A wellbore fluid performance parameters–temperature–pressure coupling prediction model during the managed pressure cementing injection stage

Managed pressure cementing (MPC) is a new technology based on managed pressure drilling, which has a greater advantage in facing narrow density window formations. However, the existing pressure prediction models during MPC injection stage consider fewer factors and have lower accuracy. To this end, combined with the characteristics of the injection stage, a predictive model of the distribution of annular fluid type was first proposed. Then, based on the experimental results, fluid density and rheology as a function of temperature and pressure were fitted. The governing equation of temperature‐pressure field was established. Eventually the fluid performance parameters–temperature–pressure coupling prediction model was developed in this paper. By comparing the predicted pump pressure with the measured pump pressure, the maximum relative error is not more than 10%. Using this model, the fluid type distribution, temperature field distribution, and pressure field distribution were investigated. The results indicated that the distribution of fluid types in the wellbore presented a complex variation, with up to 10 fluids in the casing and up to five fluids in the annulus. The trend of temperature field is complex, with three turning points. The larger the formation temperature gradient, the higher the fluid temperature in the annulus. The influence law of fluid heat conduction coefficient is reversed at 6750 m. Decreasing drilling fluid density will trigger gas channeling, while increasing drilling fluid density will increase the risk of fracturing formation, and safe operation can be realized by MPC. The variation of the static pressure in the casing is more complicated than in the annulus and the annular circulation pressure in the eccentric casing is smaller than that of the concentric casing, which is due to the smaller annular friction pressure. This study can provide a theoretical basis for the prediction of hydrodynamic parameters during the MPC injection stage.


| INTRODUCTION
With the increase of well depth, the construction process is more and more faced with high temperature and high pressure, narrow density window, narrowing of wellbore flow channel, and long bare hole section. 1,2The increasingly complicated construction conditions bring new challenges to cementing operation.For cementing in complex formations, gas kick is very easy to occur under the induction of lower bottomhole pressure.In addition, if the bottomhole pressure is increased excessively during cementing, it may also lead to downhole leakage.All these situations may cause failure of cementing construction and bring great risk to cementing construction.As the cementing injection process is complicated and involves many steps, it is extremely urgent to master the managed pressure cementing (MPC) technology on this field. 3,4PC is a new cementing technology based on managed pressure drilling (MPD), which applies the principle and hardware equipment of MPD to the liner cementing process and realizes the fine control of wellbore pressure during the liner cementing process. 5The study of MPC technology will greatly reduce the cost of cementing, improve the quality of cementing, reduce the occurrence of accidents, and ultimately further improve the level of oil and gas drilling and completion.][8][9][10] Due to the limitation of field conditions, it is difficult to launch downhole pressure monitoring tools during the cementing process, so the acquisition of wellbore pressure data relies on the prediction through mathematical modeling.
The key to accurate prediction of wellbore pressure is to determine the hydrostatic column pressure and annular friction pressure, which are closely related to the temperature field, the distribution of circulating fluid type, the friction coefficient, the flow rate, and the flow channel parameters.Soto et al. 11 proposed a real-time calculation model of wellbore pressure in cementing injection stage and demonstrated the reliability of the model through the cementing quality logging charts.Pilehvari et al. 12 and Kelessidis et al. 13 deduced the relationship model between the flow rate and the pressure drop for the Bingham fluid, the power-law fluid, the Herschel-Bulkley fluid, and the Carson fluid, respectively.Wolski et al. 14 and Dosunmu et al. 15 found that the eccentricity of the pipe column have a large effect on the annular friction pressure, and a wellbore pressure calculation model considering the eccentricity of the pipe column was established.Although there are more research on theoretical models of wellbore pressure, MPC involves the injection of multiple fluids, which has significant effects on the hydrostatic column pressure and annular friction pressure, resulting in a larger calculation error of the existing wellbore pressure profile prediction model.At present, the accuracy of the wellbore pressure prediction model still needs to be improved.
The cementing process involves many types of fluids such as drilling fluids, flushing fluids, and cement slurries.The performance parameters, including fluid density and fluid rheology, vary greatly among different types of fluids, which poses a challenge to the prediction of the pressure field in the annulus.Politte et al. 16 and Sherif et al. 17 optimized the rheological modes suitable for flusher and spacer based on the experimental results, which improved the accuracy of the description of the rheological properties of the precursor fluids.Vipulanandan et al. 18 have successively carried out experimental studies on the rheological properties of cement pastes under different temperature conditions, which have shown that the laws of temperature effect on rheology are different for different temperature ranges, and that the laws varies considerably for each range.Currently, there have been studies focusing on conducting experiments on the effects of temperature and pressure on fluid density and rheology, 19,20 but there are fewer studies on predictive modeling of fluid performance parameters, and the predictive models that have been established are not able to satisfy the application conditions of deep wells with large changes in temperature and pressure.
In addition, the prediction of wellbore temperature field is of great significance for the determination of fluid performance parameters and the calculation of wellbore pressure, and it is also an important basis for other related research.For the wellbore temperature field during drilling, a more mature prediction method has been formed due to a large number of theoretical research conducted by scholars and the application of temperature measurement devices such as measurement while drilling. 21,22While during cementing injection, the acquisition of temperature field also relies on the prediction through mathematical modeling because temperature measurement devices cannot be installed. 23Currently, the common method for predicting the temperature of the cement injection stage in the field is the API method proposed by the American Petroleum Institute. 24However, the prediction result of this method is generally high, which makes the designed cement slurry excessively slow-setting and greatly reduces the cementing quality.Bittleston et al. 25 used the method of empirical coefficients to modify the models, but the modified models had fewer considerations and were only applicable to a few blocks.Subsequently, after the development of Guillot et al., 26 the accuracy and applicability of the models have been improved, although these models are only applied to conventional cementing.
To this end, a method is first proposed to determine the distribution of fluid types by using fluid critical positions and markers, which is simpler than traditional methods.At the same time, the feasibility of the method is demonstrated by 10 types of fluid.Subsequently, the equations of fluid density and fluid rheological parameters with temperature and pressure were fitted.Finally, combined with the characteristics of the MPC injection stage and the effects of temperature and pressure on fluid density and rheological parameters, a wellbore fluid performance parameterstemperature-pressure coupling prediction model was developed in this paper.Based on the field data, the fluid type distribution, fluid density distribution, fluid rheological parameter distribution, temperature field distribution, and pressure field distribution during the MPC injection stage were predicted and analyzed.Compared with the existing models, the proposed model comprehensively considers the coupling effects of fluid performance parameters, temperature, and pressure.During the MPC injection stage, the wellhead back pressure is controlled to ensure that the bottomhole pressure is always within a safe range, which is suitable for complex cement conditions of all types of fluids.This study can provide a highly accurate prediction model of hydrodynamic parameters for MPC technology.

