time was drawn on semilog coordinate, and 10 data points at mid-to-late stage were screened to automatically regress slope, intercept, and correlation coefficient of the straight line. As shown in Figure7, all the correlation coefficients are greater than 0.9, and this indicates regression results have high confidence.Figure 7
Correlation coefficients regressed by temperature fall-off interpretation.Based on equation (14), the thermal diffusivity of the saturated oil sands for all measurement points is between 1.96×10−7 and 2.85×10−7 m2/s. The comparison curve of thermal diffusivity and half the interwell spacing along the horizontal section of producer is shown in Figure 8.Figure 8
Comparison curve of thermal diffusivity and half-interwell spacing along the horizontal section.Based on equation (18), the calculated preheating radius along the horizontal section is 2.4-5 m. The comparison curve of the preheating radius and half the interwell spacing along the horizontal section is shown in Figure 9. The calculated thermal connectivity ratio is 82.9%, and this indicates that the thermal connectivity has been established.Figure 9
Comparison curve of preheating radius and half-interwell spacing along the horizontal section.


### 5.2. Validation of Temperature Fall-Off Interpretation Results

In order to validate the reliability of the temperature fall-off interpretation model and its application method, it is compared with tracking numerical simulation, inflection point analysis of temperature curves during post fall-off period, and index analysis during the partial-SAGD and initial SAGD stages.A flexible-well model was constructed for history matching of preheating stage and judging the timing of SAGD conversion by simulated interwell temperature profile along the horizontal section. The interwell grid size was refined to 0.25 m. The historical steam injection rate is specified in long tubing while liquid-return rate in short tubing for both horizontal wells to match injection pressure and production pressure, combining with the temperature monitoring from horizontal section of the producer and observation wells. After obtaining acceptable history matching, as shown in Figure10, temperature field was drawn to analyze the preheating effect by setting 80°C temperature cutoff. Then, the relationship curve of thermal connectivity versus preheating time can be determined and drawn in Figure 11. The simulated thermal connectivity is 82.4% at the time when the temperature fall-off test started, and it is very close to the interpretation result of the proposed method.Figure 10
Preheating temperature field obtained by tracking numerical simulation.Figure 11
Thermal connectivity ratio obtained by tracking numerical simulation.Besides, after finishing fall-off test, the upper horizontal first started steam injection but without liquid production, and the lower horizontal well restored to steam circulation after an interval of about 24 h. During this post fall-off period, the pressure of the lower horizontal well was observed increasing with the pressure of the upper well, and this indicates that hydraulic and pressure connectivity has already been established. Furthermore, similar to the previous method [16], according to the producer’s temperature response of each measurement point after the injector restarts, there are 57 curves with obvious temperature inflection points, so the corresponding hydraulic connection ratio is calculated as 81.4%, which is basically consistent with the interpretation results of temperature fall-off test.Before normal SAGD conversion, the well pair first transferred from steam circulation to the partial-SAGD stage which usually lasts for a week, that is, the upper well stops steam injection and returns liquid production while the lower well continues steam circulation [16, 32]. During the partial-SAGD stage, the daily oil rate increased from less than 0.5 m3/d during the preheating stage to 5 m3/d, and the water cut decreased from 99.8% to 96.5%, as well as the ratio of total liquid production rate to steam injection rate increased from 1.5 to 2.1, indicating that it has strong interwell oil drainage capacity. After five days of work over, it transferred to the normal SAGD stage on May 8. The subsequent SAGD performance is very good, as shown in Figure 12, the initial liquid rate, oil rate, and water cut are 135 m3/d, 29 m3/d, and 78.5%, respectively. These comprehensive analyses further demonstrate that it is reliable to use the temperature fall-off interpretation method to judge of the SAGD conversion timing from the preheating stage.Figure 12
Performance curves at the preheating and subsequent SAGD stages.


## 5.1. Interpretation and Analysis of Temperature Fall-Off Data

The target oil sands SAGD project is in Athabasca, Canada. The reservoir property of a well pair is relatively good, and the thickness of the bottom transition zone is 0-1 m with little adverse effect. 70 optical fiber temperature measurement points evenly distribute along 850 m long horizontal section of the producer.On January 12, 2017, steam circulation started. After 103 days, the upper and lower horizontal wells were shut-in at the same time to conduct temperature fall-off test for 48 h, which is consistent with the previous analysis. The data of each temperature measuring point along the producer was real-time recorded, and the corresponding temperature fall-off curves of partial measuring points are shown in Figure6.Figure 6
Temperature fall-off curves of partial measuring points along horizontal section.First, the temperature data of 70 measurement points along the horizontal section were diluted at 2-hour intervals. Then, the curve of dimensionless temperature versus shut-in time was drawn on semilog coordinate, and 10 data points at mid-to-late stage were screened to automatically regress slope, intercept, and correlation coefficient of the straight line. As shown in Figure7, all the correlation coefficients are greater than 0.9, and this indicates regression results have high confidence.Figure 7
Correlation coefficients regressed by temperature fall-off interpretation.Based on equation (14), the thermal diffusivity of the saturated oil sands for all measurement points is between 1.96×10−7 and 2.85×10−7 m2/s. The comparison curve of thermal diffusivity and half the interwell spacing along the horizontal section of producer is shown in Figure 8.Figure 8
Comparison curve of thermal diffusivity and half-interwell spacing along the horizontal section.Based on equation (18), the calculated preheating radius along the horizontal section is 2.4-5 m. The comparison curve of the preheating radius and half the interwell spacing along the horizontal section is shown in Figure 9. The calculated thermal connectivity ratio is 82.9%, and this indicates that the thermal connectivity has been established.Figure 9
Comparison curve of preheating radius and half-interwell spacing along the horizontal section.


