capcis technical note - h2s partitioning

8/12/2019 CAPCIS Technical Note - H2S Partitioning

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PARTITIONING OF HYDROGEN SULPHIDE IN WELLSTREAM FLUIDS

1. INTRODUCTION AND BASIC PRINCIPLES

Hydrogen sulphide (H2S) is a highly toxic and corrosive gas (1) exerting its effects inwellstream fluids at the part per million concentration. The conceptual backgroundand a detailed mathematical description of H2S partitioning behaviour is presented forboth two and three phase systems under defined down hole and topsides conditions,thus allowing calculation of the concentrations and masses of hydrogen sulphide inall wellstream fluid phases from hydrocarbon producing wells. Statistical functionfitting has been used to enable numerical implementation of these techniques.

The term H2S in common usage is ambiguously applied to the gaseous phase, tothe undissociated dissolved gas and the aqueous sulphide ions derived from that gas(HS-and S2-). Much confusion can be avoided if the strict chemical sense of the termH2S is recognised, that relating to an undissociated molecule. In conversation, theexpression H2S molecule serves to clarify any misunderstandings. The text of thisdocument uses H2S throughout in its correct chemical sense of the undissociatedmolecule.

H2S is a mobile species readily transferring between the hydrocarbon phases and thewater phase of produced fluids in a manner that is predictable under any given set ofconditions with respect to pressure, temperature, pH and salinity of associated waterand the mass ratios of the various fluids. An understanding of this partitioningbehaviour together with the means to calculate the equilibrium concentrations of H2Sin the different wellstream fluids is an essential precursor to adopting safe wellstream

handling and processing strategies.

The literature contains many references to the solubility and partial pressures of H2S,in a wide variety of liquid organic compounds (see for example 2-5), water (see forexample 6, 7) and aqueous solutions of inorganic compounds (see for example 8, 9).There are relatively few publications which deal with the solubility and partialpressures of gases in produced crude oils (10, 11, 12) and formation waters.Literature that is available indicates a distribution ratio in the range of 3-7:1 for H2S inpure paraffin compounds and gives some data for H2S/CO2/CH4 in variouscombinations in paraffin mixtures and other organic compounds.


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Solubility data for H2S and those for other organic compounds generally give rise toa similar range of distribution ratios with water as the second liquid phase (13).Generally, H2S is considerably more soluble in organic compounds than in aqueoussolutions, except at high pH, the solubility increasing with increase in aromatic nature

and decreasing with increase in paraffin and polar nature. The effect of the pH ofassociated water is critical, as described in Section 3. The diversity of organiccompounds other than paraffin compounds present in various crude oils maytherefore markedly affect the solubility of H2S in the crude oil and its distributionbetween crude oil and water. The variability of crude oil probably explains the widerange of distribution ratios cited in the literature. Clearly, heavy, more aromatic,crude has a higher H2S solvency than a lighter, predominantly paraffinic crude.There is also a possibility that H2S may react chemically with certain compoundswhich could be present in crude oil or even formation water and appear to affect,artificially, the distribution ratios of H2S between crude oil and water.

The numerical work reported in this paper applies to typically light or medium densitycrudes and should have reasonable applicability to most oil production systems.

The method of computation of H2S solubility in crude oil and formation waters and thederivation of distribution ratios based on the respective partition coefficients coulduse Henrys Law or Gerrards Reference Line method (3,4,14) and various complexcubic equations of state(10,11-14). Gerrards elegant and realistic method and thecubic equations of state have been used to model real situations and makecorrections for the inherent non-ideal behaviour of H2S; and the use of Henrys Lawhas been criticised for this reason. Both of these methods are therefore applicable torelatively high H2S partial pressures obtained where high H2S mole fractions and totalsystem pressures cause significant deviation from ideal gas behaviour assumed byHenrys Law. The methods require comprehensive compositional data for gas, oiland water phases and, in order to use other cubic equations of state, moderatelyhigh computational power.

Where the degree of souring is not expected to rise above a few hundred mg/kg(ppmw) in the oil phase, even in the anticipated worse case, the use of Henrys Lawis fully justified. This is because at these concentrations the partial pressure of H2S,which is of paramount importance, is low at wellhead and even at reservoirpressures; and total system pressures are well below the point where non-ideal gasbehaviour starts to become measurably significant. Furthermore, under down holeconditions, at pressures above the bubble point, there is no separate gas phase, andhence the question of applicability of Henrys Law or not is irrelevant.

