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1 DOI: 0.459/mmh E-mal: : ; ; - ;.. [ ] ( [3] [4] / (. ( 0 - T 0. T e T e > T 0. : G; ; Bulletn of the South Ural State Unversty Ser. Mathematcs. Mechancs. Physcs 07 vol. 9 no.. 9
2 (. - m - [ 5]. []: t ms ρ ms ρv = Jh = GJ ( ( dv( ( msww = Jh w = ( G J t ( ( mshh = Jh Jh w = J t (3 S w Sh S = (4 S ( = w h -; ( = w h -; v - J ; - wh. ms v (5 ( rad ρ = µ ; µ ; ; -. z [6]: = zρ RT (6 T c z = 0 4l (7 T c c R ; T ; c T c -. [7] : T Sh ρc ρcmsvradt ε rad ρcmsηs = dv( λ radt mρhlh (8 t c t t T z ε = ρ c z T ηs = ε ρ c ( s s ( w w w h h h λ = ( m λs m( Sλ Swλw Shλh. ρc = m ρ c m S ρ c S ρ c S ρ c L h ; s - ; s ; c ( = s w h.. - ( (6 (8 : T z S zrt ρ ρh Sh = G (9 t T t z t S t S x mµ x S ρ t T ρc T T mρhlh Sh = ε msηs λ t ρ c µ x x µ x t ρc x x ρc t (0 S h w ρ = w0 ( ( h0 S h. ρ ( w. «..»
3 : t = 0 x x L : = T = T S = S S = 0 S = S ; ( w 0 0 h h0 w h0 x = xw : = e T = Te ; t > 0: T (3 x = L : = 0 = 0. x x x w L 0 T 0 - S h0 e T e. (9 ( (7 ( : ; - ; - ( ; -. (4 (7 (9 ( (9 (0 : ( S ( S T z ( S ( S T T z z z R T = x ρ m x m x ρ ρ ( Sh ( S h h µ µ G S t ρ ( ( ρ c ( ε ρ c µ x x x T T T T = ( ρc ( S ( S c mρhlh h h m( S ( ηs c ( ρc ρ ρ λ x T T T T λ x x. ; (4 (5 4 Bulletn of the South Ural State Unversty Ser. Mathematcs. Mechancs. Physcs 07 vol. 9 no.. 9
4 (4 (5 - A C B = F A T C T B T = F T T T T A j B j C j (j = T : A A C T z R T ρ = ( x ( S mµ ( x ( S B ( t ( S ( ( S ( S ( ρ z R T ρ mµ = = ρhg ( S ( h S h S T z z R T ρ ρ T m z x µ mµ = λ F = ( x ( ρc ( x ( ρc ; λ ρc T = ρ c µ ( B t ρc CT = ( λ λ ( x ρ c µ ( ρc ρc ( ( ( ( ( FT = T ε m S ηs ( ρ c µ x mρ ( ρc ( S ( S hlh h h (3 j j B j j Fj Aj β α = β j = j Aj α C j Aj α C j j = T: T T T = α T β = α β. : T T α = 0 β = Te T βn β N T N = T N =. α = 0 β = e. α N α N (7: z c T = 0 4 l T c c.. (6 :. (4. -. «..»
5 ( ( ( [8] 6 B B 0 Th = ex h = A z T z ; A ln 6 0 ; ; T h h - ; A B (- ( : : A = 8 486; = ; : A = 5 659; = (T new > T h ((S h ter > 0 - : ( ( ( ( ter ( c S ρ ρ T ter Sh = mn Sh = T Th Sh = h ( S h mρ hlh Gρh S S ter = S. ( ( h h h.. (T new < T h ((S w ter > 0 (S ter > 0 - : S = S = T T S = S = : S S ter = S. ( ( ( ( ter ( ( ter mn ρc S T ρ S w w ρw h h h h h h mρhlh Gρ G h ρ h ( ( h h h 5. (: ( S h w ( S ρ w ( G (( S h ( S = h. ρw 6. (4: ( S ( S w ( S h =. 7. : 6 Bulletn of the South Ural State Unversty Ser. Mathematcs. Mechancs. Physcs 07 vol. 9 no.. 9
6 ter ( S ( S ( ter ter ter z z T T δ = max ; ; ;. z T S : ter ter ter : = ; z = z ; T = T ; ter ter ter h h w w ( S = ( S ( S = ( S ( S = ( S ; ;. > ( (. [9 0]. (6. -. x ( ( ( - / /...: «..»
