Ying Xie ,Jin Meng ,*,Diwen Chen

a School of petroleum engineering,Southwest Petroleum University,Chengdu,610500,China

b PipeChina Guangdong Pipe Network Co.,Ltd,Guangdong,China

Keywords:Submarine multiphase pipeline Wax deposition law OLGA Deposition model

ABSTRACT In this study,the effects of wax deposition on submarine multiphase pipelines are investigated.In order to understand the mechanism of wax deposition in submarine multiphase pipelines,a wax deposition model in a submarine pipeline was established using the OLGA wax deposition module,and key factors influencing this phenomenon were analyzed.Additionally,a multifactor impact analysis of wax deposition was performed via the orthogonal test method.The results indicated the relative influence of five factors on oil-gas-water three-phase wax deposition,namely,oil flow rate,water content,inlet temperature,gas-oil ratio,and outlet pressure.Then,the main influencing factors of wax deposition in a multiphase pipeline flow were extracted,and the wax deposition prediction model was established.The wax deposition rate under different operating conditions was simulated using the OLGA wax deposition simulation module.The SPSS software was used to perform nonlinear regression analysis under different working conditions.In this manner,the constant terms in the wax deposition prediction model for a submarine multiphase pipeline were obtained.The prediction model could be used to programmatically predict wax deposition along a multiphase pipeline by programming the initial waxing conditions.By using this method,the wax deposition prediction model of an M-N submarine multiphase pipeline was obtained under different working conditions.After comparing the predicted and the OLGA simulation results,it was concluded that the established wax deposition model can be used to accurately calculate the wax deposition in a submarine multiphase pipeline within an allowable error range.If the physical properties and operating parameters of the conveying medium in a multiphase pipeline are given,the developed oil-gas-water three-phase wax deposition model can be used to predict the distribution of wax deposition in submarine multiphase pipelines without laboratory experiments.The results of this study can help production units understand the waxing situation of pipelines in time in order to scientifically formulate a pigging plan and avoid pipeline blockages and shutdowns.

1.Introduction

Oil and gas multiphase mixed transportation technology is widely used in marine and onshore pipeline gathering and transportation systems.The application of such a multiphase mixed transportation technology simplifies the offshore and onshore oil and gas mixed transportation facilities,so that the oil and gas can be directly transported to the processing facility for centralized processing,without prior oil-gas-water separation treatment.The application of this technology also greatly reduces the construction investment,operation and maintenance costs of pipelines and corresponding auxiliary facilities,so it has considerable economic benefits [1].With the continuous development of offshore oil and gas fields,such pipeline transportation technology has been widely used in the industry [2].In the North Sea of the United Kingdom,remote natural gas and oil and gas pipelines have been established,which have greatly promoted the development of large natural gas fields in the North Sea.In the Gulf of Mexico in the United States,the total length of submarine pipelines has reached 37,000 km,connecting the large and small oil-gas fields in the area with the onshore processing plants along the coast,thus creating a unified system of production,processing,and sales.The normal operation of the submarine pipeline network has become a key factor in the economical and effective development of oil resources in the Gulf of Mexico [3].According to statistics,China National Offshore Oil Corporation had laid a total of 315 subsea pipelines(50.8-762.0 mm in diameter)in Chinese waters,with a total length of about 6202 km from 1986 to 2016 [4].

Crude oil in China is generally characterized by high wax content,high freezing point,and high viscosity [5],which result in its poor fluidity[6].These characteristics are of particular importance in submarine pipelines,where the temperature drops rapidly in the process of crude oil transportation (the deep-sea temperature is approximately 4°C)[7].When the oil temperature is lower than the wax precipitation point,the wax crystals in the crude oil precipitate and deposit on the inner wall of the pipeline[8],reducing the flow cross-section of the pipeline,increasing friction,and decreasing the transport capacity [9].In addition,wax deposition also causes the gelation of crude oil,increasing the risk of pipeline hazards,and even causing severe blockage accidents [10],thus causing significant economic losses in terms of production [11,12].The cost of repairing a blocked pipeline at a water depth of 400 m can reach US$ 1 million per mile,according to the US Department of Energy[13].Therefore,pipeline wax deposition has become a serious flowsecurity problem in oil industry both in China and other countries involved in offshore oil and gas exploitation and transportation[14].

