Study of the Hydrodynamic Pattern in a Sedimentary Basin Subject to Subsidence

SOCIETY OF PETROLEUM ENGINEERS OF AIME 6200 North Central Expressway =&i SPE 2988 Dallas, Texas

THIS IS.A PREPRINT --- SUBJECT TO CORRECTION

RY Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/70FM/All-70FM/SPE-2988-MS/2069932/spe-2988-ms.pdf by guest on 28 September 2021 C. Jacquin and M. J. Poulet, Institut Francais du Petrole

@ Copyright 1970 American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. This paper was prepared for the 45th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houstonj Tex., Oct. 4-7, 1970. Permissionto copy is restrictedto an abstract of not more than 300 words. Illustrationsmay not be copied. The abstract should contain . conspicuous acknowledgmentof where and by wnornWle reameris nres.*m+n~..... ~~b~i~ation elsewhere afte—.— publication in the JOURNAL OF PETROLEUM fiCHNOLOGY o;”;he SOC’~TY OF PETROLEUM ENGINEERS JOURNAIJis ususJJy granted won request to the Editor of the appropriate journalprovided agreementto give proper credit is &ade.

IHsmJssiQn of this namer is invited. Three copies of any discussion shouldbe sent to the Society of Petroleum R&i;eers office. Such discussionmm be nresented at the i3bOVe meting — ad. ..> tiththe paper, may be considered for publication in one of the two SPE magazines.

ABSTRACT tion and the order of magnitude of these Qverpre~suresagree with standard observations The structure of a sedimentarybasin is made on actual sedimentarybasins. modelized, assuming that this basin is subject to subsidenceand has the following character- 3* The circulationof water through sand istics: (1) shaped like an inverted cone with horizons occurs at very low speeds of between a circular base having a radius of 300 km, - about 1 and 10 mm/year, but the volumes of (2) depth in the middle varying from O to 3,000 water involved are large (from 1012 to 1013 cu ,. m during an evolution lasting .PmL>u .nuAQw....211<*T-! years m for a period of between 40 and 150 million and (3) during this evolution, successive years). deposits of sand and clay strata occurred with gradual expulsion of water from the clay as These results may provide useful indica- the result of burial. tions for studying some of the phenomena governing the formation of petroleum accumula- This basin structure is used to study the tions, i.e., diagnesis and hydrocarbon hydrodynamic conditionsthat have occurred in migration. the different sedimentarystrata. The main conclusionsof this study are as follows. INTRODUCTION

? -b. Fhlid circIdatiQnsthrowwh the clay Hydrocarbon displacementphenomena inside are quite complex because the direction of flow stratigraphicseries (primry”wl~gra.+v..“ ++nm {n_- the has usually reversed itself, with this reversal --=nln-ce— -- -reek. end secondarymigration in occurring earlier Gr A..e.7.+ - ..--...-.=fnllnwincr t,he moment permeable layers where traps-are located) caus of deposition of clayey material. This leads the sizable accumiations making up ex@oitable to an evaluationvs time of the cumulative oil fields. The leading mechanisms assumed to amounts of water, res ectively, running upward be behind these displacementsare displacemen -(WI)and downward (W2Y over a 1 sqcm of hydrocarbonsin a dissolved or emulsion horizontal surface associated with the clay state in water and displacementof continuous deposited in a given place at a given- mumeuu.— .—.- 4. oil and gas phases (or possibly oil dissolved in gas) by gravity or aquifer movement. 2. The circulationof water through clay causes fluid overpressurescompared with the It is hoped that an understandingof the hydrostaticpressure. The vertical distribu- hydrodynamic conditions existing in a sedimentary basin during its evolution will allow References and illustrationsat end of paper. STUDY OF THE HYDRODYNAMICPATTERN IN A SEDIMENTARY —.——. 2 BASIN SUBJEET W SUBSIDENCE sm 29Ew

