3698
Langmuir 1998, 14, 3698-3703
The Temperature and Ionic Strength Dependence of the Solubility Product Constant of Ferrous Phosphonate Stephen J. Friedfeld, Shiliang He,† and Mason B. Tomson* Department of Environmental Science and Engineering, Rice University, Houston, Texas 77005 Received November 25, 1997. In Final Form: April 20, 1998 A new compound with implications in scale and corrosion control has been isolated and its solubility measured under varying conditions of temperature and ionic strength from 25 to 75 °C and from 1 to 3 M ionic strength. Ferrous phosphonate was formed using the phosphonate nitrilotris(methylene phosphonic acid) (NTMP) and was found to have the stoichiometry Fe2.5HNTMP. Using a complexation and speciation model, the stability constants for the complexation of iron(II) with phosphonate were calculated, and the solubility product constant was derived for each temperature and ionic strength; at 25 °C and 1 M ionic strength, Ksp ) 10-31.2. The temperature (T, K) and ionic strength (I, M) dependence of the negative logarithm of the ferrous phosphonate solubility product constant (pKsp) was determined to be: pKsp ) 39.54 - 6.14I1/2 + 2.18I - 1315/T. In simulated calculations using actual field data to compare iron and calcium phosphonates independently, ferrous salts were predicted to form in all instances and matured calcium salts were predicted to form occasionally. Furthermore, a relationship was established whereby the concentration of free iron in a calcium-iron-phosphonate system can be predicted for a given system.
* To whom correspondence should be addressed. † Present address: Maurer Engineering, Inc., 2916 West T.C. Jester, Houston, TX 77018. Telephone: (713) 683-8227.
have shown that calcium-phosphonate salts are relatively insoluble among the divalent metal cations commonly found in natural waters. Studies show that ferrous phosphate and ferrous carbonate exhibit low solubilities,9,10 and thus ferrous-phosphonate complexes also may be relatively insoluble. Unfortunately, the solubilities of ferrous carbonate and phosphonate have not been studied in the range of ionic strengths and temperatures of importance to the work reported herein. Though many sparingly soluble calcium salts have been studied, little work has been done with iron(II) precipitates because of the difficulty involved with maintaining an anoxic environment. This study is the first to report the solubility of iron(II) phosphonate. Knowledge of the solubility of phosphonate-metal salts under varying conditions of temperature and ionic strength can provide valuable information to the oil and gas industry as to the quantity and type of inhibitor required to inhibit scale effectively given the chemical composition of the well brine and the physical conditions in the well. Ferrous iron exists in abundance in natural and industrial systems, typically ranging from a few milligrams per liter of natural iron to as high as 100 mg/L in systems where corrosion exists.11 Thus it is likely that phosphonate inhibitors injected into gas and oil wells will react with ferrous iron. Furthermore, in addition to a possible retention and release system for the inhibition of scale, a protective layer of ferrous phosphonate may form and protect metals from corrosion, as suggested by the work of Sontheimer et al.12 with ferrous carbonate. Thus, to examine more closely the possible potential
(1) Dequest 2000 and 2006 Phosphonates; Monsanto Publication No. 9023, Monsanto: 1986. (2) Tomson, M. B.; Kan, A. T.; Oddo, J. E. Langmuir 1994, 10, 14421449. (3) Frostman, L. M.; Kan, A. T.; Tomson, M. B. In Calcium Phosphonates: Composition, Solution Chemistry, and Applications; Amjad, Z., Ed.; in press. (4) Carlberg, B. L. Oil Gas J. 1983, Dec, 152-154. (5) Malandrino, A.; Yuan, M. D.; Sorbie, K. S.; Jordan, M. M. Mechanistic Study and Modeling of Precipitation Scale Inhibitor Squeeze Processes; Society of Petroleum Engineers: San Antonio, TX, 1995; pp 597-612. (6) Browning, F. H.; Fogler, H. S. AIChE J. 1996, 42, 2883-2896.
