EXXON PROPRIETARY INFORMATION CORPORATE RESEARCH EXXON RESEARCH AND ENGINEERING COMPANY ANNANDALE. NEW JERSEY THE FATE OF C02 THE MTUNA GAS PROJECT IF DISPOSED BY SUBSEA SPARGIIG Brian P. FTannery, Andrew J. CaHegaM? Bath Nair, and Wayne G. Roberge a 5W THE FATE 0F c02 FR0tl THE IIATUM GAs PRoJEcr IF OISPOSED BY suBsEA SPARGIffi llle investjgate the consequences of disposing C02 waste gas from the Natuna project by sparging C02 into the ocean at 140 m depth near the site.- The large reservojr of natural gas discovered nean Natuna Island in the South China Sea contains over 70 percent C02. proposed levels of production amount to about 0.4 percent of the current total global Cor'emissions. This would make Natuna the world's largest point source emitter of C02 and rajses coficern for the possible incremental impact of Natuna on the C02 greenhouse probiem. While the base case production scheme calls fon atmospheric venting of C0'2, an alternative has been pr-oposed in whjch C0c would be sparged into seawater so that, perhapsi C02 would never appear in the atmosphere. ' Hene we develop models for the chemistry and transport of C02 in seawater. The js wel understood and has been investigated extensively in ionnection with the COz Greenhouse issue. Tnansport models are more complex because currents can carry C02 over the' enti re basin of the South Chjna Sea within a period of months. Data fon the three'dimensional , l chemistny exist. 0ur models consider diffusion and advectjon expected dynamics. While simplified, the models are estjmate the order of magn'itude of ljkely transport effects. time dependent cunrent distnibution do not with parametenizations characterjstic of readj ly interpretab.le, and serve to Carbon in seawater is not inert, C02 rapidly partitions itself into carbonate and bicarbonate species, changing the oceanic pH.- If the pH fa11s below 7.4, calcjte in shells begins to disso1 ve. Increases in carbon become magni fied in their effect on the partial pressure of dissolved C02.-- l,llen the partial pnessure of C02 in the ocean exceeds the partia'l pressure of C0, in the air, C02 degasses to the atmosphere. Ai sparged C02 builds up in the basin it will begin to degas. After a time which we refer to as the "retention time" C02 wil1 degas at a rate equal to the injection rate from the sparger". principal conclusions from our models are that (1) the retention time is only about ten years or less, and (2) additjon of C02 raises the acidity of seawater sufficiently to cause djssolution of calcite over an area of order 1000 square km jn sjze. These effects indjcate that sparging offens no advantage over direct atmospheric venting of C02. The At this tjme, no further work on this project is Brjan P. Flannery, Andrew planned. J. Callegari, Bahlin Nair, and Wayne G. Roberge -11. I NTRODUCT ION Init'ial plans for development of natural off gas discovered Island jn the South Chjna Sea produce as waste gas approximately 65 x metric tons of amount the of C02 C02 per to the year (1.5 x atmosphere to about 1.8 x 1010 106 Jear). Release of thjs raises concern v{ith respect to its effect on 1012 moles C02 C02 greenhouse pnoblem. Global fossi amount Natuna per l fuel emissions of C02 currently metric tons per year, so Natuna would represent about 0.4% of wor'ld C02 emissions, but viould occur as a localized point source. Various descriptions of the Natuna project c'ite different values for the amount of C02 produced. 51 ight diffenences arise depending on the assumed production capabjlities of the offshore platforms, major differences arise depending on the numben of platforms jn use. Our figure assumes total production of 5540 million standard cubjc feet per day of raw gas from three platforms required to handle the "Pipeline" and "LNG" projects. major conclus'ions of this report are material 1y affected by None slight of the changes in the overal I pnoduction rate. A possible disposal option that might not lead to release of C02 involves pumping waste gas back to the sea using the deep ocean to dispose (1977). Hoffert et al . of jndustrial atrnospheric floor. C02 was proposed (1979) investigated the proposal in The idea of by Marchetti more detail and found that injection of C02 onto the seafloor at 4000 m depth v{ould prevent C02 from entering the atmosphere for a time of order 1000 years. In this study, we investigate the consequences of shallow basin near the Natuna the ro'le C02 }Je addition to seawatelin the focus on two principal features addition on seawater chemistry, especial retention time for atmosphere. site. C02 C02 to remain dissolved in ly (l) pH' and (2) the seavrater before degassing to the -?of the site in the South China Sea basin. 0ver nuch of the basin the seafloor is not at great depth, but F'i lies on a gure 1 shows geographical features flat, Monsoons sweep shallow she'lf where the water depth does not exceed 200 m. the basin at six rmnth intervals driving and seasonal ly reversing surface currents that circulate in a gyre over the basin (Hyrtki, 1961). l,Je consider discharging C02 rich waste gas into seawater near the seafloor through a sparger system as illustrated itself in Figure 2. The sparger consists of a ring approximately 10 km in diameter from which 1.5 1012 moles per year of C02 would be degassed at a depth of there are three regions of interest. The sparged C02 140 x m. Vertjcally, rises approxirnately 30 m jn a bubble plunn before dissolving. At the surface v{ind and viave action create a well mixed layer of about 30 m depth. Finally, in the middle regions there exists a stably stratified region of about 80 n thickness. Currents near the sparger vary in magnitude and di rection with height and time of year. Typical values at depth are of order 10-50 cm s-1. At the bottom currents are persistently headed southwest, toward Eorneo 500 km distant. the characteristic velocity of 30 .n' r-1 flo* traverses the basin in only 20 days. Thus, advective transport over a basin scale can