Early warning methods of chemical agent channeling in polymer–surfactant flooding reservoirs

In the chemical flooding process, the premature breakthrough of chemical agents in production wells results in a large waste of chemical agents and increases the volume and processing difficulty of the produced fluids. The early warning method of chemical agent channeling can predict the strength of agent channeling in advance. The practice of chemical flooding shows that the production performance can be used for early warning of chemical agent channeling. In this paper, we analyze the relationship between cumulative oil production and cumulative polymer production of production wells in polymer–surfactant flooding. Three types of curves according to the enhanced oil production characteristics of chemical flooding, including convex type, S‐type, and concave type. We use the drop speed of the water–oil ratio and the rapid‐decline speed of water cut as early warning indicators to predict the channeling coefficient. A Latin hypercube experimental design method is used to design a polymer–surfactant flooding scheme with the main control factors of the channeling coefficient and early warning indicators. Numerical simulation is used to calculate samples of the channeling coefficient and early warning indicators under various conditions. The drop speed of the water–oil ratio reference value model and the rapid‐decline speed of the water cut reference value model are determined with a multiple regression method. A prediction model for the chemical agent channeling coefficient is established using the deviation coefficient of an early warning index. The method is applied in the Ng54‐61 polymer–surfactant flooding pilot area in the west of the Gudong Seventh District, Shengli Oilfield, China, and the error between the predicted result and the actual value is less than 10%. This research is helpful in taking effective antichanneling measures and improving the oil recovery degree of chemical flooding reservoirs.


| INTRODUCTION
Chemical flooding is an important method for improving the recovery of water flooding mature oilfields [1][2][3] and includes polymer flooding, surfactant flooding, and polymer-surfactant flooding. 4In polymer-surfactant flooding, polymers and surfactants work together to reduce interfacial tension and increase sweep. 5][8] However, due to the heterogeneity of a reservoir and the differences in development performance between wells, chemical agents are susceptible to channeling between wells.The channeling of a chemical agent causes it to break through prematurely in an oil production well, resulting in significant wastage of the chemical agent and increasing the volume and difficulty of processing of the produced fluid.In addition, a low-permeability zone with high remaining oil saturation cannot be produced easily, and the degree of chemical agent sweep is low, affecting the production stimulation effect.Consequently, an early warning method is required for chemical agent channeling in polymer-surfactant flooding.
Polymer-surfactant flooding synthesizes the advantages of both polymer and surfactant flooding.When a polymer and surfactant enter porous media, the polymer can not only increase the water phase viscosity, reduce the mobility ratio, reduce the fingering phenomenon, and improve the recovery degree, but it can also block hyperpermeable channels created by early water injection. 9,102][13][14] The synergistic effect of polymers and surfactants can increase oil phase permeability, increase swept volumes, reduce residual oil saturation, and improve oil displacement efficiency. 15,16Research into polymer-surfactant flooding began in the 1960s.American geologists carried out a series of field tests and achieved good results. 17Subsequently, China conducted a series of field tests and successively established development test areas in the Daqing Oilfield, Shengli Oilfield, and other oilfields, all of which achieved good development results and economic benefits. 18,19Results show that polymer-surfactant flooding can effectively reduce the water cut in mature oilfields and increase the recovery degree. 20,21owever, chemical agents may flow along the high-permeability layers and large pores of a reservoir. 22,23The quantitative identification methods used to investigate chemical agent channeling include well logging data identification, core formation correlation, tracer monitoring identification, and production performance data inversion. 24,25Production dynamic data inversion uses mathematical methods to process production dynamic data to analyze channeling channels.This method does not affect normal production and helps save costs.With the development of stochastic theory, a variety of production dynamic data inversions methods, such as gray correlation, fuzzy comprehensive evaluation, cluster analysis, and dynamic comprehensive analysis, have been constructed. 26Kou et al. 27 constructed an interpretative model of polymer channeling between wells that produced a quantitative characterization of parameters, such as the polymer-flood channel thickness and permeability breakthrough coefficient.Xu et al. 28 built a dynamic prediction model that obtained the size and direction of polymer flood channeling.Meng et al. 29 used injected water and polymers as tracers.Quantitative characterization of the channel is obtained by solving the analytical solution of the water cut and polymer concentration under the influence of water channeling and polymer channeling.
In summary, current research mainly focuses on the identification and characterization of channels in polymer flooding.Currently, there is a lack of research on quantitative characterization methods for the chemical agent channeling characteristics of polymer-surfactant flooding.A lack also exists of methods for the early warning of chemical agent channeling based on production dynamics.In this paper, the relationship between the water cut and the characteristics of agent channeling is characterized, and an early warning model of polymer-surfactant flooding is established.Using the production dynamic data of the Ng5 4 -6 1 polymer-surfactant flooding pilot area in the west of the seventh block of Gudong Oilfield, we analyze the dynamic response relationship between the water cut and the output of chemical agents for polymer-surfactant flooding.Definitions of the channeling coefficient and early warning indicator are given.Using an actual reservoir model, the main factors affecting the channeling coefficient and early warning indicator of a chemical agent are determined, as are classification criteria for the channeling degree.Finally, a Latin hypercube experimental design method and a multiple regression method are used to construct the drop speed of the water-oil ratio reference value model and the rapid-decline speed of the water cut reference value model.Using the deviation coefficient of the early warning indicator, a prediction model for the chemical agent channeling coefficient is established, and an early warning method for chemical agent channeling is obtained.AGENT CHANNELING IN POLYMER-SURFACTANT FLOODING RESERVOIRS 2.1 | Response characteristics of agent channeling in polymer-surfactant flooding reservoir