(7) Kan, A. T.; Oddo, J. E.; Tomson, M. B. Langmuir 1994, 10, 14501455. (8) Ebrahimpour, A.; Ebetino, F. H.; Sethuraman, G.; Nancollas, G. H. In Mineral Scale Formation and Inhibition; Amjad, Z., Ed.; Plenum Press: New York, 1995; p 295. (9) Al-Borno, A.; Tomson, M. B. Geochim. Cosmochim. Acta 1994, 58, 5373-5378. (10) Greenberg, J. L. High-Temperature Kinetics of Precipitation and Dissolution of Ferrous Carbonate. M.S. Thesis, Rice University, Houston, TX, 1986. (11) Patton, C. C. Applied Water Technology; Campbell Petroleum Series; Campbell Petroleum: Norman, OK, 1986.
Introduction Phosphonates are used in a wide variety of industrial applications, including scale and corrosion control, metal finishing, and industrial cleaning.1 Phosphonates inhibit scale formation via a “threshold effect”, in which small amounts (typically a few milligrams per liter) of the chemical are added to oil and gas wells to prevent the formation of scale.2 Inhibitors are typically “squeezed” into a well via pumping and are shut in for 1-2 days.3 The inhibitor squeeze works by adsorbing onto or precipitating within the rock formation. When the well is returned to production, the inhibitor slowly dissolves or desorbs into the produced brine at a low but sufficient concentration of inhibitor and effectively inhibits scale by preventing crystallites of scale from growing large enough to become stable in solution. Though both precipitation and adsorption mechanisms of effective squeeze treatments have been studied,4-6 the focus here is on the precipitation mechanism, particularly that of ferrous iron with phosphonate. The inhibitor studied was nitrilotris(methylenephosphonic acid), NTMP. This inhibitor was chosen because it is commonly used in gas and oil wells for the prevention of scale. Further, this inhibitor has been shown to form an unstable initial precipitate which is either amorphous or microcrystalline and then transforms into a less soluble, more crystalline material.7 In particular, previous studies have focused on calcium phosphonate precipitation6,8 and
S0743-7463(97)01293-6 CCC: $15.00 © 1998 American Chemical Society Published on Web 05/30/1998
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Figure 1. Schematic of the apparatus used for ferrous phosphonate solubility studies. Modified from an apparatus used to study vivianite.9
benefits of precipitation between a phosphonate inhibitor and divalent metal cation, the objectives of this study were to create a ferrous phosphonate compound, determine its solubility as a function of temperature and ionic strength, and establish a relationship between ferrous iron, calcium, and phosphonate salts as it pertains to field conditions to better predict and control scale and corrosion. Experimental Section Test Apparatus. The test apparatus (Figure 1) used in this study operates under rigorously anoxic conditions without the use of reducing agents which might interfere with the reaction. It is similar to that reported previously by Al-Borno and Tomson.9 The apparatus consists of a vacuum/purge manifold, a 1-L jacketed ACE brand glass reactor, a 316 stainless steel (SS) lid sealed to the reactor with an O-ring, one 5-L glass vessel for water deoxygenation and storage, and one 5-L glass vessel for water disposal, all connected by high-vacuum hoses. Oxygenfree argon is inlet to the system through a Firestone valve, which maintains an internal pressure of 1 atm. Three of the four twoway valves on the manifold are used to apply a positive pressure or vacuum to the reactor, storage, or disposal vessels. The SS lid has 10 1/8 in. o.d. Cajon adapters welded in place. Two-way valves connected to stainless steel tubing are installed in two of the adapters, while the remaining eight adapters contain septum ports for sampling. This apparatus was used to deoxygenate preparatory and test solutions by alternately purging and evacuating, where four vacuum/purge cycles were required to deoxygenate the system sufficiently. Materials. All chemicals used in this study were reagent grade. The nitrilotris(methylenephosphonic acid) used was a commercial product obtained from Monsanto Chemical Company as a 50% (w/w) solution (Dequest 2000). Preparation of Ferrous Phosphonate. The ferrous phosphonate precipitates were prepared at 70 °C and pH 5.7 by approximating a constant composition method13 to give a final solution containing 0.02 M phosphonate and 0.1 M ferrous iron. Approximately 1 mL of deoxygenated 0.33 M iron solution (FeCl2‚ (12) Sontheimer, H.; Ko¨lle, W.; Snoeyink, V. L. J. AWWA 1981, 73, 572-579. (13) Tomson, M. B.; Nancollas, G. H. Science 1978, 200, 1059-1060.
