A viscosity model of waxy-hydrate slurry

Hongju Chen ,Shunkng Fu ,Shui Chi ,Qingyun Lio ,Bohui Shi ,Jing Gong ,*

a State Key Laboratory of Natural Gas Hydrate/National Engineering Laboratory for Pipeline Safety/MOE Key Laboratory of Petroleum Engineering/Beijing Key Laboratory of Urban Oil and Gas Distribution Technology,China University of Petroleum-Beijing,Fuxue Road No.18,Changping District,Beijing,102249,PR China

b Key Lab of Deepwater Engineering,CNOOC Research Institute,PR China

c Sinopec Engineering Incorporation,Beijing,100101,PR China

ABSTRACT With the exploration and development of oil and gas fileds going towards into deep-water fields,high waxy reservoir has much more flow assurance issues of encourage complex solids depositions in the transportation system,especially hydrates and wax.Applying risk management such as hydrate slurry technology to control hydrate blockage,has much more economic and technical advantages,comparing to the traditional methods.It is significant to understand the viscosity of the waxy-hydrate slurry using hydrate slurry technology in high wax content reservoir.In this work,based on a simplification idea by coupling the wax content effect into the viscosity,volume and density of the water-in-waxy oil emulsion,a new viscosity model of waxy-hydrate slurry is established according to the Einstein effective medium theory,based on the experiments carried out in a high-pressure rheology system with different wax contents ranging from 0.5 wt%～2.0 wt%.The effect of the complex aggregate coupling wax-hydrate-water is considered by function the non-Newtonian coefficient by four dimensionless parameters.Well-fitting results within an improved deviation of ±15% indicate the feasibility of this method is feasibility.This work can provide a valuable reference for the application of hydrate slurry technology in deep-water fields with high wax content reservoir.

Keywords:Waxy-hydrate slurry Viscosity Flow assurance

1.Introduction

As the main strategic replacement area of the onshore oil and gas resources,deep-water offshore fields attract more attentions from the industry and academic fields.Wax and natural gas hydrates are the usual formed solids in the multiphase transportation system in the deep-water field,which are the main hazards for the safety exploitation and development in the subsea system[1].This is because the subsea condition is ideal for wax precipitation and hydrate formation,which is the main issues for flow assurance in the subsea multiphase transportation system[1,2].

To avoid hydrate formation,the main methods used in the industry are injecting thermodynamic inhibitors[3]or heating insulation[4].But,the cost and environmental issues of these traditional methods in the deep-water fields are much more than that in the shallow offshore fields[5,6].Hydrate risk management of hydrate slurry technology is proposed,where formed solid hydrate particles can suspend in the flowable main production hydrocarbon liquid phase with the help of anti-agglomerants(AAs)additives[7-10].The function of AAs is to prevent formed solid hydrate particles from aggregating to large block or sticking on the inwall of the pipe[11-15].If hydrate slurry technology is used for a waxy reservoir in deep-water filed,a waxy-hydrate slurry will form,which is a complex fluid.To master the viscosity characteristics of a waxy-hydrate slurry is significant for the application of hydrate slurry in the deep-water fields[16-19].

Experimental studies by using high-pressure flow loop[10,20-29]or high-pressure rheometer[30-39]are the main investigation methods to analyze the wax-hydrate slurry.The shear-thinng property of hydrate slurry has been found based on most published experimental work.The viscosity of hydrate slurry will increase the diversity of words can be considered of hydrate volume fraction.Based on constitutive equations,hydrate slurry viscosity models have been established by using Cross,Power Law,Herschel-Bulkley equations[24,26,28,30-33,35].All the rheological parameters are related with the hydrate volume fraction.In fact,the hydrate particles still will crash and aggregate during the flow or stir condition,although the aggregation is reduced with the help of AAs.The hydrate slurry viscosity models based on constitutive equations are difficult to involve the effects of the aggregation of hydrate particles[10,28-31].The Einstein effective medium theory would be a better way to describe hydrate slurry system[10,16,22,25,40-43].Camargo et al.[10]believed that the effective solid volume with the aggregated hydrate particles would be better to describe the effects of aggregation in hydrate slurry viscosity.A model to predict the diameter of hydrate aggregate is built which is related with the flow shear and the liquid phase viscosity.A bimodal model to predict the viscosity of hydrate slurry is proposed by Moradpour et al.[44]combining two single peak models,which is much more complex.Shi et al.[16]build a natural gas waxyhydrates slurry viscosity model based on Einstein effective medium theory by assuming the wax content as suspend solid into the effective solid volume combined with the hydrate aggregate diameter,where a weighting factor of wax volume fraction in the solid phase should be regressed.The applicability of Shi's model[16]is also complex for regressing a weighting factor of wax volume fraction.