| Classification of the relationship between oil production and polymer production
To analyze the relationship between the degree of chemical agent production and increasing oil production, the relationship curve between the cumulative oil production and the cumulative polymer production for each production well after chemical agent injection was constructed.According to the shape of the relationship curve, the stimulation characteristics of a production well in the pilot test area are divided into three types: convex type, S-type, and concave type, as shown in Figure 1.The water cut curves and chemical agent output concentration curves of the three types of characteristic wells are shown in Figure 2. The injection of chemical agents in the convex type has a rapid effect, and the oil production rate is relatively high in the early stages of chemical agent production.The oil production rate decreases, and the slope of the cumulative oil production and cumulative polymer production curve continuously decreases, the curve becoming convex.There is a long period of low polymer concentration in the early stages of polymer production and a long period of water cut decline before the concentration of the produced polymer increases.S-type characteristic wells take effect later, and the oil production rate is relatively low in the early stages of chemical agent production.After a certain period of time, after the production of the chemical agent, the oil production rate increases.In the later stages of development, the oil production rate decreases, and the slope of the cumulative oil production and the cumulative polymer production curve decreases.The curve is Sshaped.Within a short time after becoming effective, the output polymer concentration increases.Wells with concave characteristics are slow to become effective, and the degree of oil stimulation is low.The oil production rate is relatively low during the effective oil stimulation period.The shape of the cumulative oil production and cumulative polymer production curves is concave, and the water cut decreases twice before the second peak in the produced polymer concentration curve.The curves reflect the sequence between well efficiency and production agents, as well as the oil enhancing effect of the chemical agents.

| Response characteristics of water cut when chemical agent breaks through
To quantitatively analyze the relationship between chemical agent output and oil enhancement for the different types of production wells, the response time, polymer breakthrough time, and surfactant breakthrough time of the wells were examined.The response time is defined as the time elapsed from the injection of the chemical agent to when the water cut has decreased by 1%.The polymer breakthrough time is defined as the time elapsed from the injection of the chemical agent to when the concentration of the output polymer reaches 100 mg/L.The surfactant breakthrough time is defined as the time elapsed from the injection of the chemical agent to when the output surfactant concentration reaches 0.05%.The relationship between the response time and polymer breakthrough time of the production wells and the relationship between the surfactant breakthrough time and polymer breakthrough time is shown in Figure 3.In Figure 3, the polymer breakthrough time is shorter than the response time.The water cut of the production wells has a long response change period before the production of chemical agents, and the response change period is about 400 days.And the relationship between the polymer breakthrough time and the surfactant breakthrough time is not remarkable.So the change law of the water cut during the response period can be used to predict the production of chemical agents in the wells.
F I G U R E 1 Relationship between cumulative oil production and cumulative polymer production.