djstribute material injected at to seawater decreases the pH and increases pressure P(C02) of dissol ved C0Z. As descr"ibed in seawater is well in the partial Section 2, the chemistry of understood, and has recejved much attention recent'ly in the context of the role of the oceans as a sink for C02 greenhouse Natuna in a tirne of order months. Adding C02 C02 At atmospher.ic C02 problem. At the ocean's surface, gaseous C02 is in the exchanged with the atmosphere whenever a difference exists between the partial pressure of C02 in the atmosphene PA (C02) and the partia'l pressure of C02 d'i ssolved in -3surface seawater P5 (C02). C02 flows from the reservoir !,ith to the reservoi when P5 r with lower pressure. Thus, C02 will degas h'i gher pressure to the atmosphere (c02) >P4 (C02). In Sectjon 3 we define a C02 retention time for the Natuna problem according to the concept of tinre taken for seav{ater to reach a steady-state concentration of C02. For Natuna that occurs when the ocean has taken up much C02 inject that it degasses to the at the bottom. atmosphere at the sarne so rate that spargers in Section 3 illustrate the central idea of retention time, and establish its order of magnitude for a seawater basin in which C02 rapidly mixes throughout the entire volume. C02 Estimates A complete investigat'ion of mixing and transport would require detaj led current jnformation in three dimensjons and t'ime throughout the Chjna Sea basin. Such data does not exist, and, even if would require a massive computational it djd, to use it sjmulation. Instead we develop insight analysis. Nonetheless, and understanding using simplified simplen nrodels allo!, us to estimate the magnitude of the retention time impact on models and pH. In Section 4 we consider the effects of transport by diffusion timescale in 3, but retention of climate change these and several classes of models that include and advection. Typically, such predjct retention times longer than estimates model descnibed South time still based on models the simple vrell-mjxed renajns short compared with the in the C02 greenhouse problem. 0n the other hand, transpont npdels show greater pH reductions near the sparger than the wellmixed model described in Section 3. Finally, in Section 5 we discuss these results in the context of global is C02 greenhouse preferable to the problem. 0ur conclusion js that atmospheric discharge seawater sparging, In any event, seawater sparging is nearly -4equivalent to atmospheric release since the retention time with times relevant to the buildup of atmospheric through 2. a IN SEAIIATER The chemistry many influencing climate effect. greenhouse CoZ CHEI'IISTRY C02 is short compared of C02 in at length in follows that of Takahashi et al . seawater has been discussed recent references. our discussion (1980), also see Baes (1982) who developed a graphical representation of the for us. For the Natuna project' the salient features of C02 chemistry are the variation in pH and P(C02) produced by changes in the total amount of carbon, TC, dissolved in seaviater. Changes 'in pH directly influence chernical reactions, such as the oxidation of H2s and is particularly results that convenient solubility of calcium carbonate' that influence toxicity. P(C02) in surface v{ater controls the direction and rate of gaseous c02 exchange betv{een air and sea that determine the length of time that sparged C02 will remain in the ocean. The increases essential result from consideration of in TC cause decreases C02 added to in pH and C02 chemistry Iarge increases seawater rapidly dissolves to in is that small P(C02). fonrn hydrated C02 and carbonic acid H2C03. In turn, the carbonic acid can dissociate to form bicar- bonate HC0j and carbonate C0!- ions cor(s) +Hzo:H2co3(aq) Hzco3(aq) ln*+xco] HcojlH++co!- (2.1) (2.2) (2.3) -5where (g) and (aq) denote proceed rapidly enough gaseous and dissolved aqueous C02. All that the ultirnate distribution of carbon reactions among the three species can be described by equilibrium constants K1 (2.4) = [H2c03J/P(c02) rz = n+[rco5]/[H2c03] K3 Note that reactions (2.?) and (2.5) (2,6) = tH+ltco3-l/tHcoil (2.3) depend directly on the oceanic pH. The equilibrium "constants" depend on temperature, Pressure, and salinity. to seawater we want to determine the resultant change in pH and the partial pressure P(C02). In general' xe can predict those quantities given the titration alkalinity TA, the temperature, For and the total a given addition of anount of C02 carbon TC, defined as 16 = [H2co31 + tHc0!1 + tcoS-] TC nBasures carbon carbon abundance water or is concentration per unit mass, occasionally we also reference with respect to 1.025 gm cm-3. 1.98 moles (?.7) At of sea- 1930 pmole kg-l volume, 1s = pTC, where the density Natuna a typical value for m-3. Titration alkalinity, a quantity TC is measurable with precision, represents the net nolar concentration of positive ions abundance is not sensitive to pH. The excess high whose cationic charge resulting from dissociation of strong electrolytes in seav{ater is balanced by the anionic charges wh'ich are mainly generated by dissociation acid. Thus, the titration alkalinity is: of carbonic and boric -6TA = tHc0-31 + 2tc03-l + tH2B05l + [0H-] Effects of other minor species such as neglected. In quently, TA seavrater TA is js silicic - [H+] (2.8) and phosphoric acids are dominated by dissociated a function of salinity, and does not salt species. depend on Conse- TC. Given TC' TA, tempenature, and functjonal relations defining the equilibrium coeffici- ents, the set of equations can be solved for consistent values of pH' P(C02)' and the abundances of the carbon species. For the equilibt"ium coefficients use recent values supplied by Taro Takahashi et al ., of we Lamont Doherty (Takahashi 1982). Results for effects illustrate the dependence of of local chemistry ane shov/n pH and P(C02) on TA and TC in Figure 3-4 which for temperatures of 20, and 30oC, representative of surface and deep