Study on Reasonable Amount of Flushing Fluid and Flushing Time

: Oil-based drilling ﬂuid has many advantages, such as stable performance, strong anti-pollution ability, and strong inhibition, and it has been widely used in the world. However, at present, there is no uniﬁed evaluation standard for the e ﬀ ect of ﬂushing ﬂuid under this condition, and most of them are based on the ﬂushing e ﬀ ect evaluation of water-based drilling ﬂuid. However, there are few studies on wetting reversal phenomenon, reasonable dosage, and ﬂushing time between oil-based drilling ﬂuid and ﬂushing ﬂuid on the two-phase interface. Therefore, it is necessary to establish a comprehensive evaluation method for the e ﬀ ect of ﬂushing ﬂuid under oil-based drilling ﬂuid, and explore the relationship between the amount of ﬂushing ﬂuid and ﬂushing e ﬃ ciency, so as to determine the reasonable range of ﬂushing ﬂuid consumption. In this paper, using the existing experimental instruments, a type A oil-based ﬂushing ﬂuid commonly used in oil ﬁelds was selected for the experiment, and on the basis of the high-temperature and high-pressure ﬁltration meter, a ﬂushing ﬂuid evaluation device was developed. Based on the principle of equal shear rate, the ﬂushing displacement and ﬂushing time were determined, and then the ﬂushing e ﬀ ect was evaluated. In order to comprehensively consider the inﬂuencing factors of the well wall ﬂushing e ﬀ ect, ﬁve experimental factors, including di ﬀ erent core, ﬂushing displacement, ﬂushing time, ﬂushing ﬂuid type, and surfactant concentration, were selected to formulate the ﬂushing experiment scheme. The contrast method was used to test the cementation strength of core and cement slurry under di ﬀ erent conditions, and the microscopic morphology of the interface was observed and analyzed to explore the reasons for the change of cementation strength between core and cement slurry due to the existence of oil-based drilling ﬂuid. The conclusion obtained has very important practical signiﬁcance to guide the ﬁeld practice. to determine the bond strength of di ﬀ erent cores and cement paste. The results show that through the microscopic analysis of the interface between core and cement stone under di ﬀ erent conditions, the volume shrinkage of cement slurry and drilling ﬂuid results in fracture, which leads to poor interface cementation. However, the surface roughness of core is larger than the shrinkage volume spacing of cement slurry, which makes the interface cementation worse together, and the cementation strength is high. The cementation strength decreases with the increase of core permeability, which further indicates that the higher the core permeability, the more di ﬃ cult it is to be washed clean.