| Characterization parameter of the channeling degree
If the injection rate of a chemical agent is constant, the higher the concentration and output of the chemical agent produced by a well, the more serious the chemical agent channeling.Therefore, the definition of polymer-surfactant flooding chemical agent channeling coefficient is where C ps is the chemical agent channeling coefficient, a fraction; c paver is the average output polymer concentration, mg/L; Q ppro is the cumulative polymer output, t; c pinj is the injection polymer concentration, mg/L; Q pinj is the cumulative injected polymer volume, t; c saver is the average output surfactant concentration, a percentage; Q spro is the cumulative surfactant output, t; c sinj is the injection surfactant concentration, a percentage; and Q sinj is the cumulative injected surfactant volume, t.

| Early warning characterization parameter
In oilfield development, there is a long response period for a water cut change in a production well before a chemical agent is produced.Therefore, an early warning for chemical agent channeling can be established using the water cut change.The water cut change in the production wells is shown in Figure 4. Taking the inflection point of the water cut curve before the water cut reaches the valley value as the dividing point, the water cut is divided into a water cut slow-decline stage and a water cut rapid-decline stage.The characteristic parameters representing the decline rate in the water cut slow-decline stage and in the water cut rapid-decline stage serve as early warning indicators.
Using the statistical results from the mine, after the inflection point of the water cut, the relationship between the logarithm of the water-oil ratio and the dimensionless cumulative oil increment is shown in Figure 5A.The two parameters have a linear relationship: where WOR is the water-oil ratio, a fraction; N oi is the dimensionless cumulative oil increment, a fraction; D wor is the water-oil ratio decline speed, which is dimensionless; and c is a constant.N oi is the cumulative oil increment volume/pore volume.
After the inflection point of the water cut decline, the speed of the water cut decline reaches a maximum.The relationship between water cut and production pore volume multiple is shown in Figure 5B.The two parameters have a linear relationship: where f w is the water cut, a fraction; Q l is the production pore volume multiple, PV; D fw is the water cut speed drop speed, 1/PV; and b is a constant.

| Method of establishing an early warning model for agent channeling
Actually, there is usually a hyperpermeable layer or zone in the direction of the chemical agent channel.The early

| ANALYSIS OF AGENT CHANNELING LAW AND INFLUENCING FACTORS IN POLYMER-SURFACTANT FLOODING
A conceptual model of a single well group was created based on matching the production dynamics of the actual block.A numerical simulation method was used to determine the main control factors of the channeling coefficient, drop speed of the water-oil ratio, and dimensionless cumulative oil increase.According to the simulation results of different hyperpermeable layer thickness ratios and hyperpermeable layer permeability multiples, the degree of channeling of chemical agents is classified.

| Establishment of conceptual model
The Ng5 4 -5 5 single well-group area was taken from the reservoir simulation model of the Ng5 4 -6 1 polymersurfactant flooding pilot area in the west of Gudong Seventh District.A single well-group conceptual model was constructed, as shown in Figure 7.The conceptual model includes a central production well and two peripheral injection wells.The thickness of the upper layer is 8 m, and the thickness of the lower layer is 4 m.The regional area is 580 m × 150 m = 0.1102 km 2 , and the geological reserves are 25.9 × 10 4 t.To reflect the overall characteristics of the pilot test area, the average permeability, permeability variation coefficient, effective thickness, and well spacing of the conceptual model are consistent with the average value of the entire test area.The historical matching process is in the supporting material.The conceptual model consists of two sublayers: an upper sublayer that has 12 layers of simulated grids and a lower sublayer that has six layers of grids; there is an interbed between the sublayers.Considering the original rhythm of the conceptual model, the lowest two grids of the upper sublayer and the lowest grid of the lower sublayer were set as hyperpermeable layers, as shown in Figure 7B.Different hyperpermeable layer conditions can be realized by changing the permeability multiple and thickness ratio of a hyperpermeable layer.The permeability multiple of a hypertonic layer is defined as the multiple of a hyperpermeable layer relative to the average permeability of the sublayer in which it is located.The thickness ratio of a hyperpermeable layer is defined as the ratio of the thickness of the hyperpermeable layer to the total effective thickness of the sublayer in which it is located.When changing the thickness of a hyperpermeable layer, it is necessary to adjust the vertical dimensions of other grids in the sublayer to ensure that the overall thickness of the sublayer remains unchanged.Five permeability multiples of hyperpermeable layers, 2.0, 4.0, 6.0, 8.0, and 10.0, and four hyperpermeable layer thickness ratios, 0.05, 0.10, 0.15, and 0.20, were selected for research based on minefield experience.
According to the parameters of the reservoir development plan in the polymer-surfactant flooding pilot test area, a basic injection-production plan was formed for the analysis of chemical agent channeling characteristics and research on an early warning model.Injection-production parameters of polymer-surfactant flooding were selected: the prepolymer slug size is 0.05 PV, the injected polymer concentration is 2000 mg/L, the main slug size is 0.3 PV, the polymer concentration is 1800 mg/L, the surfactant concentration is 0.6%, the size of the subsequent polymer plug is 0.05 PV, and the polymer concentration is 2000 mg/L.The injection rate of the polymer-surfactant flooding and subsequent water flooding stages is 0.11 PV/year.