Internationally,research on multiphase pipe flow wax deposition mainly focuses on laboratory experiments [15,16].However,the design conditions of controlled loop experiments differ greatly from actual operating conditions of a submarine pipeline.For example,most laboratory experiments are performed in a low pressure,small diameter environment.With the continuous development of oil and gas mixed transportation technology,pipelines with low pressures and small diameters can no longer meet the needs of oil and gas system transportation[17].As a result,current research on the formation mechanism and model prediction of wax deposition of multiphase flow is still immature.More in-depth theoretical research of multiphase pipe flow wax deposition is required [1].In addition to laboratory experiments,numerical simulation has become an important method for studying wax deposition.Currently,the relatively mature software programs used to study and calculate wax deposition are mainly OLGA and PVTsim.Additionally,a number of software programs have been developed by scientific research institutions;including WaxFlow and TUWAX simulator.The OLGA wax deposition module has been widely used by scholars,especially for investigating multiphase flow wax deposition.Moreover,OLGA has a greater number of advantages for calculating wax deposition compared to the other software programs.

Therefore,this study uses the OLGA wax deposition module to:

(1) Establish a submarine multiphase pipeline model.

(2) Study wax deposition in submarine multiphase pipelines.

(3) Identify the main influencing factors of wax deposition in multiphase pipe flow.

(4) Establish a wax deposition model for submarine multiphase pipelines.

(5) Solve the established model.

The developed model can be used to predict the wax deposition distribution of submarine multiphase pipelines [18],which can help production units fully understand the wax deposition conditions of pipelines in time in order to scientifically formulate pigging plans to ensure clean pipelines,reduce corrosion risk in pipelines,avoid the occurrence of long-term pipeline blockage and shutdown accidents in pipelines that have not been pigged and improve the safe operation of pipelines.

2.Multifactor influence analysis of wax deposition in multiphase pipelines

The process of single-phase wax deposition is affected by a variety of factors,such as the composition of crude oil,the temperature difference between the oil and pipe wall,flow rate,etc.[19]Furthermore,the influence of water content and gas-oil ratio on the wax deposition process of a multiphase pipeline cannot be ignored.

For the multiphase pipeline calculation in this study(Section 3),a wax deposition model of a submarine multiphase pipeline is established using the wax deposition module within the OLGA software.Thus,wax deposition along the pipeline under different water contents and gas-oil ratios is simulated,as shown in Figs.1 and 2.

The oil-gas-water (three-phase) wax deposition rate is related to multiple factors,and each factor has a different degree of influence.If single-factor analysis is used,the influence of other factors cannot be accurately analyzed.Therefore,in order to accurately analyze the behavior of wax deposition in multiphase pipelines,it is necessary to comprehensively analyze the importance of each factor’s effect on wax deposition.

When there are three or more changing factors in a test,the test is referred to a multifactor test.A multifactor test is seldom used because it includes many redundant combination factors without a reference value and requires a significant amount of time,manpower,and materials with results of little significance.Therefore,partial tests such as orthogonal tests,are considered.

2.1.Orthogonal test

The orthogonal experimental design is a multifactor optimal experimental method.It selects some representative points that are uniformly dispersed and neatly comparable from the complete design of experiments based on orthogonality [20].An orthogonal test design refers to the different states of the factors that need to be investigated as horizontal or level.

Kenichi Taguchi,a famous Japanese statistician,listed the horizontal combinations selected by orthogonal experiments into a table,known as the orthogonal table.The orthogonal table is constructed on the basis of the orthogonal Latin method,which is based on the idea of uniform dispersion and the theory of combinatorial mathematics.The notation of the orthogonal table is as follows [21]:

where L is the orthogonal table code;a is the level of each factor;n is the number of rows in the orthogonal table,that is,the number of tests;and q is the number of orthogonal table columns,that is,the number of factors.