4H2O dissolved in deionized water) and 1 mL of deoxygenated 0.669 phosphonate solution (NTMP dissolved in deionized water and NaOH) to give 25 mL total of each were alternately injected with syringes into the reaction vessel. The reaction vessel contained a deoxygenated solution of 850 mL deionized water, 0.7 M NaCl, and 0.01 M acetic acid (used as a buffer). The pH was maintained approximately constant by adding deoxygenated 1 M HCl and 1 M NaOH appropriately, as determined by measuring the pH of withdrawn samples periodically. The addition of iron and phosphonate to the reaction vessel formed an off-white precipitate immediately. The solution settled overnight, and the precipitate was washed with an oxygen-free solution of 0.05 M NaAc/0.05 M HAc at 1 M I (NaCl), where the buffer fixed the pH at about 4.4. The deoxygenated washing solution was introduced to the contents of the reaction vessel from the deoxygenation flask and stirred for several hours using a magnetic stirrer, and the supernatant liquid was removed to the disposal flask after settling. The concentration of total iron in the supernatant was measured using spectrophotometric methods after each wash and decreased from 5000 to 27 mg/L after nine washes. Numerous attempts were made to maintain a constant ferrous iron concentration in addition to the constant buffered pH to reduce potential error and requiring measurement of only phosphonate. However, this increased the likelihood for oxygen to enter the system and caused the precipitate and solution to oxidize. Thus, only the pH was fixed and both total iron and total phosphonate were measured instead. The washed precipitates were kept under positive pressure of oxygen-free argon in the reaction vessel. No change in color was observed during the washing. The seed crystals were characterized by electron microprobe and X-ray diffraction. The sample was prepared for X-ray diffraction on a glass slide with doublesided tape; the X-ray source was Cu KR at a wavelength of 1.5418 Ångstroms. The average stoichiometry of the precipitate was determined by withdrawing samples of the seed material with syringes and measuring the ratio of iron to phosphonate in the filtrate. The samples used for stoichiometric determination were taken after the completion of the solubility tests and thus were considered to be mature precipitates. Solubility Tests. Solubility experiments were performed at 25, 50, and 70 °C and 1, 2, and 3 M ionic strength for each temperature, where NaCl was the electrolyte used. A Neslab circulating pump was used to maintain a constant temperature
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Friedfeld et al.
((0.1 °C) within the jacketed reaction vessel. After equilibrium was established (as determined by a constant total concentration of iron and phosphonate for several hours), the ferrous phosphonate saturated solution was sampled every few hours for several days and up to 21 days. Samples were withdrawn from the reaction vessel with plastic syringes injected through the septa and forced through a filter (Acrodisc 0.45 µm filter) into 30-mL plastic centrifuge cuvettes for storage. The capped centrifuge tubes were placed in a cool water bath to bring the temperature down to 25 °C for the higher temperature studies. The samples were divided and diluted to measure independently the total iron and phosphonate concentrations using HACH FerroVer and PhosphoVer spectrophotometric methods. The solubility experiments were run from high to low temperature for each ionic strength, in order of increasing ionic strength. A high-to-low-temperature ramp was used because it was assumed that the solubility decreased with an increase in temperature, which is common for scale formers. Further, the low-to-high ionic strength order was used because of the difficulties in creating dilute solutions from strong solutions in an anoxic system. Fe2+-NTMP Complexation. A factor termed bM (where M is the metal of interest) used in determining complexation constants was defined by Tomson et al.2 for calcium phosphonates. This factor was determined in this study under the assumption that calcium and ferrous iron phosphonate complexes behaved similarly and were stoichiometrically equivalent. In particular, a specific concentration on the titration curve used to determine bCa2+ was used to determine the analogous bFe2+. In the iron(II) study, the pH change was measured by insertion of the pH electrode into the reaction vessel, thus potentially exposing the solution to oxygen. The exposure time was minimized by immediately replacing the stainless steel lid and maintaining a positive pressure of oxygen-free argon over the solution. Four independent measurements were made to measure the pH change. Data Interpretation. The solubility of a ferrous phosphonate precipitate is given by the general dissolution reaction