| MATHEMATICAL MODEL
Combined with the characteristics of the MPC injection stage, a model for predicting the distribution of fluid types was developed for calculating the distribution of different fluid types with time.Based on the experimental results, fluid density and rheology as a function of temperature and pressure were fitted.The effect of casing eccentricity on annular friction pressure was considered, and the governing equation of temperature-pressure field was established.Eventually the fluid performance parameters-temperature-pressure coupling prediction model was developed.

| Determination method of fluid type distribution
During the injection process, multiple fluids exist in the wellbore, and the fluid positions change continuously with time.To describe the distribution of each fluid position with time, the fluid injection process is simplified as shown in Figure 1.The key time points include the following: 1.The moment of injection of the different types of fluid, such as spacer, flusher, and cement slurry.2. The moment the spacer, flusher, and cement slurry reach the bottom of the well.3. The moment when the MPC injection stage ends.
According to the key time points, a method is proposed to determine the distribution of fluid types by using fluid critical positions and markers, which is simpler than traditional methods.
The distribution of different types of fluids interfaces in the wellbore can be expressed by F I G U R E 1 Schematic of fluid type distribution during managed pressure cementing injection stage.
After the fluid reaches the bottom of the well from the wellhead, it continues to flow out along the annulus toward the wellhead.At this point, the flow direction changes.Using the number 0 to mark that the fluid is in the casing and the number 1 to mark that the fluid is in the annulus, whether the fluid is located in the casing or in the annulus can be determined using the following equation: where L i t and L t ( ) i are the notation for the location of fluid i.
Considering the different structure of casing and annular flow path, the casing area is A in and the annular area is A out .The specific calculation is formulated as where A in is the casing area, m 2 ; A out is the annular area, m 2 ; d a is the outer diameter of the casing, m; λ is the casing wall thickness, m; D a is the outer diameter of the annulus, m.According to Equations (1)-(3), the equations for the distribution of different types of fluid interfaces with time can be obtained by where f t ( ) i is the fluid interface position function.The inverse function of Equation ( 4) can be calculated by . The same type of fluid is located between two adjacent interfaces, so the density of the fluid can be predicted by where ρ h t ( , ) and ρ h H L ( , , ) t are the density of the fluid at depth h at moment t, kg/m 3 ; ρ i is the density of fluid i, kg/m 3 ; ρ i+1 is the density of fluid i + 1, kg/m 3 .
The drilling fluid, prefluid, and cement slurry in the cementing process are all non-Newtonian fluids with yield-pseudoplastic properties, so the Herschel-Bulkley rheological model 27 is chosen to describe the rheology of these types of fluids where γ  is the shear rate, s −1 ; τ is the shear force, Pa; τ 0 is the dynamic shear force, Pa; μ is the viscosity, Pa s; K is the consistency factor, Pa s n ; n is the fluidity index.
Similarly, the rheological parameters of different types of fluids can be predicted by where Γ is the set of rheological parameters n K τ { , , }.In addition to Herschel-Bulkley rheological model, Bingham rheological model, power-law rheological model, and Carson rheological model can also be used in this model.By replacing the rheological parameters in Equations ( 7) and ( 8), the subsequent wellbore temperature and pressure calculations can be achieved.Therefore, the proposed model can be applied to different types of fluids.