7 ... - /......: /.... // /.. // ( /.... // / // / : /......: / : / : Bulletn of the South Ural State Unversty Seres Mathematcs. Mechancs. Physcs 07 vol. 9 no DOI: 0.459/mmh7003 MATHEMATICAL MODEL AND ALGORITHM FOR SOLVING THE PROBLEM OF NON-ISOTHERMAL GAS FILTRATION IN RESERVOIR IN CASE OF HYDRATE DECOMPOSITION N.G. Musaaev S.L. Borodn D.S. Belsh Tyumen Branch of Khrstanovch Insttute of Theoretcal and Aled Mechancs SB RAS Tyumen Russan Federaton Tyumen State Unversty Tyumen Russan Federaton E-mal: bedeser@yandex.ru The aer formulates a roblem of njecton nto orous bed flled u n the ntal condton wth hydrate and as warm (wth the temerature hher than the ntal temerature of the bed as. A mathematcal model of non-sothermal as fltraton n case of as hydrate dssocaton s develoed to solve ths roblem. The artcle resents a soluton alorthm where an mlct dfference scheme a swee method and a method of smle nteraton are aled. The method for calculatn hydrate saturaton from several lmtn condtons s suested. It can be used for soluton of other hase-chane roblems also for multdmensonal Stefan roblems as well as roblems wth an extended hase transton zone. After that the roblem s consdered n one-dmensonal lane-arallel formulaton wth reard to requred ntal and boundary condtons for fndn a comutatonal soluton of a set of equatons descrbn ths model. At the end the aer resents the roblem calculaton results usn the suested method on the bass of whch the dstrbuton of arameter values for some tme ntervals are shown. In the erformed calculatons the reservor n the ntal condton s flled u wth methane and ts hydrate. Keywords: non-sothermal fltraton of as; as hydrate; numercal method; hase transton. Bulletn of the South Ural State Unversty Ser. Mathematcs. Mechancs. Physcs 07 vol. 9 no.. 9
8 References. Maoon Yu.F. Gdraty rrodnyh azov (Natural as hydrates. Moscow Nedra (n Russ... Shaaov V.Sh. Musaaev N.G. Dnama obrazovanya razlozhenya dratov v sstemah dobych transortrov hranenya aza (Dynamcs of hydrate formaton and decomoston n the systems for as roducton transortaton and storn. Moscow Naua Publ (n Russ.. 3. Kollett T.S. L'yus R. Uchda T. Nefteazovoe obozrene Autumn (n Russ.. 4. Borodn L.S. Tyumen State Unversty Herald. Physcal and Mathematcal Modeln. Ol Gas Enery 05 Vol. no. 3( (n Russ.. 5. Musaaev N.G. Khasanov M.K. Tyumen State Unversty Herald. Physcal and Mathematcal Modeln. Ol Gas Enery 04 no (n Russ.. 6. Latonov V.V. Gurevch G.R. Gazovaya romyshlennost' 969 no (n Russ.. 7. Basnev K.S. Kochna I.N. Masmov V.M. Podzemnaya dromehana (Subsurface hydromechancs Moscow Nedra Publ (n Russ.. 8. Istomn V.A. Yaushev V.S. Gazovye draty v rrodnyh uslovyah (Gas hydrates n natural envronment Moscow Nedra Publ (n Russ.. 9. Varaft N.B. Sravochn o telofzchesm svoystvam azov zhdostey (Reference boo on heat-transfer roertes of as and lqud. Moscow Naua Publ (n Russ.. 0. Varaft N.B. Flov L.P. Tarzmanov A.A. Totsy E.E. Sravochn o telorovodnost zhdostey azov (Reference boo on heat conductvty of lqud and as. Moscow Eneroatomzdat Publ (n Russ.. Receved January «..»
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