Abstract
In the production of oil and gas fields, horizontal wells can obtain larger reservoir drainage area. Single well production is large and the production cycle is long. Especially for the development of reservoirs with thin production layer, small porosity, and low permeability, it shows the incomparable effect of vertical wells. Due to gravity separation in horizontal wells, the distribution of fluids in horizontal cross sections is more complicated. There are many influencing factors, such as gas lock, water lock, and flow instability. In horizontal well oil–water two-phase flow, the flow separation in different flow zones complicates the reading of the turbine flowmeter due to the change the cross-sectional area of the fluid. A small deviation of the horizontal well inclination causes significant changes in holdup and flow velocity. Well deviation causes backflow and circulation. In this paper, the capacitance water holdup and turbine flowmeter data processing method of FILT in oil–water two-phase flow are studied by the oil–water, two-phase flow experiment. The stratified flow interpretation model of oil–water two-phase flow and the chart fitting calculation method are proposed and realized. This is the innovation of this paper. Through the verification of experimental data, the relative errors under various conditions are less than 10%. Only when the moisture content is 20%, the error is greater than 10%. The interpretation accuracy of oil–water two-phase flow can fully meet the actual needs of production. It provides a strong basis for accurately finding the producing water point and scientifically plugging water in horizontal wells. The findings of this study can help the better understanding of the oil–water two-phase flow stratification flow interpretation model and the chart fitting calculation method.
1. Introduction
Fluid conditions in horizontal and large-slope wells are completely different from those in conventional straight wells due to the long-distance fluctuating wellbore conditions and the gravity-induced separation of heavy and light phases of fluids in the wellbore [1, 2]. Likewise, it poses more complex challenges for logging and fluid production dynamics monitoring [3]. A leading foreign oilfield technical service company has developed a horizontal well production logging instrument with its own intellectual property. Schlumberger developed Flow View, a water content imaging instrument, and Flow scan Image, a fluid scan imaging instrument, which can determine the content and flow rate of each phase of the fluid in the wellbore and map the distribution of oil, gas, and water in the wellbore section. Atlas developed MCFM multi-electrode array logging instrument in the late 20th century, which measures the information of oil, gas, and water by the difference in the dielectric constant of each phase of the fluid. Sondex used CAT, RAT, and SAT multi-array imaging logging to measure oil, gas, and water retention and flow data. In 2021, China National Petroleum surveyed the structural principles of domestic and foreign tools and designed a single-turbine, single-capacitance probe with adjustable support arms. In this paper, it is called the FILT. This paper takes fluid imaging logger as the research object, and investigates the interpretation method of stratified flow imaging logging for oil and water two-phase flow in horizontal wells, and proposes a new kind of stratified flow interpretation model applicable to the FILT. The flow interpretation method is given by fitting plots of turbine speed, flow rate, and water content. Figure 1 below presents the general sketch of the problem under study.
2. Introduction of the Fluid Image Logging Tool
The FILT (Fluid Imaging Logging Tool) has a length of 4 m and an outside diameter of 56 mm [4]. The tool can withstand a maximum temperature of 175°C and a maximum pressure of 80 mpa. A 5.5-inch casing has a starting discharge of less than 25 m3/d (accuracy ±1 m3/d). When the tool is not measuring, the arm is closed, as shown in Figure 2. The height of the measurement point on the wellbore section can be controlled by adjusting the angle of the support arm according to actual needs. The maximum height is 145 mm, as shown in Figure 3; [5].