Introduction
With the deepening of exploration and development to deep oil and gas reservoirs and unconventional oil and gas reservoirs, the number of complex deep wells and shale gas wells is increasing year by year, and the requirements for drilling fluid performance are higher and higher [1,2]. Among them, oil-based drilling fluid has obvious advantages in drilling complex wells, especially in drilling high-temperature deep wells and water-sensitive formations due to its excellent inhibition and temperature resistance, which can more effectively protect water sensitive oil and gas reservoirs Energies 2020, 13, 4483 3 of 22 combined with the size of the self-developed experimental device and the fluid performance measured in the laboratory, the displacement required for this experiment can be obtained.
As shown in Figure 1, for the annulus with inner and outer radius distributions of R 1 and R 2 , the r coordinate is established along the radial direction with the center line of the annular space as the origin. At the place away from the entrance and exit, the strip flow element with thickness of 2r, length of L, and width of π(R 1 +R 2 ) is taken. Considering the steady flow of cement slurry, the momentum of flow microelement is conserved. The external force acting on it-that is, the resultant force of pressure at both ends π(R 1 +R 2 )2r∆P, whose direction is the same as the flow direction, is the driving force-that is, the flow resistance caused by shear stress τ on the upper and lower sides of the element 2Lτπ(R 1 +R 2 ). The momentum balance equation is obtained as follows: Energies 2020, 13, x FOR PEER REVIEW 3 of 28 wellbore fluid performance that have been cemented on site. Then, using the shear rate, combined with the size of the self-developed experimental device and the fluid performance measured in the laboratory, the displacement required for this experiment can be obtained. As shown in Figure 1, for the annulus with inner and outer radius distributions of R1 and R2, the r coordinate is established along the radial direction with the center line of the annular space as the origin. At the place away from the entrance and exit, the strip flow element with thickness of 2r, length of L, and width of π(R1+R2) is taken. Considering the steady flow of cement slurry, the momentum of flow microelement is conserved. The external force acting on it-that is, the resultant force of pressure at both ends π(R1+R2)2r△P, whose direction is the same as the flow direction, is the driving force-that is, the flow resistance caused by shear stress τ on the upper and lower sides of the element 2Lτπ(R1+R2). The momentum balance equation is obtained as follows: It can be easily obtained that the shear stress is in a straight line distribution in the annular space gap. The shear stress at the pipe wall is the largest, and the shear stress at the pipe axis is the minimum τw, which is zero: If the mathematical model of fluid rheology is power-law model and the rheological parameters are determined, the velocity distribution of fluid can be deduced according to the flow dynamic balance equation [ (3) where n' is the fluidity index and τy is the static shear force.
The shear rate can be obtained by deriving the above equation. In addition, Chen Jialiang [33] also deduced the velocity distribution equation.
Similarly, the shear rate can also be obtained by deriving the above equation. Chen Jialiang [33] also derived the annular shear rate distribution equation. 21 12 2 where V is current speed. It can be easily obtained that the shear stress is in a straight line distribution in the annular space gap. The shear stress at the pipe wall is the largest, and the shear stress at the pipe axis is the minimum τ w , which is zero: If the mathematical model of fluid rheology is power-law model and the rheological parameters are determined, the velocity distribution of fluid can be deduced according to the flow dynamic balance equation [30]: where n' is the fluidity index and τ y is the static shear force. The shear rate can be obtained by deriving the above equation. In addition, Chen Jialiang [33] also deduced the velocity distribution equation.
Similarly, the shear rate can also be obtained by deriving the above equation. Chen Jialiang [33] also derived the annular shear rate distribution equation.
where V is current speed. Assuming that the annular velocity is constant, considering the balance between pressure and shear stress, the expression of shear rate at the outer wall of annulus is obtained [33].
where δ is flow core distribution and k is consistency coefficient. Taking the construction data of a well in the oil field as an example, the density of the third spud isolation fluid is 2.42 g/cm 3 , n = 0.543, k = 1.398 Pa·s n , the hole diameter of the third spud in is D = 0.3112 m, and the casing size is d = 0.2445 m. The displacement is 33 L/s and the flow rate is 1.134 m/s. The shear rate is 261.26 s −1 , 261.28 s −1 , 261.25 s −1 , and 261.26 s −1 . It shows that Chen Jialiang's equation can be used for relevant calculation [33]. The inner diameter of flushing device barrel is 0.0536 m, and the outer diameter of simulated formation screen is 0.0305 m. Based on the principle of equal shear rate, the flow rate of the fluid in the flushing cylinder is 0.367 m/s and the displacement is 0.5333 L/s.

Design Principle of Experimental Device
There are many methods to evaluate the flushing effect of flushing fluid, but the rotary viscometer method or improved rotary viscometer method is still the main method for indoor flushing experiment, based on the principle of equal shear rate or replacing rotating stator with core for flushing experiment.
In this paper, based on the high-temperature and high-pressure filtration instrument, the water loss device is reformed and a new flushing fluid evaluation device is developed. The flow chart of the experimental device is shown in Figure 2.
Energies 2020, 13, x FOR PEER REVIEW 4 of 28 Assuming that the annular velocity is constant, considering the balance between pressure and shear stress, the expression of shear rate at the outer wall of annulus is obtained [33]. where δ is flow core distribution and k is consistency coefficient.
Taking the construction data of a well in the oil field as an example, the density of the third spud isolation fluid is 2.42 g/cm 3 , n = 0.543, , k = 1.398 Pa·s n , the hole diameter of the third spud in is D = 0.3112 m, and the casing size is d = 0.2445 m. The displacement is 33 L/s and the flow rate is 1.134 m/s. The shear rate is 261.26 s −1 , 261.28 s −1 , 261.25 s −1 , and 261.26 s −1 . It shows that Chen Jialiang's equation can be used for relevant calculation [33]. The inner diameter of flushing device barrel is 0.0536 m, and the outer diameter of simulated formation screen is 0.0305 m. Based on the principle of equal shear rate, the flow rate of the fluid in the flushing cylinder is 0.367 m/s and the displacement is 0.5333 L/s.

