Study on Predicting Liquid Production Profile in Horizontal Wells Considering the Mechanism of Annular Flow Resistance and Water Control

The coated particle ICD water control technology has been widely used in horizontal well completion in offshore oil fields in recent years, but there is a lack of research on the simulation and prediction methods for liquid production profiles. By analyzing the dynamic inflow process of fluid, starting from the laws of momentum conservation and mass conservation, a coupled mathematical model of horizontal well reservoir wellbore pressure drop considering the mechanism of annular flow resistance was established, and solved through programming. Based on the actual well data of a certain block in an offshore oilfield, a horizontal well reservoir production model was established. The calculation results of the example show that the annular flow resistance and water control technology can effectively control the balanced liquid production of horizontal wells, thereby increasing the anhydrous oil recovery period and improving the oil recovery rate of the oilfield; The coupling model simulation and prediction method can fully reflect the mutual influence between the oil reservoir, wellbore annulus, ICD, and horizontal wellbore; The effective diameter of the ICD valve affects the changes in oil production and water content. The placement of the ICD well section has a significant effect on water control, and the compactness of the filled particles has a certain impact on pressure and water content changes.


Introduction
Annular flow control is the process of filling the annulus between the wellbore and the screen tube with small coated particles, increasing the axial flow resistance of fluid in the annulus, preventing water channeling in the annulus, and not affecting the radial flow of oil.By designing ICD water control devices for each well section, the radial flow control effect of ICD and the axial flow blocking effect of coated particles significantly reduce the water output in high water cut sections, achieving the goal of segmented water control and oil increase.Without the need to insert a packer, it can achieve unrestricted segmentation of the annulus and fine water control.
The coated particles have lipophilic and hydrophobic properties, and have certain water control functions, which can enhance the water control effect; It has both sand control functions and can achieve integrated sand and water control; The particles are easy to carry and can be used for filling long horizontal sections above 800m and small wellbore filling; Can achieve non flushing pipe construction, with a wide range of applications, saving costs and construction period; The requirements for understanding geological reservoirs are relatively low.
Li Yong et al. studied the construction of a horizontal well model considering annular pressure drop [1], and An Yongsheng et al. conducted model construction and numerical simulation research on the coupling model of horizontal well ICD water control and completion integration [2].However, they did not achieve the model construction and production performance profile prediction considering the filling of particles in the annulus.On the one hand, domestic and foreign numerical simulation software cannot consider the complex and complex comprehensive flow of horizontal well completion, and there is also a lack of research on multi stage flow coupling numerical simulation.On the other hand, based on the demand for energy security confidentiality and localization of numerical simulation software in China.How to use numerical simulation methods to couple the flow models in different spaces such as stratigraphic reservoirs, annulus filled with particles, ICD water control devices, and horizontal wellbore is an urgent problem that needs to be solved to accurately depict and finely describe the production performance of horizontal wells in oilfield sites.
In response to some of the above issues, a coupled model for predicting the liquid production profile of horizontal wells considering the principle of annulus resistance flow control water was established based on mathematical model derivation.An example was calculated and analyzed, and the results showed that the model can accurately describe the dynamic flow process of annulus resistance flow control water, providing an effective means for predicting the production performance of horizontal wells, and can judge the changes in the water content and liquid production profile of horizontal wells, Furthermore, it provides basis and guidance for water control measures in horizontal wells.

Inflow Dynamics Description
Assuming that the reservoir is a reservoir with edge and bottom water, ignoring the flow of gas phase, only oil-water two-phase flow exists, following Darcy's law and not considering the influence of temperature.After production start-up, the dynamic change process of reservoir fluid inflow driven by production pressure difference can be mainly divided into four flow stages: reservoir seepage, annular filling layer seepage outside the pipe, ICD device throttling, and oil pipe flow along the wellbore [3].Next, establish mathematical models for different flow stages and couple them between the models [4].