The structure of the fluid imaging logging instrument is shown in Figure 4. The uppermost part of the FILT is the swing arm assembly of the support arm. The arm angle measurement and signal processing module under the swing assembly is used to measure the status of the support arm, process the water flow signal, and upload it. The middle part is the support arm sensor assembly. It can be turned on and off as required. It is fitted with a turbine flow sensor with a 28 mm outer diameter and a capacitive water-holding rate sensor for measuring the flow and water content at the arm position. The bottom part is the arm opening power and control assembly. It is used to control the opening and closing dimensions of the arm and to measure the well diameter.(1)the arm swing component(2)the arm angle measurement and signal processing module(3)the arm component(4)the flow sensor(5)the water sensor(6)the arm power and well diameter measurement component
The FILT turbine flowmeter has an outside diameter of only 28 mm [6, 7]. The principle of the turbine flowmeter is to use the interaction of physical forces. It will rotate with the flow of the mixed fluid in the wellbore. By processing the data and using the turbine speed, the relative flow rate of the fluid within the measurement range around the turbine can be calculated, thus calculating the total flow rate in the wellbore. Like a conventional turbine flow meter, it has a very small magnet mounted on the turbine. As the turbine rotates due to the flow of the mixed fluid, cutting the magnetic induction lines produces an AC signal. As shown in Figure 5, the magnetic sensor measures information about the response of the turbine to the fluid, i.e., the number of cycles per second the turbine spins with the fluid, and transmits it to the surface acquisition system via a transmission cable. Due to the special nature of the fluid imaging logging instruments, the FILT turbine flow meter can only perform point measurements.
As shown in Figure 6, the FILT also has a capacitive water content meter [8]. The measurement principle of the capacitive sensor uses the different dielectric constants of oil, gas, and water in the wellbore. It is due to this difference that mixed multi-phase fluids flow through the capacitive water-holding rate meter and the LC oscillation circuit records different frequencies due to the different contents of oil, gas, and water in the mixed fluid, and the recorded frequency signals are transmitted to the surface acquisition system via cable. The water-holding rate of the fluid can be back-calculated from the scale response values of the capacitive sensor in different single-phase fluids.
In formula (1), L is the inductance measured by the oscillation circuit in the capacitive sensor at the current position h (Henry). C is the capacitance value of the response of the capacitive probe to the fluid within the current detection range in the wellbore, f (Farah). f is the oscillation frequency measured by the capacitive water content meter, Hz (Hertz).
The working principle of the FILT is described below. After the instrument reaches a certain target layer, adjust the ground voltage to make the pendulum motor work and complete the instrument pendulum. After the swing is completed, adjust the ground voltage to control the lifting arm motor. When the arm is lifted, the data of water content, flow rate, and arm height are collected at the same time. Make the arm fixed in a certain position, complete the measurement of water content and flow rate, and collect the data of arm height. After the test is completed, the arm is restored by adjusting the voltage of the cable head on the ground. Profile data collection and water flow verification can also be completed during the oil recovery process. After the instrument is fully recovered, the instrument is lifted to other layers for data acquisition.
The data acquisition system of the FILT is WELLSUN3000 Production Logging System [9]. The acquisition system includes an associated output interface and a composite input interface. The output interface controls the switching of the arm and the height of the probe. The input interface displays the data measured by the turbine probe and the capacitance probe on the data acquisition system in real time.
As shown in Figure 7, [10], the measured data of the FILT is in the format of .dat. The XCHD curve editing software compiled by the instrument development unit is needed to convert the data into an international logging data format . Las.
As shown in Figure 8, [11], it is the interface of the XCHD curve editing software used for logging data format conversion. This software can edit the logging curve for depth selection, draping, horizontal stretching, manual drawing, curve extraction, depth inversion, curve filtering, etc. It can meet the basic editing needs of users [12].
After data processing, such as curve editing, the well section data can be exported [13]. It is possible to select any or more curves of a specified depth section for export. The export path can be made by clicking the “…” button and the curve data in . Las format can be exported by clicking Confirm.
The accuracy and stability requirements of the laboratory oil and gas flow rate are shown in Table 1. The adjustable range and the accuracy of the experimental system water content: 0–100% (±3%). The accuracy of the flow calibration system is the liquid phase error between ±0.2% and ±0.5%. The time to reach steady-state flow in the experiment does not exceed 3 min, and the maximum displacement can last at least 1 hour of the operation. The flow control is divided into automatic and manual modes. The wellbore can be simulated at any angle in the range of 0–90°. Test medium: oil is industrial 10# white oil, viscosity 5 mPa-s, density 0.84 g/cm3, gas is air, and water is tap water. Table 1 shows the technical specifications of the flow accuracy and stability of the experimental device.
The experimental setup mainly consists of the following nine parts: (1) Simulated wellbore, (2) oil, gas, and water stabilization system, (3) oil, gas, and water mixer, (4) oil, gas, and water separation system, (5) oil, gas, and, water flow meter calibration system, (6). (7) up and down fluctuating wellbore, (8) electric winch, and (9) hydraulic system.
