Langmuir 1996, 12, 5231-5238
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Effect of Precipitating Conditions on the Formation of Calcium-HEDP Precipitates F. Henry Browning and H. Scott Fogler* Department of Chemical Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2136 Received April 5, 1996. In Final Form: August 13, 1996X Phosphonates are water treatment chemicals that are effectively utilized in many industrial processes as dispersants, bleaching agents, or scale and corrosion inhibitors. In many of these applications, the phosphonates are able to react with divalent cations such as calcium to form stable divalent cationphosphonate precipitates. The focus of this paper is to define the conditions under which distinct calciumphosphonate precipitates will form and to study how each of these precipitate’s unique chemical and physical properties govern the release of phosphonate from porous media. The phosphonate used in this study was (1-hydroxyethylidene)-1,1-diphosphonic acid (HEDP). By variation of the pH and calcium/ HEDP molar ratio in solution, two distinct precipitates were formed: (1) a soluble, fibrous 1:1 calcium/ HEDP precipitate; and (2) a less soluble, spherical 2:1 calcium/HEDP precipitate. Critical pH values that define the conditions under which each distinct precipitate forms were identified. Below the first critical pH value, the 1:1 precipitate formed, while above the second critical pH value, the 2:1 precipitate formed. Finally, coreflood and micromodel experiments showed that the release of 2:1 precipitate from porous media was significantly slower than that of 1:1 precipitate, suggesting that the 2:1 precipitate is better suited for phosphonate treatments in oil field applications. The release of a precipitate mixture (one which contains both distinct precipitates and has a calcium/HEDP molar ratio of 1.4:1) from a micromodel reconfirmed this phenomenon.
Introduction Phosphonates are threshold scale inhibitors that are commonly used to prevent undesirable solids from forming in industrial systems involving large quantities of highsalinity brine solutions. Phosphonates are advantageous in scale prevention treatments because they have the ability to inhibit many different types of scale and are stable over a wide range of conditions, i.e., temperatures and pressures.1-3 These advantages are evident when phosphonates are used to slow or completely prevent scale formation in petroleum production systems where scales and conditions may vary considerably from well to well. The injection of phosphonates into a reservoir to prevent scaling, commonly referred to as a “squeeze treatment”, can potentially lead to the mixing and precipitation of phosphonates with divalent cations (most likely calcium in carbonate reservoirs) contained in the formation. This precipitation process is, in many cases, desirable in oil field treatments because (1) a large volume of phosphonate can be retained in the formation after injection and (2) the dissolution kinetics are favorable in ensuring a slow release of phosphonate into the produced fluid. These resulting precipitation characteristics will, in turn, significantly enhance squeeze treatment lifetimes and improve treatment performance. Hence, with phosphonates and their precipitates playing such an important role in petroleum production systems as well as in other industrial operations, it becomes important to understand the precipitation mechanism of phosphonates with divalent cations and to identify the conditions which will result in the formation of divalent cation-phosphonate precipitates with different properties. Recently, research on the precipitation of calcium with diethylenetriaminepentakis* To whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, October 1, 1996. (1) Dequest 2010 Phosphonate; Monsanto Technical Bulletin; 1986; Publication 9024. (2) Nancollas, G. The Growth of Crystals in Solution. Adv. Colloid Interface Sci. 1979, 10, 215. (3) Hach Company report. Phosphonates; Hach Chemical Co.: Loveland, CO, 1980.