It is on the above basis, therefore, that the present determination and calculationmethodology were developed. The mathematical treatment in this paper details themethod of calculation of the full wellstream concentrations and mass of H2S and

derived sulphides for either two or three phase systems under defined down hole andtopsides conditions. Note that, although outside the scope of the current paper, thistreatment is applicable to the study of other components, such as carbon dioxide(CO2).

A comprehensive list of literature references can be found in Chapter 7 of Reference1.


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2. GLOSSARY OF TERMS

G = Pressure of system in mm Hg (abs).H = Total wellstream mass of H2S, in kg/day.

HG = Mass of produced H2S in the gas phase, in kg/day.HO = Mass of H2S in the oil when above bubble point, in kg/day.

HO = Mass of produced H2S H2S in the oil phase, in kg/day.HW = Mass of produced H2S in the water phase, in kg/day.KG = Effective partition rate coefficient for gas.KO = Partition rate coefficient for oil.KOW = Concentration ratio of H2S, oil to water.KW = Partition rate coefficient for water.KWO = Concentration ratio of H2S, water to oil.

K WO*

= Apparent KWOvalue not corrected for pH.

M = Total wellstream production mass, in kg/day.MG = Mass of produced gas, in kg/day.

mG = Average molecular mass of partitioned gas (typical value = 20).mH = Molecular mass of H2S = 34.mO = Average molecular mass of wellstream hydrocarbon fluids.

MO = Mass of oil above bubble point, in kg/day.mN = Molecular mass of N2= 28.MO = Mass of produced oil, in kg/day.MW = Mass of produced water, in kg/day.p = Partial pressure of H2S in the gas phase in mm Hg (abs).P = Pressure of system in atmospheres (abs).QN = Mass, of purge nitrogen, in kg.QO = Mass, of purged oil sample, in kg.rG = Proportion by mass of produced gas.rO

= Proportion by mass of produced oil when above bubble point.

rO = Proportion by mass of produced oil.rW = Proportion by mass of produced water.STP = Standard Temperature and Pressure, 0o Centigrade and 1 atmospheres

(abs).T = Temperature of system in degrees Centigrade.V1 = Volume occupied by one mole of any gas at STP, namely 22.4 litres.VN = Volume of purge nitrogen, measured at STP.XG = Concentration of H2S in the gas phase, in mg/kg.

XO = Concentration of H2S in the oil phase when above bubble point, in mg/kg.XO = Concentration of H2S in the oil phase in mg/kg.XW = Concentration of sulphide species (H2S + HS

-+ S2-) in the water phase inmg/kg.

XWE = Concentration of H2S as the undissociated molecule in the water phase atspecified pH, in mg/kg.

y = Mole fraction of H2S in gas phase.Y = Concentration of H2S in gas phase in ppmv.YN = Concentration of H2S in purge nitrogen measured at STP, in ppmv.Z = Overall concentration of sulphide species (H2S + HS

-+ S2-) in wellstream inmg/kg.


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outgasses, this raises the pH of the water which consequently locks-up additional

H2S, in the water phase, as HS-

ions.

It is therefore most important to take account of the pH effect when using measured

amounts of H2S in a gas phase to deduce the corresponding concentration (s) in theassociated phase(s) or in determining the necessary partition coefficients.

From (6.1) we derive linking the effective concentration of H2S as theundissociated molecule in the water (available for partitioning) to the pH of thesystem:

X XWE W= (3.8)

Z r X r X r XE O O G G W WE= + + (3.9)

[ ]or Z above the bubble pointE O O W WEr X r X= + ( . )3 9

Conversion from atmospheres to mm Hg:

G = 760P (3.10)

4. THREE-PHASE PARTITIONING (BELOW BUBBLE POINTPRESSURE)

Light or medium density crude oil bubble point pressures are generally within therange 35 - 540 atmospheres over the operating temperatures of the wellstream. Thatis to say, the particular bubble points for the various gas molecules typically present

in any quantity lie within this range. As pressures are lowered, so more gascomponents partition out, raising the oilstream G.O.R. and the average molecularweight of the produced gas. The bubble point pressure for a given molecule will notvary muchover the usual range of separator temperatures (T, ambient up to 120oC,say), as can be seen from examining the standard relationship: P (bubble) = Pexp

[1/(T + 273)] with P70 atmospheres say, for a typical well head gas component.