The area of the experimental piping is shown in Figure 9. It is used to connect the oil, gas, and water stabilization system, storage tank for each phase of the fluid, gas and liquid (oil and water) separation system, various phase piping required for simulation experiments, and valves for controlling each phase of the fluid.
The control table of the multi-phase flow experimental simulator is shown in Figure 10. It is mainly used to control the displacement and proportion of oil, gas, and water phases.
The simulated wellbore and table etc., are shown in Figure 11. The size of the simulated borehole is 159 mm (7in) and 124 mm (5.5in) in two different sizes of glass borehole. The length of the laboratory simulated borehole is 12 m, with a 10 m clear borehole in the middle. Each section of the clear borehole was 2 m long and the stainless steel borehole at each end of the borehole was 1 m. The center distance between the two boreholes was 800 mm. The gas–liquid mixer was installed at a height of 5 m at the bottom of the borehole. Three pressure sensors and three temperature sensors are evenly arranged from top to bottom in each borehole. They are used to measure the pressure and temperature variations in the glass of the simulated borehole.
3. Experimental Design of Oil–Water Two-phase Flow
The FILT studied in this paper was subjected to oil–water two-phase flow experiments in a multi-phase flow laboratory. The response characteristics data of the fluid in the wellbore were analyzed [14]. The response values of the FILT in each phase were calibrated and the applicability of the instrument was studied. It provides sufficient reference data for the instrument’s interpretation method and wellbore imaging algorithm.
According to the actual production requirements of the study area and laboratory conditions, a comprehensive analysis was conducted and an experimental program was designed for different oil–water ratios in the near-horizontal section of the 85°∼95° (0° in the vertical gravity direction and 90° in the full horizontal well) horizontal section. There are 360 sets of data, as shown in Table 2.
Industrial 10# white oil (viscosity of 5 mPa-s, density of 0.84 g/cm3) and tap water (viscosity of 1.16 mPa-s, density of 0.9884 g/cm3) were used for the experiment at room temperature and pressure. The braces were used to hold the instrument. By adjusting the height of the fluid imaging logger arm, the corresponding positions of the logger capacitance probe and turbine in the wellbore section were determined. The fluid is matched using an oil–water mixer and the mixed fluid is injected into the simulated wellbore through a pipe at 5.5 in. After 3 minutes, when the fluid is stable, data acquisition begins. A capacitive probe on the tool arm records fluid information. A turbine flow meter records the current fluid flow rate in the wellbore section. A high-definition video camera is used to record and film the experimental process, providing visual image data for instrumentation studies and experimental data analysis [15].
In this experiment, five different heights of 48 mm, 64 mm, 76 mm, 88 mm, and 100 mm from the bottom of the well were simulated. From top to bottom, the position of the first measurement point is 100 mm. The position of the turbine in the wellbore section at full horizontal (i.e., inclination angle of 90°) is shown schematically in Figure 12. The red part is the schematic diagram of the turbine at different measurement heights. The above measurement point locations were chosen because these five measurement points can basically cover most of the vertical fluid in the wellbore section.
The file name of the measurement in this experiment is OWL-PD□□QT□□W□□□. OWL stands for oil–water two-phase measurement record, PD is the pipe inclination angle (°), QT is the total flow rate (m3/d), and W is the water content (%). For example, when the angle between the wellbore and the vertical direction is 88°, the total flow rate of the fluid in this experiment is 300 m3/d, and the water content of the mixed fluid is 50%; it is named OWL-PD88QT300W50%. By observing the experimental process and the electronic image information recorded by the camera and other photographic equipment, the flow model of oil–water two-phase in horizontal wells was analyzed and studied by combining the existing technology and related literature.
4. Data Analysis and Processing of Multi-Phase Flow Experiment
4.1. Data Processing of Capacitance Water Holdup
In order to avoid the influence of the inclination angle on the value of the capacitance water content meter, the experimental measured value of single-phase oil and water at an inclination angle of 90° or completely horizontal condition was chosen as the calibration value of the FILT capacitance water content meter. As shown in Figure 13, the response values of pure oil and pure water are very different. The red circle point is the FILT scale response value of the capacitive single-phase oil holding water rate meter, and the average value of the sample data points is about 36300 CPS. The small blue triangle indicates the scale response value when the FILT capacitive probe is full string water, and the sample arithmetic average value is 12900 CPS. It provides effective data support for the subsequent gas content and flow rate calculation.