FexH6-2xPhn T xFe2+ + (6 - 2x)H+ + Phn6-
(1)
where Phn is the phosphonate NTMP (with six ionizable protons) and x is the stoichiometric coefficient. The corresponding solubility product is
Ksp ) (Fe2+)x{H+}(6-2x)(Phn6-)
(2)
where ( ) refer to molar concentrations and { } refer to activity. Free concentrations of iron, (Fe2+), and NTMP, (Phn6-), were required to calculate the solubility product, and were determined from the measured total concentrations of phosphonate and iron and pH using the electrostatic speciation and complexation model developed by Tomson, et al.2,14 The complexation constants for the reaction
Fej-1HiPhn(8-i-2j)- + Fe2+ T FejHiPhn(6-i-2j)-
(3)
are given by
Kij )
(FejHiPhn(6-i-2j)-)
for (Fe2+)(Fej-1HiPhn(8-i-2j)-) 2 e i e 6, 0 e j e (B - i)/2 (4)
Similar to previous work with calcium, the values of Kij were assumed to be represented by the following equation:
log Kij ) bFe2+|q2j-2+i|
for i >1, j g 1
(5)
The validity of this model is tested below. The value of the acid association constants for NTMP were given by log Ki ) aH+ + bH+|qi-2| where3 (14) Tomson, M. B.; Kan, A. T.; Oddo, J. E.; Gerbino, A. J. In Mineral Scale Formation and Inhibition; Amjad, Z., Ed.; Plenum Press: New York, 1995; p 307.
aH+ ) 2.296 - 0.567xI + 0.184I - 314/T bH+ ) 1.439 - 0.160xI + 0.0255I - 54.3/T and log K1 ) 12.30 for protonation of the sp3-hybridized N. At 25 °C and 1 M I the six successive dissociation constants of NTMP as log Ki (for 2 e i e 6) are calculated to be 1.2, 3.1, 4.2, 5.4, and 6.5.
Results and Discussion Characterization of Fe2+-NTMP Seed Material. Chemical analysis of the precipitates yielded a molar ratio of iron to phosphonate of 2.46 ( 0.18. Thus, the stoichiometry of the precipitate is assumed to be Fe2.5HNTMP, rounding to the nearest small whole-number ratios. This value is supported by the chemical formula of NTMP, HN+(CH2PO32-)3, and data for an amorphous form of CaNTMP with the stoichiometry Ca2.5HNTMP.3 In previous work with calcium phosphonates,7 a second phase for CaNTMP formed after the initial precipitate had undergone a dialysis-filtration process and was found to have the stoichiometry Ca3NTMP. The relatively large standard deviation for the stoichiometry in this study may partially be explained from the method of crystal formation, since the size and size distribution of the solid particles may change during the course of formation when a constant composition is not used,10 as was required here by the need for an anoxic environment. Ferrous phosphonate precipitates that had undergone the various temperature and ionic strength conditions showed no sharp peaks when examined by X-ray diffraction (Figure 2). Instead, a rounded hump appeared at 26 2θ, possibly indicating that the solid is microcrystalline with large aggregates of micrometer-sized particles.3 An electron microprobe analysis confirmed qualitatively the chemical composition of the solid and the absence of other elements. Fe2+-NTMP Complexation. A computer program written in FORTRAN15 and revised for Ca-inhibitor studies was used to calculate the value for bFe2+ given the I, T, pH, etc. values from titrations. The value for bFe2+, from eq 5, was found to be 0.86. The reasonableness of the value bFe2+ ) 0.86 was tested using outer-sphere complex formation theory, as in Tomson et al.2 At 1 M I and 70 °C, this corresponds to a stability constant of 101.72 M for the complexation of Fe2+ with a dinegative phosphonate ion, and the distance of closest approach using the value bFe2+ ) 0.86 approximates that found for calcium phosphonate complexes.2 Solubility of Fe2+-NTMP Precipitates. From the respective total concentrations measured, the free concentrations of iron and phosphonate were determined, and along with the pH, were used to calculate the Ksp. Table 1 lists the resultant log Ksp values along with the average value for each T and I condition. The mean values lie between 30.755 (for 25 °C/2 M I) and 31.798 (for 50 °C/1 M I), indicating that temperature and ionic strength have a small effect on the solubility product Fe2+-NTMP throughout the experimental ranges. The standard deviations are below 0.200 except that for 70 °C/1 M I. The pKsp mean value drops successively when the temperature is lowered from 70 to 25 °C within one ionic strength except for the value at 70 °C/1 M I; also, the pKsp decreases from 1 M I to 2 M I and then increases again at 3 M I, within one temperature, again with the exception of 70 °C/1 M I. The different behavior of the solubility at 70 °C and 1 M I may be explained as follows. This was the first (15) Wentworth, W. E. J. Chem. Educ. 1965, 42, 96.