definition of the physical or chemical mecha- Laws of Evolution nism by which such migrations occur. There- fore, we shall attempt to reconstitutethese Sedimentationis assumed to have occurred hydrodynamic conditionsby comput@. Our underneath a water depth which is unifo?xnin reasoning will be based on a basin pattern space but does not need to be defined nor even whose structure and evolution are defined from assumed constant in time. what is known about sedimentarybasins and from hypotheses (choosingones that are as simple The sand is assumed to be an incompress- as possible) concerningwhat is poorly known. ible homogeneousmaterial with constant sand Although such hypotheses,like the approxi- layer porosity and thiclmess. mations that may be made during the project, may appear to be entirely justified,and even The clay is assumed to be compressibleand

though computingmay provide results with an at all times to have a porosity dIat a given Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/70FM/All-70FM/SPE-2988-MS/2069932/spe-2988-ms.pdf by guest on 28 September 2021 nr.rm~vsow wh< -h Aenanrlc ~~~~ay ~p. ~~.~ ~~t,~ ~~- no-in+..wi+.h +.hi .- nnvnsi+.v rltaneniiinu nnlv op. ~.~.~ -“.- -“J ....*”.. -“y”..-” =-—.. , ..-”-- “-.-w y-. -W . . . -vy”..-_. ~ ----~ voted to this operation, these results are depth y of this point. The relation between still nothing more than an order of magnitude. porosity and depth is 0= l/(L.y+A),with

FACTS OF THE PRf)BIJ!l!ANDBASIC HYPOTHESES =Oogfor y=O = 0.2for y= 1,000m. Shape, Structure and Evolution of the Basin (Fig. 1) This equation is suggestedby bibliographic data. Compression of the clay leads to the Reasoning is based on a sedimentarybasin that expulsion of the fluid filling up the clay has undergone subsidence. pores. This fluid mainly consists of a water phase possibly contax hydrocarbons (in a Shape and Dimensions form that we will not fix) in small amounts. The characteristicsof this fluid will be taken The basin consideredis in the form of an up later on. inverted cone with a circular base having a radius R = 300 km. The depth in the center, It is assumed that solid clay material is H, varies with time from O to 3,000 m at the added to the center of the basin, with a terminal state of an evolu ion correspondingtc constant deposit rate in time (expressedin k a total duration of 150.10 years. It can be mass per time unit) snd constant character- seen that this is a very flat structure [(R/H) istics of the deposited material (porosity, ~ 100] and that the representativediagrams grain size, morphology). use two very different scales for the horizontal and vertical dimensions. It is assumed Laws Governing Fluid Flow that the. ..w -—=l]rfa~e--”w nf-- +.he. ..” a-Lwmmd---- .-.Pan he-. =mlat.d.=—-.- to a plane. Thro~h Sand

Structure of the Basin The permeabilityof the sand is assumed to be constant and identical at all points in The sedimentary series filling the basin the sand material. is assumed to be made of two parts which will be called “clay” and “sand”. The clay Through Clay represents the source rock for the hydrocarbons. It is compressibleand has low Flow through the clay is assumed to follow permeability. It was through this rock that Darcy’s law (for a possible criticism of this primary migration took place. The sand hypothesis,Cf. 2). The permeability of the represents permeable and not very compressible clay material is assumed to depend only on the 1 . ----- :...-:A- -s . ..L< ,.L . ..A-A.-. .“.< -t...+< 6.- J_dyC~b JJ1=4UG UL W1lLGL1 =CGUJM=lJ lLl*~J-cLb*UA1 porosity according to a relation of the type took place. They may form reservoirs in place~ K = A .05 (Cf. 2), with K being the perme- where their structure is suitable for hydro- ability and k being a constant. carbon accumulations. Fluid Characteristics With regard to the relative arrangement of the sand and clay parts inside the series, The fluid circulatingin the sand and clay it is considered to be a single sand layer is consideredto be in a monophasic state (or originally deposited on an impermeablebase- at least that it makes up a phase whose satu- ment with a constant thickness and covered by ration at all points is very close to 1 so that clay. the correspondingrelative permeability can also be assumed equal to 1). The fluid is assumed to be similar to a simple viscous fluid, with its viscosity at any given point SPE 2988 C. JACQUIN and M. J. POULET 3