Commonly used orthogonal tables are L4(23),L9(34),L16(45),L25(56),and L50(511).For example,L4(23) implies that four experiments are performed,three factors are considered,and each factor includes two levels.The orthogonal test arrangement is shown in Table 1.

Table 1 L4(23) orthogonal test table.

The orthogonal table is selected according to the following criteria [22].

(1) The number of influencing factors and the horizontal number of the selected orthogonal table are equal to or greater than the number of factors or the horizontal number to be tested,and the number of tests is minimized.

Fig.1.Thickness variation of wax deposition in pipeline at different water content.

Fig.2.Thickness variation of wax deposition in pipeline under different gas-oil ratios.

(2) The columns of an orthogonal table are orthogonal;that is,each level of each factor is combined with each level of another factor.

The orthogonality of the orthogonal table is expressed in the following two aspects:

(1) Uniform dispersion:in each column of an orthogonal table,the number of occurrences at all levels is equal.

(2) Neat comparability:For any two columns of an orthogonal table,the two levels in the same row are considered to be an ordered number pair.Each ordered number pair occurs at the same time.

2.2.Multifactor orthogonal test

The orthogonal experiment method was applied to analyze the main influencing factors of wax deposition in an M-N submarine multiphase pipeline.The wax content of the selected crude oil is 14.77 %wt,and the WAT is 32.5°.Five factors were selected:inlet temperature,outlet pressure,water content,gas-oil ratio,and oil flow rate.For each factor,four levels were selected for the orthogonal experiments.The selected influencing factors and levels are shown in Table 2.

Table 2 Influencing factors and level table of wax deposition rate.

Among the five influencing factors,each factor has four levels.If a comprehensive test is carried out,a total of 45=1024 tests will be carried out.Evidently,the workload of such a multifactor test would be high and unscientific.According to the construction principle of the orthogonal table,the L16(45)orthogonal test table is selected in this paper;only 16 simulation tests need to be performed to reflect the importance of each influencing factor in the oil-gas-water three-phase wax deposition [23].The designed orthogonal test and simulation results are shown in Table 3.

Table 3 Orthogonal test scheme and simulation results of oil-gas-water three-phase wax deposition.

The simulation results of the orthogonal texts were evaluated using direct analysis,and the importance of each influencing factor was ranked according to the range of the test results[24].The mean value and range of each factor at different levels were calculated based on the results of 16 groups of simulations,as shown in Table 4.

Table 4 Mean and range table of the influencing factors at different levels.

According to the range analysis,the influence of various factors on wax deposition rate can be determined.The value whose range produces the greatest difference in the corresponding wax deposition rate is the main influencing factor.On the contrary,the factor whose range produces a lesser variation in the wax deposition rate is a secondary factor.According to Table 4,the primary and secondary relationship of each factor on the wax deposition rate is shown in Table 5.

Table 5 Primary and secondary relationship of the influence of various factors on wax deposition.

3.Establishment of a wax deposition model for multiphase pipelines

Multiphase pipe flow wax deposition is commonly analyzed and modeled based on the mechanism of single-phase pipe flow wax deposition.

According to Table 5,the amount of oil flow rate plays a key role in the change of wax deposition thickness,mainly because it increases the total wax content,and thus,the amount of wax precipitation naturally increases.Unlike single-phase pipe flow,the influence of the additional gas and water phases cannot be ignored.In particular,the water phase affects the viscosity of oil and the heat transfer process of the fluid.According to the results in Fig.1,if the wax deposition rate is calculated by the average wax deposition thickness,the wax deposition rate decreases exponentially with increasing water content.The gas phase mainly affects the formation of wax deposits by shear peeling.Therefore,based on the universal waxing model [25],this study established the oil-gaswater three-phase wax deposition model by including the effect of gas shear and water content on wax deposition:

where W is the wax deposition rate in g/(m2h);τLand τGare the shear stresses of the liquid and gas phases at the pipe wall in Pa;μ is the dynamic viscosity of crude oil in mPa·s;is the solubility coefficient of the wax crystal at the pipe wall in 10-3/°C;is the radial temperature gradient at the pipe wall in°C/mm;fWis the volumetric water content of crude oil;and k,m,n,p,and q are all constants that can be determined by experiments or simulations.