| Fitting functions for fluid performance parameters
Using the method in Section 2.1, the distribution of fluid types in the wellbore can be predicted, and the fluid performance parameters are represented by Equations ( 7) and (8).However, the fluid performance parameters are not only related to fluid type but also closely related to temperature and pressure.
The physical diagram of the experimental equipment is shown in Figure 2. The name of the equipment in the figure is Anto Paar density meter, which can be used to complete the density measurement experiment.The working pressure range of the equipment is atmospheric pressure to 120 MPa, and the working temperature range is from −50°C to 200°C.Experiments were conducted to investigate the effects of temperature and pressure on the performance of drilling fluids.The fluid performance parameters include fluid density and rheological parameters.The experimental data were fitted with polynomials and the fluid density and rheological parameters were expressed by Equations ( 9) and (10), respectively.
Higher temperatures produce an expansion effect in the drilling fluid and a decrease in drilling fluid density; higher pressures produce a compression effect in the drilling fluid and an increase in drilling fluid density.The effects of temperature and pressure can be shown by where ρ 0 is the density at standard conditions, kg/m 3 ; ϕ is the density correction coefficient; ξ p , ξ pp , ξ T , ξ TT , and ξ pT are the regression coefficients; p is the pressure, Pa; T is the temperature, °C; p 0 is the standard pressure, Pa; T 0 is the standard temperature, °C.Different temperatures and pressures affect the effective viscosity of a fluid.The effective viscosity decreases when the temperature increases and increases when the pressure increases, and the viscosity is influenced by the coupling of temperature and pressure. 28e experimental data show that the rheological parameters are quadratic with temperature and primary with pressure under different temperature and pressure conditions.The equations can be described as The regression coefficients in the equations are shown in Table 1.The value of the change in mass per unit volume of fluid per unit time is equal to the difference in mass between inflow and outflow.The equation for the conservation of mass of the fluid can be given by

| Temperature-pressure governing equation
where v is the density at standard conditions, m/s.The density of a fluid is related to the type of fluid, temperature, and pressure, which can be converted to a function of time with the following equation: As shown in Figure 3, the forces on the cemented fluid microelements were analyzed.These forces include interfacial pressure, gravity, and friction pressure loss.The momentum balance equation is represented by the following equation: where g is the gravitational acceleration, m/s 2 ; z is the vertical depth, m; p f is the friction pressure loss, Pa.The frictional resistance of the fluid in the casing can be calculated by where p f c is the friction pressure in the casing, Pa; f c is the frictional coefficient in the casing.The frictional resistance of the fluid in the annulus can be deduced as where p f a is the friction pressure in the annulus, Pa; f a is the frictional coefficient in the annulus.
Casing eccentricity is unavoidable due to the small gap in the annulus of ultradeep wells.Compared with concentric annulus, the frictional resistance in the annulus of eccentric casing can be minimized by up to 40%.Therefore, it is necessary to correct the frictional resistance of eccentric annulus.Eccentric annulus correction coefficient is the ratio of eccentric annulus friction resistance to concentric annulus friction resistance.The eccentricity correction coefficient can be replaced by 29 R p p = , where R is the eccentricity correction coefficient; p f ecc is the friction pressure in the eccentric annulus, Pa; p f con is the friction pressure in the concentric annulus, Pa.
Based on the Herschel-Bulkley fluid, the eccentric annulus correction coefficient for laminar flow can be expressed as 30 T A B L E 1 The regression coefficients in the equations.
where R lam is the eccentricity correction coefficient for laminar flow; e is the casing eccentricity.
The eccentric annulus correction coefficient for turbulent flow can be expressed as 31 where R turb is the eccentricity correction coefficient for turbulent flow.
Considering the heat transfer modes between casing, annulus, and formation, the corresponding energy conservation equations are established for describing the heat transfer process in the MPC injection stage.
The heat transfer process of the fluid inside the casing includes axial heat transfer and radial heat transfer between the fluid and the casing. 32,33The equations are as follows: where c ρ is the specific heat capacity, J/(kg °C); T c is the fluid temperature of the casing, °C; k l is the heat transfer coefficient of the fluid, W/(m °C); T a is the fluid temperature of the annulus, °C.
The heat transfer process of fluids in the annulus includes heat conduction between fluids, forced convection heat transfer between fluids and the outer casing wall and well wall.The equations are as follows: where h w is the convective heat transfer coefficient between the fluid in the annulus and the well wall, W/(m 2 °C); T c is the fluid temperature of the well wall, °C.
Considering only axial and radial heat conduction in the formation, the governing equations for the formation temperature field are as follows: where h w is the heat transfer coefficient of the formation, W/(m °C); T e is the fluid temperature of the formation, °C; r is the radial distance, m.