depending only on the local temperature. Fig. Depth-Time Relationship 2 shows the relationshipexisting between these two parameters. The temperaturedepends The law governing the evolution of depth linearly on depth as defined by the following with the in the center of the basin is first two conditions: (1) surface temperature = 20° determined. At a given moment the shape of C and (2) a temperatureincrease of 3°C for the basin is thus lmown, along with the dis- each depth increase of 100 m (correspondingto tribution of porosity values at sll points in a mean value of the geothermal gradient). the clay, as well as the rate of burial. Fig. 3 shows the graphic representationof how deptk The other factors capable of changing the evolves with time in the center of the basin. viscosity values of the fluid are pressure and salinity. A study of Fig. 2 with regard The rate of burial (slope of the curve in Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/70FM/All-70FM/SPE-2988-MS/2069932/spe-2988-ms.pdf by guest on 28 September 2021 to s~~ty and Fig. 253.1 in Ref. 3 with Fig. 3) can be seen to reach a maximum at the regard to pressure shows that the possible initial moment and to become almost constant role of these two factors is entirely negli- once the depth reac es 1,000 m, which corre- gible in the case with which we are concerned. sponds to t = 40.1d years. It can be seen that this depth of 1,000 m correspondsto a Relative Importance of Pressure Drops in the degree of burial beyond which the organic Two Parts of the Series material.of the sediments can be considered capable of becoming transformedinto hydro- Pressure drop in the sand will be ignored carbons (Cf. 4). This gives us consideringthe great difference between the permeabilityvalues in both types of material. H= C+B.t An a posteriori check of this approximation 6 shows that it is acceptableprovided the ratio with H = 1,000 m when t . 40.10 years between the s d and clay permeabilityvslues H = 3,000mwhent = 150.106 years reaches 0.5.109 . This proves to be the case if the clay material permeabilityvalues Flow of Water in Clay mentioned in the bibliography and standard ssnd permeabilityvalues are used. When this ..-L,—..-l Consideringthe structure of the basin, ratio becomes iess tinantineiimit menuonea water is expelled from the clay, which is put above, the results (water volumes and rates) under compressionas the result of progressive are overestimated. burial$ and this water is driven vertically both upward toward the surface representingth Consequencesof this Approximation seabottom and downward toward the clay-sand contact. At every moment within the clay mass It is assumed that flow inside the sand there is a surface z where the rate of flow is runs parallel to lines intersectingvertical. nil; thus, z separatestwo zones (Fig. 4). =——.–.nlanes running via the @s of the basin and AL....- -,-. ,.n.r.ww+ R.lnw ~i f~~w nuuvtz z, flmw L U.o Uymw.u. -“-”.. the surfaces separating clay and send, hence runs downward. This surface~ is determined b that it is almost horizontal (consideringthe assuming that the pressure drops P1 and P2 ?~~+.+.hn+. +.he vsllle nf the R./H ~~~~Q ~S very A-”” “..-” . ..- .—-- -- J--- --, -- for Plow fiong the same v-ertiealIim L-ieaeh~ high). Likewise, flow through the clay is of these two zones are equal. then nearly vertical. Stice flow is vertical, surfaceZ is such APPFU)ACHOF THE PROBLEM AND RESULTS that its point of intersectionwith any verti- csl line is located at a depth h-z that depend Evolution of the geometric character- solely on the depth h of the point of inter- istics of the sedimentarybasin thus defined, section of the same vertical line with the and hence evolution of fluid circulationin clay-sand separation surface. Therefore, the clay snd sand, can be calculatedvs time. merely knowing the relationshipbetween z and The problem of evaluating them at a given is sufficientto determine surface Z corre- moment actually means writing sn equation ~nondin~r..-——..=to a given age (i.e.! a given geometr which expresses a material balance and which of the basin). is solved h,nalyticallyor numerically, depending on the case. The graph in Fig. f+represents the relation between the depth h of a point located In the following description,no attempt on the clay-sand contact surface and the will be made to explain all stages of thickness z, measured on a vertical from this computation. The main points in the reasoni!q point, of the clay mass located underneath .X. will merely be pointed out, end the results .w-~ k...... As soon as h reaches a value of 300 m, the UC &_vGLL. reiations-hipbetween z and h may be considere( to be linear: . STUDY OF THE HYDRODYNAMICPATTERN IN A SIZUMENTARY BASIN SUBJE12TTO SUBSIDENCE SPE 2988