Among these parameters,the shear stress of the liquid phase,τL,can be calculated using the rheological equation of pseudo-plastic fluids [26].The shear stress of gas,τG,relative to the pipe wall can be calculated by the Fanning formula in the process of intermittent flow[13].The radial temperature gradient at the pipe wall,,can be solved according to the thermal balance on the microelement section,and the solubility coefficient of the wax crystal at the pipe wall[27],,can be calculated by interpolation from the relationship curve between the solubility coefficient of the wax crystal and temperature measured during the experiment[28].

It should be noted that this model is established based on the data of a three-phase submarine multiphase pipeline transporting oil,gas,and water,and that the transportation volume is low.The wax content of the oil used is 14.77 %wt,which is relatively high,and the wax precipitation point is 32.5°C,which is relatively low.Because different oil products have different physical properties,this model is only suitable for three-phase mixed pipelines with low throughput,high wax content,and low wax precipitation point.By applying this model,the wax deposition along the mixed transportation pipeline can be predicted according to the physical properties of the conveying medium and the operating parameters of the pipeline.The calculation program block flow diagram is shown in Fig.3:

(1) Input each flow parameter into the program and set the maximum simulation time.

(2) Segment the pipeline to calculate the temperature at each position along the axial direction of the pipeline.

(3) Calculate the radial temperature gradient and wax molecular temperature concentration gradient at the pipe wall [29].

(4) Substitute this information into the wax deposition model.

(5) Calculate the thickness of the wax deposition layer.

(6) Calculate the wax deposition thickness of the next interval until the simulation time is reached.

4.Example calculations

M-CEPA transports partially dehydrated and partially degassed crude oil from the A and B oil fields to the N-CEPA base through submarine pipelines (referred to as the “M-N submarine pipeline”).The total length of the M-N submarine pipeline is 30.6 km,and the burial depth is 1.5 m(the distance from the top of the pipe to the surface of the sea floor).The average temperature at the burial depth during summer and winter is 21.7°C and 3.7°C,respectively.The average water depth of the sea is approximately 20 m,and the annual average temperature is 13.6°C.

The pipes are insulated with rigid polyurethane foam with a total heat transfer coefficient of 0.85 W/(m2·°C).The transmission ratio of A and B crude oil is A:B=1:1,the wax precipitation point is 32.5°C,and the freezing point is 11°C.The initial total oil flow rate of the M-N submarine pipeline is 4435 m3/d.The main transportation gas is natural gas from C-BOP.The initial total gas transport volume is 13.42×104 m3/d(P0=0.101325 MPa,T=20°C;the same as below),and the total water transport volume is 1066 m3/d.

Fig.3.Block Flow diagram of wax deposition calculation.

According to the allocated production volume,the gas-oil ratio is 30.26 m3/m3and the water content is approximately 19.38%(according to the following analysis,the gas-oil ratio is 30 m3/m3and the water content is 20%,except in the cases where these variables are specified).

The basic parameters of the M-N submarine pipeline are listed in Table 6.

Table 6 Basic parameters of the M-N submarine pipeline.

According to the transportation conditions and the physical properties of the oil,OLGA was applied to simulate the wax deposition of the M-N submarine pipeline under different working conditions [12].The wax deposition parameters and simulation results of the pipeline are shown in Table 7.

Table 7 Wax deposition parameters of the M-N submarine multiphase pipeline.

The nonlinear regression analysis was carried out using the SPSS software,and the calculated results are shown in Table 8.

Table 8 Estimated values of the wax deposition parameters.

According to the regression analysis of wax deposition parameters,the regression parameters of the wax deposition model are as follows:

k=4171.219,m=-0.846,n=2.213,p=-2.349,q=-1.880.