water near the drilling site. (Takahashi et Based on al ., the globa'l correlation between salinity and TA 1982), Takahashi estimates that TA near Natuna shou'ld about 2300 ueq/kg. Air sea exchange tends to majntain equatorial nearly in equilibrium with atmospheric P(C02) at a surface v{aters at Natuna Natuna have a value TC val ue of 340 be watens vatm. Thus, = i930 u mol/kg as shown in Figure 3. in Figures 3-4 is the strong increase in p(c02) and decrease in pH for increases in TC at fixed salinity and temperature which arises from the well known buffer factor in seawater. Notice that increases of only lOx in TC increase P(C02) from 340 uatm to over 1000 uatm The important feature shown and decrease pH from 8.2 to 7.4. In the stipled cal c.ium carbonate j s undersaturated so unless b.io1 that shel I regjons of Figunes 3-4 materi a1 wi 11 di ssol ve ogical activity offsets the dissolutjon rate. The ' figures illus- trate that c02 is less soluble at higher temperature. Thus, for a 9iven absolute value Tc, pH is lower and P(C02) higher at higher temperature. -t - That P(C02) increases rapidly with is well Tc known (e.9. lleiss, f974); the ratio of proportional variation for small increments is the Revelle factor .r, defined as knoyrn as (2.e) aP(C02)/P(c02; = 1 aTc/Tc For surface waters Revel le factor at Natuna we calculate ranges from 8 averaging 10 (Broecker et al in ., r = 9.2. to 15 in cold riaters, globally 1979; Takahashi et al ., 1980). The Revelle waters v{arm factor is especially useful for analysis of the descnibed sparging C02 C02 as in the near vicinity of the sparger itself, on length scales of order local influx, seawater transport Q = 1.5 x bubble plune (hg). Then is dominated by 1012 moles/year, water flowing over the sparger l0 km wide the change in tc is by 30 m high, the height of the by sparging caused fl ow rate water flow rate (mo'les ,-3) = t.O ( = =a advection. llle assume that released uniformly into a sea- C0" ^tc netention time in the next section. l,le can use results of this section to estimate the impact of 10 km when the For surface v{ater, the is given a D. hr. (2. v km" 30 m" = f-0 ) f(-J .--J\ by 1o ) l0 cms-l' " ' tc vs. velocity in the range l-100 cm s-1, and the corresponding variation in local P(C02) and pH. Note that if local stagnation events occur they will be accompanied by large changes in 1oca1 pH. Onsite measurements i ndi cate that velocities less than l0 cm s-l do occur occasionally. Figure 5 sho!,s -83. THE SEA-ArR EXCHANGE 0F C02 AND THE C02 RETENTIoN TIi4E Gaseous C02 migrates across rate FSA in the the sea air surface interface at a net proportional to the difference between the partial pressures of C02 tv{o reservoi rs Fsn= E I The expression has been scaled average - Ps(co2) PA(co2) (3.1) 340 uatm to units appropriate for the pantial pressure of atmospheric C02, Pt(C02) = calibrations give E = 20 moles/(m2 annual mean yearly uatm. Empirical yr) (Peng et al . 1979). For surface condi340 tions at Natuna, tc.O. 2.0 nroles m-3 is required for Pr(C02) = 340 uatm, at which F5n vanishes. Surface waters over rnost carbon abundance such that FSA . of the worlds oceans maintain a 0. t.O, for air-sea gas exchange to equilibrate, consider a situation in which a well-mixed layer of seawater of depth h contains no C02 initially, and is in contact nith air" at P4(C02) = To estimate the appropriate timescale, 340 75 patm. For typical oceanic conditions the well-mixed layer has a depth h = meters. To reach equilibrium the mjxed layer requires the addition of h.tc = 140 moles m-2, and the initial filling rate is 20 nroles/(m2 yr). Thus, a characteristic estimate for the equilibration time scale is Cq After time of order teq the net and tc reaches steady h tc eo 'SA exchange state jn the (3.2) ocean. of C02 between ajr and sea vanishes -9t,lhile the estimate for air considered no additional sources, in seav{ater sea exchange for the equilibration tine Natuna pnoblem will not reach equilibrium until the C02 (3.2) concentration the ocean waters lose rate identical to the influx fron the sparger in C02 at a Q. In iater sections we will consider mone detai led models including djffusion and transport, our goal hene is to obtain simple estimates for the characteristic timescale of the problem. !,le estimate the retention time rp for C02 by first estimating what the carbon concentratjon tc.O in surface waters rnust be in order for surface outflux to equal Q. lie then estimate the equilibration tifi€ assuming by that the necessary increase in tc occurs at a rate Q. Nothing in the estimates used here actually allows us to the basin size, or surface area over which degassing occurs, to estimate basin size in later sections. a function of R. in Because P(C02) assumed surface atea for a circular region will attempt for retention time as of arbitrary radius the carbon chemistry of seawater produces such a strong increase with increase in total small basin Here we solve bre determine sizes. limiting value that C02 the retention time is very short for For large basin size, the retention time approaches a does not depend on radius. Thus, we wilI obtain useful (lower) bounds on the retention tifiE even without knowing the size of the affected regi on. For a circular surface area sea of radius R the net outflux of C02 from to air will equal the sparger influx for onzFro = aP (C0, ) 340 u atm Q 100 = 2.4 1.5 x 1012 moles yr-l 2 km' (3.3) -10To estimate sol ve the increase in TC requi red to produce the change aP(C02) we must the non-linear chemistry equations of the previous section. for small changes in TC we can use concent rat i on change di However, the Revelle factor to determine the rectly. ,nt r tilc) =a for fp.. r (3.4) ff = Note l lo0 li o.zo krn 2l that initially Pr(C02) = P4(C0Z) = 340 uatn, and that Atc/tc = aTC/TC. Given the increase in TC, either from (3.4) or by solution of the tirE for the ocean to for t"O in (3.2). Assume that the nonlinear equation (3.3) we can crudely estimate the reach equilibrium as entire basin of use the in the discussion volume nR2h must increase its C02 concentration by initial influx rate Q to estimate the filling and time Atc .R For the Natuna basin we use h = 140 atc, m. If the required (3.5) change atc is small, then v{e can use (3.4), based on the Revelle factor, to determine rq. 