Negative Compressibility

No reasons to share it with one person. I tink it is very common problem. So, Sometimes ECLIPSE will calculate negative total compressibility values even if the P! tables are not e"trapolate#. !his issue seems to occur #ue to either P! tables create# by P! packages that #o not have total compressibility compressibility checks as in P!i, or user errors when tables are e"porte#. $hatever the reason, it is possible to %" the total compressibility compressibility by slightly changing &o values as shown in the attache# tables. !hese small changes shoul# improve simulation convergence. 'as an# oil P! properties are #e%ne# in the ECLIPSE #eck using P(' an# P!) *or PC)+. ECLIPSE then issues the following message -$/0NIN' /! !I1E 2.2 (/3S * 45/N4662+ - NE'/!IE C)1P0ESSI&ILI!3 C)1P0ESSI&ILI!3 7)8N( IN '/S - P0ESS80E !/&LE 4 /N( )IL P0ESS80E - !/&LE 4 /! / S/1PLE P0ESS80E /L8E - 9644.:94;: . /(58S! S/!80/!E( 7L8I( - P0)PE0!3 /L8ES /! !4 $hy #oes ECLIPSE issue this message? $hat #oes it mean? + !hen Sg J  Ct,o  *Ct,g  Ct,o+  *;+ !he eect of a negative total compressibility compressibility is usually to cause the simulator to e"perience numerical #iKculties *convergence failures an#or erratic changes in the solution+.

/ complete table of total compressibility evaluation can be written to the .(&' %le by activating switch :4 of the (E&8' keywor# in the P0)PS section. If the range of sample pressures e"ten#s above the ma"imum bubble point entere# in the P!) table or above the ma"imum #ew point entere# in the P!' table, then ECLIPSE will be force# to e"trapolate above the highest entere# 0s or 0v. !his e"trapolation is linear in 0s, 4&o, 4*&oBisco+, 0v, 4&g, an# 4*&gBiscg+. In this case, it is not unlikely that negative compressibilities coul# occur as a result of e"trapolation. It is recommen#e# that the highest bubble point no#e in the P!) table is constructe# so as to avoi# e"trapolations above the highest entere# 0s in the table. Similarly, in a run with vaporie# oil present, it is recommen#e# that the highest #ew point no#e in the P!' table is constructe# so as to avoi# e"trapolation above the ma"imum entere# 0v #uring the simulation. !hree e"amples of P! tables are provi#e# below for a mo#el with #ry gas *0vA2+ an# live oil *0sM2+   E"ample 4. P(' an# P!) are #e%ne# with a single @un#ersaturate# line@. ECLIPSE e"trapolates &o an# 0s from =24=.; to 624=.; psi along the saturate# line. !his may cause negative total compressibilities to be calculate#. P('  P' &' IS' 4=.; 4;;.92> 2.22O> :>=.; 44.:4O 2.226O 94=.; 9.6=G 2.2444 424=.; G.42O 2.24G9 :24=.; 4.>4= 2.24O: :94=.; 4.G2> 2.2:29 G24=.; 4.26O 2.2::O =24=.; 2.OG9 2.2:;: 924=.; 2.>;9 2.2G4= >24=.; 2.9>O 2.2G99 ;24=.; 2.=62 2.2G6= O24=.; 2.=G: 2.2=G: 624=.; 2.GO> 2.2=>O  P!)  0S *P&8&+) &) IS) 2.22>4 4=.; 4.44; 2.66=   saturate# 2.26== :>=.; 4.4>2 2.69G   saturate# 2.4;;> 94=.; 4.:2: 2.64G   saturate# 2.GGO= 424=.; 4.:O= 2.OGO   saturate# 2.>=6: :24=.; 4.=G9 2.;2>   saturate# 2.O24= :94=.; 4.929 2.>=O   saturate# 2.69:2 G24=.; 4.9;4 2.969   saturate# 4.:=6; =24=.; 4.>64 2.92:  Psat 924=.; 4.>>O 2.9=6 >24=.; 4.>=> 2.96; ;24=.; 4.>:G 2.>=9 O24=.; 4.>24 2.>6:

624=.; 4.9;O 2.;=2     E"ample :. P(' is the same as that in the E"ample 4 but P!) has multiple @un#ersaturate# lines@. Since the saturate# P! #ata e"ists for the complete pressure range *4=.; to 624=.; psi+, ECLIPSE #oes not e"trapolate &o an# 0s along the saturate# line. P!)  0S *P&8&+) &) IS) 2.22>4 4=.; 4.44; 2.66=  2.26== :>=.; 4.4>2 2.69G  2.4;;> 94=.; 4.:2: 2.64G  2.GGO= 424=.; 4.:O= 2.OGO 2.>=6: :24=.; 4.=G9 2.;2> 2.O24= :94=.; 4.929 2.>=O 2.69:2 G24=.; 4.9;4 2.969 4.:=6; =24=.; 4.>64 2.92: 924=.; 4.>>O 2.9=6 >24=.; 4.>=> 2.96; ;24=.; 4.>:G 2.>=9 O24=.; 4.>24 2.>6: 624=.; 4.9;O 2.;=2  4.9=G> 924=.; 4.;6> 2.=:G >24=.; 4.;;: 2.=>G ;24=.; 4.;=O 2.92G O24=.; 4.;:= 2.9=G 624=.; 4.;22 2.9OG  4.OG=> >24=.; 4.OO> 2.G9> ;24=.; 4.O>4 2.G62 O24=.; 4.OG9 2.=:= 624=.; 4.O42 2.=9O  :.4:G: ;24=.; 4.6>2 2.G22 O24=.; 4.6G= 2.G:6 624=.; 4.62O 2.G9;  :.=26; O24=.; :.246 2.:9G 624=.; 4.66: 2.:;;  :.>6=9 624=.; :.2>G 2.:4G 4224=.; :.2G9 2.:G=  

     Psat

 saturate#

 saturate#

 saturate#

 saturate#  saturate#

  E"ample G. P(' is the same as that in the E"ample 4 but PC) has the multiple compressibilities *C)+ an# viscosibities *C+ of the un#ersaturate# oil. Since the saturate# P! #ata e"ists for the complete pressure range *4=.; to 624=.; psi+, ECLIPSE #oes not e"trapolate &o an# 0s along the saturate# line. PC)  *P&8&+) 0S &) IS) C) C 4=.; 2.22>4 4.44; 2.66= 4.GG=E29 6.924E29  saturate# :>=.; 2.26== 4.4>2 2.69G 4.GG=E29 6.924E29  saturate# 94=.; 2.4;;> 4.:2: 2.64G 4.GG=E29 6.924E29  saturate# 424=.; 2.GGO= 4.:O= 2.OGO 4.GG=E29 6.924E29  saturate#

:24=.; :94=.; G24=.; =24=.; 924=.; >24=.; ;24=.; O24=.; 624=.; 

2.>=6: 2.O24= 2.69:2 4.:=6; 4.9=G> 4.OG=> :.4:G: :.=26; :.>6=9

4.=G9 4.929 4.9;4 4.>64 4.;6> 4.OO> 4.6>2 :.246 :.2>G

2.;2> 2.>=O 2.969 2.92: 2.=:G 2.G9> 2.G22 2.:9G 2.:4G

4.GG=E29 4.GG=E29 4.GG=E29 4.GG=E29 4.GG=E29 4.GG=E29 4.GG=E29 4.GG=E29 4.GG=E29

6.924E29 6.924E29 6.924E29 6.924E29 6.924E29 6.924E29 6.924E29 6.924E29 6.924E29

        

saturate# saturate# saturate# saturate# saturate# saturate# saturate# saturate# saturate#

/ttache# e"cel sheet illustrates how a small change in speci%c &o values can remove negative total compressibilities. 5ust turn on option :4 in (E&8' keywor# to generate the check table. 58S! 0EN/1E the attache# B.#oc %le in to B."ls 0egar#s, /le"