S0743-7463(96)00327-7 CCC: $12.00
(methlyenephosphonic acid) (DTPMP, a phosphonate containing five phosphate groups) has shown that between a pH of 4.0 and 5.5, three calcium cations attack and bond with DTPMP.4,5 In addition, the flow of freshwater over this amorphous, calcium-DTPMP precipitate resulted in the transformation to a more crystalline, less soluble precipitate. More recently, a systematic study identified the parameters that affect the resulting properties of calcium-HEDP (a phosphonate with two phosphate groups) precipitates.6 This research showed that two distinct calcium-HEDP precipitates could be formed under different precipitating conditions. The work presented here elucidates how different precipitating conditions affect the properties of calcium-HEDP precipitates. More specifically, the goals of this paper are to define the conditions under which different calcium-HEDP precipitates form and to delineate how different calciumHEDP precipitate properties can affect the release of HEDP in porous media, i.e., in oil field applications. Formation and Characterization of Distinct Calcium-HEDP Precipitates The general reaction mechanism of calcium with HEDP is shown in Figure 1. To form a stable calcium-HEDP precipitate, a calcium cation has to replace two hydrogens from the phosphonate molecule. Because the HEDP molecule has two phosphate groups (each containing two hydrogens), two distinct calcium-HEDP precipitates can form: (1) a calcium-HEDP precipitate having a calcium to HEDP molar ratio of 1:1, i.e., a 1:1 calcium-HEDP precipitate; or (2) a calcium-HEDP precipitate having a calcium to HEDP molar ratio of 2:1, i.e., a 2:1 calcium(4) Kan, A. T.; Oddo, J. E.; Tomson, M. B. Acid/Base and Metal Complex Solution Chemistry of the Polyphosphonate DTPMP vs. Temperature and Ionic Strength. Langmuir 1994, 10, 1442. (5) Kan, A. T.; Oddo, J. E.; Tomson, M. B. Formation of Two Calcium Diethylenetriaminepentakis (methylene phosphonic acid) Precipitates and Their Physical Chemical Properties. Langmuir 1994, 10, 1450. (6) Browning, F. H.; Fogler, H. S. Effect of Synthesis Parameters on the Resulting Properties of Calcium-Phosphonate Precipitates. Langmuir 1995, 11, 4143.
© 1996 American Chemical Society
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Figure 1. Precipitation reaction mechanism between calcium and phosphonate (HEDP).
HEDP precipitate. The proposed precipitate structures include five molecule rings, which are known to be extremely stable molecular structures.7 In addition to forming stable precipitates, HEDP has the ability to chelate calcium cations, resulting in the formation of soluble calcium-HEDP complexes.3,7 The resulting calcium-HEDP species that form are highly dependent upon the conditions under which the reaction takes place. The two parameters that have the most adverse effect on the precipitate properties are the pH of the precipitating solution and the calcium to HEDP molar ratio in the precipitating solution. Both parameters affect the extent of hydrogen deprotonation from the HEDP molecule which, in turn, affects the number of potential calcium bonding sites and the resulting precipitate composition. Solution conditions of low pH and small calcium to HEDP molar ratios limit the amount of hydrogen deprotonation from the HEDP molecules and increase the potential of forming precipitates that have a 1:1 calcium to HEDP molar ratio. Conversely, at precipitating conditions of high pH and large calcium/HEDP molar ratios, the amount of HEDP deprotonation increases and potentially results in the formation of precipitates with a 2:1 calcium/HEDP molar ratio. Materials and Experimental Procedures. To examine the effects that solution pH and calcium/HEDP molar ratio have on the resulting precipitate properties, batch synthesis experiments were performed at different conditions using the simple titration apparatus illustrated in Figure 2. The method for preparing precipitates was the same as that described previously.6 All titrations were carried out at 298 K, and a nitrogen gas blanket was maintained to minimize the effect of carbon dioxide. Each precipitate was formed by titrating a calcium solution with HEDP in 5 mL increments. In most of the experiments, concentrated sodium hydroxide was added to the precipitating solution to maintain the pH at the desired level; otherwise, the pH would decrease as the reaction proceeded. The resulting precipitates were filtered, washed with deionized water, and then characterized. Experimental Results and Discussion. Although titrations were carried out at many different conditions (7) Martell, A. E.; Calvin, M. Chemistry of the Metal Chelate Compounds; Prentice-Hall: Englewood Cliffs, NJ, 1956.