| Initial and boundary conditions
Pressure and temperature data at some moments and locations are known and need to be solved for temperatures and pressures at other moments and locations.Initial and boundary conditions are given to help the model to be solved.At the initial moment, the fluid temperature in the wellbore is the same as the formation temperature where T s is the ground temperature, °C; G is the temperature gradient of the formation, °C/m.At the wellhead, the fluid temperature can be measured in real time by means of a sensing device where T in is the temperature of the injected fluid, °C.At the bottom of the well, the temperature of the fluid in the casing and the fluid in the annulus are equal:

| Model solution
The principle of MPC is to realize accurate control of bottomhole pressure through real-time calculation of wellbore hydraulics parameters and control of wellhead back pressure in the cementing process, so as to keep bottomhole pressure within the safe range.Combined with the principle of MPC and the model in Sections 2.1-2.3 (the role of each model in the calculation process has been marked with red boxes), the solution method of cyclic iterative method is proposed, and the above model is coupled.Each iteration ensures the convergence of wellbore pressure, wellbore temperature and wellhead back pressure, and calculates the current annular fluid distribution before entering the next iteration.According to the above method, the pressure control process of cementing injection stage is simulated, and the specific calculation flow is shown in Figure 4.The geological conditions in Sichuan Basin are complicated, and the cementing process faces such difficulties as HTHP, narrow density window, long cementing time, and so forth.Gas intrusion and well leakage are very likely to occur by conventional cementing methods (CCMs), and the quality of cementing can hardly meet the later production requirements.To solve the above problems, well X decided to adopt the MPC for cementing operation. 5The basic parameters of the simulated well: well depth of 7800 m, borehole size of 139.7 mm, tail pipe outer diameter of 114.3 mm, inlet temperature of 30°C, surface temperature of 15°C, ground temperature gradient of 0.028°C/m, and the design parameters of the fluid are shown in Table 2.Because fluid 8 and fluid 11 are identical, a total of 10 fluid types are used in this well X.