Historical Review of Water Circulation in the cblV

For different values of r snd of final At any stage in the evolution of the basin depth y at Point M, the cumulativevolumes let us consider the clay present at Point M were calculatedfor the water having circulated located at a distance r from the axis and at a through a horizontal surface measuring 1 sq m depth y. Depending on the value of y, the flow centered around M. The results of this are at Point M will run either upward or downward: plotted in Figs. 6 to 8. In order to differen- for h-y>z, the flow runs upward; for h-y = z, tiate flow directions, these results are there is no flow; for h-y< z, the flow runs plotted as follows. Each of the Figs. 6 to 8 d~wn~afi_: correspondsto a .@ven value of r. Time in millions of years is plotted on the abscissa. Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/70FM/All-70FM/SPE-2988-MS/2069932/spe-2988-ms.pdf by guest on 28 September 2021 During the evolution of the basin, the For a given value of the final depth of M, value of h-y, representingthe depth of sedi- the cumulativevolumes of water having run ments deposed prior to the clay present at M, through the 1 sq m reference surface are can only decrease as the result of the progres- plotted on the ordinates: (a) toward positive sive expulsion of water. On the other hand, values for volumes correspondingto upward the value of z increases with time, while z flow (Wl) and (b) toward negative values for depends on h according to the relation de- volumes correspondingto downward flow (W2). scribed in Fig. 4. Depending on the position We have defined of M at the.moment t = 150.106 years, three cases can occur (Fig. 5).

1 ~~ ~~,e~,Gr,eTL~~ = 1cm 1 n 6 ..=.-= M<” JGGU3, L-l L= locat~~ at the sand-clay co~&~ This means that the clay present at M was deposited at the very beginning of the basin!s existence. There In the general case (Case 3), to each fore, we still have y = h; hence h - y = 0< z value of the final depth of Point”M correspond when t > 0, and flow constantly runs downward. two curve portions limited by to and ti for the curve portion concehg upward fiow, and 2. At the moment t = 150.106 years, M is ti snd 150 for the curve portion concerning located above surface Z , and (h-y)t=1507 downward flow. Since h-y can only decrease during time,‘z)t=l~~Le zconttiues toticrease, the in- h Cases 1 and 2, which have a constant equality h - YEZ is always valid. The clay flow direction, the figure is reduced to only present at M was deposited at a moment to one of these curve portions. The following correspondingto a fairly well advanced stage can elso be seen on Figs. 6 to 8. The number in the basin’s evolution and has always been at the far right of each curve portion subject to upward drainage. indicates the final depth of Point M. The numbers written along the curves give the 3. At the moment t = 150.106 years, M is momentary depth of Point M. located between the sand-clay contact and surface Z. This means that (h-y)t=lo< Distribution of Upward and Downward Flowing Water Volumes in the Clay at the Final Stage (z)= O* The clay present at M was zhus subject %? downward flow, at least toward the end of Basin Evolution of the basin’s existence. However, this was not always the stiuation. Indeed, at moment to Figs 9 and 10 show tinedistributionof of deposition of the clay present at M, we had the total volume of water that has flown through a 1 sq m horizontal surface located in ‘t. = 0; hence the clay, with Fig. 9 showing the upward (h-y)t=t = %o’ flowing volume and Fig. 10 the downward flowing o volume. Since we still have z