Figure 2. Schematic showing the apparatus used to synthesize calcium phosphonate precipitates.
(the pH was varied from 1.5 to 6.0 while the calcium to HEDP molar ratio in the precipitating solution was varied from 1:1 to 10:1), only two distinct precipitates were identified: a 1:1 calcium-HEDP precipitate that was comprised of polydispersed, fibrous spindles and a 2:1 calcium-HEDP precipitate consisting of powdery, spherical particles (see Figure 3). In addition to these distinct precipitates, two additional precipitates (with average calcium/HEDP molar ratios of 1.2:1 and 1.4:1, respectively) were formed. However, a micrograph of the 1.4:1 precipitate indicated that this precipitate was a mixture of the distinct 1:1 and 2:1 precipitates (see Figure 3). Further analysis of the two distinct precipitates, along with the precipitate mixtures, continued to show extreme differences in the resulting precipitate properties. Batch dissolution experiments performed with each of the precipitates indicated that the 1:1 precipitate dissolved much faster than the 2:1 precipitate while the 1.4:1 precipitate mixture dissolved at an intermediate rate (see Figure 4). The initial dissolution rates of the 1:1, 1.4:1, and 2:1 precipitates were 2.89, 2.01, and 0.414 mg/(h cm2), respectively, while the HEDP solubility levels were 1380, 760, and 12.2 ppm, respectively. In addition to the batch dissolution experiments, X-ray diffraction (XRD) measurements were taken for the precipitates, and the resulting patterns are shown in Figure 5. These XRD patterns illustrate two important points. First, the 1:1
Ca-HEDP Precipitates
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Figure 3. Morphological structures of distinct calcium-HEDP precipitates.
Figure 4. Coupled effects of solution pH and calcium/HEDP molar ratio on the resulting dissolution curves of calciumHEDP precipitates.
These results clearly show that the precipitation reaction between calcium and HEDP can form two distinct precipitates with significantly different physical and chemical properties. In addition, under certain precipitating conditions, it is also possible to form precipitates that are mixtures of these extreme precipitates. The differences between the precipitate properties (morphologies, dissolution rates) can play an important role in squeeze treatments where a slow release of phosphonate from porous media is desired. Previous experimental work has shown that the slow dissolving 2:1 precipitate can, in fact, enhance the shape of the elution curve and potentially enhance treatment lifetimes. However, to design more efficient squeeze treatments by inducing a desired precipitate into a porous medium (which will be discussed in a later section), it becomes extremely important to understand the underlying factors that govern the formation of each distinct precipitate and to define the precipitating conditions under which each will form. Defining the Precipitating Conditions for Each Distinct Precipitate
Figure 5. Effect of the calcium-HEDP molar composition on the resulting XRD patterns.
precipitate shows two distinct peaks, indicating that this precipitate is crystalline in nature while the 2:1 precipitate had no distinct peaks, signifying an amorphous precipitate. Second, when the XRD patterns are plotted as a function of the precipitate’s molar ratio (from 1:1 to 2:1), the XRD patterns evolve from having two large peaks at a 1:1 molar ratio to having two smaller peaks at a molar ratio of 1.4:1 to having no peaks at a 2:1 molar ratio, further verifying that each precipitate was a mixture of the 1:1 precipitate and the 2:1 precipitate.