After calibration, the FILT measurement reflects the fluid properties in the wellbore around the capacitance probe. The water content at the i-th height position is calculated from the response value of the capacitance water content meter at the i-th measurement position, as shown in formula (1); [16, 17].
is the water holding at the i-th measurement height position, after the decimal point. is the response value of the capacitive probe at the measurement height, after the decimal point. is the response value of the capacitive probe in pure water. HYDO is the response value of the capacitive probe in pure oil.
Taking the data of five measurement points in the multi-phase flow experiment conducted in this paper as an example, the local water-holding rate of these five measurement points can be calculated by formula (1). Taking the midpoint of two measurement points as the boundary, the wellbore can be divided into five different areas, as shown in Figure 14. First, the water content of each area is calculated using the water content of each measurement point. Then, the water content of the wellbore section can be obtained by adding the calculated water contents of the five areas and dividing them by the total area of the wellbore section, as shown in formula (3).
is the water-holding rate of the wellbore section at the point measurement depth. is the water content at location i. Si is the area of area i.
According to the above calculation method, five measurement points were measured at a well slope angle of 90° and a water content of 40% for seven different flow rates of 50 m3/d, 70 m3/d, 100 m3/d, 120 m3/d, 160 m3/d, 200 m3/d, and 250 m3/d, respectively. The locations of the measurement points are shown in Figure 15. The water content measured by the water content meter was used to calculate the water content at different flow rates. The relationship between the water content of the wellbore and the flow rate was obtained.
As shown in Figure 15, the water content of the wellbore fluctuates with an increase in the oil–water two-phase mixed flow, but the overall trend is increasing. As can be seen from Figure 16, the calculated water-holding rate at small flow rates is relatively close to the water content rate. This is because the oil–water mixture in the wellbore shows a horizontal, smooth stratified flow due to the gravity partitioning effect. When the total flow rate is larger, the fluid velocity difference leads to the dispersed flow of oil–water and oil–water–water in the wellbore. Since the sensor of the capacitive water content meter is sensitive to the response of water, the measured water content will increase when the flow rate is higher.
Table 3 shows the experimental images of 50 m3/d, 70 m3/d, 100 m3/d, 120 m3/d, 160 m3/d, 200 m3/d, and 250 m3/d, and the corresponding water contents were obtained from formula (3) under the condition of PD90W40%.
As shown in Table 3 and Figure 17, the applicability of the FILT is better at low flow rates. Therefore, water-holding rate measurements were selected for seven cases with different water contents (20%, 40%, 50%, 60%, 70%, 80%, 90%) in the wellbore under low-flow rate conditions in horizontal wells. Based on this, the values of the water-holding rate in the wellbore under different conditions were calculated. The relationship between water content and the water-holding rate of the wellbore section at the same inclination angle and the same flow rate was established, as shown in Figure 18.
From Figure 16, it can be seen that there is a good linear relationship between water content and the water-holding rate of horizontal wells under low flow rate conditions, with the correlation coefficient above 0.97. It also verifies the feasibility of the FILT in low-flow horizontal well measurements[18]. To further explore the rationality of the measurement points selected in the FILT experiment, the local holding rates of five measurement points under each water content condition were plotted and analyzed. The area of bubbles reflects the water content rate.
Figure 17 shows the bubble plots of the local water-holding rate for five measurement points in the experiment at an inclination angle of 90°, a total flow rate of 50 m3/d, and a water content of 20%. It can be seen from the figure that the FILT only measures the response of water at a detection height of 48 mm.
Figure 18 shows the bubble diagram of the local water-holding rate at each measurement point at an inclination angle of 90°, a total flow rate of 50 m3/d, and a water content of 40%. Under this measurement condition, the FILT at measurement point 5 (48 mm) and measurement point 4 (64 mm) can detect the water information and the water-holding rate increases in the wellbore section.