Design Principle of Experimental Device
There are many methods to evaluate the flushing effect of flushing fluid, but the rotary viscometer method or improved rotary viscometer method is still the main method for indoor flushing experiment, based on the principle of equal shear rate or replacing rotating stator with core for flushing experiment.
In this paper, based on the high-temperature and high-pressure filtration instrument, the water loss device is reformed and a new flushing fluid evaluation device is developed. The flow chart of the experimental device is shown in Figure 2.      Operation steps of flushing experiment: (1) Install the core on the mud cake forming device and pour oil-based drilling fluid as shown in Figure 3g. Fix the core on the base of the dehydration device, connect the nitrogen cylinder, and open the air inlet switch; (2) Open the valve of the nitrogen cylinder, adjust the pressure value to 5 MPa, open the bottom switch, and stand for 30 min; (3) After 30 min, close the lower and upper air inlet switches and close the nitrogen valve; remove the mud cake forming device and remove the core and weigh it as W 1 ; (4) Prepare a certain flushing fluid, pour it into the heating cylinder, heat it to 80 • C, and then put the core into the inner barrel of the flushing device. As shown in the Figure, the flushing device is placed on the dehydration base, the lower end is the liquid inlet and connected with the pump, and the upper end is the liquid outlet, which is connected to the heated flushing liquid cylinder through three pipes, and the pump is started to flush at a certain displacement; (5) After washing for a period of time, stop the pump, remove the core, and weigh it as W 2 ; (6) Clean the rock sample in step (5) and weigh it as W 3 ; (7) Calculate the flushing efficiency of flushing fluid as follows:

Experimental Sample
Five pairs of samples (as shown in Figure 4) are selected for flushing experiment. They are field sandstone (Figure 4a), ultra-low permeability core (0.01 mD) (Figure 4b), low permeability core (0.15 mD) (Figure 4c), medium permeability core A (10 mD) (Figure 4d), and medium permeability core B (150 mD) ( Figure 4e). The morphology of some rock samples after washing is shown in Figure 5.   Figure 5. Morphology of core after washing.- Figure 5 (a-e) shows the appearance of core in Figure 4 (a-e) after washing

Experimental Methods
In this paper, the test methods of interfacial bonding strength are as follows: take out the core which has been washed out from the flushing device and place the core in the middle of the steel sleeve; according to the requirements, prepare the cement slurry, lead the prepared cement slurry into the annular space formed by the steel sleeve and the core, put it into the constant temperature water bath for curing, take it out after the curing time, and cool it to room temperature. A certain pressure is slowly applied to the upper end face of the core by the digital bending and compression testing machine, and then the artificial core is slowly pressed out from the cement sheath. When the interface between the artificial core and the cement stone falls off, the value displayed by the instrument is the size of the shear force. The bond strength of the interface is calculated as shown in where σ is the interfacial bond strength, N/m 3 ; F is the interfacial shear stress, Pa; S is the core side area, m 2 ; r is the core radius, m; and h is the core height, m.  Figure 5 (a-e) shows the appearance of core in Figure 4 (a-e) after washing.

Experimental Methods
In this paper, the test methods of interfacial bonding strength are as follows: take out the core which has been washed out from the flushing device and place the core in the middle of the steel sleeve; according to the requirements, prepare the cement slurry, lead the prepared cement slurry into the annular space formed by the steel sleeve and the core, put it into the constant temperature water bath for curing, take it out after the curing time, and cool it to room temperature. A certain pressure is slowly applied to the upper end face of the core by the digital bending and compression testing machine, and then the artificial core is slowly pressed out from the cement sheath. When the interface between the artificial core and the cement stone falls off, the value displayed by the instrument is the size of the shear force. The bond strength of the interface is calculated as shown in Equation (8).
where σ is the interfacial bond strength, N/m 3 ; F is the interfacial shear stress, Pa; S is the core side area, m 2 ; r is the core radius, m; and h is the core height, m.

