Study On Two-phase Flow Of Supercritical Carbon Dioxide And Proppants In Fractures

Unconventional natural gas?tight gas and shale gas?reservoirs are generally characterized by low porosity,low permeability,low pore-throat radii and high gas flow resistance.Therefore,fracturing-based reservoir stimulation is mainly applied to the exploitation of unconventional natural gas reservoirs so as to improve the production per well and the duration of the stable production.Although hydraulic fracturing is often used to achieve commercial hydrocarbon recovery,it suffers from a series of problems such as water sensitivity and formation damage in unconventional natural gas reservoirs.The supercritical carbon dioxide?SC-CO₂?waterless fracturing can avoid such issues,and it is a potential economically efficient novel fracturing technology with advantages regarding carbon-reduction.It has evolved into an academic focal point all over the world.This work targetes the key scientific issue in the SC-CO₂ hydraulic fracturing stimulation of unconventional gas reservoirs,illustrates the filtration regularity of the SC-CO₂ in unconventional gas reservoirs and builds the mathematic description of SC-CO₂ fracturing fluid filtration via both theoretical and experimental approaches.On the basis of multi-flow-field coupling,namely coupling of the temperature and pressure fields,wellbore and fracture,fracture and filtration zone,and fracturing fluid and proppant,the regularity of the proppant transportation through fractures assisted by the mass-variable SC-CO₂ is analyzed,and the flow parameter of proppant transportation in SC-CO₂ fracturing is optimized.Given the physical property characteristic of the SC-CO₂ and the effects of the SC-CO₂-rock-CH₄ adsorption,a two-phase filtration rate calculation model for SC-CO₂fracturing in unconventional gas reservoirs is built.Experimental validation using the self-developed fluid filtration experimental apparatus for core samples from unconventional reservoirs indicates that the average absolute error between the calculated and measured data is 1.99%,for the cases of filtration pressures respectively of 2 MPa,4 MPa,6 MPa,8 MPa and 10 MPa.By solving the proposed model,the filtration characteristic of SC-CO₂ fracturing in unconventional gas reservoirs is presented as follows:the filtration rate declines as time lapses,and the reduction rate eventually reaches its equilibrium.A non-linear relationship is found between the filtration rate and the permeability,in which with the increasing permeability,the filtration rate growth slows,and yet the area affected by the pressure and the filtration invasion expand.The relationship between the pressure of the SC-CO₂ fracturing fluid and the stable filtration rate is found to be almost linear.The filtration slows down as the viscosity of the SC-CO₂ fracturing fluid increases.A filtration rate control chart in terms of the SC-CO₂ fracturing operation parameter is plotted.A device that is capable of measuring the Joule-Thomson coefficient in cases of temperatures from 283 K to 423 K and pressures from 2 MPa to 40 MPa is developed.By measuring the temperature and pressure differences before and after CO₂ going through the insulated throttling unit,the Joule-Thomson coefficients of gaseous,liquid and supercritical CO₂ are obtained.Then,the CO₂ Joule-Thomson coefficient is calculated using eight frequently-used state equation,and the variation pattern of the CO₂ Joule-Thomson coefficient with temperatures is analyzed.An improved CO₂ Joule-Thomson calculation formula that contains 25-parameters is proposed,which can calculate the CO₂ Joule-Thomson coefficient with the known temperature and pressure.It is capable of precisely determining the Joule-Thomson coefficient of gaseous,liquid and supercritical CO₂,with known pressures and temperatures.Compared with the experimental results,the average absolute errors of the gaseous,liquid and supercritical CO₂ are respectively 1.52%,4.59%and 3.08%.The reverse curve calculated from the modified CO₂ Joule-Thomson coefficient calculation formula is also well consistent to the result of molecular simulation.Considering the physical characteristics of SC-CO₂,the variations of internal energy and flow work in fractures,and the characteristics of filtration and fractures,the calculation formulas of the friction resistance coefficients of SC-CO₂ in the wellbore and fracture are obtained based on experimental data.The SC-CO₂ temperature and pressure field models in the wellbore and fracture are also proposed,which are used to analyze the effects of the geothermal gradient,and fracturing fluid pump rate,injection temperature and pressure on the SC-CO₂ fracturing fluid temperature and pressure fields and phase distribution regularity.The calculation results suggest that the transition from the liquid state to the supercritical state during the flow process of the SC-CO₂ fracturing fluid occurs in the wellbore or fracture.The phase change position may migrate inside the fracture.With higher injection temperatures and geothermal gradients,or lower pump rates,the phase change position moves towards the fracture root.In the case study of this paper,with the rising injection pressure,the phase transition is correspondingly located at the places from a distance of 12 m,9 m,5 m,3 m and1 m to the fracture root.Given the unsteady SC-CO₂ fracturing fluid system with the variable density and viscosity inside the fracture,the equilibrium velocity equation for SC-CO₂ flow carrying proppants is derived.The deviations between the calculation results and the experimental SC-CO₂ equilibrium velocities obtained at varied densities and grain sizes are 3.32%and4.54%,respectively.Considering the variations of SC-CO₂ internal energy and flow work,filtration characteristics,physical property evolution,and the effects of the SC-CO₂-rock-CH₄adsorption during the SC-CO₂ fracturing operation,the sand-carrying flow calculation model of the SC-CO₂ fracturing fluid is built,on the basis of coupling the temperature and pressure fields,the fracture and filtration zone,and SC-CO₂ and proppant.The experimentally the proppant body heights of nine experiment cases is measured,with an average error in terms of the theoretical prediction of 3.43%.According to the sand body profile,the comparison between the fresh water and SC-CO₂ fracturing fluid indicates that their proppant-carrying capacities in cases of high Reynolds numbers are generally close each other.Based on the SC-CO₂ fracturing proppant body distribution prediction model,the sand-carrying characteristic of the SC-CO₂ fracturing fluid is studied,and the time-dependent proppant concentration distribution and sand body profile are obtained.Calculation results show that the proppant buildup presents a relatively small reduction in height and yet considerably extended length along the fracture length,as the fracturing fluid pump rate grows,the proppant density declines,the proppant grain shrinks or the SC-CO₂ fracturing fluid system thickens.This work concluded the design fundamental of the flow parameter regarding proppant transportation in SC-CO₂ fracturing,on the basis the proposed filtration coefficient calculation model of SC-CO₂ fracturing fluids in unconventional gas reservoirs,wellbore and fracture temperature and pressure field models of SC-CO₂ fracturing,and the two-phase flow model of SC-CO₂ fracturing fluids and proppants.Combined with the SC-CO₂ fracturing technology and practice,the optimal design program applicable for the flow parameters of proppant transportation in SC-CO₂ fracturing is also proposed.