Figure 19 shows the bubble diagram of the local water-holding rate at each measurement point at an inclination angle of 90°, a total flow rate of 50 m3/d, and a water content of 50%. Under the condition of 40% water content, although only two measurement points detected moisture information, the local water-holding rate measured at the second measurement point (64 mm) was larger, i.e., the water phase and trace oil bubbles are more in the 50% detection range.
Figure 20 shows the bubble diagram of the local water-holding rate at each measurement point at an inclination angle of 90°, a total flow rate of 50 m3/d, and a water content of 70%. By the FILT calculation, the water-holding rate at measurement point 3 (76 mm) to measurement point 5 (48 mm) is 1. The water-holding rate at the second measurement point (88 mm) is about 0.1. It can be assumed that the fluid in the detection range of the second measurement point is still dominated by the continuous oil phase.
Figure 21 shows the bubble diagram of the local water-holding rate at each measurement point at an inclination angle of 90°, a total flow rate of 50 m3/d and a water content of 90%. It can be clearly seen that the measured and calculated water content of all four measurement points is 1, except for the first measurement point (100 mm) where the water content is 0.33. It can be seen that the second measurement point (88 mm) to the fifth measurement point (48 mm) is in a continuous water phase, and there are a few bubbles in the fluid at the first measurement point.
Table 4 shows the comparison between bubble plots and laboratory images of the local gas content variation at the measurement points for a 90° inclination angle, a total flow rate of 50 m3/d, and different water content. It was further determined that the wellbore water-holding rate increased with increasing water content under constant flow rate and well inclination angle. The results show that FITL has good applicability for horizontal smooth stratified flow and interfacial mixed wave stratified flow.
4.2. Turbine Flowmeter Data Processing
The FILT has only one micro-turbine flow meter. It measures at five measurement points at different heights and acts as a capacitive water content meter. The centers of the turbine flowmeter and the capacitive water content meter are parallel to the wellbore in the same line. The experimental data were analyzed to obtain the starting flow rate at each measurement point. Under horizontal well conditions, the start-up flow rates are different for different measurement methods. The start-up flow rate in pure oil is greater than that in pure water due to the viscous force of the oil and the flow rate of the pure oil phase. The turbine speed at the corresponding start-up flow rate can be calculated from formula (4). As shown in Table 5.
In formula (4), i = 1, 2, …, 5. is the starting velocity of the i-th measurement point in pure fluid, m/min. Gas is the starting flow rate of the i-th measurement point in pure fluid, m3/d. Pc is the line constant, (m3/d)/(m/min).
The turbine speeds calculated for pure water and pure oil tilt the angle of 90°, as shown in Tables 6 and 7. It can be found that at the 5th measurement point (48 mm), the turbine does not rotate and does not operate at a low-flow rate [19].
The rendezvous diagram analysis of flow rate and turbine speed at different measurement points in horizontal wells was performed to obtain the slope in pure oil and pure water as shown in Figures 22 and 23, [14].
The response coefficients Ko and Kw of the turbine in pure oil and pure water were obtained after correcting the fitted slopes of the horizontal well flow rate Q and turbine speed RPS shown in equations (3)–(5), as shown in Table 8. As shown in equations (3)–(5), the response coefficients Ko and Kw of the turbine in pure oil and pure water were obtained
In formula (5), i = 1, 2, …, 5. is the response coefficient of the i-th measurement point in pure oil. k1i is the slope of the fit of Q and RPS for the i-th measurement point. pc is a tube constant, (m3/d)/(m/min).
The starting speed of the turbine and the instrument response coefficient are obtained, and the local fluid velocity at the position of the i-th measurement point can be calculated according to formula (6).wherewhere
In formula (6), is the local fluid velocity at the i-th measurement point. is the local response coefficient at the i-th measurement point. is the turbine speed measured at the i-th measurement point. koi is the instrument response coefficient at the i-th measurement point in pure oil. is the instrument response coefficient at the i-th measurement point in pure water. is the turbine start-up speed at the i-th measurement point in pure oil. is the turbine start-up speed at the i-th measurement point in pure oil.
After obtaining the local fluid velocity at each measurement point, it is usually necessary to calculate the average velocity of the wellbore section to calculate the flow rate in the wellbore. We have tried three methods of calculating the average velocity. These three calculation methods are the arithmetic average method, the weighted average method, and the integral method.
