advanced equations for natural gas

8/10/2019 Advanced Equations for Natural Gas

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THE SPE I MAGE LI BRARY SPE 4692

Advanced Equat i ons f or Natural GasFl ow Predi ct i on

4692

Franci s, M. A. ,Texas East ern Tr ansmi ssi on Corp.

Copyri ght 1973, Amer i can I nst i t ut e of Mi ni ng, Metal l ur gi cal andPet r ol eum

Engi neer s I nc.

Thi s paper was prepared f or t he 48th Annual Fal l Techni cal Conf erenceand Exhi bi t i on of t he Soci et y of Pet r ol eum Engi neer s of AI ME, hel d i nLas Vegas, Nev. Sept . 30 - Oct . 3, 1973. Per mi ssi on t o copys restr i ct ed t o an abst r act of not mor e t han 30 wor ds. I l l ust r at i ons

maynot be copi ed. The abst r act shoul d cont ai n conspi cuous acknowl edgmentofwhere and by whom t he paper i s pr esent ed. Publ i cati on el sewher e af t er

publ i cat i on i n t he J OURNAL OF PETROLEUM TECHNOLOGY or t he SOCI ETY OFPETROLEUM ENGI NEERS J OURNAL i s usual l y grant ed upon request ed to t heEdi t orof t he appr opr i at e j our nal , pr ovi ded agr eement t o gi ve pr oper credi ts

made.

Di scussi on of t hi s paper i s i nvi t ed. Thr ee copi es of anydi scussi onshoul d be sent t o t he Soci ety of Pet r ol eum Engi neers of f i ce. Suchdi scussi ons may be pr esent ed at t he above meet i ng and, wi t h t he paper ,maybe consi dered f or publ i cat i on i n one of t he t wo SPE magazi nes.

ABSTRACT

I sother mal pr essure- di st ance equati ons aregi ven f or l i near and quadr ati c vol ume- di st ancedi st r i but i ons, bot h wi t h and wi t hout t hest andard const ant sl ope el evati on cor r ect i on.Basi c appl i cat i ons t o pi pel i ne r eal gas f l ow,evel of f , and bl owdowns are i ncl uded. The

el at i onshi p of t r ansmi ssi on f act or s t o Reynol dsNumber dependent ef f i ci enci es, vel oci t y pr of i l es,and or i f i ce met er equati ons i s di scussed. Ent hal pyef f ect s on temper ature predi ct i on ar e consi dered.

NTRODUCTI ON

The descr i pt i on of i sother mal gas f l ow hasbeen r est r i ct ed by usual i nt egr ati on methods i nhat pr essur e- di st ance pol ynomi al s are avai l abl e


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onl y f or t he const ant vol ume case. By expr essi ngvol ume as a l i near f unct i on of di st ance, wi t h t hepar t i al der i vat i ve of vol ume wi t h r espect t odi st ance hel d const ant , an i nf i ni t e number ofsi mpl i f i ed vol ume- di st ance di st r i but i ons may bedef i ned. I nt egr at i on of t he moment umbal anceequat i on, wi t h t hi s i ndi cat ed subst i t ut i on, l eadso a f ami l y of pr essur e- di st ance pol ynomi al s i n

whi ch the square of t he pressure i s expr essed asa cubi c equat i on of pi pel i ne l engt h.

The above met hod may be ext ended t o a quadrat i cvol ume di st r i buti on, where a vol ume at t he pi pe

sect i on mi d- poi nt i s est i mat ed, and t he resul t i ngpr essur e- di st ance pol ynomi al s are expr essed t hroughhe f i f t h degr ee of pi pel i ne l engt h. I f t he moment um

bal ance equat i on i n t he above cases contai ns anel evat i on t er m, i t has t he f or m of t he Ber noul l idi f f er ent i al equati on and may be so i nt egr ated.

MOMENTUM BALANCE EQUATI ON

The moment um bal ance equat i on i s gi ven byFl ani gan and has t he f orm

=0. . . . ( 1)

where t he second and thi r d f actors are t henert i a t erms and t he f our t h and f i f t h dealespecti vel y wi t h el evat i on and f r i cti on ef f ects.

The Fanni ng f ri cti on t er m i s t he quot i ent of t heshear coef f i ci ent and t he hydr aul i c radi us

. . . . . . . . . . . . . ( 2)

where

. . . . . . . . . . . . . ( 3)

andR = d

h - - -4 . . . . . . . . . . . . . ( 4)

Eq. ( 3) i s i n the f orm r ecommended by Shapi r oand def i nes t he fr i cti on fact or as t he rat i o ofhe shear coef f i ci ent t o the dynami c head. Eq.4) gi ves t he hydr aul i c radi um f or a ci rcul ar

pi pe f l owi ng ful l , see Daugher t y.

Eq. ( 1) i s i n uni t s of t he f oot - pound- second


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syst emand may be conver t ed t o gas f l ow uni t s asgi ven by Eq. ( 24) . The pr i mar y steps i n t hi spr ocess wi l l be l i st ed her e and ar e si mi l ar t ohose gi ven by J ohnson, Smi t h, and Uhl .


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advanced equations for natural gas

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