'R Notice that rate Q. = \te ' this estimate is r'4 Yr independent .. for ltc EC I (3.6) of the basin size R and the i nfl ux - 11 - The crude estimate derived here represents an approximation corres- ponding to adding C02 to the entire cylindrica'l the concentration remained well mixed at volume of the basin as though all times. This is unlikely to occut' is stably stratified vertically and because advective transport controls horjzontal distribution. In later sections v{e consjder such additiona.l effects. Nonetheless, these estimates place the characteristic timescale in perspective, it is of order years. both because the water Using these estinates, and accurate solution of the nonlinear equa- tion (3.3) to determine tc appropriate to equilibrium degassing for P(C02), we illustrate several features of the results in Figure 6. In Figure 6a and b we shov{ the required change in P(C02) and tc as a function of basin size. Figure 6c shows the retention time estimated from in tc vie also show the pH corresponding important point is that, if (3.5). Gjven the increase to equilibrium conditions. rapid mixing occurs on smal l The length scales, of order of sparger diameter, l0 km, then the degassing time is very short regardless of the exact size of the affected region. 0ver larger scales the degassing tinre Detai these ti 4. rne will still be only a few years led nrodels of transport if COZ phenomenon reaches the surface. as discussed below increase esti mates. TRANSPORT MODELS Iniected plume within C02 from 30 m of the sparger dissolves into seav{ater in a the seafloor. Measurements bubble of vertical profiles of tenperature and density at the s'ite indicate that below a well-mixed surface layer 30 m deep the water proceed by eddy is stably stratjfied, so vertical mixing must diffusion, sporadic upwelling events, or transport by currents. 0ur estimates below will shov{ complex non-local that vertical d'i ffusion -t?to bring C02 to the surface. times of order a few years are required in the introduction, described tneasured horizontal velocities of 30 cm s-1 carry material over basin scale djstances measurements time. As onder in only months. Site also indicate that current varjes significantly with depth Consequently, a realjstic model of seawater transport of South China Sea requires current information covering the enti C02 re in bas'i and the n in three spatial dimensions and time. To date no complete data set exists port calculation on the scale of the basin, formjdable numerical exercise even if assumed and such a calculation presents C02 we investigate a hjerarchy of current and djffusion profiles, that do include tirc will of order a decade at most, barring unlikely current patterns, be dependence. Cumulatively, they indicate anomalously low that C02 retention times or vertical diffusion rates, as we describe. The models described be'low have dependent a the data were avajlable. To gain insight into the 1ikely retention time for simpler npdels based on to carry out a realistic trans- variation of concentratjon dependence on concentration, using analytical solutions for the time when F5q can be approxinated by the Revel le factolin (3.1). a linear However' numerical solutions are simple to obtain, even with non-l inear relations for the loss term, and simple to interpret based on known characteri stic behavior for the diffusion equation. Table I contains a listing of model parameters and typical values for thei r magnitude. K(V) and K(H) representing vertical and horizontal diffusion in the ocean are the only parameters listed in Table l that have not yet been discussed. Below the mixed layer of the ocean, var^iation of temperature and density produce stable strat'i fication that inhibits vertical flow of any sort' 'i ncluding diffusive mixing. K(v) is particularly important in this problem -13since it sets the timescare for carbon to diffuse to the surface where rosses can occur by air-sea exchange. The value bre list, 4000 m2 yr-l (- 1.3 cm2 s-1) is typical 0f verticar diffusion through stabry stratified layers in the ocean as a whole (Broecker and peng, l9g2). A recent study of Berelson et a1 . (1982), based on the vertical distribut.ion of radon-222 in the of the California coast, found K(V) = a.r2 s-l at water depths of 500 m. No measurements of K(V) exist for the liatuna basin. It is possible that v{ave action and currents in a confined basin Santa Barbara basin K(v) becorc larger, neducing the upward diffusion time, or that special circumstances cause K(v) to be smaller than for the ocean as a whole. No a make priori theory exists that can accurately predict values Horizontal diffusion is known to for K(V). be dramaticalry larger than vertical, K(H) = sarmiento et ., 1982). However, the model results are less sensitive a1 107 K(V), is generally accepted (Kuo and Veronis, 1973; to K(H), since advective current flow tends to dominate diffusion as a cause for hori zontal mixing. a. l.lith Rapid Holi zontal l4ixing and Vertical Diffusion In the pnevious section mixed cylindricar moder based initial infrux rate. the retention time of a we on the required equilibrium concentration and we estimated Here we considen the time history of such a nrdel , and effects due to vertical diffusion. Since surface losses r.ise as C02 increases in the reservoir, the actuar history of outgassing causes the retenadd tion time to increase over that estimated in the previous section. -14In this of radi us R occurs that horizontal mixing throughout the basin rapidly at any depth, but that vertical transport occurs model v{e assume only by diffusion in the stratified layers below the surface m'ixed layer of depth hp. The C02 injection rate per unit volume q(z) is taken to be uniform per unit volume at depths within the bubble plume, z < hB = 30 m. equation defining the time h'istory *tt of concentration .a = q(z) +-az K( v) The 'is ?tc (4. 