## 5.2. Validation of Temperature Fall-Off Interpretation Results

In order to validate the reliability of the temperature fall-off interpretation model and its application method, it is compared with tracking numerical simulation, inflection point analysis of temperature curves during post fall-off period, and index analysis during the partial-SAGD and initial SAGD stages.A flexible-well model was constructed for history matching of preheating stage and judging the timing of SAGD conversion by simulated interwell temperature profile along the horizontal section. The interwell grid size was refined to 0.25 m. The historical steam injection rate is specified in long tubing while liquid-return rate in short tubing for both horizontal wells to match injection pressure and production pressure, combining with the temperature monitoring from horizontal section of the producer and observation wells. After obtaining acceptable history matching, as shown in Figure10, temperature field was drawn to analyze the preheating effect by setting 80°C temperature cutoff. Then, the relationship curve of thermal connectivity versus preheating time can be determined and drawn in Figure 11. The simulated thermal connectivity is 82.4% at the time when the temperature fall-off test started, and it is very close to the interpretation result of the proposed method.Figure 10
Preheating temperature field obtained by tracking numerical simulation.Figure 11
Thermal connectivity ratio obtained by tracking numerical simulation.Besides, after finishing fall-off test, the upper horizontal first started steam injection but without liquid production, and the lower horizontal well restored to steam circulation after an interval of about 24 h. During this post fall-off period, the pressure of the lower horizontal well was observed increasing with the pressure of the upper well, and this indicates that hydraulic and pressure connectivity has already been established. Furthermore, similar to the previous method [16], according to the producer’s temperature response of each measurement point after the injector restarts, there are 57 curves with obvious temperature inflection points, so the corresponding hydraulic connection ratio is calculated as 81.4%, which is basically consistent with the interpretation results of temperature fall-off test.Before normal SAGD conversion, the well pair first transferred from steam circulation to the partial-SAGD stage which usually lasts for a week, that is, the upper well stops steam injection and returns liquid production while the lower well continues steam circulation [16, 32]. During the partial-SAGD stage, the daily oil rate increased from less than 0.5 m3/d during the preheating stage to 5 m3/d, and the water cut decreased from 99.8% to 96.5%, as well as the ratio of total liquid production rate to steam injection rate increased from 1.5 to 2.1, indicating that it has strong interwell oil drainage capacity. After five days of work over, it transferred to the normal SAGD stage on May 8. The subsequent SAGD performance is very good, as shown in Figure 12, the initial liquid rate, oil rate, and water cut are 135 m3/d, 29 m3/d, and 78.5%, respectively. These comprehensive analyses further demonstrate that it is reliable to use the temperature fall-off interpretation method to judge of the SAGD conversion timing from the preheating stage.Figure 12
Performance curves at the preheating and subsequent SAGD stages.


## 6. Summary and Conclusions

(1)
Based on the thermal conduction theory of horizontal well and temperature fall-off data along the horizontal section of the producer, the temperature fall-off interpretation model and application method were presented to calculate the preheating radius and thermal diffusivity along the horizontal section as well as determine the timing of SAGD conversion from preheating stage(2)
For Athabasca oil sands in Canada, when thermal conduction penetration thickness is 1 m, the corresponding shut-in time for temperature fall-off test is about 2 days, which can reflect the temperature decline of the reservoir near the wellbore without seriously damaging the preheating process(3)
The flow chart of temperature fall-off interpretation method was proposed. Based on the temperature fall-off data measured by simultaneous shut-in injection and production wells, the dimensionless temperature and shut-in time can be first calculated and drawn on the semilog coordinate, then the slope, intercept, and correlation coefficient of the linear section in the mid to late stage are regressed. Thermal diffusivity and preheating radius at different temperature measurement points along the horizontal section can be calculated, and then, the thermal connectivity ratio can be obtained by comparing the preheating radius and half the interwell spacing(4)
Compared with conventional methods, this proposed method can apply to preheating ways including steam circulation and electrical heating under the condition of weak thermal convection. It has the advantages of being independent of the static geological model and easy to develop interpretation template or software to fast judge the timing of SAGD conversion especially for long horizontal well section deployed with more temperature measurement points, and its main limitations come from neglecting the influence of thermal convection and interwell interference



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*Source: 6343707-2022-08-13.xml*