(a) Gas Phase

Typically start with Y measured directly in ppmv. The common commercial detectortube techniques are very quick and simple to apply on site at production wellheads orgas separators. Also, they are qualitatively better than the usual techniques formeasuring concentration in the oil phase, although not so accurate as the titrimetricmethods for water. Titrimetric methods for water are not, however, amenable for useon site at the production wellheads and the dissolved sulphides need to bechemically fixed to avoid loss by oxidation and degassing during transit to thelaboratory. Measurement of H2S concentrations in gas phase is, therefore, the mostcommonly adopted practice.


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From the glossary above it can be seen that gas phase measurements may besupplied as, or be needed to be expressed as: ppmv (Y), partial pressure in mm Hg(p), mg/kg (XG ppmw) or mole fraction (y). The various relationships betweenthese units are summarised in the table of transformations given below:

Y (ppmv)

Converting from

p (mm Hg) XG(ppmw) y (mole fraction)

Converting YTo

Y 106 p/G mG XG /mH 106 y

p 10-6 YG p 10-6 GXG mG /mH yG (4.1)

XG mHY/mG 106 mH p/(GmG) XG 10

6 mH y/mG

y 10-6 Y p/G 10-6 XG mG /mH y

We have,

X p K p KO O WE w= =/ & / X (4.2)

Then (3.8) implies:

X XW WE= / (4.3)

and Z comes from (3.6) directly.

(b) Water Phase

One standard technique starts by 'fixing' the H2S in the water entirely as HS

-

or S

2-

,by the addition of alkali to raise the pH. The implied total mg/kg of H2S that couldhave been found in the water at a low enough pH (below 5.0) is then back-calculated.This method therefore supplies a value for XW, rather than XWE, which must becalculated from (3.8); which in turn supplies a value for XO via (3.7) and for p via(4.2). Finally, observe that (4.1) and (4.2) together imply

X KG G= p / (4.4)

(c) Oil Phase

One standard technique is to purge a sample of oil with nitrogen gas so as to(nominally, at least) remove all the H2S, and then to find the ppmv, YNsay, at STP, of

this purged H2S in the nitrogen. This figure must be converted back to recover the oilconcentration via the mass balance equation:

X Q X QO O N N= (4.5)

which implies


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Xm

mY

V m

V QO

N

GN

N N

O

=

1

(4.6)

Then (4.2) followed by (4.4) and (4.1) recovers p, XWE, XG, y and Y in turn. These canbe applied to (4.3) then (3.6) for Xwand Z, if required.

(d) Overall Mixture

An alternative situation occurs when the overall figure for H2S production, H, is given(in kg/day). This typically arises either as a design parameter for oilfield equipment orfrom modelling of H2S production down hole by bacterial activity. Then (3.4) gives Zimmediately, whilst substituting for XGfrom (4.4) and for XOand XWEfrom (4.2) andhence into (3.6) using (3.8), we find:

[ ]p Z r K r K KO O G G WE= + + / 1 1 1rW (4.7)

Then

Y = p 106/G (4.8)

whilst (4.2) gives XO and XWE , (4.4) gives XG , (3.6) gives Z and finally (3.8)recovers XW.

5. TWO-PHASE PARTITIONING (ABOVE BUBBLE POINT PRESSURE)

Here the two phases are oil and water in the proportions r'Oand rWrespectively. Wehave

=X X KO WE OW/ (5.1)

(a) Water Phase

Given XWas measured from a sample of water, (3.8) and (5.1) imply

=X KO OW WX (5.2)

with (3.6') for the overall concentration. Note that this water sample measurement willproduce an apparent value for the partition coefficient equal to X'o/Xw . From (5.2)we see that this is proportional to the fundamental diffusion ratio, KOW, coinciding with

it only when =1.(b) Oil Phase

Given a direct measurement of XO , (5.1) and (5.2) give XWEand XW, then (3.6') givesZ. When H2S is given as a mole% concentration in the wellstream downholehydrocarbon phase, this can be converted into mg/kg by


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Xmole m

mO

H

O

=

%

100

10 6

(5.3)

(c) Overall Mixture

Given Z, perhaps derived from a top-side three phase analysis, we can substituteboth for XO from ( . )3 7 and for XWfrom (3.8), into ( . )3 6 to give

X r K r WE O OW W= + Z / ( ) (5.4)

and hence Xwfrom (3.8), and XO from (5.1).

