# ASTM D4056-16

Designation: D4056 − 16Standard Test Method forEstimation of Solubility of Water in Hydrocarbon andAliphatic Ester Lubricants1This standard is issued under the fixed designation D4056; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope*1.1 This test method covers a procedure for estimating theequilibrium solubility of water and its vapor in hydrocarbonand aliphatic ester lubricants, at temperatures between 277 Kand 373 K. The test method is limited to liquids of low tomoderate polarity and hydrogen bonding, with predicted solu-bilities not over 1000 ppm by weight in hydrocarbons, or30 000 ppm by weight in oxygenated compounds, at 298 K.1.2 Specifically excluded are olefins, nitriles, nitrocompounds, and alcohols.1.3 This test method is recommended only for liquids notcontaining widely different chemical species. This excludesblends of esters with hydrocarbons, and lubricants containingdetergents, dispersants, rust preventives, or load carryingadditives.1.4 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D94 Test Methods for Saponification Number of PetroleumProductsD1218 Test Method for Refractive Index and RefractiveDispersion of Hydrocarbon LiquidsD1298 Test Method for Density, Relative Density, or APIGravity of Crude Petroleum and Liquid Petroleum Prod-ucts by Hydrometer MethodD2502 Test Method for Estimation of Mean Relative Mo-lecular Mass of Petroleum Oils from Viscosity Measure-mentsD3238 Test Method for Calculation of Carbon Distributionand Structural Group Analysis of Petroleum Oils by then-d-M Method3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 charge transfer parameter—the portion of the solubil-ity parameter not attributed to London or Keesom forces.3.1.1.1 Discussion—It includes hydrogen bonds, induceddipoles, and other quasichemical forces.3.1.1.2 Discussion—The square of the solubility parameterequals the sum of the squares of the three partial parameters.3.1.2 dispersion parameter—the portion of the solubilityparameter attributed to London forces.3.1.3 polar parameter—the portion of the solubility param-eter attributed to Keesom (permanent dipole) forces.3.1.4 solubility parameter—the square root of the cohesiveenergy density (heat of vaporization minus work ofvaporization, per unit volume of liquid), at 298 K.3.2 Symbols:CA= percentage of aromatic carbons,CN= percentage of naphthenic carbons,d = density of lubricant at 298 K, g/mL,G = solubility by weight, mg/kg (ppm),M = molecular weight of lubricant, g/mol,nD= refractive index of lubricant at 298 K,RH = relative humidity, %,S = saponification number, mg of KOH/g of lubricant,T = system temperature, K,V = molar volume of lubricant, mL/mol,x = mole fraction of water in equilibrium mixture,y = Lorentz-Lorenz refractivity function,δd= dispersion parameter, (MPa)0.5,P = polar parameter, (MPa)0.5,H = charge transfer parameter, (MPa)0.5,1This test method is under the jurisdiction of ASTM Committee D02 onPetroleum Products, Liquid Fuels, and Lubricants and is the direct responsibility ofSubcommittee D02.L0.07 on Engineering Sciences of High Performance Fluids andSolids (Formally D02.1100).Current edition approved Jan. 1, 2016. Published March 2016. Originallyapproved in 1981. Last previous edition approved in 2010 as D4056 – 01 (2010).DOI: 10.1520/D4056-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1φ1= volume fraction of lubricant in equilibrium mixture,andφ2= volume fraction of water in equilibrium mixture.4. Summary of Test Method4.1 Data required are the density, refractive index, andmolecular weight of a hydrocarbon. The saponification numberis also required for an ester. From these are calculated thecarbon distribution for a hydrocarbon, and then the partialsolubility parameters. These in turn are used to calculate thevolume fraction of water dissolved at 298 K at saturation. Thisis converted to mole fraction, and adjusted to system tempera-ture. The mole fraction is then converted to solubility byweight. If the system atmosphere is not saturated, the solubilityis multiplied by the relative humidity.5. Significance and Use5.1 Knowledge of the water content is important inlubrication, as large amounts of water can cause corrosionfatigue in steel bearings, and the complete absence of water cancause metal scuffing.5.2 High water content has an accelerating effect on oxida-tion of lubricants, and can also contribute to foaming, espe-cially at high altitude or temperature, or both.6. Procedure6.1 Calculate the molar volume of the lubricant as follows:6.1.1 Determine the density at 298 K byTest Method D1298or equivalent. If the density at 293 K is known (as required forTest Method D3238) multiply it by 0.996 to obtain d withsufficient accuracy.6.1.2 Determine the molecular weight by Test MethodD2502.6.1.3 Calculate the molar volume as follows:V 5 M/d (1)6.2 Calculate the dispersion parameter by these steps:6.2.1 Determine the refractive index at 298 K by TestMethod D1218.If a value at 293 K is known (as required for Test MethodD3238) multiply it by 0.998 to obtain nDwith sufficientaccuracy.6.2.2 Calculate the refractivity function as follows:y 5 ~nD22 1!