Pressure Drop Model for Annular Flow Filled with Particles
The stage in which the formation fluid flows into the outer annulus of the horizontal well tubing through the formation.Due to the filling of water control and flow blocking film coated particles in the annulus, the annulus can be regarded as the fluid's seepage stage in another layer with different permeability and wettability.According to Darcy's law, it can be concluded that [4]: In the formula:  is the opening degree; H A is the cross-sectional area of the oil tube microelement, 2 m ; h x  is the length of the annular segment, m ; h k is the fluid permeability of the annulus layer, mD ; h  is the fluid viscosity of the annulus layer, mPa s  ; h q is the total flow rate at the end of the annular section, 3 / ms .

ICD Flow Pressure Drop Model
According to relevant research at home and abroad [5][6][7][8], the flow of fluid through nozzle/orifice type ICD devices mainly generates throttling pressure drop, and its mathematical flow model can be written as: In the formula: ICD p  is the pressure drop between the inflow and outflow ends of the ICD device, MPa ; ICD  is the density of the fluid during the flow phase in ICD, 3 / kg m ; ICD q is the total fluid flow rate during the ICD flow stage, 3 / ms ; n is the number of ICD devices in the annulus segment; d is the diameter of the ICD nozzle, m ; D C is the flow coefficient of the fluid passing through the ICD device.

Pressure Drop Model for Wellbore Flow in Horizontal Wells
Assuming that the fluid flow in the wellbore tubing is an isothermal variable mass flow, a horizontal well grid is divided using the finite element method.According to the law of mass conservation and momentum theorem, the pressure drop model of the horizontal wellbore can be obtained as follows: In the formula:  is the fluid density inside the tubing,  is the pressure drop of oil pipe flow; w  is the frictional resistance of the internal pipe wall of the oil pipe; D is the diameter of the oil pipe, m ; x  is the length of the tubing micro segment, m .

Reservoir Seepage Model
Considering the mechanism of annular flow resistance and water control, a coupled model is constructed and solved by combining the reservoir model and wellbore model.Based on the law of conservation of mass and Darcy's law, a mathematical model for three-dimensional oil-water twophase flow is derived, ignoring the effect of gravity.The oil-water two-phase model is [9][10]: ( ) ( ) In the formula: o  and w  are the density of the oil-water phase fluid in the reservoir, o q and w q are the volumetric flow rate of oil and water phases in the reservoir, 3 / ms ; o s and w s are the saturation of oil and water phases in the reservoir;  is the porosity of the formation in the oil reservoir.

Coupling Model for Predicting Production Performance of Horizontal Wells
Assuming that the mass of the formation fluid is conserved throughout the entire inflow process, the outflow rate of the fluid from the formation is equal to the inflow rate of the fluid in the annulus, the outflow rate of the fluid in the annulus is equal to the inflow rate of the ICD throttling device, and the outflow rate of the ICD throttling device is equal to the inflow rate of the fluid in the tubing.Based on the law of mass conservation and the theory of seepage mechanics, it can be concluded that [11][12][13][14]: In the formula: Fi p is the reservoir formation pressure, MPa ; Ri p and 1

Ri
p + are the pressure before and after the flow of the micro element section of the oil pipe, respectively, MPa ; 1 is the throttling pressure drop of the ICD device, MPa ; fi q  is the phase flow rate of the formation fluid, 3 / ms ; hi q  is the annular fluid phase flow rate, 3 / ms ; Ri q is the flow rate flowing out of the micro element section of the previous oil pipe, 3 / ms ; 1 i q + is the fluid flow rate flowing into the micro element section of the tubing from the annulus, 3 / ms ; f k and h k are the absolute permeability of the formation and annulus, respectively, mD ; ( ) The flow pressure at each stage can be obtained through the pressure drop relationship [15][16]: The solution process is shown in Figure 2.

Basic Model Parameters
A horizontal well in a certain offshore oilfield block has applied annular flow resistance and water control technology.Based on the basic data of the oilfield reservoir and wellbore, a reservoir model and a horizontal well model have been established to simulate the production of a horizontal well with one injection and one production method in the bottom water reservoir of the oilfield.The relevant parameters are shown in Table 1.