The precipitation reaction between calcium and HEDP resulted in the formation of only two distinct precipitates, a soluble, fibrous 1:1 precipitate and an insoluble, spherical 2:1 precipitate. Considering the nature of the phosphonate (HEDP) under study, these results are not altogether surprising because HEDP has only two phosphate groups available to bond with calcium. Hence, by varying the precipitating conditions, the availability of these phosphate groups for calcium attachment can be altered, resulting in the formation of two distinct precipitates. Previous work showed that at the precipitating conditions of low pH and small calcium/HEDP molar ratios, the 1:1 precipitate is likely to form while at high pH and large calcium/HEDP molar ratios, the 2:1 precipitate is likely.6 However, to define the conditions under which each of the 1:1 and 2:1 precipitates, along with the precipitate mixtures, will form, a systematic set of batch synthesis experiments was performed at varying precipitating conditions. Two sets of titrations were performed. In the first set of titrations, the calcium to HEDP molar ratio in solution was held constant at 1:1 while the pH was varied from 1.5 to 6.0. In the second set of titrations, the calcium to HEDP molar ratio was maintained at 10:1 while the pH was varied from 1.5 to 6.0. In each titration at the desired pH value, concentrated NaOH or HCl was used to keep the pH constant while not appreciably diluting the solution. The calcium/HEDP molar ratio of the resulting precipitate is shown as a function of pH in Figure 6. At a calcium to HEDP molar ratio of 1:1 in solution, the precipitate’s calcium/HEDP molar ratio remains at approximately 1:1
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2Ca2+ + HEDP3- T Ca2HEDP + H+
(3)
while equilibrium constant is defined by the following equation
K2 )
aCa2HEDPaH+ )
2
a
Ca2+aHEDP3-
1 Ksp2
(4)
In addition to the two precipitation reactions, the following deprotonation reaction also occurs at these conditions
HEDP2- T HEDP3- + H+
(5)
where the equilibrium constant is expressed as Figure 6. Coupled effects of solution pH and calcium/HEDP molar ratio on the resulting precipitate’s molar composition.
until a pH of 4.7 is reached where it abruptly jumps to 2:1 and remains constant thereafter. In the series of titrations having a calcium to HEDP molar ratio of 10:1 in solution, the calcium/HEDP molar ratio remains essentially constant at 1:1 until the pH value reaches 3.9 where the precipitate ratio increases to 2:1 and stabilizes. A closer examination of Figure 6 reveals several interesting phenomena. First, it is obvious that every titration performed at constant pH resulted in the formation of one of the two distinct precipitates (1:1 or 2:1 precipitate) and not a mixture, indicating that at a given pH value, one precipitate is inherently more stable than the other. Second, the transition from formation of a 1:1 precipitate to a 2:1 precipitate occurred at a lower pH in the series of titrations having a solution molar ratio of 10:1 than in the series of titrations performed at a 1:1 calcium to HEDP molar ratio, signifying that the presence of excess calcium played an important role in determining which precipitate formed. Third, the shift in the resulting precipitate’s molar ratio from 1:1 to 2:1 occurred abruptly in each series of titrations, suggesting that in this short transition region, a drastic change in the system chemistry occurs. Finally, by simultaneously examining the results from each series of titrations, it becomes apparent that “critical pH values” can be identified and used to determine which distinct precipitate will form at a given set of conditions. Below the first critical pH value (∼3.9), all resulting precipitates will be 1:1 precipitates while above the second critical pH value (∼4.7), the resulting precipitates will be 2:1 precipitates. At pH values between these critical pH values, the molar ratio of the resulting precipitates depends upon the calcium to HEDP molar ratio in solution. To provide a clearer understanding of this phenomenon, the reactions that govern the formation of each distinct precipitate must be examined. At pH values where both the 1:1 and 2:1 calcium-HEDP precipitates are capable of forming, the precipitation reaction for the 1:1 precipitate can be written as