The arithmetic averaging method is suitable for single-phase flow in the wellbore or when the fluid is uniformly distributed and the velocity difference is small. It is used to calculate the average velocity of the fluid from the local velocity calculated at each measurement point. This is shown in (9).
In formula (9), is the average velocity of the fluid in the wellbore. is the local fluid velocity at the i-th measuring point. n is the number of all measurement points.
The weighted average method is used here to calculate the total water-holding capacity, similar to the capacitive holding probe. Based on the center height of each measurement turbine, the wellbore is divided into five unequal zones, as shown in Figure 24. By calculating the proportion of each zone and adding a weighting factor to the local velocity calculated for each zone, the water retention rate of the wellbore section is obtained as shown in formula (10); [20]. This method is only applicable to stratified flow.
In formula (10); [21], is the average velocity of the fluid in the borehole [22]. is the local fluid velocity at the i-th measurement point. n is the number of all measurement points. is the area of the borehole section.
As shown in Figure 25; [23], the velocity profile can be obtained by numerically fitting the local velocity (turbine speed) calculated by the integration method at each point [24]. The maximum and minimum velocities of the velocity profile can be calculated as shown in Figure 25, with the wellbore section as the horizontal axis and the fluid velocity as the vertical axis. The integral of the function should be satisfied as shown in formula (11); [25]. The average velocity can be obtained as:
is the average fluid velocity of the desired solution. f(x) is the functional relationship fitted by the velocity profile. is the minimum value of the fitted curve. Vmax is the maximum value of the fitted curve. The average velocity can be calculated by solving the above integral.
This method can be applied to stratified flow with low flow velocity and low water content or dispersed flow with high water content and high flow velocity. However, it is influenced by the choice of the velocity profile fitting function.
The stratified flow interpretation model is a flow interpretation method based on an array holding rate meter and array turbine flowmeter in oil–water two-phase stratified flow in horizontal wells. The idea of this method is to grid the wellbore cross section and create a water-holding rate grid data layer, a flow rate grid data layer, and an area grid data layer on the basis of the same grid. As shown in Figure 4, the grid division is decided according to the position of each probe of the array water-holding rate meter and each turbine of the array turbine flow meter, which makes each water-holding rate grid have a velocity grid and an area grid corresponding to it.
Compared with the gridded model, this calculation model approximates the area of the entire cross section by integration, which improves the accuracy in comparison [26].
5. Interpretation Model Research
In the multi-phase flow laboratory of Yangtze University, the oil–water two-phase calibration experiments of high-slope wells and horizontal wells were conducted using the FILT. The flow patterns of oil–water two-phase in the near-horizontal section of horizontal wells were analyzed based on the flow pattern division theory of horizontal wells proposed by Trallero and the image information collected by the laboratory camera. When the flow rate is low and the water content is low, the oil and water two-phases are mostly in a homogeneous stratified flow. When the flow rate and water content are high, oil and water will be in the form of dispersed flow in the wellbore. Based on the actual experimental data from the FILT, the data from the capacitive water-holding instrument and turbine flow meter were processed. The good suitability of the instrument for low-flow stratified flows was determined. The calculation of water accumulation in the wellbore and the three average velocities are given. However, the turbine flowmeter at this measurement point could not operate at low measurement heights at low flow rates and low water content due to defects in the chosen measurement point.
The stratified flow interpretation model uses a similar approach to calculate the fluid flow rate for smooth horizontal stratified flow based on the data processing scheme of the water accumulator and turbine flow meter. A schematic diagram of the five measurement points recorded by the FILT is shown in Figure 26. The midpoint of the adjacent measurement points is found according to the height position of each measurement point. The wellbore cross section is unevenly divided into five zones. The flow rate of each phase in the wellbore can be calculated by the method shown in formula (13).
In formula (13), Qo is the total flow rate of the oil phase in the wellbore, m3/d. is the area of the i-th measurement point, as shown in Figure 27, m3. is the local water content of the i-th measurement point, fractional. Vi is the local fluid velocity of the i-th measurement point, m/min.
The area of each measurement point Si can be calculated by a mathematical formula. As an example, the area of each measurement point is calculated for the five selected measurement points in the laboratory test.