Evaluation of Flushing Experiment
According to the existing cementing literature reports [2,14], the main factors affecting the cementing displacement efficiency are displacement, displacement time, formation core properties, and flushing fluid system. Therefore, based on the investigation results and combined with the field cementing data, the type A flushing fluid system was selected to evaluate the flushing experiment of this project (A is a kind of flushing fluid equation for flushing evaluation).
Energies 2020, 13, 4483 8 of 22 As shown in Table 1 above, the type A flushing fluid system was selected for the experiment. Different flushing time, displacement, concentration of flushing fluid, and core type were used for flushing experiment, and the core flushing efficiency was calculated. As shown in Figure 6, the selected cores are 0.1 mD core (Φ 2.54 cm × 4.7 cm) (Figure 6a), 10 mD core (Φ 2.54 cm × 8.4 cm) (Figure 6b), and 150 mD core (Φ 2.54 cm × 4.7 cm) (Figure 6c).

Evaluation of Flushing Experiment
According to the existing cementing literature reports [2,14], the main factors affecting the cementing displacement efficiency are displacement, displacement time, formation core properties, and flushing fluid system. Therefore, based on the investigation results and combined with the field cementing data, the type A flushing fluid system was selected to evaluate the flushing experiment of this project (A is a kind of flushing fluid equation for flushing evaluation).
As shown in Table 1 above, the type A flushing fluid system was selected for the experiment. Different flushing time, displacement, concentration of flushing fluid, and core type were used for flushing experiment, and the core flushing efficiency was calculated. As shown in Figure 6, the selected cores are 0.1 mD core (Φ 2.54 cm × 4.7 cm) (Figure 6a), 10 mD core (Φ 2.54 cm × 8.4 cm) (Figure 6b), and 150 mD core (Φ 2.54 cm × 4.7 cm) (Figure 6c).

Evaluation of Flushing Effect of Type a Flushing Fluid
(1) The concentration of flushing solution is 10% Using the above flushing fluid evaluation device, sandstone cores with permeability of 0.1 mD, 10 mD, and 150 mD are flushed with type a flushing fluid with concentration of 10% under different displacement and time conditions. The flushing efficiency under different conditions can be calculated by Equation (7), as shown in Table 2 below.
According to the flushing time and displacement in Table 1, the amount of flushing fluid can be obtained, and the relationship between the amount of flushing fluid and the flushing efficiency can be obtained, as shown in Figure 7.  (7), as shown in Table 2 below. According to the flushing time and displacement in Table 1, the amount of flushing fluid can be obtained, and the relationship between the amount of flushing fluid and the flushing efficiency can be obtained, as shown in Figure 7.     (Figure 7a), which means that it can be washed clean. However, for cores with high permeability of 10 mD or even 150 mD, a greater amount of flushing fluid is needed to clean the cores (Figure 7b,c).
According to the data in Table 2, the relationship between flushing time and flushing efficiency under different cores can be obtained, as shown in Figure 8.   Figure 8 shows the evaluation of flushing results of different cores at the same discharge rate under the condition of 10% A-type flushing fluid concentration. It can be seen from the Figure that under the same displacement, for cores with different permeability, the flushing effect becomes worse with the increase of permeability. Under the condition of osmotic pressure, the core with high permeability forms thick and dense mud cake on the core surface, while the core with low permeability forms thin mud cake on the core surface. In addition, the flushing effect under the condition of 35 L/min (Figure 8c) is obviously better than that of 25 L/min (Figure 8b) and 10 L/min (Figure 8a). When the core permeability is 0.1 mD and 10 mD and the flushing time is about 25 min, the flushing efficiency is 90%.
(2) The concentration of flushing solution is 20% Using the above flushing fluid evaluation device, sandstone cores with permeability of 0.1 mD, 10 mD, and 150 mD are flushed with type a flushing fluid with concentration of 20% under different displacement and time conditions. The flushing efficiency under different conditions can be calculated by Equation (7), as shown in Table 3 below. According to the flushing time and displacement in Table 3, the amount of flushing fluid can be obtained, and the relationship between the amount of flushing fluid and the flushing efficiency can be obtained, as shown in Figure 9.      (7), as shown in Table 11. According to the flushing time and displacement in Table 11, the amount of flushing fluid can be obtained, and the relationship between the amount of flushing fluid and the flushing efficiency can be obtained, as shown in Figure 11. According to the flushing time and displacement in Table 4, the amount of flushing fluid can be obtained, and the relationship between the amount of flushing fluid and the flushing efficiency can be obtained, as shown in Figure 11. It can be seen from Figure 11 that when the core permeability is 0.1 mD, 10 mD, and 150 mD, the flushing efficiency is 90% when the flushing fluid consumption is 0.2 m 3 (Figure 11a), 0.36 m 3 ( Figure  11b), and 0.6 m 3 (Figure 11c), respectively. The flushing effect is better than that of 20% solution.
According to the data in Table 4 above, the relationship between flushing time and flushing efficiency under different cores can be obtained, as shown in Figure 12. It can be seen from Figure 11 that when the core permeability is 0.1 mD, 10 mD, and 150 mD, the flushing efficiency is 90% when the flushing fluid consumption is 0.2 m 3 (Figure 11a), 0.36 m 3 (Figure 11b), and 0.6 m 3 (Figure 11c), respectively. The flushing effect is better than that of 20% solution.
According to the data in Table 11 above, the relationship between flushing time and flushing efficiency under different cores can be obtained, as shown in Figure 12.  It can be seen from the Figure 12 that, under the same displacement, with the increase of core permeability, the worse the flushing efficiency. When the displacement of flushing fluid is 10 L/min, the permeability is 0.1 mD and 10 mD, and the flushing time is 25 min, the flushing efficiency reaches 90% (Figure 12a); when the displacement of flushing fluid is 25 L/min, the flushing efficiency of 0.1 mD flushing time is 15 min, and 10 mD and 150 mD core flushing time is 20 min, the flushing efficiency reaches 90% (Figure 12b); when the displacement of flushing fluid is 35 L/min, the flushing efficiency of 0.1 mD and 10 mD flushing time is 10 min, and 150 mD core is 15 min, the flushing efficiency is 90% (Figure 12c). When the concentration of flushing fluid is 30%, good results can be achieved for cores with different permeability under certain flushing time.

