裂缝中气液二相流体临界渗流机理与理论研究
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摘要
在石油天然气开采、煤层气开发及煤矿瓦斯抽放等工程领域中,都存在着裂缝中气液二相流体渗流的问题。气液二相流体的相对渗透率决定着油气、煤层气、瓦斯等资源的采收率。我们在进行低渗透煤层裂缝渗透特性实验的过程中,发现当气液相对饱和度达到某一临界值时,气液二相流体的相对渗透率都会迅速下降,甚至发生二相流体的流动都停止的现象。我们称这种现象为气液二相流体在裂缝中渗流的临界渗流现象。为了揭示这种奇特现象产生的机理,采用了理论推演、数值实验、物理模拟、实验室岩石裂缝渗流试验、现场工程数据分析等手段,对裂缝中气液二相流体临界渗流的机理与理论进行了全面的、详细的研究,取得了如下主要成果和结论:
1.通过对气体、液体以及气液二相流体各自在裂缝中的渗流规律,进行详细的理论分析和推演,建立了裂缝中气液二相流体渗流的混合数学模型,该模型主要包括五个控制方程;
连续性方程:div(P_w(?)_w+P_g(?)_g)+(?)(P_wS_w+P_gS_g)/(?)t+I=0
气体裂缝渗流达西定律:q_g=(-b~2/12μ_g)S_g((?)P/(?)S)
液体裂缝渗流达西定律:q_w=(-b~2/12μ_w)S_w((?)P/(?)S)
In many engineering such as oil-gas exploitation, coalbed methane exploitation and extraction, there always occurs gas-liquid two-phase flow through a fracture. The gas-liquid relative permeability in fracture always determines the recovery ratio of oil, nature gas, coalbed methane, and gas. When we are studying the fracture seepage characters of low permeability coal, we find that when the gas relative saturation closed to a certain value, the relative permeability of gas and liquid will fall down rapidly and sometimes the flow of the two-phase will stop. We name this phenomenon as critical seepage phenomenon of gas-liquid two-phase flow in single fracture, and the gas relative saturation as critical gas relative saturation where the critical seepage phenomenon occurs. In order to reveal the mechanism of critical seepage phenomenon of gas-liquid two-phase flow in single fracture, we study the gas-liquid two-phase seepage law in detail by means of theory deduce, numerical simulation, physical simulation, fracture seepage test of rock samples, analyses with in situ data from one gas production well. The main achievements and conclusions are listed as follows:[1] After analyzing the fracture seepage law of gas, water and gas-liquid two-phase fluid in detail, a combined mathematical model of gas-liquid two-phase flow in single fracture is set up. This model involves five control equations:Continuity equation: divDarcy law of gas seepage in fracture:Darcy law of liquid seepage in fracture:
Gas-liquid relative saturation equation: g ￡>(l - Sg0)+ p0Sg0Equation of state for an ideal gas: pg = ——RTWith proper definite condition, these five control equations make up of the complete combined mathematic model of gas-liquid two-phase flow in single fracture. While substitute the five equations into one combined equation, we get the final control equation of gas-liquid two-phase fluid seepage in single fracture:2 U C ^ ?r r.2 ? C Va2 2 ,2 2\V~^go) M 0 Po^go \\ P P~ P(\ -sj+ Ptss,+ It 24//, P(i - s,,)+ P,st, }Caxr+"v"J dt{p(\-SgO)+PoSgO)+ XT p(l-SgO)+PoSgO dt[2] The numerical solution of above combined mathematic model is researched, and the Finite Element Simulating program is designed by using Fortran computer language.[3] After a great deal of numerical simulating, the critical seepage phenomenon is proved objective. The probable critical gas relative saturation ranges from 44% to 70%. When the probability is above 80%, the critical gas relative saturation is about 47-65%. When the gas saturation is about 57-60%, then the pabobility of critic phenomena occuring is 1. The mechanism of generating critical seepage phenomenon is due to the extraordinary different of gas-liquid seepage properties and the high compressibility of gas. If the gas relative saturation is out of the critical saturation range, the flow of gas and water is lamina. If the gas relative saturation is right among the critical seepage saturation, the seepage state of the gas and liquid will change entirely. The flow of two fluids is disorderly and unsystematic, the flow path is zigzagged and discontinued, and the gas bubble is shrinking and expanding from time to time, so the energy is storing and releasing. The flow of two fluids lost all its forward energy, the critical seepage phenomenon occurs and the flow of two-phase fluid will stop.[4] After a great deal of experiment research of gas-liquid two-phase flow in an artificial fracture, the critical seepage phenomenon also occurs objectively. In addition, the experiment proved that the gas-liquid two-phase relative saturation is the main factor affecting the