1) n where q(z) = rrR zh, q(z) = Q r.hB fon for .thB z represents height above the seafloor in a water column of total depth H. Boundary conditions for (4.1) correspond to separate treatment of the C02 balance in the mixed layer and zero diffusive flux across the seafloor. Here #--K(v) r FsR *FlH-hr,r- (4. 2a ) (4.2b) fftr=o=o several features of the model should be noted. F'irst' from the form of (4.1-Z) the solution depends only on the basin area rRz, but not on the assumed cylindrical geometry; and we use R simply as volume nR2H, a conveni ent -15of basin size. Second, in the limit where K(V) becornes very large this model becomes vertically (and holi zontal ly) wel 1 mixed, as in the simpler model of Section 3. I'lathematically, the vertically well nixed model corresponds to just using the boundary conditions (4.2a) and letting the mixed layer measure depth equal H. Third, just as in Sect'ion 3, these equations reach equilibrium injection. Therefore, equilibrium when surface degassing balances sparger for surface concentration as found in (3.3). However, vrith vertical diffusion tc increases with depth; thus, for a given value of tc requires the same value at the surface, the reservoir has a higher capacity for C02. The retention time increases from the estirnate in Section 3, both because some degassing occurs as the C02 concentration rises and because the basjn capacity i ncreases. l{e illustrate the character of the time Figure 7 which shov{s the rate of surface injection rate for a series of curves ane for (1) a vertically which is the npst reasonable model with K(V) = 469 *2 models degassing well -mixed fill fo1 lowed 500 km. The three , (2) K(V) = 4000 fiz yr-l estimate fon the diffusion coefficient, and (3) yr'I, an order of the degassing rate increases the basin, model solutions in relati ve to the sparger with basin size coefficient typical of the global ocean. phase whene dependent a magnitude lower than the diffusion These nrodels re1 al1 display an initial atively rapidly as C02 begins laten by a slow relaxation to steady state to where influx from the spargen. l,,lhile the rnodel takes 'infjnite tjme to reach the exact steady state, degassing would equal the the condition that C02 degassing equals some large fraction of the 'injection rate, say 90%. Figure we can assign shows a nominal retention time, rR, the retention tirne estimated in that based on way fon a serjes of models with varying radjus and diffusivity. Note that vertical diffusion increases the 8 -16retention tin€ relative to well nixed mode'l best estimate of K(V), the retention tirne s, as discussed above, but is stil'l for only about 3.5 years our even for the largest basjn sjze. Figur"e 9 shows pH for models in steady the variation with depth of Thus the nearly linear with depth. (The relation C02 concentration and the are bubble the source function varies with depth.) Notice that models with Finally, time t0 sparger we use this model depth. Figure l0 y.-1, or. depth. In tc constant profiles becomes curved 'i nside longer retention tirne also have hi gher concentrations of 4000 n2 concentration state. In steady state the flux of C02 is with depth so K(V)dtc/dz = F5g. plume where C02 at the seafloor. to illustrate sensitivity of retention shows a series of best estimate, and a range models with K(V) of values for H, the = sparger of 30 m and a mixed layer of H from 60 to 1000 m. The results follow the basic each case, we include 30 m, but we vary the depth C0Z a bubble plurne scaling appropriate to propagation of a djffusion front over a distance 12. L (4.3) Kt Thus, retention times become dramatically longer as the spargen depth i ncreases. 0ur results showing very long retention tines fot' disposal at great depth are in agreement with those of Hoffert et disposal in the deep ocean at 4000 South China Sea basin m. If a1 . (1979) who investigated currents along the bottom of the fortuitously carried C02 from the Natuna site to deep water, then retention times would be increased. An area of deep water (>1000 m) does exist a few currents could carry C02 hundred ki lometers to the northeast. Although over such distances, buoyancy effects are prevent currents from penetrating to great depth. likely to b. 17 - Rectanoular I'lodels l{'ith Horizontal Advection and Vertical Diffusion l'lodels nothing in Section (4a) in the physical description establ interplay between C02 for a series of basin sizes, but size. In nature the ished the basin horizontal and vertical transport establishes a scale: is not lost until it rise, were shown encounters the surface C0Z but, durjng the tire taken to also migrates horizontally. For the Natuna sjte there is no ques- tion that significant horizontal motion occurs, the problem is that time and velocity scales are sufficiently long that basin scale circulation must be included to evaluate the spreading. directed southeast at depth, of Borneo, 500 km djstant, C02 t,rljth a typical velocity of injected at the in only 20 days, which Natuna is short retention time (unless rapid vertical mixing occurs). that far, then at Borneo the directjon site If 30 cm reaches conpaned Bearing in the coast with the the current persists will deflect along the coast, and enter into circulation on a basin scale size, for whjch three dimensional dependent data do not s-l time exist. mind the preceding discussion, we consider two dinen- sional advective, diffusive flow merely to establish the general character of the solution, rather than to model basin scale circulat'ion. lle consider unifonm advection with velocity v along the x direction, in a rectangular basin of width I'l, transverse to the l,le assume that COZ flow. l,l is not determined by the model . mixes rapidly along