| Changes in channeling coefficient and early warning indicators of highpermeability layer model
Figure 8A shows the channeling coefficient for different permeability multiples of the hyperpermeable layer when the thickness ratio of the hyperpermeable layer is 0.1.As the permeability multiple of the hyperpermeable layer increases, the channeling coefficient increases.Figure 8B shows the channeling coefficient for different hyperpermeable layer thickness ratios when the permeability multiple of the hyperpermeable layer is 4.0.The thickness ratio of 0.1 is the cut-off point.As the thickness ratio of the hyperpermeable layer increases, the channeling coefficient first increases and then decreases.
Figure 9A shows the early warning indicators of chemical agent channeling for different permeability multiples of the hyperpermeable layer when the thickness ratio of the hyperpermeable layer is 0.1.The permeability multiple of the high-permeability layer significantly influences the early warning indicators of chemical agent channeling.As the permeability multiple increases, the drop speed of the water-oil ratio and rapid-decline speed of the water cut increase.Figure 9B shows the early warning indicators of chemical channeling for different hyperpermeable layer thickness ratios when the permeability multiple of the hyperpermeable layer is 4.0.The thickness ratio of the highpermeability layer considerably influences the drop speed of the water-oil ratio and the rapid-decline speed of the water cut.As the permeability multiple of the hyperpermeable layer increases, the drop speed of the water-oil ratio and rapid-decline speed of the water cut increase.

| Quantitative relationship between early warning indicators and channeling coefficient
To analyze the quantitative relationship between the early warning indicators of chemical agent channeling and the channeling coefficient, the relationship curves between the drop speed of the water-oil ratio, rapiddecline speed of the water cut and the channeling coefficient of the model without hyperpermeable layer and the model with hyperpermeable layer were drawn, as shown in Figure 10.In the hypertonic layer model, the permeability multiples of the hypertonic layer are 2.0, 4.0, 6.0, 8.0, and 10.0, and the thickness ratios of the hypertonic layer are 0.04, 0.08, 0.12, 0.16, and 0.20.A full-scheme design was adopted, and 25 sets of hyperpermeable layer model samples were obtained.The quantitative relationship between the drop speed of the water-oil ratio, the rapid-decline speed of the water cut, and the channeling coefficient are good, and the correlation coefficients R 2 are 0.9535 and 0.8933, respectively.This indicates that the obtained early warning indicators of chemical agent channeling can indeed be used to provide such an early warning.

| Main factors influencing the channeling of chemical agents
On the basis of the numerical simulation method, the sensitivity of the channeling coefficient and the early warning indicators to each influencing factor were analyzed using the coefficient of variation C v .The coefficient of variation C v is defined as shown in Equation (4) 30 F I G U R E 8 Variation in channeling coefficient for (A) different permeability multiples of a hypertonic layer (thickness ratio of a hypertonic layer is 0.1) and (B) different thickness ratios of a hypertonic layer (permeability multiple of a hypertonic layer is 4.0).