(d) apparent partition constant

For fixed pH the ratio

=X X KO W OW/* (5.5)

defines an 'apparent' partition constant, which is not however a true partition constantsince it is not a ratio of diffusion speeds and it depends on pH. From (3.8) and (5.1)we see that

K OW OW* = K (5.6)

Also, solving for ZE, we find

[ ][ ]Z Z r K r

r K rE

O OW W

O OW W= + +

(5.7)

for (down-hole) two-phase mixtures, and

[ ]

[ ]Z Z

r K r K r K

K K r KE

O O G G W W

O G W W

= + +

+ +

1 1 1

1 1 1(r rO G ) (5.8)

for (top-side) three-phase mixtures.


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6. RESPONSE SURFACE FITS TO TABULATED VALUES

Plotting a standard table of retention proportions on a base 10 logistic scale, shows a

clear linear trend with unit slope, crossing the pH axis at 6.7, and therefore implyingthe following relationship between and pH :

= + ( ).1 10 6 7 1pH (6.1)

The partition K constants depend on pressure, temperature and the precise chemicalcomposition of the various phases. They can be difficult to measure and variousvalues can be found in the literature.

Access to a table of partition coefficients for a typical light to medium densitypetroleum production system has enabled another function fitting exercise to producethe following formulae for the two necessary partition coefficients, KOand KW:

K C C A CA A C A CA CA C AO O= + + + + + + + + + 1 22

32

4 53

62

72

83

92 2 (6.2)

[ ]K X CW o= + +0 86 1. exp (6.3)

where C = T/100, A = P/100, X = |A - 0.75|, and the & values are given in thetable below:

parameter value parameter value

0 0.0527417 0 -0.3955801 0.1381160 1 -0.681974

2 0.13080903 0.04312124 -0.08985115 -0.01515936 -0.12320307 0.16883308 -0.05989669 0.0371972

The tabulated values for both KOand KWcovered the ranges 0P150 and 0T100.A plot of the 4th order response surface, given below, as fitted to these supplied KOvalues, can be seen in Figure 1. The corresponding plot for Kwcan be seen in Figure

2, extended out to T 160 and P = 250. The extrapolated sections of this lattergraph appear to be consistent with the pattern of fit seen for the interpolated regionand hence this formula is perhaps usable out to the higher parameter values.Although some extra, statistically significant, terms could have been included in themodel for KW , they were of little practical significance within the interpolated region,and unfortunately became unstable for extrapolations. Hence the simplified modelgiven above was considered to be preferable.


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7. REFERENCES

(1) Oilfield Reservoir Souring, UK Health & Safety Executive OTH 92385

HMSO Publication 1993.

(2) CHEUNG, H. and ZANDER, E. H. Chem. Eng. Prog. Symp. Ser., 64(88), 34,(1968).

(3) EAKIN, B. E. and DEVANEY, W. E. Aiche, Symp. Ser., 70, 80, (1974).

(4) GERRARD, W. J. Appl. Chem. Biotechnol, 22, 623, (1972).

(5) HSU, C. and LU, B.C.Y., J. Chem. Eng., 50, 144, (1972).

(6) REAMER, H. H., SAGE, R. H.. and LACEY, W. N. Ind. Eng. Chem., 43, 975,(1951).

(7) ROBINSON, D.B., Proc. Ann. Conv. Gas Process Assoc., Tech. Pap., 54, 25,(1975).

(8) ANDREWS, J. C. and KENDALL, J. JACS, 43, 1545, (1921).

(9) ANDO N., SADA, E. and KITU, S. J. Appl. Chem. Biotechnol., 22 1185,(1972).

(10) ERBAR, J. H. and MAJEED, A.I., EFCE Publ. Ser., 27, C15/1-C15/7 (Int.Conf. Inf. Genie Chim., 2) (1983).

(11) ERBAR, J. H. MOSHFEGIAN, M. and SHARIAT, A. ACS Symp. Ser., 133,

333, (1980).

(12) WAGNER, J. and MAJEED, A.I. ACS Symp Ber., 300, 452, (1986).

(13) RORSCHACH, R. P. and GARDINER, F. T. Ind. Eng. Chemical., 41, 1380,(1949).

(14) GERRARD, W. Solubility of gases and liquids, Plenum Press, (1976).

capcis technical note - h2s partitioning

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