the width, and that the C02 source is distributed smoothly along a 10 km section in x of width l.l. The flndel is defined by the following equations and boundary conditions F =h !l#u K(v) a(;;tc) + q(x,z) :* - aIv.tc(M)] = -K(v) FtH_hM ax (4.4 ) Fsn ht4 (a. 5a ) -18- 4e=o dz at 9!e=o AX atx=xl atc ax where xl, - in (4.5b) at *=x2 of the rectangulan model . x2 denote the endpoints conditions ^ z=0 boundaries. Thjs will be zero diffusive flux through is a good approximation ) (4.6b ) The boundary (4.6a,b) apPly at the "x" boundaries of the rectangle. conditions imply that there (a.6a These the since advection dominates the flow. l{e consider two rnodels of the advective diffusive class' both have width W = with a spargen source distributed along 10 km length in x. nndel is well mixed vertically (K(V) + 6)' the second has K(V) = 10 knr, first 4000 m2 yr-l. The Figure 11 illustrates the variation of concentration with dis- tance fon the well mixed nrodel . w'ith the sparger source centened total length of the model is 104 km, at x = 505 km. Because the model is well Here the mixed, degassing commences directly over the sParger, and the concentration decays (x2 with d.i stance downstream from the - x1)/v = 1Jr, sparger. The advective timescale' controls approach to steady state in this nrodel , so that concentration achieves steady state values as the flov{ front passes a gi ven point. At this relati vely high rate of flow, even withjn 104 km of the surface degassing only reaches about 50 percent of sparger, the net rate of the sparger injection rate. Further degassing of c02 would occur beyond x2' the downstream limit of our computational domain. However, we terminated the calculation at 104 km because the geometrical distance greatly size of the South China Sea basin. exceeds the -19The second advective diffusive model resembles the first, but includes vertical diffusion with K(v) = 4000 mZ yr-l rather than being welI mixed. The basin length in this model is only 103 lm, with the sparger at 95 km. For this nodel both the advective and diffusive times play a role in the approach to steady state. Here advected flow crosses the grid horizontally in a time (x2 - xl/u = 0.1 year, but the vertical diffusion time, H2lK(V) = 3 year^s, is much longer. Figure 12 illustrates the tirne dependent solution for the total rate of surface outgassing over the entire located grid. Net outflow only approaches steady state after 3 years, the diffusive timescale. At that time, the surface outgassing rate is 35 percent of injection rate. Again, as in the previous occur beyond the downstream boundary at model x2. the , further degassing would Figure 13 shows contours of constant pH for th'is model after the flow achieves equilibrium. Notice that pH indicates large increases in acidity near the sparger. The essential nodels discussed here point to be learned frorn the advective diffusive is that the vertical diffusion that advection can transport C02 over distances size of the South China Sea. time large is sufficiently long compared It is unrealistic to assune that with the basin such flow would to a geometry resembling flow in a basin of rather narrow rectangular cross section as assumed here, i.e. with li constant. It follows that current behavior far from the Natuna site might control the ultimate fate remain confined of C02. For instance, it is possible that currents flowing at depth near the site, night upwe1l as they approach the coast of Borneo, so that outgassing occurs at that poi nt. 0n the other hand, currents could carry C02 to deep water i ncreasi ng the retenti on time. One dominates other point learned from this model is that, when advection the flow, the local concentration in the vicinity of the sparger is -20governed by the considerations described in section peak local concentration simply by constructing the rate to the water flow CoZ rate. The imPortant 2. There we analyzed for ratio of the c02 injection point from that analysis was that concentrations become very large' and pH'is strongly reduced, during periods when the flow vetocity stagnates over the sparger. tric c. l'lodels Guided by llith Radial and Vertical Diffusion insight from the previous models we consider one final in both the vertical and radial dimensions' but without advection. The motivatjon for this model is an attempt to approximate the effect of variable horizontal currents on transport as a diffus'ion process. 0ur estimate for the horizontal diffusion coefficient K(H) model in which diffusion occurs in this fashion, agrees approximately with oceanographic estimates for K(H) suitable for open ocean conditions. such estimates show that the ratio K(H)/K(V) is of order 107 or more (Kuo and Veronis, 1973; Sarmiento, obtained 1982). The enormous enhancement occurs because horizontal dynamical processes stratification, as in vertical diffusion. t.le estimate the horizontal eddy diffusivity for random horizontal current patterns in which the velocity persists at a given value for a are not damped by specific length of time At, such a model, the Fickian product and then changes its direction completely. diffusion coefficient is the average value of the of length and velocity . To estimate a characteri stic K(H) we use v = 30 cm s-1, and . 2.5 , value for a persistence tirne of one day K(H) = r(H) For 1011 rn2 * Y2a1 y.-1 1-----l--.,;214t 30cms' day I (4.7 ) -21 He the actual values of K(H) or K(v) at the Natuna Our estimate for K(H) is solely for motivational purposes. It does, stress that site. we do not however, agree roughly In the know with estimates characterizing the model below we use K(H)/K(v) open ocean. = 5 x 107' For this ratio' a typical basin size, diffusive transport over the vertical distance' occurs in times comparable and 100 m' with transport horizontally over 500 km. This follows from (4.3) since (R/H)2[r(v)/r(H)] = O.s I'lith this picture for diffusion t{e can rnodel the basin as an axi- symetric tvro dimensional diffusion problem: l{e = o(.,.) ateju) at = JL r ar +--1a r ar K(H) ' a ar t. * xlvy Aeztc K(V) atc a .