The area of the first measuring point:
The area of all regions can be calculated by analogy. The area of the i-th measuring point:
In the formula, R is 0.5 times the radius of the borehole size or the diameter curve (assuming the borehole is completely circular). He is the bottom boundary of each area.
The relationship plot shown in Figure 28 can be obtained by fitting the turbine speed and flow rate data for the second measurement point (probe height 88 mm) at a 90° tilt. It is not difficult to find that there is a good quadratic function relationship between turbine speed and flow rate. The correlation coefficients are both greater than 0.99. Therefore, a functional relationship between the two can be established.
The red line in the graph means that the fluid in the wellbore is pure oil, which means that there is a functional relationship between the turbine speed f at the measurement point and the flow rate Q in the wellbore when the water retention is equal to 0, as shown in formula (17):
When the fluid properties in the wellbore are all water, there is a quadratic function relationship between the turbine speed f and the flow rate Q as shown in formula (18):
It can be seen from Figure 29 that he flow rate in the wellbore decreases with an increase in the water-holding capacity at the same turbine speed. Therefore, it is assumed that the variation of the flow rate ΔQ with the water-holding capacity is constant for a certain turbine speed. Based on this idea, the F and Q lines are straightened in pure water. Then, when the wellbore is filled with oil, the functional relationship can be expressed as formula (19).where
Therefore, under the condition that the turbine speed and the water accumulation in the wellbore are known, the flow rate value at the second measurement point (88 mm) in the wellbore can be obtained based on the above flow rate calculation method combined with the water accumulation calculation method.
Likewise, the flow rate values can be calculated for each measurement point in the area location as shown in formula (22).
Then, the total flow rate in the wellbore satisfies formula (23).
In formula (22), is the water holdup at the i-th position, decimal. is the area of the i-th region. is the area of the borehole section.
Since the FILT fluid imaging logging interpretation evaluation software has not yet been used in actual oilfield logging production, it still lacks the test of actual production data. Therefore, only experimental data of oil–water two-phase flow were used to test the application of the logging interpretation model. As shown in Table 9, the flow rates and errors interpreted by the software when the inclination angle is 88°are: the flow rate is 50 m3/day and the water content varies.
As can be seen from Table 9, the relative error of the FILT fluid imaging logging interpretation model is less than 10%, except that the error is greater than 10% when the water content is 20%. Its interpretation accuracy can still meet the actual needs of production. The error of the calculated flow rate is larger when the water content is 20%. This may be due to the fact that the turbine at the fifth measurement point (48 mm) selected in the experiment does not work due to the low water content.
6. Summary and Conclusions
The data measured by the capacitive water-holding rate meter were processed and analyzed based on the experimental data of oil and water phases.(1)The calculation method of the water-holding rate of the FILT in the wellbore is given.(2)Three different methods of calculating the average flow rate are given for the turbine flow meter of FILT logging. Among them, the integral method is more suitable for the FILT.(3)By comparing the domestic and foreign flow calculation methods, a new stratified flow interpretation model is applicable to the FILT.(4)The flow interpretation method is given by the fitting diagram of turbine speed, flow rate, and water content.(5)The flow of each phase of the fluid in the wellbore is calculated based on the area occupied by the measurement points when the FILT technique is applied to the low flow rate and low water content stratified flow in horizontal wells.(6)The strength of this study is that it improves the precision of the results with the new model.(7)The disadvantage of this study is that its experimental environment is limited by the conditions.
Data Availability
All data are included with the paper.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by Xinjiang Uygur Autonomous Region Innovation Environment (talent, base) Construction Foundation (Xinjiang NSFC Program Foundation 2020D01A132): Research and implementation of horizontal inversion optimization interpretation method. Hubei Science and Technology Demonstration Foundation (2019ZYYD016); Cooperative Innovation Center of Unconventional Oil and Gas, Yangtze University (Ministry of Education & Hubei Province), NO UOG2020-10; Logging simulation of gas water two-phase production in shale gas horizontal wells (2020CB21-25); Digital core graphic virtual simulation teaching system based on Alicloud; Ideological and political education of postgraduate courses in Yangtze University: Python for Data Analysis; and Quality courses for Postgraduates in Yangtze University: Artificial Intelligence and Machine Learning.