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Figure 4. Equation-fitted curves of the pKsp for Fe-NTMP as a function of ionic strength using eq 6. Data were collected for solutions at 1, 2, and 3 M ionic strength, and the functional form of the fit was derived by analogy to the well-characterized calcium-phosphonate system. Figure 2. X-ray diffraction diagram for a matured precipitate of ferrous phosphonate. The sharp peaks are for NaCl, the electrolyte used throughout the solubility studies. Table 1. Summary of Chronological Experimental Solubility Data for Fe2+-NTMP time (h)
T IS (°C) (M)
pH
no. of measurements
av pKsp
std dev
5.50-48.50 63.50-115.25 123.75-232.25
70 50 25
1 1 1
4.48 4.48 4.48
9 7 10
31.410 0.216 31.798 0.081 31.222 0.180
238.00-309.50 325.50-385.50 395.67-422.25
70 50 25
2 2 2
4.42 4.42 4.42
8 5 6
31.468 0.142 31.117 0.118 30.755 0.126
429.25-472.75 494.50-563.00 569.75-1193.50
70 50 25
3 3 3
4.38 4.38 4.38
3 13 10
31.653 0.082 31.488 0.133 30.883 0.198
Figure 3. Plot of the log concentration of total iron and phosphonate over the course of the solubility studies.
dissolution condition, and thus the solid may have been in an initial microcrystalline phase which had not undergone complete phase transformation. Furthermore, the precipitate was formed using a large excess of iron, and thus incomplete washing of the solid created an initial excess of total iron and limited the dissolution of ferrous phosphonate. Figure 3 is a plot of the logarithm of the concentration of total iron and total phosphonate in the batch dissolution experiments as a function of time, where the ratio of iron to phosphonate appears to be stable at around 3-4 h after the initial experiments. A curve fit using the statistical code Psi-Plot16 was performed to determine pKsp as a function of ionic strength and temperature given the data in Table 1, resulting in
pKsp ) 39.54 ((1.24) - 6.14 ((1.63)xI + 2.18 ((0.6)I - 1315 ((205)/T (6)
The temperature-dependence and ionic strength dependent pKsp for Fe2+-NTMP in eq 6 was tested by changing the solution pH after the completion of the solubility experiments from ∼4.4 to 3.90 by the addition of 20 mL of deoxygenated 0.1 M acetic acid. The total iron and total phosphonate increased to 0.071 and 0.013 mM, respectively. The resultant mean pKsp changed by less than 1.00%. This closeness of fit suggests that the pKsp function determined from this study may be applicable to other pH, temperature, and ionic strength conditions, and thus it is useful in real field situations. Application to Field Data. The solubility data from this study were used with field data from 10 gas and oil wells (Table 2) to simulate precipitation conditions during the “shut in” period of well treatment because of the relevance of this work to the oil and gas industry and the apparent influence of calcium and ferrous cations on phosphonate inhibitor fate in precipitation squeezes. The ferrous and calcium systems within a given well were assumed to be independent of each other, and the total phosphonate concentration was set at 1 mg/L NTMP for each well to represent typical phosphonate return concentrations following a squeeze treatment. The functional form of bCa2+3 was used for calcium data, and bFe2+ ) 0.86 from this study. Following an inhibitor treatment, the produced brine composition and pH (except for low concentration of phosphonate) return to original values within a short period of time, typically a few days. Given total iron or calcium, the free iron and calcium concentrations were determined and used to calculate the ion product (IP) for the iron-NTMP precipitate and the amorphous and crystalline calcium-NTMP precipitates:
for Fe2.5HNTMP, IP ) (Fe2+)2.5{H+}(NTMP6-) for Ca2.5HNTMP, IP ) (Ca2+)2.5{H+}(NTMP6-) for Ca3NTMP, IP ) (Ca2+)3(NTMP6-) From the values for pIP and pKsp (where pX ) -log X), the saturation index (SI) was calculated:
SI ) log
( ) IP Ksp
where numbers in parentheses are standard deviations. Figure 4 shows the curve fit of eq 6 for all three temperatures used in this study over a range of ionic strengths. The standard enthalpy change is ∆H° ) -25.2 kJ mol-1 for the solubility product.