- - -r:57-l rtxt I5F rH-h, "' az r atc, Dz tz E 'sA o =0 (4.eb) 3r lr = 0 =0 (4.10a ) i*el. = * = (4. r0b ) o Figure 14 shows that the time dependent variation of outgassing 90% with a radius of 500 krn, typical of the basin outgassing (4.9a) hll = atc, model (4.8 ) size. for a single The model reaches in 6.5 years. l,lithout detai led data and simulations of three dimensional time dependent C02 transport, the model described here represents our most real- time. From previous nrodels it is clear that, for typical values of vertical diffusi vity' C02 will mix to the surface istic simulation of the C02 netention -22in a timescale of a fefl years, after v{hich outgassing to the atmosphere w'i ll match C02 injection rates. Also, the npdels, and simple physical estimates' show that a timescale of a few years alloYrs transport to distribute C02 throughout the South China Sea basjn. 5. SUMMARY Because of waste of concern about gas C02 from the Natuna direct atrnospheric release. reaches CoZ greenhouse project t{as proposed as an alternative to However, our results indicate i nc rea ses aci d tht sparged C02 and degasses Furthermore, increasing the concentration doubl i ng. jssue, seawater sparging to the atmosphere within a period less than a is short cornpared with the 100 year period proiected for C02 the surface decade, which the i of C02 in seawater ty. For our best estimates of transport properties, vertical diffusion from 140 m depth to surface only requires 6.5 years before the r"ate of C02 outgassing through the sea surface nearly equals the sparger iniection rate. Those estimates are based on parameter values determined from studies 91oba1 ocean, condjtions could be China Sea. If faster. more rapid of different in the shallow basin of the vertical mixing occurs, the outgassing occurs Possibly, current patterns might transport C02 below the South even the surface for rather large distances, and then upwell in localized regionsr perhaps near coastlines. Once C02 degassing would carry C02 to contacts the surface at high concentration rapid occur. Alternatively, it is possible that currents deeper water giving could a longer netention tine, but buoyancy effects probably prevent currents fron flowing to great depth. -23For typical diffusion rates, the only way quickly is to sparge at far to keep C02 from degassing greater depths. Below 1000 km the C02 netention years. A regjon of much deepen watelis available several hundned km to the northeast, but sparging there would be far nnre costly since a pipeline would be required, and waste gas must be pumped to greater depth t'ime exceeds 100 and pressu re. C02 in seawater decreases pH (increases is not inert; increasing the concentration of acjdity). Present ambient conditions have pH = 8.3 in our models. Reduction of 0.7 units aragonite form to begin C02 to 7.6 pH allovrs calcium canbonate in the to dissolve. our models indicate that pH reductions unjt or more will affect regions of order 1000 km2. A tradeoff occurs: if the vertical diffusion coefficient decreases, so that C0Z is of one retajned longer, then the concentratjon of when C02 at depth rises. the retention time increases, the impact associated with increases. Either the size of the affected region the pH change increases, or grows Consequently' pH change also or the magnitude of both. l{e also estirnated the peak local concentration of C02 and associated change in pH, based on advection dominated flow in the vjcinity of the sparger, where concentration changes rnaximize. Those estimates sholr appreci - falls below 50 cm s-1, which occurs commonly. Furthenmore, changes rise dramatical ly during stagnatjon events when flow speed drops below 10 cm s-l which do occur occasionally. 0un conclusion is that sparging of C02 offers little advantage over direct atmosphelic release of C02, since the retention times is short in any case, but that spanging of large amounts of C02 does cause a negative impact in seawater by its affect on pH. able pH changes whenever flow speed -?4REF ER EI{CES Baes, C. F. (1982), "Effects of Carbon Dioxide," 187-204, ocean Chemistry and Biology on Atnosphe ic in 1982" }'l. C. Clark "Carbon Dioxide Review: editor, 0xford University Press: New York' 1982. l{. l,il., Hannond, D. E. and Fuller, C. (1982), Radon-?22 as as tracer for mixing in the water column and benthic exchange in the southern Berelson, California borderland, Earth and Planetary Sciences Letters, 61, Broecker, !{. S. and Pen9, T. H. (1982), "Tracers Palisades, New York, 690 Broecker, H. S., Takahashi, fossil fuel in the Sea," 41-45. ELDIGI0 Press' PP. T., Sinpson, H. J. and Peng, T. H. (1979), Fate of carbon dioxide and the global carbon budget, Science' 206' 409-418. Hoeffert, M. I., },ley, Y. Atmospheric response Cl imate Change, 2' C., Callegari, A. J., of deep sea model , 53-68. Deep-Sea 68. of oxygen as a test for an abyssal Res., 20, 871-878. Marchetti, C. (1977) on geoengineering the - Il. S. (1979), iniections of fossil -fuel carbon dioxide, Kuo, H. H. and Veronis, G. (1973), The use circulation and Broecker, C02 Problem, climate change' 1' 59 -25Pens, T. H., Broecker, tJ. S., Mathieu, G. G. and Li, Y. H. (1979), Evasion rates in the Atlantic GE0SECS Pr"ogram, Sarmiento, J. 1., and Radon Pacific 0ceans as determined during the Jour. Geophys. Res., 84, 2471-?486. Rooth, C. G. H., and Broecker, H. S. (1982), Radium-228 as tracer of basin wide processes in the abyssal ocean, Jour. a Geophys. Res., 87,9694-9698. Takahashi, T., Broecker, ll. S., Carbonate chemistry t.lerner, S. R. and Bainbridge, A. E. (1980), of the surface waters of the world oceans, in "lsotope Marine Chemistry," E. D. Goldberg, Y. Horibe and K. Saruhashi editors, Uchi da Rokakuho Pub., Japan, 291-326. Takahashi, T., fJilliams, R. T. "GE0SECS and Bos, D. Pacific Expedition, Vol L. (1982), Carbonate chernistry, . 