| Predicted and measured pump pressure results
During the MPC injection stage, the pump pressure curve with time can be observed at the wellhead.Therefore, the measured pump pressure results can be obtained by exporting the data using the controlled pressure cementing software.The pump pressure results predicted using the model in this paper are compared with the measured pump pressure results, as shown in Figure 5.It can be found that the predicted results have the same trend with the measured results, and the maximum relative error is less than 10%, which makes the model of this paper have high accuracy.
The reason for the error is, on the one hand, due to the frequent changes in the displacement during the injection stage, which makes the measured pump pressure unstable and difficult to be accurately predicted by the model in this paper.On the other hand, it is due to the complexity of the field process, the uncertainty of the process has an impact on the pump pressure.slurry, enter the annulus, the annular fluid density distribution changes continuously with time.On the other hand, during the whole injection stage, the temperature and pressure field of the wellbore keeps changing, and the change of temperature and pressure will have an effect on the density of the fluid in the annulus, so that the density of the same type of fluid is variable at different well depths.The effect of temperature and pressure on fluid density is not negligible, and this is less considered in conventional cementing models.Therefore, the fluid performance parameters-temperature-pressure coupling model proposed in this paper is very helpful to the accuracy of pressure control.
The laws of rheological parameters of the fluid were analyzed in terms of viscosity.The distribution of different types of fluid viscosity in the annulus at different moments was calculated as shown in Figure 9.
It can be found that the viscosity change of the annular fluid is small before the spacer enters the annulus (101.76 min), which is due to the fact that at this time the distribution of the annular fluid type is a single-column structure, and the type of the annular fluid does not change.At the moment when the spacer (101.76 min), flusher (122.88 min), leading slurry (125.44 min), and tailing slurry (142.08 min) enter the annulus, the viscosity distribution of the annular fluid changes significantly, which is due to the change of the type of the fluid in the annulus.Similarly, the magnitude of viscosity values varies at different well depths due to differences in temperature and pressure.Viscosity has an effect on frictional heat generation and circulating frictional resistance, which in turn has an effect on the temperature and pressure field.Thus, the relationship between the two is coupled.In the field, the drilling fluid has been circulated in the wellbore for a period of time.To make the simulated conditions more in line with the field situation, the temperature field formed after the drilling fluid has circulated in the wellbore for 10 h is used as the initial condition of the temperature field in the injection stage.The distributions of fluid temperatures in the casing and in the annulus with well depth at different moments were calculated as shown in Figure 10 and Figure 11, respectively.
Overall, the fluid temperature in the annulus is greater than that in the casing, which is mainly due to the fact that the formation temperature is greater than the fluid temperature at the inlet, and the fluid is continuously heated in the process of flowing from the casing down to the bottom of the well and then returning from the annulus to the wellhead, and the fluid in the annulus rises its temperature higher because of the long heating time.At the same time, with the increase of the circulation time, the temperature change amplitude is getting smaller and smaller, which indicates that the temperature field of the casing-wellbore-formation system develops in the direction of thermal equilibrium, and this trend is in line with the classical thermodynamic theory.
As can be seen from the temperature variation curve of the fluid in the casing as shown in Figure 10, the temperature of the fluid in the section above the turning point "T IF1 " (the depth of the well is about 1600 m) increases gradually with the increase of the circulation time, while the fluid temperature increases continuously with the increase of the circulation time in the section below the turning point "T IF1 ."The fluid temperature decreases with the increase of circulation time in the section below the turning point "T IF1 ."This is because the fluid temperature difference between different regions in the upper well section is small, so that the heat generated by viscous dissipation of the fluid is larger than the heat generated by convection and heat transfer, which leads to a gradual increase of the temperature, while the opposite is true in the lower well section, and the same phenomenon exists in the turning point "T IF2 " in Figure 11.In addition, at the turning point "T IF3 " in Figure 11, the temperature of the annulus fluid reaches the maximum value, which is consistent with the changing pattern of the temperature field in the drilling process.
The distributions of fluid temperature in the casing and in the annulus with time are calculated for different well depths as shown in Figure 12 and Figure 13, respectively.Comparing the calculation results in Figure 12 and Figure 13, it can be seen that the temperatures at different locations of the casing and the annulus gradually tend to equilibrate with the increase of time.Meanwhile, the rate of temperature change decreases with the increase of injection time, which indicates that the temperature field of the casing-annulus-formation system moves toward thermal equilibrium, which is consistent with the classical thermodynamic theory.For the wellhead position, the temperature at the wellhead gradually increases with time because the high temperature fluid in the annulus flows from the bottom of the well to the wellhead.For the bottomhole position, the temperature gradually decreases because the low-temperature fluid enters the annulus from the casing.
However, for the middle portion of the well depth location (including 2000 and 5000 m), the temperature inside the casing and the temperature inside the annulus show opposite patterns of change.The fluid temperature inside the casing decreases gradually with time, and the temperature in the annulus increases gradually with time.The decrease of the temperature in the casing is due to the injection of low-temperature fluid, while the increase of the temperature in the annulus is due to the warming effect of the formation.
The change of annulus temperature will affect the density and rheology of the fluid, and then change the bottomhole pressure.To accurately control the bottomhole pressure, it is necessary to analyze the influence of wellbore parameters on the annular temperature field, such as formation temperature gradient and heat conduction coefficient.For different formation temperature gradient and thermal conductivity conditions, the variation pattern of the annular temperature distribution is different.Especially for the bottom hole circulation temperature (BHCT), these two factors have a great influence.
The distributions of fluid temperature in the annulus with well depth under different formation temperature gradients (2.2°C/100 m, 2.5°C/100 m, 2.8°C/100 m, and 3.1°C/100 m) are calculated as shown in Figure 14.
According to the calculation results, the larger the formation temperature gradient, the higher the overall temperature of the annulus fluid.This is due to the fact that the larger the formation temperature gradient, the higher the formation temperature, the greater the temperature difference between the formation and the annulus fluid, the more heat is transferred from the formation to the annulus fluid, and the higher the temperature of the annulus fluid increases.At the wellhead location, the annular fluid temperature difference caused by the different formation temperature gradient is small and can be ignored.However, at the bottom of the well, the BHCT difference caused by the different formation temperature gradient is large, about 62°C.This indicates that the effect of the formation temperature gradient on the annulus fluid temperature is more pronounced for deep and ultradeep wells.
The distributions of fluid temperature in the annulus with well depth under different fluid heat conduction coefficients (1.2 W/(m* °C), 1.7 W/(m* °C), 2.2 W/(m* °C), and 2.7 W/(m* °C)) are calculated as shown in Figure 15.