Figure 5 shows the saturation index for each production well as a function of ionic strength. Any value of SI > 0 indicates that a precipitate might form, since the solution is oversaturated with respect to the relevant species; if SI < 0, the solution is undersaturated and a precipitate cannot form.17 From Figure 5, ferrous phosphonate is predicted to precipitate in each well, while the amorphous
(16) Psi-Plot 1993. Poly Software International, Salt Lake City, UT.
(17) Oddo, J. E.; Tomson, M. B. Oil Gas J. February 1994, 33-37.
b
pKsp (Ca2.5HNTMP)3 ) 29.34 - 5.39xIS + 1.79IS
Friedfeld et al.
aPhn :Fe or :Ca refers to the free phosphonate concentration in the respective simulation. Total phosphonate was set for each well at 1 mg/L. f - 1780/T. c pKsp (Ca3NTMP)3 ) 26.80 - 5.00xIS + 1.73IS - 1910/T.
22.349 20.877 18.483 18.927 18.882 18.43 18.913 17.726 20.368 17.762 18.673 19.137 18.807 18.762 18.643 18.078 18.689 19.005 19.884 18.670 25.955 25.386 23.672 24.170 24.406 23.969 24.438 23.831 25.747 24.233 21.112 21.697 21.163 21.262 21.242 20.682 21.288 21.460 22.586 21.263 30.798 29.987 26.955 28.867 28.236 28.238 29.296 28.007 31.527 28.449 32.107 32.664 32.313 32.237 32.335 31.873 32.375 32.366 33.712 32.348 4.09e-6 1.95e-2 2.39e-3 0.41 9.40 21.60 8.64 0.044 2.27 98.30 2.04e-6 1.12e-2 2.87e-2 0.79 5.72 7.69 8.56 4.70 4.03 140.00 10.3 1.90 24.00 3.07 1.12 1.20 1.12 16.20 0.57 1.21 6.26 1.36 17.20 1.24 1.59 1.41 0.51 2.13 8.86e-2 0.86 3.34 3.34 3.34 3.34 3.34 3.34 3.34 3.34 3.34 3.34 10.30 1.90 24.00 3.07 1.12 1.20 1.12 16.20 0.57 1.28 6.27 1.36 17.2 1.25 1.61 1.43 0.52 2.15 0.09 0.88 1.75 0.76 2.91 1.20 0.74 0.88 0.73 1.40 0.23 0.75 4.10 5.37 5.50 6.00 6.50 6.50 6.50 6.50 6.50 7.43 Gladys McCall O’Daniel #2 Pleasant Bayou #2 High Island A-9 #2 Huff A N. R. Smith #4 Pretts #1 A. E. Guerra #43 Maxus ZEE-6 Thompson Trustee #1
420.78 413.55 424.67 411.89 371.89 344.11 374.11 444.11 388.56 374.67
pIP FeT (M) CaT (M) PhnT (M) Fef (M) Caf (M) Phnf:Fe (M) Phnf:Ca (M) pKsp pIP pKsp (×10-4) (×10-2) (×10-6) (×10-4) (×10-2) (×10-13) (×10-14) Fe2.5HPhn Fe2.5HPhn Ca2.5HPhnb Ca2.5HPhn IS (M) pH well name
T (K) (bottom hole)
Table 2. Input Parameters for Solubility Simulationsa
pKsp Ca3Pc
pIP Ca3P
3702 Langmuir, Vol. 14, No. 13, 1998
Figure 5. The saturation index (SI) as a function of ionic strength for the wells listed in Table 2.