Analysis of Water Control Parameters for Annular Flow Resistance
The ICD completion technology that considers the mechanism of annular flow resistance and water control is influenced by multiple factors, and different parameters have different impacts and adaptability [17]; Analyze and evaluate the main factors affecting ICD water control completion through the established actual well model [18].Using a numerical simulation model for dynamic production simulation, Set the number of 3D reservoir grids to 75 × 50 × 5, Corresponding grid step sizes are 20, 10, and 2 respectively.The wellbore grid step size should be consistent with the reservoir grid step size, and an ICD water control device should be arranged for each corresponding well section of the grid.Simulate the production of a horizontal well for three years, and compare the predicted cumulative production curve, water cut curve, and other results by controlling parameter changes [19][20].

Liquid Production Volume.
When the recovery rate is low, the fluid flow in the reservoir is slow, and crude oil is easily extracted along with the injected water.The water content of the produced liquid is low, resulting in a higher cumulative oil recovery.If the liquid extraction speed is too fast, due to the influence of the viscosity difference between oil and water, a portion of the crude oil will be trapped in the reservoir during each cycle of oil recovery, thereby reducing the final cumulative oil recovery.
Set different production work systems for a typical well to analyze the production performance of the horizontal well after taking measures under different working systems with different liquid production volumes.By changing the injection and production work system after water control measures, the production volume was set to 350, 550, 650, and 750 m3/d.The production comparison is shown in Figure 3 and Figure 4.  increases significantly, but the increase in oil pressure per unit reservoir is relatively small.From the graph, it can be seen that increasing the amount of liquid produced can increase the daily average oil production rate, but it will shorten the production time, thereby reducing the cumulative oil production under the same formation energy.During actual production, the production system should be dynamically adjusted based on the actual needs of oilfield production.

ICD Current Limiting Intensity.
The different ICD flow limiting intensities (the size of the effective nozzle diameter) affect the uniformity of the water injection profile in a horizontal well; At the same time, the variation amplitude of the uniformity of the water absorption profile also changes with the change of the effective nozzle diameter.The magnitude of ICD flow limiting intensity not only reflects the uniformity of the water injection profile, but also affects the water absorption index of the water injection horizontal well (with an increase in injection pressure difference and a decrease in water absorption index).By designing different ICD nozzle diameters, dynamic prediction of liquid production profile after production is carried out to analyze the impact of ICD flow limiting intensity on the dynamic changes of horizontal well production.ICD valves with diameters of 3.5, 4, 5, and 6mm were designed for comparison, as shown in Figures 5 and Figures     It can be seen that as the diameter of the ICD device increases, the cumulative oil production slightly increases, but no more oil is added after 5mm, and the risk of water breakthrough in the later stage increases; Meanwhile, as the diameter of the ICD device increases, the non-uniformity of the inflow profile along the horizontal wellbore increases.

Tightness of Filling
Layer.The control of the particle size of the annulus filling is the key to the effectiveness of sand control and water control in the filling layer, and the size of the filled particles is difficult to accurately analyze in actual simulation.Therefore, the compactness of the filling particles and the size of the filling particles are fitted by combining on-site experimental results and certain mathematical relationships; By analyzing the relationship between particle compaction and annulus permeability, the three factors can be linked to achieve an analysis of their impact.
The compactness of the filling layer particles, combined with the physical and chemical properties of the surface film coating, can effectively control water and flow, adjust the high permeability profile, and make the seepage stable, effectively reduce water content, improve the oil-free period, and achieve the implementation effect of on-site measures for increasing production and oil production.Maintain the same other parameters in the model and change the permeability value of the annular filling layer within   From the figure, it can be seen that as the compactness of the coated particles in the filling layer increases, the overall permeability of the filling layer is lower, making it more difficult for aqueous fluids to flow in; On the contrary, the blocking effect of coated particles on oil phase fluids is relatively not significant.After the measures, the water content profile has significantly improved, the cumulative oil production has increased, and the water control effect of the well is obvious, resulting in better development effects.
On the other hand, as the particle size of the filling particles increases, i.e. the permeability of the filling layer increases to a certain extent, the water control effect does not change; The compactness of the filling layer can only produce a significant effect under certain limiting conditions, so there is an interval for optimizing this influencing factor.