| Predicted results for the pressure field distributions
According to the definition of heat conduction, the larger the heat conduction coefficient, the faster the heat transfer, and the more sufficient the heat transfer of the annulus fluid in the same time.This phenomenon is fully reflected in the figure .According to the simulation results, when the well depth is less than 6750 m, the heat transfer coefficient is larger and the annulus temperature is lower; when the well depth is greater than 6750 m, the heat transfer coefficient is larger and the annulus temperature is This is because when the well depth is less than 6750 m, the temperature of the annulus fluid is greater than the formation temperature, and the annulus transfers heat to the formation.The larger the heat transfer coefficient is, the more heat is released from the annulus fluid, and the lower the temperature of the annulus fluid is.However, when the well depth is greater than 6750 m, the temperature of the annulus fluid is less than the formation temperature, and the formation transfers heat to the annulus.The larger the heat transfer coefficient is, the more heat is absorbed by the annulus fluid, and the higher the temperature of the annulus fluid is.At the bottomhole position, the annular temperature change caused by the heat conduction coefficient is the largest, and the difference in the BHCT is about 10°C.It is worth mentioning that this will not only have an impact on the bottomhole pressure but also have an impact on the waiting setting time of the cement slurry, so it must be paid attention to.
Back pressure cannot be applied at the wellhead during CCMs, so the bottomhole pressure can only be adjusted by changing the density of the drilling fluid.The bottomhole pressure prediction results for the two CCM are predicted as shown in Figure 16.
The first method is to use a drilling fluid with a density of 2.1 g/cm 3 (Figure 16A).Since the density of the flusher is 1.0 g/cm 3 , when the flusher enters the annulus, the bottomhole pressure will gradually decrease to less than the pore pressure, and then gas channeling may be triggered.Subsequently, the cement slurry enters the annulus, and the bottomhole pressure gradually increases to be greater than the breakdown pressure, which is easy to fracture the formation.To avoid fracturing the formation, the second method is to use a low-density drilling fluid of 2.0 g/cm 3 (Figure 16B).Although the bottomhole pressure remains within the safe pressure window after the cement slurry enters the annulus, the bottomhole pressure is still less than the formation pressure until 140 min, and the gas channeling still cannot be solved.Therefore, this method is also unfeasible.
In summary, decreasing drilling fluid density will trigger gas channeling, while increasing drilling fluid density will increase the risk of fracturing formation, and safe operation cannot be realized by CCM.
MPC can realize precise control of bottomhole pressure through real-time calculation of wellbore hydraulics parameters and application of wellhead backpressure.During the MPC injection stage, the bottomhole pressure is kept within a safe range.The bottomhole pressure prediction results of the MPC are predicted as shown in Figure 17.As fluids such as flusher are injected, the annular hydrostatic column pressures (Figure 18) and annular friction pressure (Figure 19) are constantly changing due to variability in displacement and slurry column structure.To control the bottomhole pressure unchanged, the value of wellhead backpressure keeps changing.After the cement slurry enters the annulus, to avoid fracturing the formation, the wellhead back pressure becomes 0. At this time, the bottomhole pressure is constantly changing, but it is always within the safe range.Therefore, safe operation can be realized by MPC.
The annular hydrostatic column pressures and annular friction pressure are important components of bottomhole pressure.To better understand the change law of bottomhole pressure, these two pressures are calculated and analyzed.
The hydrostatic column pressure is closely related to the fluid type distribution.The casing and annular hydrostatic column pressure calculation results are shown in Figure 18.After analyzing the distribution of different types of fluids in the casing (Figure 6) and annulus (Figure 7), we can see that there are up to 10 types of fluids in the casing (79.74 min) while there are up to five types of fluids in the annulus (156.3 min), so the variation of the static pressure in the casing is more complicated than in the annulus.In addition, it is found that at the end of the injection stage, the hydrostatic column pressure is less than the pore pressure and the circulating friction is 0. If the CCM is used, which does not apply the wellhead backpressure, the bottomhole pressure will be less than the pore pressure, and gas channeling is bound to occur.
During casing running, the casing is often eccentric, and the eccentricity varies from 0 to 1.To facilitate the study, the casing with eccentricity 0 and 0.4 was selected as the research object for calculation and analysis.Figure 19 illustrates the annular circulation pressure and annular friction pressure prediction results at different eccentricity conditions.The annular circulation pressure is the sum of annular friction pressure and annular hydrostatic column pressure.It can be seen that the annular circulation pressure in the eccentric annulus is smaller than that of the concentric annulus (Figure 19A), which is due to the smaller annular friction pressure in the eccentric annulus (Figure 19B).However, the eccentric annulus does not affect the distribution of fluid types and hydrostatic column pressure in the annulus, so the focus should be on correcting the annular friction pressure for eccentric annulus.According to the calculation results, the magnitude of the annular friction pressure is influenced by the displacement and fluid type distribution, which are also coupled with each other.