(h-y)t=t> z~o. Flow through the clay produces the exis- o tence, at all points M the clay mass, of a Immediatelyafter its deposition, the clay water overpressurecompared with hydrostatic present at M was thus subject to upward flow. pressure. Along a given vertical line, this In this case, an inversion of the flow directior overpressureP is nil at the point of contact can be seen to have occurred at moment ti. between sand and clay as well as at the point of contact between clay and the seabottom. It Fig. 5 summarizesthe three cases. is a msximum at the point of intersectionwith ‘E2988 C. JACQUIN an M. J. YUULlfl’

surface Z. ~~,i~.h.~~~ ~~ ~o~sib~e to calculate linear flow rates in sand at each moment for any value In order to determine the distributionof of r (Fig. 15) and the amount of water that, the values of P according to depth ’slonga between two given periods, flowed through a given vertical line and at a given moment, in given zone in the sand layer (Fig. 16). addition to the hypothesis slready adopted, it is necessa~ to know the value of the constant CONCLUSIONS . ...-----l---J :- A1“- .-.1 .+

There is no point in attempting to deter- bution and order of magnitude of overpressures Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/70FM/All-70FM/SPE-2988-MS/2069932/spe-2988-ms.pdf by guest on 28 September 2021 ,. m-l.J mine 1 and in consideringthat tihisparameter n me ILUM comlpar~u-a .+&l..W&U1~1...A=+.+4n4n~lyuJu=u=uAUpres- has a well defined value. Aside from the clay sure. permeabilityand porosity values found in the bibliography, L can be seen to be strongly 1. It was found that fluid circulations influenced by the nature of the clay material. through clay are quite complex and that in the It is possible to find values of k (expre~sed normal case the flow direction is reversed. M I/darcy) arying from 10-3 (kaolinite This phenomenon occurs fairly early, depending Ventura clay?), to 1CY7 (montmorillonite$b). on the time when the clay material considered intermediatevalue of approximately10-5 was deposited. appears plausible and, for example, corresponds to that of a natural clay (McKelveyand Milne 2. The distributionand order of magni- in Ref. 6). Therefore,we have adopted this tude of the overpressuresof the fluid, com- value A = 10-5 for evaluating overpressures pared with hydrostaticpressure, in clay P due to flow in the clay. The results are layers conform to the data provided by conven- given in Figs. 11 and 12. The distributionof tional observationson actual sedimentary fluid pressure values (sum of P and hydrostatic basins. pressure) is shown in Fig. 11. The values of I are capable of being rather high, rising to as 3. Water circulationthrough sand layers much as 2&0 kg/ sq cm. This value represents occurs at very low rates of between 1 and 10 a maximum, at least for the basin model mm~year. However, the volumes of water ti- studied. The pressure reached by the water in volved are large, approximately1012 to 1013 the clay located on the axis of the basin and cu m for a period between 40 and 150 million at depths in the ticinity of 2,000 m (sum of P years. and hydrostaticpressure, Fig. 11) is almost equal to geostatic pressure, which for reasons 4. These findings may possibly provide of stability:it cannot surpass (Fig. 12). significantindicationsfor studying various phenomena governing the formation of Oii and It is interestingto compare the values gas fields, i.e., the diagenesis and migration obtained in this way with the overpressures of hydrocarbons. observed in sedimentarybasins. For this reason, Figs. 13 snd 14 present the data taken NcMENcLAm from the bibliography on this subject.T-9 The general aspect of pressure distributionwith A, B, C,L,l= constants depth as well as the orders of magnitude can be h= local depth of sand-clay ,. .,. seen to De qw~e similar to thse cbtaimd %-ltk Cnn+.ar+.------. the model studied here. H= depth at center of basin K= permeabilityof clay F1OW in Sand M= point located in clay P= overpressurein fluid (comparec Only t,hezone of the clay mass located with hydrostaticpressure) underneath z contributesto feeding the sand r= distance between Point M and iayer* !nL_ -n L..-<.1 .wA +ha mne<+inm nf me rate UA UIXA- -Au v..= ~v-.-- . . the MS of the basin are lmown at all points at a given moment. R= radius of sedimentarybasin Therefore, for each moment it is possible to t= time calculate the amount of water entering during to = time at which clay present at a unit of time into the sand layer portion M was deposited located inside a cylinder with a radius r and ti = time at which Point M was having the same axis as the basin. Then it car located on~ merely be said that this amount of water is W1 = volume of water having crossed equal to that expelled from the clay located through a 1 sqm horizontal underneath z and inside the same cylinder. In surface centered around M STUDY OF THE HYDRODYNAMICPATTERN IN A SEDIMENTARY EASIN SUBJECT TO SUBSIDENCE SPE 298E