Ca2+ + HEDP2- T CaHEDP
(1)
while the equilibrium constant is expressed as,
K1 )
aCaHEDP 1 ) aCa2+aHEDP2- Ksp1
(2)
In a similar manner, assuming that the HEDP species has to deprotonate at least three hydrogens to form a 2:1 precipitate (which is consistent with experimental findings and will be discussed later), the precipitation reaction for the 2:1 precipitate can be written as
Ka3 )
aHEDP3-aH+ aHEDP2-
(6)
By coupling these equations together, a simple equilibrium expression relating the 1:1 and 2:1 precipitates can be written
Ca2+ + CaHEDP T 2H+ + Ca2HEDP
(7)
Assuming an activity of 1 for the solid precipitates, the equilibrium constant can be expressed as
K ) Ka3
K2 aH+2 Ksp1 ) ) Ka3 K1 aCa2+ Ksp2
(8)
To simplify this equation for the purpose of using easily measurable data in the discussion of the titration results, each solute’s activity was expressed as its molar concentration. It should be noted that at the experimental conditions, the use of mean activity coefficients to account for the nonidealistic behavior of electrolytic solutions would provide a better approximation for the calculation of the equilibrium constant (see below). In addition, it should also be noted that the calcium species in the expressions above represents the free calcium cations in solution. However, because HEDP has the potential to chelate free calcium, the addition of calcium to the solution will increase the amount of free calcium in the precipitating solution but not by as much as expected due to the chelation of some calcium cations. It is apparent from eqs 7 and 8 that an increase in the calcium concentration or a decrease in the hydrogen concentration (increase in the pH) will drive the equilibrium reaction to favor the formation of the 2:1 precipitate at the expense of the 1:1 precipitate. In each series of titrations (at 1:1 and at 10:1 calcium/HEDP ratios in solution), the transition point from a 1:1 precipitate to a 2:1 precipitate occurs when the precipitating solution’s [H+]2/[Ca2+] ratio is essentially equal to the equilibrium constant, K (the point where the direction of the equilibrium reaction shifts). At a calcium/HEDP molar ratio of 10:1 in solution, this transition point will occur at lower pH values (pH ∼3.9 for 10:1 ratio vs pH ∼4.7 for 1:1 ratio) because the free calcium concentration is greater than that in the 1:1 titrations. These transition points, in turn, are equivalent to the critical pH values that define the conditions under which each distinct precipitate forms. The magnitude of the [H+]2/[Ca2+] ratio in solution (experimentally determined to be 7.50 × 10-8 and 7.14 × 10-8 mol/dm3 at critical pH values of 3.9 and 4.7, respectively; the inclusion of mean activity coefficients in these calculations slightly improved the agreement) with respect to the equilibrium constant dictates which distinct
Ca-HEDP Precipitates
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Figure 8. Effect of calcium in solution on the resulting titration curves of HEDP. Figure 7. Effect of pH on the deprotonation of HEDP and the resulting species composition.
precipitate is more favorable, i.e., which reaction direction is dominant. Because the titrations were performed at constant pH, the magnitude of the [H+]2/[Ca2+] ratio relative to the equilibrium constant was maintained and resulted in the formation of one distinct precipitate at the expense of the other. The batch experiments suggested that this phenomenon was governed by the reaction kinetics and the initial relative amounts of each reactant. In addition, by knowing the initial and final amounts of calcium and HEDP present in a given precipitation reaction, along with the solubility limits for both the 1:1 and 2:1 calcium-HEDP precipitates, we were able to verify that only one distinct precipitate formed at constant pH as the reactants used to form one distinct precipitate left insufficient amounts of calcium and HEDP needed to form the other distinct precipitate, i.e. the final solution contents remained at saturation (or undersaturation) with respect to the precipitate not formed. In addition to the batch experiments that were performed at constant pH, two additional titrations were carried out by initially mixing the reactants at a pH of 6 and allowing the pH to vary during precipitation. The resulting molar compositions of the precipitates were 