Based on the experimental data carried out in the previous work[16],a new waxy-hydrate slurry viscosity model is proposed by classifying wax content into the viscosity of the water-in-waxy emulsion based on the Einstein effective medium theory.This work can highly important to provide technical support for the application of hydrates slurry flow in waxy oil field.

2.Method

2.1.Experimental data

By using a high-pressure hydrates slurry rheological measurement system[37],waxy-hydrate slurry was prepared and its viscosity was measured by the high-pressure rheometer(Anton Paar Mcr101)with a geometry of concentric cylinders.The materials used include Mineral oil LP14(0.837 kg/m3),deionized water,AAs(composed of Span 20 and complex-type inhibitors[45]),wax and civil natural gas[37].Experiments are carried out under the initial pressure of 7.0 MPa and bath water temperature of 276.15 K for wax-hydrate slurry formation with different stirring rate in the high-pressure reactor.The water cut is constant as 20%with 1 wt%AAs additives,and different wax contents with 0.5 wt%,1.0 wt%,1.5 wt%and 2.0 wt%are discussed.Details of these experiments can be found in our previous paper[16].

From the mean final hydrate volume at different wax contents under different stirring rates listed in Table 1 and shown in Fig.1,it can be concluded that higher stirring rate enhances hydrateformation amount.The effect of wax content on hydrate formation amount is not significant.

Table 1 Mean final hydrate volume fractions at different wax contents under different stirring rates(vol%).

The apparent viscosity data at different wax contents under different shear rates forming with different stirring rates is listed in Table 2 and shown in Fig.2.It can be recognized that wax-hydrate slurry shows shear-thinning behavior being as non-Newtonian fluid.And,it can be seen that with the increasing of wax content,the apparent viscosity raises.This is because that the viscosity of the continuous liquid phase will be enhanced with the increasing of wax content without hydrate formation in the liquid phase.Meanwhile,complex aggregates caused by precipitated wax adsorbed the surface of hydrate particles will still form in the waxhydrate slurry with the presence of AAs additives[19].The influence of stirring rate during hydrate formation process on the apparent viscosity reduction is not very obvious.With higher stirring rate,the effective solid aggerates in the liquid phase are smaller,which proves the shear-thinning property of this complex fluid.Therefore,the influence of these complex aggregates suspended in the liquid phase should not be ignored for the investigation of wax-hydrate slurry viscosity.

2.2.Viscosity model

The model was proposed by Shi et al.[16]with a weighting factor of wax volume fraction based on the classical effective medium theory,which was believed being better to describe waxhydrate slurry viscosity comparing with the constitutive equations[20,46-50].But,the weighting factor and the precipitated wax fraction in the liquid phase is difficult to determine.It would be simplified to couple the wax content effect directly involving into the viscosity,volume and density of the water-in-waxy oil emulsion.A new viscosity model of waxy-hydrate slurry is built as Eqs.(1)-5)referring to our previous work[16,37,40].K,the non-Newtonian coefficient,is defined as a function related with four dimensionless parameters[37],including the aggregate numberNNum[40],aggregate Reynolds numberNRe[51,52],aggregate Weber numberNWe[52],stirring speed factorNStir.The effect of complex aggregates coupling wax-hydrate-water on the waxyhydrate slurry viscosity is merging intoKbyNNum,NRe,NWeandNStir[10,22].The dispersion degree of the aggregates,the viscosity and density of water in waxy-oil emulsion,the shear affection and interfacial tension of the aggregates,and the string rate during hydrate formation process are considered byNNum,NRe,NWeandNStir,respectively.

where,Kis the non-Newtonian coefficient ranging from 0 to φmax;μsis the waxy-hydrate slurry viscosity;μLVL,ρLare the viscosity,volume and density of the water in waxy oil emulsion,respectively;ηris the relative viscosity;φhydis the final hydrate volume fraction calculated based on the pressure and temperature data with time during hydrate formation process[37];φmaxis the maximum solid particles volume fraction where particles packed randomly as spheres with the same diameter;dAis diameter of complex aggregates predicated by the Camargo method[10,22]coupling with the inward and outward hydrates shell growth model[53];γ represents shear rate;σ is the waxy oil-water interfacial tension,which is measured of 7.589 mN/m.NStirare 1.0,1625 and 2.25 for the stirring speed of 800 rpm,1300 rpm and 1800 rpm,respectively;IfKφhyd/φmaxis close to 0,μsis close to μL.