3, Hydrographic in Data, 1973-1974, National Science Foundation, I'lashington, D.C. 78-82. lleiss, R. F. (1974), Carbon dioxide in water a non-ideal gas, l.lari ne Chem., 2, llyrtki, K. (1961), NAGA and seawater: The so1 ubility of 203-215. Report, Scientific Results of Ma i ne Investigations of the South China Sea and the Gulf of Thailand, 1951-61, Physical 0ceanography of of the 0ceanography La Southeast Asian l,laters, Univ. JolIa, California, Vo1 Calif. Scripps Instit. . 2, 195 pp. -26TABLE I PARNIETERS 'OOEL tc Q Total p Seawaten densi TC Total 1.5 x lo12 moles C02 source C02 ty concentration R Basi n radi us H Basi n depth yr-l 1.025 gn cm-3 pTC Total C02 concentration = Typical or Starti ng Value Identi fi cat i on Symbol (mass) (volume) 1930 ymol es kg-1 1.98 moles m-3 10-1000 130 hB Height of bubble plume hil Depth FSR C02 km m 30m of surface mixed layer 30m flux from sea to air mol es / (m2 yr) F5s = EIP5(C02)-Pn(C02)1/340 uatm E Exchange coefficient for F54 K(V) Vertical diffusion coefficient K(H) Horizontal diffusion coefficient v Hori zontal current speed 20 moles/(m2 4969 p2 2 x yp-l 1011 m2 0. 30 m yr) yr_l s-l -27FI6URE CAPTIONS FIGURE 1. Geography of the FIGURE 2. Schematic of the sparger configuration. FIGURE 3. Variation of total carbon Natuna site. P(C02) and pH as tc a function of alkalinity (per unit volume) at a salinity of 35 o/oo temperature 20oC corresponding site. s FIGURE 4. Calcium carbonate 5. is As in Figure 3, but for' 30"C corresponding at the Natuna to surface water at the te. total carbon abundance tc (a), P(C02) (b), and pH (c) with current, for flushing at a uniform flow rate over the Variation of local is moles per year uniformly over 6. bottom water unsaturated and dissolves when pH 10 krn sparger diameter. C02 FIGURE to and 7.4. Natuna si FIGURE TA and injected at a rate of 1.5 x the bubble column of height 1012 30 m. Valiation of carbon abundance TC (a), P(C02) (b), retention time t (c), and pH (d) as a function of basin diameter nixed reservoir achieves steady state model C02 degasses sparger i njects CoZ that a well concentration. For each to the atnosphere at the C02. R such same rate as the -28FIGURE 7. C02 surface degassing mixed cylindrical rate versus titne for a horizonta'l ly well model with radius 500 km. The degassing rate is scaled relative to the C02 injection rate from the subsurface sparger. The top curve is fon a ventically wel 1 mixed model. The is for our best estinate of the vertical diffusivity. The bottom curve is for diffusivity a factor of ten below our best middle curve estinate. FIGURE 8. Retention time as a function cylindrical rnixing. F IGURE 9. model of basin size with vertical diffusion The retention time is defined as and di and ffus i vi ty the time when su Variation of (a) C02 concentration and (b) pH with height mode'ls above with varying basin size and diffusivity. These nrodels have reached steady state. f'lith diffusion the concentration varies linear'ly with depth except in the layer, rfa ce of the sparger iniection rate. of seafloor for the rapid hori zontal degassing C02 reaches 90% for where concentration mjxed is constant, and inside the bubble plure layer where the source function varies. FIGURE 10. C02 surface degassing rate vensus time as a function of variable sparger depth, H. As in Figune 7 the degassing relative to the spange injection rate, rate is scaled is cylindrical with rapid horizontal mixing and vertical d.i ffusion. For all tirB curves K(V) = aggg nZ y.-1 . The and the model results increases r.oughly as H2 for fixed shovr that retention diffusivity. -?9FIGURE 11. Tine dependent solution for a well mixed model with advective velocity s-l 30 cm and width 10 km: (a) carbon concentration, (b) surface flux F54, (c) total surface C02 outgassing relatjve to sparger injection. The 10 km long spanger source is centered at 505 km. FIGURE 12. Variation of the surface degassing rate with time for a two sional advective, diffusive model . The model is 1000 km long by wide and 140 m high, with the sparger source centered at 10 km 95 km. The horizontal advection velocity is 30 cm s-1, and the vertical diffusivity K(V) = 4000 n2 yr-l. After 3 years degassing rate 35 percent FIGURE 13. dimen- Contours within 900 km the of the sparger equals approxinately of the injection rate. of pH for the advective diffusive model shown in Figure 12, after attaining steady state. FIGURE 14. Variation of the surface degassing rate with time for an axisymmetric model with both vertical and horizontal model K(V) = 4000 m2 y.-1, basin radius is 500 km. diffusion. In this r(H)/r(V) = 5 x 107, H = 140 m, and the Fi gure I o o r UJ \ I 8( EI o c oq @t t a0 3;,; pa#. I I {! -,\. c 93 zG *;?i {tt -? l.o ---El 1G \:/ o coo O) g ah o r t-t/ )tt ,r! / rE t=J o o ,aJ g E c(! =lE o 3 G oo E E F o o G g UJ AtmosPhere 30m Mixed taYer Surface -4 ---+ lrl kol --_----*.> lEg 1-, lrD 4 140m Current L ,rolii -> ---> o ! or t' Sea Floor lokm !* ii: ;ii: ;ir: r :-, :...:, :..* 1 r.. t :".l r :t: +ril#iri - -.^.iri".i:i' ::;ii;i.:'t':.:.:Z 30m Bubble Plume - ?t Fi gure 3 2600 2500 E) .Y ff' 2400 P(COr) .T 2200 2600 i t! t t t , ,t 6 a i 2500 v a € {F:i i i^'j E) .! '5 ffr 2400 i ilr tt;t tt;t tt;, ,t;tl F 'illi !!!i { o s 6 t {lllt !,i ! i 2200 1800 pH 2000 2200 2400 , t,t ,\ t -6-- t 6 ).' , 2600 2800 TC(pmole/kg) 3000 33Fi qu re 4 2600 o ao oo o alt 6o ^8 E -l ao 24oo a 1 P(CO2) s o c' lrJ o oo "r" F 6' 2300 G ct a aa" ooQ *d aoQ s'/ lyr, 2200 2600 (o € ,t t, , ,t t, .t,t \t, ot ., ta € i !r ,t ct) ta '5 q llt 2400 5- t,,t tt t, ,t ,,t, 6 , 6 pH t , t) 'o , tt t, ,, , ttt o (o' , t a (o o 2200 1800 2000 2200 24oO 2600 2800 TC(pMole/kg) 3oo0 e, -34- , Figure 5 (a) ;t E go o =tr ttoL ao lg P 0 100 (b) E .F o J- o o tra c 103 102 I (c) 8 -CL 7 6 'l 1 10 100 V(cm/sec) 1000 4.5 E 4.0 = o € 3.5 a (.) o FJ () 6 6 F 1.5 (a) (c) 1.0 tE P 3.0 0.5 2.s 2.0 tl 0.0 lc l(lt 10s l- (d) (b) 8.0 E (o 1oo 7.5 1 o o (L 4 o7.O 103 6.5 102 1 0 100 R(km) 1000 6.0 10 100 R(km) 1000 , ('r (Flux In) BJHE 1d ?, a - 37- Fi gure 8 o (> o o o