1.2:1 for the 1:1 calcium/HEDP solution and 1.4:1 for the 10:1 titration, while the final pH values in the two titrations were 3.97 and 3.62, respectively. These precipitate compositions indicate that the variable pH titrations provide the precipitating conditions necessary to form a mixture of the two distinct precipitates (see Figure 3). This observation is important because when precipitation occurs in-situ in porous media, the pH of the solution will change if no buffering agents are present, resulting in the formation of a mixture of the two distinct precipitates. Factors Governing the Formation of Calcium-HEDP Precipitates It is not surprising that both the solution pH and calcium/HEDP molar ratio affect the calcium-HEDP precipitate properties because changing these conditions can potentially alter the amount of HEDP deprotonation and, therefore, dictate the composition of the precipitate species. However, what is surprising is that the chemical compositions of the precipitates cannot be predicted solely from the reported HEDP pKa values (see Figure 1). This point can be clarified with the aid of Figure 7 where the fraction of each deprotonated HEDP species is shown as a function of solution pH. The pH where the fraction of two different deprotonated species is equal defines a pKa value. It is apparent from Figure 7 that at a pH of 5.5, all HEDP molecules have deprotonated two to three
hydrogens. The titration of calcium with HEDP (at both a 1:1 and 10:1 calcium/HEDP molar ratio) at pH 5.5, however, showed that a 2:1 calcium-HEDP precipitate formed, indicating that four hydrogens had deprotonated from each HEDP molecule. This phenomenon was observed in other experiments at different pH values as well. It is evident from these results and others that the presence of calcium enhances the ability of the HEDP molecule to deprotonate and subsequently precipitate. To better understand the effect that calcium cations have on the ability of HEDP to deprotonate, two standard titration curves were obtained, one by titrating an HEDP solution with sodium hydroxide and one by titrating an undersaturated 1:1 calcium-HEDP solution with sodium hydroxide. The resulting titration curves are shown in Figure 8. The pK3 value is equal to the pH where the inflection point of the titration curve occurs. The titration curve obtained with only HEDP reveals that the pK3 value was approximately 7, which is in good agreement with that determined from Figure 7 while the pK3 value in the 1:1 calcium-HEDP titration curve was approximately 6. This phenomenon, consistent with other work studying phosphonate titration curves, shows that the presence of calcium in solution effectively reduces the apparent pKa values by chelation reactions involving calcium and HEDP, resulting in a shift of the solution equilibrium.4,5,7-9 It is also likely that the stability of the calcium-HEDP precipitates relative to soluble calcium-HEDP chelates and the nonideality associated with electrolytic solutions enhanced the amount of HEDP deprotonation and subsequent precipitation. Finally, the reaction of calcium with HEDP to form a stable 2:1 precipitate seemed to occur only when the HEDP molecules had deprotonated at least three hydrogens. This observation is most likely due to the fact that HEDP molecules having one or two deprotonated hydrogens inherently favor the formation of a 1:1 calcium/HEDP precipitate. Precipitate Performance in Porous Media As previously mentioned, the use of phosphonates to prevent scale formation in petroleum production systems is one of the most important industrial applications for phosphonates. Previous research has shown that the placement of phosphonate into porous media by precipitation has proven extremely efficient in providing long (8) Cilley, W. A. Grabenstetter, R. J. Complexation Between Ca++and Ethane-1-Hydroxy-1,1-Diphosphonic Acid. J. Phys. Chem. 1971, 75 (5), 676. (9) Grabenstetter, R. J.; Quimby, O. T.; Flautt, T. J. The Acid Dissociation Constants of Substiuted Methanediphosphonic Acids: A Correlation with P31 Magnetic Resonance Chemical Shift and with Taft σ*. J. Phys. Chem. 1967, 71 (13), 4194.
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Figure 9. Schematic showing the apparatus used to test the performance of precipitates in consolidated porous media (coreflood apparatus).