F I G U R E 9
Channeling early warning indicators for (A) different permeability multiples of a hypertonic layer (thickness ratio of a hypertonic layer is 0.1) and (B) different thickness ratios of a hypertonic layer (permeability multiple of a hypertonic layer is 4.0).
where n is the number of samples, y i is the ith simple value, and y ¯is the sample mean.
Table 1 shows the coefficient of variation of the chemical agent channeling coefficient and the early warning indicators corresponding to each influencing factor.
To quantitatively obtain the main influencing factors of the chemical agent channeling coefficient and early warning indicators, it was necessary to establish influencing factor selection criteria.The selection criteria must take full account of differences in the variation coefficients of influencing factors, and the factors included should be as comprehensive as possible on the basis of meeting the conventional understanding.We selected influencing factors whose coefficient of variation value was greater than twothirds of the average variation coefficient of all factors as the main influencing factors.The main factors affecting the channeling coefficient of a chemical agent are the permeability variation coefficient, oil viscosity, main slug polymer concentration, surfactant concentration, main slug size, injection rate, injection timing, polymer accessible pore volume fraction, and maximum polymer adsorption capacity.The main factors affecting the drop speed of the water-oil ratio are the permeability variation coefficient, oil viscosity, main slug size, injection rate, injection timing, polymer accessible pore volume fraction, and maximum polymer adsorption capacity.The main factors affecting the rapid-decline speed of the water cut are the permeability variation coefficient, reservoir temperature, oil viscosity, main slug polymer concentration, main slug size, injection rate, injection timing, maximum permeability reduction coefficient of the polymer, and maximum polymer adsorption capacity.

| Classification of the degree of channeling of chemical agents
The relationship between the channeling coefficient C ps , water flooding recovery η w , polymer-surfactant flooding recovery η ps , and enhanced recovery η Δ is shown in Figure 11.The channeling coefficient has a good relationship with the recovery factor for each development method and enhanced recovery factor.This shows that the channeling coefficient not only reflects the production status of the chemical agents, but reflects the oil displacement effect of polymer-surfactant flooding.Therefore, the chemical agent channeling conditions of polymer-surfactant flooding can be classified according to the channeling coefficient.
An analysis of the change law of the channeling coefficient for different hyperpermeable layer parameters and Figure 11 show that the permeability multiple of the hyperpermeable layer has a greater influence on channeling than the thickness ratio of the hyperpermeable layer.For a given permeability multiple of the hyperpermeable layer, the channeling coefficient and recovery factor values for different thickness ratios of the hyperpermeable layer are relatively concentrated.Therefore, referring to the distribution interval of the channeling coefficient for different permeability multiples of a hyperpermeable layer the classification criteria of the channeling degree of a chemical agent are obtained, as shown in Table 2.

Influencing factor Range
Channeling

| EARLY WARNING MODEL AND APPLICATION METHOD OF POLYMER-SURFACTANT FLOODING AGENT CHANNELING
The deviation coefficient of the early warning indicator is defined as the ratio of the difference between the actual value and the reference value of the early warning indicator to the reference value of the early warning indicator.The deviation coefficient of the early warning indicator includes the drop speed of the water-oil ratio deviation coefficient and the rapid-decline speed of the water cut deviation coefficient.where T Dwor is the drop speed of the water-oil ratio deviation coefficient, dimensionless; D wor is the actual value of the drop speed of the water-oil ratio, dimensionless; D′ wor is the drop speed of the water-oil ratio reference value, dimensionless; T Dfw is the rapid-decline speed of the water cut deviation coefficient, dimensionless; D fw is the actual value of the rapid-decline speed of the water cut, 1/PV; and D′ fw is the rapid-decline speed of the water cut reference value, 1/PV.The deviation coefficient of the channeling coefficient is defined as the ratio of the difference between the actual value and the reference value of the channeling coefficient to the reference value of the channeling coefficient