Conclusion
(1) We have established a reservoir wellbore coupling model suitable for horizontal wells in offshore oil fields using annular flow resistance and water control technology.By comparing the measures before and after, it is reflected that the annular flow resistance and water control technology can effectively control the water coning at the bottom of the horizontal well.After the measures are taken, the liquid production in the horizontal well is more balanced, and the development stage has increased the anhydrous oil recovery period, which can effectively improve the oil recovery rate of the oilfield; (2) A coupled model simulation and prediction method for oil reservoir wellbore has been established, which fully considers the dynamic changes in inflow of two-phase fluids under complex flow conditions.By using pressure drop changes and mass conservation as the connecting points, prediction and calculation of liquid production and pressure drop profiles at each flow stage can be carried out, fully reflecting the flow changes and mutual effects between the reservoir, wellbore annulus, ICD, and horizontal wellbore; (3) The effective diameter of the ICD device reflects its current limiting strength, which affects the length of production time under a certain production system, and thus affects the changes in oil production and water content; The placement of the well section of the ICD water control device has a significant effect on the water control effect; The compactness of the filling particles reflects the permeability law of the filling layer and has a certain impact on the dynamic production pressure and water content changes.For a reasonable selection of comprehensive parameters, optimization design can be carried out.

Figure 1 .
Figure 1.The flow process of fluids at different stages.

3 / kg m ; 1 R v and 2 Rv 1 RA
is the cross-sectional velocity before and after transverse flow in the micro element segment, / ms ; R v is the average flow velocity of the fluid flowing into the micro element section of the tubing, / ms ; is the crosssectional area of the micro element section of the oil pipe, 2 m ; R A is the area of the micro element section flowing into the tubing from the annulus, 2 m ; R p

3 /
kg m ; ro B and rw B are volume coefficient of the oil-water phase in the reservoir; ro k and rw k is the permeability of the oil-water phase in the reservoir, mD ; o  and w  are the viscosity of the oil-water phase in the reservoir, mPa s  ; fo p and fw p is the oil-water phase pressure of the formation in the oil reservoir, MPa ;

Hip
is the pressure on the outer wall of the annulus layer, MPa ; 2 Hi p is the pressure on the inner wall of the annulus layer, MPa ; Fi p  is the pressure drop of formation inflow, MPa ; Hi p  is the pressure drop of the annular flow, MPa ; ICDi p 

3 /
 are the relative permeability of the formation and annulus, respectively, mD ; f   and h  are the fluid phase viscosities of the formation and annulus, respectively, mPa s  ; f B  and h B  are the volume coefficients of the fluid phase in the formation and annulus, respectively; i  is the fluid density inside the tubing, kg m ; i f is the friction coefficient of the fluid inside the tubing.

Figure 2 .
Figure 2. Solution process of reservoir wellbore coupling model.

Figure 3 .
Figure 3.Comparison of cumulative oil production under different liquid production rates.

Figure 4 .
Figure 4. Comparison of daily oil production under different liquid production rates.With the increase of liquid production after measures, the initial cumulative oil production 6.

Figure
Figure 5.Comparison of cumulative oil production under different ICD flow limiting intensities.

5 .
Figure 5.Comparison of cumulative oil production under different ICD flow limiting intensities.

Figure 6 .
Figure 6.Comparison of liquid production profiles under different ICD flow limiting intensities.

2023
International Conference on Applied Mathematics and Digital Simulation Journal of Physics: Conference Series 2747 (2024) 012029 IOP Publishing doi:10.1088/1742-6596/2747/1/0120299 the range of 1000-6000mD to analyze the water control effect, as shown in Figures 7 and Figure 8.

Figure 7 .
Figure 7.Comparison of cumulative oil production under different compaction levels of filling layers.

Figure 8 .
Figure 8.Comparison of water content profiles under different compaction levels of filling layers.

Table 1 .
Model related parameters.