Bond Strength Test Results
The compressive testing machine is used to load test the curing test sample. The following sample Figure 13(1-5) are as follows: in situ sandstone, ultra-low permeability core (0.1 mD), low permeability core (0.15 mD), medium permeability core A (10 mD), and medium permeability core B (150 mD)) to determine the interfacial bonding strength. The following Figure 14 shows the sample diagram of clean core and washed core after curing in 80 • C water bath box for 48 h.   Table 5 shows the comparison test data of the interface cementation strength between clean core and core after flushing. It can be seen from the Table that although the interfacial bonding strength of clean core is not high, the interfacial bonding strength of clean core is higher than that of washed core; and the greater the permeability of core, the smaller the interfacial bonding strength of core. The main reason is that during the setting process of cement slurry, the water of cement slurry continuously permeates into the rock core under the condition of osmotic pressure. Under the condition of the same osmotic pressure, the greater the permeability of the core, the greater the water infiltration into the core. The infiltration of water has a certain hydration effect on the core, which reduces the strength of the interface with cement slurry and the bonding strength of the interface. In addition, from the ultra-low permeability core to the medium permeability core, the solid particles in the drilling fluid will be continuously compacted on the rock surface in the process of mud cake formation under the condition of pressure difference, so the core with larger porosity and permeability will have greater thickness of mud cake attached to its surface, which will lead to it becoming more difficult to wash in the washing process. Therefore, the permeability of rock is an important factor affecting the second interface cementing-that is, the lower the permeability, the greater the cementing strength; and the greater the permeability, the smaller the cementing strength.