DCPS
ps ps ps (7)   where T DCPS is the channeling coefficient deviation coefficient, dimensionless; and C′ ps is the channeling coefficient reference value, dimensionless.The channeling DU ET AL.
| 2189 coefficient reference value is the chemical channeling coefficient calculated for a given set of dynamic and static parameters of the reservoir and no high-permeability layer.
The channeling coefficient deviation coefficient reflects the influence of the hyperpermeable layer on channeling.
A dynamic analysis of mine development shows that the water cut in the production wells has a long response period before chemical agents are produced.Therefore, the deviation coefficient of the channeling coefficient can be expressed as a function of the deviation coefficient of the early warning indicator T f T T = ( , ) where a 1 , a 2 , a 3 , a 4 , a 5 , and b are the constants.There are nine main reservoir dynamic and static parameters and chemical agent parameters that affect the chemical agent channeling coefficient.These include the permeability variation coefficient, oil viscosity, main slug polymer concentration, surfactant concentration, main slug size, injection rate, injection timing, polymer accessible pore volume fraction, and maximum polymer adsorption capacity.Therefore, C′ ps is a function of the above parameters: where V k is the permeability variation coefficient; μ o is the oil viscosity, mPa s; c pinj is the main slug polymer concentration, mg/L; c sinj is the surfactant concentra- tion, %; V c is the main slug size, PV; q inj is the injection rate, PV/year; f wi is the injection timing, fraction; ϕ D is the polymer accessible pore volume fraction, fraction; and c ˆp max is the maximum polymer adsorption capacity, mg/g.Combining Equations ( 7)-( 9) yields the regression equation for the chemical agent channeling coefficient, Equation (10).Moreover, ,  ,  , ,  , , , ˆ)   where b′ and c are the constants.A multinomial regression method was used to obtain early warning indicators for chemical agent channeling and a reference value model for the channeling coefficient.The influence of a single factor is represented by a quadratic polynomial, and the influence of factors compound is represented by a quadratic product term.A sample set was generated using a Latin hypercube experimental design.The design constitutes a stratified sampling method that not only ensures that sampling points fully cover the variable combination space, but also that the correlation between the independent variable sample values is minimized.

| Drop speed of water-oil ratio reference value model
The drop speed of the water-oil ratio reference value D′ wor satisfies the functional relationship f V μ V q ( , , , , Five levels of these seven factors were taken to generate a sample set for a scheme without a hypertonic layer.The drop speed of the water-oil ratio reference value model for no hyperpermeable layer was obtained by a regression method, as shown in Equation (11).
where D′ wor is the drop speed of the water-oil ratio reference value, which is dimensionless.The relationship between the calculated value of the water-oil ratio reference value model and the actual value of the drop speed is shown in Figure 12.The predicted absolute error is less than 17 (within the range of the error standard line), which meets the engineering requirements.

| Rapid-decline speed of the water cut reference value model
The rapid-decline speed of the water cut reference value D′ fw satisfies the functional Five levels of these nine factors were taken to generate a sample set for a scheme without a hypertonic layer.The rapid-decline speed of the water cut reference value model for no hyperpermeable layer was obtained by a regression method, as shown in Equation (12).
DU ET AL.
| 2191 where D′ fw is the rapid-decline speed of the water cut reference value, 1/PV; T is the reservoir temperature, °C; and R kmax is the maximum permeability reduction coefficient of the polymer, dimensionless.
The relationship between the calculated value of the rapid-decline speed of the water cut reference value model and the actual value is shown in Figure 13.The predicted absolute error is within 1.21/PV (within the range of the error standard line), which meets the engineering requirements.

| Predictive model for the chemical agent channeling coefficient
The chemical agent channeling early warning indicators, the main influencing factors of the channeling coefficient, and the parameters of the hyperpermeable layer (permeability multiple of the hyperpermeable layer, thickness ratio of the hyperpermeable layer) were used as parameters.A Latin hypercube experimental design was used to generate sample sets without a hypertonic layer and different hypertonic layers.Early warning indicators and channeling coefficients for each sample were obtained via simulation.According to the definition of the early warning indicators deviation coefficient and the channeling coefficient deviation coefficient, the deviation coefficient of the early warning indicators and the channeling coefficient deviation coefficient were calculated.Equation (8) shows the relationship between the deviation coefficient of the channeling coefficient and the deviation coefficient of the early warning indicators.The prediction model for the channeling coefficient was obtained by regression of Equation (10), as shown by Equation (13).The relationship between the calculated value of the channeling coefficient and the actual value is shown in Figure 14.The predicted absolute error is within 0.008 (within the range of the error standard line), which meets the engineering requirements.