| CONCLUSIONS
Combined with the characteristics of the MPC injection stage and the effects of temperature and pressure on fluid density and rheological parameters, a wellbore fluid performance parameters-temperature-pressure coupling prediction model was developed to investigate the laws of fluid type distribution, wellbore pressure field and wellbore temperature field.The main conclusions are as follows: 1. Compared with the existing models, the proposed model comprehensively considers the coupling effects of fluid performance parameters, temperature, and pressure.During the cement injection stage, the wellhead back pressure is controlled to ensure that the bottomhole pressure is always within a safe range, which is suitable for complex cement conditions of all types of fluids.By comparing the predicted pump pressure with the measured pump pressure, the maximum relative error is not more than 10%, which can show that the model has high accuracy.2. There are many fluids in the wellbore during MPC injection stage, up to 10 fluids in the casing and up to five in the annulus.Changes in fluid type distribution have a direct impact on casing hydrostatic static column pressure and friction pressure.3. The trend of the cementing temperature field is complex, with three turning points.The temperatures at different locations of the casing and the annulus gradually tend to equilibrate with the increase of time.
For the middle portion of the well depth location, the fluid temperature inside the casing decreases gradually with time, and the temperature in the annulus increases gradually with time.4. The larger the formation temperature gradient, the higher the fluid temperature in the annulus.The influence law of fluid heat conduction coefficient on the annulus fluid temperature is reversed at the position of 6750 m.The BHCT change due to the formation temperature gradient is 62°C, and the change due to the fluid heat transfer coefficient is 10°C. 5. Decreasing drilling fluid density will trigger gas channeling, while increasing drilling fluid density will increase the risk of fracturing formation, and safe operation cannot be realized by CCM. the bottomhole pressure is constantly changing, but it is always within the safe range by MPC. 6.The annular circulation pressure in the eccentric casing is smaller than that of the concentric casing, which is due to the smaller annular friction pressure in the eccentric casing.However, the eccentric casing does not affect the distribution of fluid types and hydrostatic column pressure in the annulus, so the focus should be on correcting the annular friction pressure for eccentric casing.
With the injection of different types of fluids during the MPC injection stage, there are both drilling fluids and cement slurry with different physicochemical properties in the wellbore.The distribution of fluid types, changes in fluid density and rheological parameters, casing eccentricity, and other factors will affect the temperature and pressure field of the wellbore.In this regard, the corresponding mass conservation equation, momentum balance equation, and energy conservation equation are established.To facilitate the modeling, the following assumptions are made: 1.The fluid movement in the wellbore is onedimensional flow.2. Ignoring the effect of diffusion between different types of fluids on the pressure distribution in the annulus.3. The rate of hydration reaction of cement slurry during the injection stage is zero.4. Neglecting wavering pressures due to changes in wellhead backpressure.5. Ignoring the influence of the instantaneous change of the wellhead back pressure on the annular fluid density and fluid rheology.6.The effect of casing eccentricity on heat transfer is neglected.7. Since flushing fluids generally consist of clear water with nearly constant rheology, the effect of flushing fluids rheology on the wellbore pressure of MPC is not considered.8. Assuming that the bottomhole pressure remains constant, the wellhead back pressure is adjusted as needed.Assumptions (1)-(3) are the conventional cementing model assumptions, and (4)-(8) are the unique assumptions of the proposed model.