calcium-phosphonate salt would not precipitate in any of these wells. If the calcium salt has the Ca3NTMP stoichiometry, a precipitate is predicted to form in three of the wells, though the degree of saturation of Ca3NTMP is low relative to the saturation levels of ferrous phosphonate. A relationship among iron(II), calcium (from the Ca3NTMP, since this is the form predicted to precipitate in some of the wells), and phosphonate was established to predict the concentration of free iron in the water system:
KspFe KspCa
)
(Fe2+)2.5{H+}(Phn6-) (Ca2+)3(Phn6-)
therefore,
(Fe2+) )
( ) ( ) (Ca2+)3 {H+}
1/2.5
KspFe
KspCa
1/2.5
(7)
This equation is useful since the pH and calcium concentration are easily measured or calculated.18 Table 3 was constructed using the functional forms derived for the Ksp’s of Fe2.5HNTMP and Ca3NTMP, (Ca2+)f, and the pH for each well. The ratio of the free iron concentration calculated with the simulations to that calculated using eq 7 was within an order of magnitude for each well; the predicted concentration usually approaches the actual concentration as the pH is increased. The free (Fe2+) concentrations calculated with eq 7 can serve as a good estimate of actual downhole concentration and thus are useful in predetermining the appropriate concentration of phosphonate inhibitor required to prevent scale. Conclusions Ferrous phosphonate was formed under anoxic conditions, and its solubility was determined as a function of temperature and ionic strength. The precipitate, with a stoichiometry of Fe2.5HNTMP, may have interesting implications for the oil and gas industry regarding scale and corrosion control. Furthermore, a method of determining downhole free iron concentrations has been developed. Because of the solubility of the precipitates, it is apparent that indeed the ferrous iron in downhole environments may control the fate of squeezed inhibitors, (18) He, S. L.; Kan, A. T.; Tomson, M. B.; Oddo, J. E. A New Interactive Software for Scale Prediction, Control, and Management. SPE Paper 38801 presented at the 1997 SPE Annual Technical Conference and Exhibition, Oct 5-8.
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Table 3. Calculation of the Concentration of Free Iron in a System Containing Calcium, Ferrous Iron, and Phosphonatea pH
{H+} (×10-7)
(Ca2+)f (M) (×10-2)
KspFe (×10-33)
KspCa (×10-19)
(Fe2+)f,calc (M) (×10-4)
(Fe2+)f,meas (M) (×10-4)
ratio of (Fe2+)f,meas to (Fe2+)f,calc
4.10 5.37 5.50 6.00 6.50 6.50 6.50 6.50 6.50 7.43
794.0 42.7 31.6 10.0 3.16 3.16 3.16 3.16 3.16 0.4
10.30 1.90 24.00 3.07 1.12 1.20 1.12 16.2 0.57 1.21
7.81 2.17 4.86 5.79 4.62 13.40 4.22 4.30 0.19 4.49
2.12 0.73 1.56 1.73 2.27 8.36 2.05 0.99 0.13 2.14
0.121 0.047 1.130 0.156 0.061 0.060 0.061 2.030 0.020 0.158
6.26 1.36 17.20 1.24 1.59 1.41 0.51 2.13 0.09 0.86
51.7 28.9 15.2 7.9 26.1 23.5 8.4 1.1 4.5 5.4
a The value for (Fe2+) 2+ f,calc was calculated using eq 7; (Fe )f,meas is the concentration of free iron determined to be in the wells based on spreadsheet calculations using the input values for pH, total iron, and 1 mg/L phosphonate (NTMP).
especially phosphonates. That calcium phosphonates are believed to precipitate downhole in wells and have been the subject of many precipitation studies while Fe2+NTMP precipitation has not may be the result of the low initial concentrations of ferrous iron. Similarly, the large amount of total calcium found downhole may compensate for the slight degree of supersaturation for the Ca3NTMP solid and yield a large amount of calcium phosphonate precipitate. The data suggest that the potential for ferrous phosphonate to form is high and thus may be especially important in corrosion control where iron concentrations are considerably higher. Nonetheless, ferrous phospho-
nate precipitates may play an important role in scale inhibition as dictated by their solubility characteristics. Acknowledgment. This work was supported by members of the Rice University Brine Chemistry Consortium: Amoco, Aramco, Baker/Petrolite, Champion Technologies, Chevron, Conoco, Exxon, Shell, Texaco, and Unichem. The authors also acknowledge Milton Pierson, Department of Geology, Rice University, for his help with X-ray and electron microprobe analyses, and Lynn M. Frostman and Amal Al-Borno for their helpful discussions. LA971293L