| Flowchart for predicting the chemical agent channeling coefficient
Equations ( 5)-( 6) and ( 11)-( 13) are used to predict the channeling coefficient of the production wells using field data and to provide further early warning of channeling.An early warning flowchart for chemical agent channeling is shown in Figure 15.The specific steps are as follows: (1) Collect water cut curve data from the production wells, and early warning indicators of chemical agent channeling (D wor and D fw ) can be obtained.(2) Combining the dynamic and static parameters of the reservoir and the parameters of the chemical agent, Equations (11) and ( 12) are used to calculate the reference values of the chemical agent channeling early warning indicators D′ wor and D′ fw , respectively.(3) Equations ( 5) and ( 6) are used to calculate the drop speed of the water-oil ratio deviation coefficient T Dwor and the rapid-decline speed of the water cut deviation coefficient T Dfw , respectively.(4) Combining the reservoir's static parameters, dynamic parameters, and chemical agent parameters, the predicted value of the chemical agent channeling coefficient is calculated using Equation ( 13).( 5) Determine the channeling degree of each production well according to the classification criteria given in Table 2.

| CASE STUDY
Using the reservoir's geological parameters and the single well performance of the Ng5 4 -6 1 polymer-surfactant flooding pilot area in the west of Gudong Seventh District, the constructed polymer-surfactant flooding chemical agent channeling early warning model was used to carry out an early warning of a single well in this block; the prediction results of the model was analyzed and verified.Because the peripheral production wells were disturbed by the peripheral injection wells before the expansion of the polymer-surfactant flooding pilot test area, the applicable conditions of the channeling early warning model were not met.Therefore, seven central production wells were selected as objects of analysis.The associated parameters of the early warning model are shown in Table 3.
Table 4 shows the actual value of the channeling coefficient and the classification of the corresponding channeling degree of the central production wells in the polymer-surfactant flooding pilot test area.The values  were calculated according to the definition of the chemical agent channeling coefficient.The results show that the channeling degree in the pilot test area is below medium channeling for each well.The channeling coefficients of wells 32-3135 and 32-3186 are less than 0.05, indicating that no chemical agent channeling has taken place; the channeling coefficients of the other wells are between 0.05 and 0.10, indicating weak channeling.The output of the chemical agent channeling coefficient prediction model consists of two parts: the reference value of the early warning indicators and the predicted value of the channeling coefficient.Table 5 shows the prediction results and prediction errors.The prediction errors of the chemical agent channeling coefficients are all within 10%, indicating that the established chemical agent channeling coefficient prediction model has good prediction accuracy.

| CONCLUSIONS
In this paper, an early warning model for the channeling in polymer-surfactant flooding was established.This will provide an accurate early warning of the channeling of chemical agents based on the change of water cut at the early stage.It is helpful to determine appropriate measures to improve the development effect of chemical flooding reservoirs.The main conclusions are as follows: (1) On the basis of the relationship between cumulative oil production and cumulative polymer production, the stimulation characteristics of production wells were classified as convex type, S-type, and concave type.The convex-type characteristic wells took effect early and produced a good oil-increasing effect.The S-type characteristic wells took effect late but also produced a good oil-increasing effect.The concave-type characteristic wells, however, took effect late and produced a poor oil-increasing effect.Before a chemical agent was produced, the water cut of the production well had a long response change period and it was used to predict the production of a chemical agent.(2) The drop speed of the water-oil ratio, the rapiddecline speed of the water cut, and the channeling coefficient had a good quantitative relationship.This indicated that an early warning index of chemical agent channeling could be used for the early warning of chemical agent channeling.And the main control factors of the channeling coefficient and early warning indicators were determined.(3) Combined with the main control factors of the early warning indicators, a reference value model of the drop speed of the water-oil ratio and a reference value model of the rapid-decline speed of the water cut were constructed using a Latin hypercube experimental design and a multiple regression method.Using the deviation coefficient of the early warning index, a prediction model for the chemical agent channeling coefficient was established and an early warning method of chemical agent channeling obtained.(4) The channeling coefficient early warning method of polymer-surfactant flooding proposed in this paper was applied to the Ng5 4 -6 1 polymer-surfactant flooding pilot area in the west of Gudong Seventh District, Shengli