F
I G U R E 2 Physical diagram of the experimental equipment.LIU ET AL.| 253

3
Mechanical analysis of fluids in casing and annulus.

F I G U R E 4
Flowchart of model calculation.3| MODEL VERIFICATION 3.1 | Basic data of the well X

4 | RESULTS AND DISCUSSION 4 . 1 |
Predicted results of fluid performance parameter distributions Based on the data in Section 3.1, the fluid performance parameter prediction situation was predicted.The fluid types distribution in the casing at different moments was calculated as shown in Figure 6.Fluid types 1-11 represent, respectively, low density mud, spacer, flusher, leading slurry, tailing slurry, rubber plug press fluid, afterflush, mud, afterspace, heavy weight drilling fluid, and mud.When the weighted drilling fluid was injected (79.74 min), 10 types of fluids existed simultaneously in the casing.When the injection stage is over (156.3 min), the fluids no longer flow and the distribution of fluid types in the annulus remains steady.Changes in fluid type distribution have a direct impact on casing hydrostatic column pressure and friction pressure.The distribution of different types of fluids in the annulus at different moments is calculated as shown in Figure 7. Fluid types 1-5 represent respectively low density mud, spacer, flusher, leading slurry, and tailing slurry.When the spacer reaches the bottom of the well (103 min), the distribution of fluid types in

|
257       the annulus changes from a single-column structure to a multiple-column structure.When the injection stage is over (156.3 min), five types of fluids exist in the annulus.Different types of fluids correspond to different fluid densities and rheological parameters, which affect the temperature and pressure fields.At the same time, the density and rheological parameters of the fluids are also affected by the temperature and pressure, and the values of these parameters in the annulus vary continuously with time.Therefore, the influences of fluid type, fluid density, fluid rheological parameters, temperature, and pressure are coupled with each other.The distribution of different types of fluid densities in the annulus at different moments was calculated as shown in Figure 8.On the one hand, it can be found that before the flushing fluid enters the annulus (122.88 min), the change of the annulus fluid density is small, especially when the spacer enters the annulus (101.76 min), the annulus fluid density is not affected.This is due to the fact that the density of the low-density drilling fluid is the same as that of the spacer, while the difference between the density of the flusher and the spacer is large, so that the distribution of the annular fluid density remains unchanged, although the type of the annular fluid changes at 101.76 min.When fluids with different densities, such as flusher and cement F I G U R E 6 The distribution of different types of fluids in the casing at different moments.F I G U R E 7 The distribution of different types of fluids in the annulus at different moments.

F I G U R E 8
The distribution of different types of fluids density in the annulus at different moments.F I G U R E 9 The distribution of different types of fluids viscosity in the annulus at different moments.temperature field distributions

F
I G U R E 10 Distribution of fluid temperature in casing with well depth at different moments.F I G U R E 11 Distribution of fluid temperature in the annulus with well depth at different moments.F I G U R E 12 Distribution of fluid temperature in casing with time at different well depths.

F
I G U R E 13 Distribution of fluid temperature in annulus with time at different well depths.F I G U R E 14 of fluid temperature in the annulus with well depth under different formation temperature gradients.

F
I G U R E 15 Distribution of fluid temperature in annulus with time at different different fluid heat conduction coefficients.

F
I G U R E 16 Bottomhole pressure prediction results for two conventional cementing methods.(A) The first method.(B) The second method.F I G U R E 17 Bottomhole pressure prediction results for managed pressure cementing.F I G U R E 18 Casing and annular hydrostatic column pressure prediction results.

F
I G U E 19 circulation pressure and annular friction pressure prediction results at different eccentricity conditions.(A) Annular circulation pressure.(B) Annular friction pressure.

t is the cementing injection time, s; T i initial the initial injection time of the fluid I, s; T i bottom is the time that fluid i reaches the well bottom, s; Q t ( ) the injected displacement at moment t, m 3 /s; A H L ( , )
i are the depth of the fluid i at moment t, m; t , m 2 ; H well is total well depth, m.
The injected schedule and parameters of fluids.
T A B L E 2 F I G U R E 5 Predicted and measured pump pressure results.LIU ET AL.