since moment to Exploitationdes Gisements, IFP R6f. 13024 W2 = volume of water having crossed (Feb., 1966) through a 1 sq m horizontal 4. Tissot, B.: ‘!~problbmesg~ochimiquesde la surface centered arotid M gen?se et de la migration du p&role”, since moment tl Revuede 1’IFP (Nov., 1966)XXI, No. 11, 1621-1671. y = depth of Point M 5. Darle~. H.C.H.: 11ALaboratO~ Investi- z = local thickness of clay lo- gatio~’of BoreholeStabilityf’jJ. Pet. cated underneath Z ~. (Jdy, 1969) 883-892. @ = porosity of clay 6. Bredehoeft,J. D. and Hanshaw, B. B.: “on Z = surface separatingupward and the Maintenance of Anomalous Fluid Pres- downwand flow directions in sures. I. Thick SedimentarySequences.

clay II. Source Layer at Depth”, Bull., GSA Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/70FM/All-70FM/SPE-2988-MS/2069932/spe-2988-ms.pdf by guest on 28 September 2021 (Sept., 1968) ~, 1097-1122.— REFERENCES 7* Moulenes, B.: ffofigfie Cles pressions anormales clansles gisements de p~trole..—.- - 1. Poulet, M: ?tprobl~mes pOS&s par la Etude blbiiographiqtieii,Revue fie-l’lkr migration secondairedu p~trole et sa mise (Feb., 1964) XIX, No. 2, 196-212. en place clansles gisements”,Revue de 1’ 8. Magara, K.”: “Considerationsof Upward and ~ (Feb., 1968) ~111, No. 2, 159-173. Downward Migrations of Fluidsll~+ (Ina, Tm . . ..s...-..\ T T.-.-a.a A..fiz. 2. Jacqti, C.: ‘i-nteractions entre i:argiie UapaJicac/ u . uapa.LLGoG noclub. s Gu. A=ti... et les fluides - Ecoulementsa travers les (July, 1968)~, Part I, No. 4, iO-17; argiles compactes- Ekude bibliographique”, Sept., 1968)Part II, No. 4, 40-47. IISomeAspects of High Pres- R&he de 1’-~ (Oct., 1965)XX, NO.-lO, 9* Watts, E. V.: lfb75-1501. sure in the D-7 Zone of the Ventura Avenue 3. Mondrah, P.: “Cours de Production”,Tome Field”, Trans., AIME (1948) l&, 191-205. II (Tempora~ Text) ~SFM-CES Forage et

R .300 km I 7

cloy

Thickness of send bed = 50 m ...... , :“.,...”..” Send Send porosity = 200/’ I h\\\\\\Y Impermeable bosement

Fig. 1 - Diagram of sedimentarybasin. m meters

Vtscoslty inc% 1.4

1.2

L ,Q ~Q / 1.0 Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/70FM/All-70FM/SPE-2988-MS/2069932/spe-2988-ms.pdf by guest on 28 September 2021

0.8 Colculoted / evolution / /

Lt”eor opproximoi ion / !000 H=C+B t ‘k / /“ ;~ ,.rewaer< / 7“ / / / I 01 , , > 1000 10 30 50 70 90 110 130 / Temperoi. re “C / / Fig. 2 - Viscosity of water and brines.3 ( 40 50 100 150 , > t ,“ millions of years

Fig. 3 - Evolution of center “basin depth with time.