2
Water cut curves and chemical agent output concentration curves: (A) convex type, (B) S-type, and (C) concave type.F I G U R E 3 Production dynamic response relationship: (A) relationship between response time and polymer breakthrough time and (B) relationship between surfactant breakthrough time and polymer breakthrough time.(The dashed line in figure (A) represents the response time is 400 days earlier than the polymer breakthrough time.) Division of water cut decline stage.F I G U R E 5 Water cut change curve: (A) relationship between water-oil ratio and dimensionless cumulative oil increment and (B) relationship between water cut and production pore volume multiple.warningindicators of chemical agent channeling and the dynamic and static parameters of the reservoir are known conditions.However, high-permeability layers or zones in the reservoir cannot be obtained directly.Therefore, when establishing a prediction model for the chemical agent channeling coefficient, the main control factors of the early warning indicators (the drop speed of the water-oil ratio and rapid-decline speed of the water cut) should be determined first.A numerical simulation model without a highpermeability layer was constructed using different control factors, and the drop speed of the water-oil ratio reference value model and the rapid-decline speed of the water cut reference value model were obtained by regression.Then, the main control factors of the channeling coefficient of a chemical agent were determined, and numerical simulation models with and without hyperpermeable layers and different factors were established.Finally, the deviation coefficient of the drop speed of the water-oil ratio and the deviation coefficient of the rapid-decline speed of the water cut were calculated.These were combined with the regression of the main control factors of the chemical agent channeling coefficient to produce the channeling coefficient prediction model.The flowchart of the established model is shown in Figure6.

3. 1 . 1 |
High-permeability layer model setting and injection-production scheme The channeling of chemical agents in polymer-surfactant flooding is characterized by premature and rapid chemical agent production and poor oil enhancement.The main reason for chemical agent channeling is the strong heterogeneity of the reservoir.Due to the original characteristics of the reservoir and the long-term scouring effect from injected water, local large pores and high-permeability layers F I G U R E 6 Flowchart of the model used to predict the channeling coefficient.DU ET AL. | 2185 are formed in the late stages of water flooding.This creates conditions for the channeling of chemical agents in the polymer-surfactant flooding stage.To analyze the dynamic characteristics of chemical agent channeling, a hyperpermeable layer was set up in the conceptual model.The dynamic change law of chemical agent channeling under different hyperpermeable layer conditions was examined by changing the characteristic parameters of the hyperpermeable layer.

F I G U R E 7
Regional selection and conceptual model: (A) whole district model and (B) conceptual model.

F
I G U R E 10 Relationship between the early warning indicators of chemical agent channeling and the channeling coefficient: (A) drop speed of water-oil ratio and (B) rapid-decline speed of water cut.T A B L E 1 Coefficient of variation of the chemical agent channeling coefficient and early warning indicators corresponding to each influencing factor.
k o pinj sinj c inj wi D p max is a polynomial function, and the influence of a single factor is represented by a quadratic polynomial function.The influence of factors compound is represented by the quadratic product term:

F
I G U R E 11 Variation in channeling coefficient: (A) water flooding recovery, (B) polymer-surfactant flooding recovery, and (C) enhanced recovery.T A B L E 2 Classification criteria of the channeling degree.

F
I G U R E 13 Relationship between the calculated value and the actual value of the rapid-decline speed of the water cut.F I G U R E 14 Relationship between the calculated value and the actual value of the channeling coefficient.F I G U R E 15 Flowchart of the chemical agent channeling early warning of chemical flooding.T A B L E 3 Parameters of the central production wells in the polymer-surfactant flooding pilot test area.
Channeling coefficient actual value of the central production wells in the polymer-surfactant flooding pilot area.
Prediction results of central production well channeling coefficients.
T A B L E 5