3.Results and discussion

3.1.Determination of the non-Newtonian coefficient K

Define the function off1as Eq.(6),sinceNNumandNStirdirectly related with final hydrate volume fraction listed in Table 1.From the mean final hydrate volume fraction data at different experimental conditions,the specific function off1(NStir,NNum)can be regressed with ln(NNum)as Eqs.(7)-9),where the coefficientsAandBare related withNStirbased on the regressed data as shown in Fig.3 and Fig.4.

Table 2 Apparent viscosity at different wax contents under different shear rates forming with different stirring rates(Pa·s).

And,if φhydequals to φmax,f1is 1.0 based on Eq.(6).Thus,f2can be expressed as Eq.(10)[16,37],which can be determined based on the apparent viscosity data listed in Table 2 and the properties of this complex waxy-hydrate slurry.The specific function off2(NRe,NWe)can be given as Eqs.(11-12).

Therefore,the non-Newtonian coefficientKcan be determined by combing Eqs.(7)-9)and Eq.(11)involving withNNum,NRe,NWeandNStir.This new viscosity model of waxy-hydrate slurry built in this work,not only considers the dispersed,sheared and collided complex aggregates with waxy-hydrate-water,but also couples the wax affection on the viscosity,volume and density of the water-inwaxy emulsion.

3.2.Model validation

Fig.5 shows the experimental and predicted apparent viscosity data of the waxy-hydrate slurry with 0.0～2.0 wt%wax content and 300 s-1under different stirring rates,which indicates a good fitting.The experimental and predicted apparent viscosity data of the waxy-hydrate slurry with 800 rpm and 400 s-1under different wax contents also shows a good agreement in Fig.6.From Figs.5 and 6,it can be seen that this model can describe the effects of stirring rate and wax content on its apparent viscosity.The apparent viscosity of waxy-hydrate slurry increases with the increasing of wax content and the decrease of stirring rate.

The presence of the complex aggregates with wax-hydratewater is the main factor affecting the apparent viscosity of the waxy-hydrate slurry as shown in Fig.7.It is obvious that the apparent viscosity of the waxy-hydrate slurry increases in the increasing of the size of aggregates.Fig.8 and Fig.9 show the apparent viscosity of the waxy-hydrate slurry decrease with the increasing ofNReandNWe.Based on the definition of these two parametersNReandNWe,the shear function enhances with high values of them,which proofs the shear thinning behaviors of waxyhydrate slurry.

The deviation between the predicted and experimental relative viscosity values is within ±15% illustrated in Fig.10,which is improved comparing with the results reported by Shi et al.[16].It should be noted that this method to establish the effective medium theory viscosity model can obtain a well-fitting result statistically.All the effects of complex aggregates such as collapsed and sheared can be described.Its applicability can be enhanced by using more experiments.

4.Conclusions

To understand the viscosity characteristics of waxy-hydrate slurry is significant for the hydrate slurry risk management technology application in deep-water fields.In this work,a new viscosity model of waxy-hydrate slurry is established according to the Einstein effective medium theory,based on the experiments carried out in a high-pressure rheology system with different wax contents ranging from 0.5 wt%～2.0 wt%.The effect of the complex aggregate coupling wax-hydrate-water is considered by function the non-Newtonian coefficient by four dimensionless parameters.To simplify the model,the wax content effect is assumed directly involving into the viscosity,volume and density of the water-inwaxy oil emulsion.Well-fitting of predicted and experimental data can be found,which proofs the method of this work is feasibility.The deviation is within ±15% which improved comparing with our previous model[16].This work can provide a valuable reference for the application of hydrate slurry in deep-water fields with high wax content reservoir.

Declaration of competing interest

There is no conflict of interest of this manuscript.

Acknowledgements

This work was supported by the Beijing National Natural Science Foundation of China(Grant No.3192027);National Natural Science Foundation of China(Grant No.U20B6005,52104069,51874323);Science Foundation of China University of petroleum-Beijing(Grant No.2462020YXZZ045,2462020XKBH012),which are gratefully acknowledged.