Z m meters f

.3500

-3000

?,=O t = 150 I + .-” .2500 @“- I IM I 7’ I

-2000 M under ~, downword flow

/~;’;, /,J I=to l=f, t = 150 / ; /4 :// M on~ ] I ( -1500 . . . . ( .2-.”” %$! p ~ 7/ 7 M under~ downword flow . 100a W , M above ~ upword flow ,/ ,, /,’4 / ,/ /! /;,. ,?,, ,,

.500 ,,/;/,;?;, /, ~~ /, “’’’” ~~ p ‘p undepos$fed ,, /);/, ” ‘ ,.’ 2000 3000 ,//,, , /,,,,,; , + M above ~,upword flow h !. reelers

Fig. 4 - Relation between local depth h Fig. 5 - Direct on of flow in clay. and thickness Z of the argillaceous mass located under ~ and feeding the sand bed. IWl, m31m2 + W, ,m31mZ

200 Imcom 1200 1 / Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/70FM/All-70FM/SPE-2988-MS/2069932/spe-2988-ms.pdf by guest on 28 September 2021 +q: k/’= -100 1“n“oo”f //

o 150 T,me, loeye.ars

,W)on

- 100

w ~ ,m3(mZ 200 200 i I Fig. 6 - Flow in clay, r = l(lkm Fig. 7 - Flow in clay, r = 100km.

W,, m3/mZ

ZQo

o Oeptll,m

50 -

100

200 / ’00” ~zoom”? /“09 ///79

‘ooY’

10 50 !00 150 200 I (Z .m’ /mz O,sloncer Ir.m Cenlm .atbmnn,km

’00

Fig. 9 - Clistrihution of the values of wl

at the final stage. (t = 150 “ lo~ Fig. 8 - Flow In clay, r = 200km. years). Depth, m

1000 Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/70FM/All-70FM/SPE-2988-MS/2069932/spe-2988-ms.pdf by guest on 28 September 2021 I!500 I

2000 .. / 0

2 y 5

10 170m3 /mz

30 ~/ 50 10 / /

Fig. 10 - Distribution of the value~O~f ‘2 at the final stage. (t = 150 “ years) .

2CQ 250 100 150 0 50 , O,stonce r from cenier of bown, km

r300hq /cm2 Fig. 11 - Distribution of water pressures in

the clay at the moment t = 150 ● 106 years. pressure, kq)cd 200 400 600 o m Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/70FM/All-70FM/SPE-2988-MS/2069932/spe-2988-ms.pdf by guest on 28 September 2021

pressure

Fig. 12 - Water pressure in the clay vs depth,

at the center of the basin and at the moment t = 150 “ 106 years.

P0r0s8! y o o 0.2 04 06

2CO0 500

4000 1000

ecoc , ,,,,...,., .. ..’.a, ) 1500

8W0 2000 TExAS ,0”! S,,.. o GuLF COAST FIELDS ( P,.,.,,. ..,,. ”., E 250Q loom c“ a

=. 12000 : 3~ O 0.2 0.4 0.6 0 205 400 5 kqlcmz : m 14w o c+ B 0 20X3 0 6000 8000 100CO12CQ314000t6~0 Pressure, osi Fig. 14 - Vertical distribution

C; -l?= D,--ee,,ra iism+h ~~~atlon of porosity values(A) and of rug. La 88 ---”,- --r---- 9 pressure values(B). Niigata gas in high-pressure zones. field in Shiunji prefecture.8

300 lo” 10mm/yec. r 250

200 300 250 150 200

100

,~lz Imnl/yeor I

...... ,,. ”! ,).. ,-. ni, r ...... -- ..-

of the basnn

50 70 90 110 130 I 50 1 8. m,ll, ons O( yeors 50 70 90 110 130 ! 50 1 ‘n “’’’O”s ‘f years 10”

Fig. 16 - Volumes of water having flowed through sand bed since moment Fig. 15 - Mean fluid flow rate in the sand t = 40 . 106 years, measured at different bed measured at different distances from distances from the center of the basin. the center of the basin.