Thus,the M-N submarine pipeline wax deposition model is:

According to Fig.3,the wax deposition distribution of the M-N submarine pipeline can be calculated using MATLAB;these results can then be compared with the results of OLGA simulation.Fig.4 shows four different working conditions:a) oil flow rate 57.10 m3/h,gas-oil ratio 86.33 m3/m3,and water content 38%;b)oil flow rate 65.18 m3/h,gas-oil ratio 56.83 m3/m3,and water content 29%;c)oil flow rate 75.17 m3/h,gas-oil ratio 64.14 m3/m3,and water content 28%;d)oil flow rate 88.86 m3/h,gas-oil ratio 49.47 m3/m3,and water content 20%.The model established in this paper and OLGA were used to predict the wax deposition distribution of M-N submarine pipeline [18].As shown in Fig.4,under the four working conditions,the thickness distribution of wax deposition and maximum waxing position of the pipeline predicted by our model are slightly different from the results predicted by OLGA,but the deviations are not large.

Since the model is based on the average wax deposition thickness,it cannot reflect the effect of model regression if only comparing the distribution thickness of wax deposition along the pipeline.Therefore,it is necessary to calculate the average wax deposition thickness obtained by the two methods.As shown in Table 9,the relative errors between the model prediction results and the OLGA prediction results are-11.67%,0.76%,17.04%,and 5.37%under the four working conditions(a negative sign indicates that the model prediction result is less than the OLGA prediction result).The average relative error is 8.71%,which indicates that the results predicted by the model based on regression are in good agreement with the results predicted by using OLGA,and the regression effect is better [30].

Table 9 Comparison of model prediction results with OLGA prediction results.

5.Conclusions

(1) According to the multifactor orthogonal test analysis of wax deposition in a multiphase pipeline,the factors influencing oil-gas-water three-phase wax deposition can be ranked in order of their importance (high to low) as follows:oil transportation volume,water content,inlet temperature,gas-oil ratio,and outlet pressure.Water content greatly influences wax deposition.In future research,this influence factor should be further investigated.Future work should include the influence of physical properties such as crude oil viscosity.

(2) On the basis of the universal wax deposition model of singlephase wax deposition,considering the effects of gas-phase shear and water content,a prediction model of wax deposition in an oil-gas-water three-phase multiphase pipeline was established,and the solution method of the model wasstudied.When the physical parameters of the conveying medium and the operating parameters of the submarine pipeline are known,the established oil-gas-water three-phase wax deposition model can be used to predict the wax deposition distribution of low-volume submarine multiphase pipelines.Because the developed model isbased on limited experimental data and on the OLGA simulation results,it has certain limitations when used,which need to be improved in future work.

(3) According to the operating parameters of an M-N submarine multiphase pipeline under different working conditions,the wax deposition model was determined by calculations performed using the SPSS software.By comparing the results predicted by the model and results predicated by using OLGA under four different working conditions,the maximum relative error was found to be 17.04%,the minimum relative error was 0.76%,and the average relative error was 8.71%.This indicated the model had a good regression effect.Due to limited conditions,this study first verified that the OLGAbased wax deposition prediction is feasible by consulting relevant literature.On this basis,comparing our model prediction results with the simulation results obtained using OLGA indirectly proves the reliability of the model established in this study.However,this method has certain limitations;therefore,we recommend the use of different oil products and pipeline operating parameters in order to obtain more experimental results that can be used to verify the accuracy of the mathematical model when the experimental conditions allow it.

(4) The oil-gas-water three-phase wax deposition model established in this study was obtained by numerical simulation regression only on the basis of the physical properties of crude oil,the single-phase wax deposition model developed using laboratory experiments,and the effects of gas phase shear and water content.It is suggested that future research should be conducted based on the results of loop experiments,the wax deposition mechanism and flow pattern be considered when establishing an improved multiphase flow wax deposition model.

Fig.4.Comparison of the predicted results of the regression model and the OLGA predicted results under different working conditions.

Author statements

All persons who have made substantial contributions to the work reported in the manuscript:

Conception or design of the Manuscript:Ying Xie;

Draft work,Writing review and editing:Jin Meng;

The acquisition,analysis,or interpretation of data for the Manuscript:Diwen Chen.

Declaration of competing interests

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.