/~nD212! (2)6.2.3 Calculate the parameter as follows:δd5 45y32 119y21108 y 2 4.58 (3)6.3 For hydrocarbons, calculate δdand P as follows:6.3.1 Determine CAand CNby Test Method D3238.6.3.2 Calculate the parameters as follows:P 5 0.0143CAand (4)H 5 0.0286CA10.0143CN(5)6.4 For esters, calculate P and H as follows:6.4.1 Determine the saponification number by Test MethodsD94.6.4.2 Calculate the parameter as follows:P 5 0.00815 Sd and (6)H 5 0.00173 SM/V0.5(7)6.5 Calculate the volume fraction of water at 298 K andsaturation as follows:1⁄φ25 exp@0.00726 φ21~~18.00 2 δd!21 2.39 ~15.552P)212.39 ~16.27 2 H!2)1~1 2 18/V!φ1] (8)NOTE 1—For hydrocarbons, it may be safely assumed that φ1= 1.00.However, that can introduce a significant error for some esters, socalculate φ2stepwise. Start with φ1= 1.00, next step φ1=1−φ2from thefirst step, and so on until no further significant change is noted.6.5.1 Rarely are more than three steps needed to obtainconstancy to three significant figures. A small programmablecalculator, which is strongly recommended for the wholeprocedure, can readily be set into the interative cycle described.6.6 Calculate the mole fraction at 298 K as follows:x 5 Vϕ2/18 (9)6.7 Calculate the solubility by weight at 298 K, using Eq 10:G 5 18 3106X/M~1 2 X! (10)6.8 If the system was not saturated at equilibrium, with atleast a trace of liquid water present, multiply X by RH/100;then convert to G as before. (Unless G is larger than 1000, thisadjustment can be made directly on it.)6.9 Multiply G by RH/100, if the system was not saturated,with at least a trace of liquid water present. If G is greater than1000, multiply X by RG/100 before converting to G.7. Precision and Bias7.1 Precision—The repeatability and reproducibility inter-vals arise entirely from those of the experimental methodsemployed for n, S, CAand CN. The intervals due to the statedprecision of Test Method D1218 will both be 0.4 % of thecalculated solubility. The effects of the intervals stated for TestMethods D94 and D3238 are such that no blanket statementcan be made. However, the intervals for any specific lubricantcan readily be calculated by processing the values of S, CA, andCNthrough the equations alone and plus the intervals from theexperimental methods.7.1.1 Predictions have been made for all pure hydrocarbonsfor which solubilities of water at 298 K were listed, exceptingthe olefins, by API,3Riddick,4and Polak.5On aliphatics,Polak’s values were chosen if available since they werecarefully compared against the older data, giving 14 points.Riddick yielded three, and API two accepted, plus six rejectedsimply because they appeared “wild.” All 18 points werepredicted within 610 %. The API and Riddick values weresimilar on naphthenes; five values were predicted within 20 %and one within 50 %. Polak’s six values for aromatics werepredicted within 10 %, and five others from Riddick within15 %.API had only one that was neither redundant nor wild; itwas predicted within 10 %.3API Technical Data Book, American Petroleum Institute, Washington, DC1970.4Riddick, J. A., and Bunger, W. E., Organic Solvents, (Techniques of OrganicChemistry, Vol. 2, A. Weissberger, Ed.) Wiley-Interscience, John Wiley and Sons,New York, NY 1970.5Polak, J., and Lu, B. C.-Y., “Mutual Solubilities of Hydrocarbons and Water,”Canadian Journal of Chemistry, Vol 51, 1973, pp. 4018–4023.D4056 − 1627.1.2 Predictions at elevated temperatures had to be checkedagainst API data, and were within 10 % of the correct slopefrom 298 K to 373 K for the three liquids covering this range.Most of the data stop at 323 K or less, and have not beenanalyzed.7.1.3 API lists eight commercial oils with solubilities atelevated temperatures. Assigning plausible δd, CA, and CNvalues gave predictions on five of these within 50 % or betterfor solubility, and 25 % or better for slope. The gasolinetemperature range was too short to test, and the JP-3 and 4 dataappeared wild.7.1.4 Data by Cantley6on a petroleum (SAE 5W) oil, asynthetic hydrocarbon, and two esters at 311 K were predictedwithin 20 %, and the dependence on RH within 10 %. Otherdata also illustrate the problems caused by additives.7.1.5 Riddick shows data on 34 esters. However, only 13 ofthose meet the criteria in the scope, and two of these wereclassified as wild because of obvious conflicts with closeisomers. The remaining eleven were predicted within 50 % ofthe true value, and most within 30 %.7.2 Bias—No general statement is made for bias for this testmethod since the data used to determine the correlation cannotbe compared with accepted reference material.8. Keywords8.1 lubricants; solubility; waterSUMMARY OF CHANGESSubcommittee D02.L0 has identified the location of selected changes to this standard since the last issue(D4056 – 01 (2010)) that may impact the use of this standard. (Approved Jan. 1, 2016.)(1) Revised Eq 8.ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or service@astm.org (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standard may also be secured from the Copyright Clearance Center, 222Rosewood Drive, Danvers, MA 01923, Tel: (978) 646-2600; http://www.copyright.com/6Cantley, R. E., “The Effect of Water in Lubricating Oil on Bearing FatigueLife,” ASLE Transactions, Vol 20, 1977, pp. 244–248.D4056 − 163