seepage state. By adjusting the gas relative saturation, the critical seepage phenomenon could be controlled to occur or not. The critical gas saturation ranges from 49.12% to 63.47%. The observed results proved the conclusion of last chapter, when the flow is falling into critical seepage, the gas and water will disperse along the seepage path disorderly and unsystematically.[5] Based on the results of gas-liquid seepage in coal sample's fracture, the critical seepage phenomena is also in existence.[6] The effect of gas relative saturation on gas-liquid two-phase seepage law in rock fracture is not sole; there exists a critical value of gas relative saturation Sgc. When the gas' relative saturation Sg > Sgc, the gas-liquid composite seepage coefficient varies exponentiallywith [Sg - Sgc f, and can be expressed as exp a(sg - sgcj ; When Sg < Sgc, the gas-liquid composite seepage coefficient varies exponentially with [Sg - Sgc) and can be expressed ; from the experiment, the critical gas relative saturation is 59.275%.[7] Besides the gas relative saturation, the stress state and the connectivity of the fracture also have influence on gas-liquid two-phase flow in single fracture. While all these factors taken into account, the gas-liquid two-phase seepage coefficient in single fracture can be expressed as: 2[cr, + uia, +cr,) -kf =rkoP p I" *n[8] After analyzing the well test data of a coalbed methane extraction well, we found there also has critical seepage phenomenon in coalbed methane extraction engineering. The critical gas saturation ranges from 43.9% to 60.0%. Within this range, the output of gas and water decrease to the nadir. So in order to get the continuous high output of gas, the drainage of gas and water should be taken into control to avoid the gas relative saturation to fall into the range of critical relative saturation range.In this paper, the theory and mechanism of gas-liquid two-phase critical flow in single fracture is researched in detail, both detailed theory deduce and a great numbers of experiments including numerical and physical are brought out, and the generating mechanism
of gas-liquid two-phase critical seepage phenomenon is revealed at last. This research is useful not only to understanding the science meaning of critical seepage phenomenon, but also to providing an important theoretic base in how to improving the coefficient of gas recovery, so the achievement of this research has great science values as well as has widest application foreground.
1.通过对气体、液体以及气液二相流体各自在裂缝中的渗流规律,进行详细的理论分析和推演,建立了裂缝中气液二相流体渗流的混合数学模型,该模型主要包括五个控制方程;
连续性方程:div(P_w(?)_w+P_g(?)_g)+(?)(P_wS_w+P_gS_g)/(?)t+I=0
气体裂缝渗流达西定律:q_g=(-b~2/12μ_g)S_g((?)P/(?)S)
液体裂缝渗流达西定律:q_w=(-b~2/12μ_w)S_w((?)P/(?)S)
In many engineering such as oil-gas exploitation, coalbed methane exploitation and extraction, there always occurs gas-liquid two-phase flow through a fracture. The gas-liquid relative permeability in fracture always determines the recovery ratio of oil, nature gas, coalbed methane, and gas. When we are studying the fracture seepage characters of low permeability coal, we find that when the gas relative saturation closed to a certain value, the relative permeability of gas and liquid will fall down rapidly and sometimes the flow of the two-phase will stop. We name this phenomenon as critical seepage phenomenon of gas-liquid two-phase flow in single fracture, and the gas relative saturation as critical gas relative saturation where the critical seepage phenomenon occurs. In order to reveal the mechanism of critical seepage phenomenon of gas-liquid two-phase flow in single fracture, we study the gas-liquid two-phase seepage law in detail by means of theory deduce, numerical simulation, physical simulation, fracture seepage test of rock samples, analyses with in situ data from one gas production well. The main achievements and conclusions are listed as follows:[1] After analyzing the fracture seepage law of gas, water and gas-liquid two-phase fluid in detail, a combined mathematical model of gas-liquid two-phase flow in single fracture is set up. This model involves five control equations:Continuity equation: divDarcy law of gas seepage in fracture:Darcy law of liquid seepage in fracture:
Gas-liquid relative saturation equation: g ￡>(l - Sg0)+ p0Sg0Equation of state for an ideal gas: pg = ——RTWith proper definite condition, these five control equations make up of the complete combined mathematic model of gas-liquid two-phase flow in single fracture. While substitute the five equations into one combined equation, we get the final control equation of gas-liquid two-phase fluid seepage in single fracture:2 U C ^ ?r r.2 ? C Va2 2 ,2 2\V~^go) M 0 Po^go \\ P P~ P(\ -sj+ Ptss,+ It 24//, P(i - s,,)+ P,st, }Caxr+"v"J dt{p(\-SgO)+PoSgO)+ XT p(l-SgO)+PoSgO dt[2] The numerical solution of above combined mathematic model is researched, and the Finite Element Simulating program is designed by using Fortran computer language.[3] After a great deal of numerical simulating, the critical seepage phenomenon is proved objective. The probable critical gas relative saturation ranges from 44% to 70%. When the probability is above 80%, the critical gas relative saturation is about 47-65%. When the gas saturation is about 57-60%, then the pabobility of critic phenomena occuring is 1. The mechanism of generating critical seepage phenomenon is due to the extraordinary different of gas-liquid seepage properties and the high compressibility of gas. If the gas relative saturation is out of the critical saturation range, the flow of gas and water is lamina. If the gas relative saturation is right among the critical seepage saturation, the seepage state of the gas and liquid will change entirely. The flow of two fluids is disorderly and unsystematic, the flow path is zigzagged and discontinued, and the gas bubble is shrinking and expanding from time to time, so the energy is storing and releasing. The flow of two fluids lost all its forward energy, the critical seepage phenomenon occurs and the flow of two-phase fluid will stop.[4] After a great deal of experiment research of gas-liquid two-phase flow in an artificial fracture, the critical seepage phenomenon also occurs objectively. In addition, the experiment proved that the gas-liquid two-phase relative saturation is the main factor affecting the
seepage state. By adjusting the gas relative saturation, the critical seepage phenomenon could be controlled to occur or not. The critical gas saturation ranges from 49.12% to 63.47%. The observed results proved the conclusion of last chapter, when the flow is falling into critical seepage, the gas and water will disperse along the seepage path disorderly and unsystematically.[5] Based on the results of gas-liquid seepage in coal sample's fracture, the critical seepage phenomena is also in existence.[6] The effect of gas relative saturation on gas-liquid two-phase seepage law in rock fracture is not sole; there exists a critical value of gas relative saturation Sgc. When the gas' relative saturation Sg > Sgc, the gas-liquid composite seepage coefficient varies exponentiallywith [Sg - Sgc f, and can be expressed as exp a(sg - sgcj ; When Sg < Sgc, the gas-liquid composite seepage coefficient varies exponentially with [Sg - Sgc) and can be expressed ; from the experiment, the critical gas relative saturation is 59.275%.[7] Besides the gas relative saturation, the stress state and the connectivity of the fracture also have influence on gas-liquid two-phase flow in single fracture. While all these factors taken into account, the gas-liquid two-phase seepage coefficient in single fracture can be expressed as: 2[cr, + uia, +cr,) -kf =rkoP p I" *n[8] After analyzing the well test data of a coalbed methane extraction well, we found there also has critical seepage phenomenon in coalbed methane extraction engineering. The critical gas saturation ranges from 43.9% to 60.0%. Within this range, the output of gas and water decrease to the nadir. So in order to get the continuous high output of gas, the drainage of gas and water should be taken into control to avoid the gas relative saturation to fall into the range of critical relative saturation range.In this paper, the theory and mechanism of gas-liquid two-phase critical flow in single fracture is researched in detail, both detailed theory deduce and a great numbers of experiments including numerical and physical are brought out, and the generating mechanism
of gas-liquid two-phase critical seepage phenomenon is revealed at last. This research is useful not only to understanding the science meaning of critical seepage phenomenon, but also to providing an important theoretic base in how to improving the coefficient of gas recovery, so the achievement of this research has great science values as well as has widest application foreground.
引文
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