Micro-Morphology Analysis of Interface Cementation
The microscopic morphology of the interface between core and cement paste was analyzed by depth stereomicroscope under different conditions. It can be more intuitive to observe the cementation of the interface between core and cement stone and provide certain guidance for further analysis of the interface bonding. One of the instruments used in this experiment is the depth stereomicroscope: select a certain core and cement paste cementation sample and core, and observe the sample with depth stereomicroscope, as shown in Figure 15.  Table 5 shows the comparison test data of the interface cementation strength between clean core and core after flushing. It can be seen from the Table that although the interfacial bonding strength of clean core is not high, the interfacial bonding strength of clean core is higher than that of washed core; and the greater the permeability of core, the smaller the interfacial bonding strength of core. The main reason is that during the setting process of cement slurry, the water of cement slurry continuously permeates into the rock core under the condition of osmotic pressure. Under the condition of the same osmotic pressure, the greater the permeability of the core, the greater the water infiltration into the core. The infiltration of water has a certain hydration effect on the core, which reduces the strength of the interface with cement slurry and the bonding strength of the interface. In addition, from the ultra-low permeability core to the medium permeability core, the solid particles in the drilling fluid will be continuously compacted on the rock surface in the process of mud cake formation under the condition of pressure difference, so the core with larger porosity and permeability will have greater thickness of mud cake attached to its surface, which will lead to it becoming more difficult to wash in the washing process. Therefore, the permeability of rock is an important factor affecting the second interface cementing-that is, the lower the permeability, the greater the cementing strength; and the greater the permeability, the smaller the cementing strength.

Micro-Morphology Analysis of Interface Cementation
The microscopic morphology of the interface between core and cement paste was analyzed by depth stereomicroscope under different conditions. It can be more intuitive to observe the cementation of the interface between core and cement stone and provide certain guidance for further analysis of the interface bonding. One of the instruments used in this experiment is the depth stereomicroscope: select a certain core and cement paste cementation sample and core, and observe the sample with depth stereomicroscope, as shown in Figure 15. From the macroscopic observation in Figure 15, it can be seen from the macroscopic observation that during the cementation process, the cement stone is cemented with the mud cake on the core surface, which makes the mud cake adhere to the cement stone ( Figure 15a); when the clean core is cemented with the cement stone, the cement stone and the core are directly cemented (Figure 15b). Therefore, the bond strength between the undrained core and the cement stone is lower than that between the clean core and the cement stone.
In view of the interface cementation under the above two conditions, the micro-morphology under the two conditions was analyzed with the help of depth stereomicroscope, as shown in Figure  16. From the macroscopic observation in Figure 15, it can be seen from the macroscopic observation that during the cementation process, the cement stone is cemented with the mud cake on the core surface, which makes the mud cake adhere to the cement stone ( Figure 15a); when the clean core is cemented with the cement stone, the cement stone and the core are directly cemented (Figure 15b). Therefore, the bond strength between the undrained core and the cement stone is lower than that between the clean core and the cement stone.
In view of the interface cementation under the above two conditions, the micro-morphology under the two conditions was analyzed with the help of depth stereomicroscope, as shown in Figure 16.
It can be seen from the micrograph in Figure 16 that when the mud cake attached to the core is cured with the cement slurry at a certain pressure and temperature, the cement slurry gradually coagulates during the curing process, and the mud cake contacting with the cement slurry also gradually solidifies; then, during the condensation process of the two substances, their volume will shrink, and the cement slurry will be cured (Figure 16a,c,e). The formation of fractures makes the cementation interface difficult to bear the effect of certain shear stress, which makes the interface cementation strength less when mud cake is attached to the core surface and cement slurry. In addition, when cementation occurs between the core and the cement slurry, firstly, because the core surface has a certain roughness, the cement slurry is closely attached to the surface of the rock sample. Although the volume shrinkage of the cement slurry will occur during the setting process, the volume shrinkage spacing is smaller than the roughness of the core surface, so that the two can be connected together, as shown in the right of the above Figure. Therefore, the clean core and cement paste are closely cemented, and the interface cementation strength is high (Figure 16b,d,f), while it is easy for the cementation interface between the clean core and the cement stone to form cracks in the cementation process, which leads to the decrease of the interface bonding strength. It can be seen from the micrograph in Figure 16 that when the mud cake attached to the core is cured with the cement slurry at a certain pressure and temperature, the cement slurry gradually coagulates during the curing process, and the mud cake contacting with the cement slurry also gradually solidifies; then, during the condensation process of the two substances, their volume will shrink, and the cement slurry will be cured (Figure 16a,c,e). The formation of fractures makes the cementation interface difficult to bear the effect of certain shear stress, which makes the interface