treatment lifetimes and ensuring successful scale inhibition in oil fields.10,11 Having defined the conditions under which each distinct precipitate will form, we will now examine how the unique chemical and physical properties of the 1:1 and 2:1 precipitates govern the release of HEDP from porous media. Experimental Apparatus and Procedure. To study the performance of calcium-HEDP precipitates in porous media, both coreflood experiments and micromodel experiments were performed. A schematic of the experimental apparatus used for the coreflood experiments is shown in Figure 9. One inch diameter, three inch long ceramic cores (K ∼ 33 mD, porosity ∼ 40%) were placed in a Hassler cell where an overburden pressure was applied. Ceramic cores are relatively clean, inert cores comprised of silicon dioxide and aluminum oxide, making them ideal for fundamental studies. Fluid (DI water or phosphonate solutions) was passed through the core using a constant volumetric flow rate FDS-210 pump. When any solution other than DI water was pumped into the core, an accumulator was placed in-line with the system to hold the desired solution. Pressure taps were placed at various positions down the length of the core for pressure measurements: at the core inlet, 0.5 in. into the core, and 1.5 in. into the core. A 0.22 µm filter was placed in-line with the entering fluid to collect any foreign particles. The effluent was collected and analyzed for phosphonate using the Hach technique.3 The procedure for precipitation coreflood experiments was similar to that used in an actual reservoir system. First, a supersaturated calcium-HEDP solution was passed through the core until the core became saturated. This placement procedure was possible due to the induction period (1-2 h) before the onset of precipitation in the supersaturated solutions. The solution was then shutinto the core for approximately 24 h, allowing in-situ precipitation to occur. After the shut-in period, the core was eluted with deionized water and effluent samples were collected and analyzed to obtain an elution curve. During elution, pressure readings were recorded to monitor the extent of formation damage (if any) throughout the course of the experiment. Performance Comparison of Distinct Precipitates in Ceramic Cores. Previous studies in micromodels comparing precipitate performance showed that the release of 2:1 precipitate was governed by hydrodynamic dissolution of the spherical particles while the release of 1:1 precipitate was dictated by both hydrodynamic and (10) Carlberg, B. L. Scale Inhibitor Precipitation Squeeze for NonCarbonate Reservoirs. Paper SPE 17008 presented at the Production Technology Symposium, Lubbock, TX, November 1987. (11) Bellasol S29-Phosphorous-Containing Polymeric Scale Inhibitor; Ciba-Geigy Corp.: Hawthorne, NY, 1989.
Figure 10. Effect of precipitate type of the release of HEDP from ceramic cores.
diffusion-controlled dissolution.6 The coreflood experiments, however, provide a more realistic representation of consolidated porous media with which to compare the performance of the two distinct precipitates. Using the precipitating conditions previously described, each of the two distinct precipitates were induced into ceramic cores and eluted with deionized water at pH 6.5. The resulting elution curves are shown in Figure 10. It is apparent from these two curves that the shapes differ considerably. The initial release of HEDP from the coreflood performed with 1:1 precipitate was significantly greater than that in the 2:1 precipitate coreflood, subsequently resulting in a steadier decline in the effluent phosphonate concentration and faster depletion of the precipitate. These results were similar to those obtained from micromodel experiments and were somewhat expected considering the fact that the equilibrium solubility level of the 1:1 precipitate is 2 orders of magnitude higher than that for the 2:1 precipitate, resulting in a faster dissolution of HEDP from porous media. These observations show that because the 2:1 precipitate offers a slower release of HEDP from porous media, this precipitate may be better suited for phosphonate treatments in oil field applications. And knowing the conditions under which this precipitate forms (as defined earlier) will enable oil producers to induce this desirable precipitate into porous media and further enhance phosphonate treatments in petroleum production systems. Release of Mixed Precipitates from Micromodels. In oil field applications where precipitation occurs in-situ in porous media and buffering agents are not present, the pH changes when the precipitation of calcium with HEDP occurs (as in variable pH batch experiments). Hence, a study of how precipitates formed under variable pH are released from porous media is applicable to phosphonate treatments in many reservoirs.
Ca-HEDP Precipitates
Figure 11. Effect of a precipitate’s molar composition on the release of HEDP from a micromodel.
Micromodel experiments were used to study the performance of precipitates formed at variable pH. Micromodels offer the advantage that the release of HEDP precipitates can be visually observed. The experimental setup is described in a previous paper, and the procedure used to perform these experiments is essentially the same as that used in the coreflood experiments.6 Precipitate placement was performed by injecting a 10:1 calcium/HEDP solution at pH 6.0 into the micromodel where in-situ precipitation occurred. Note that the precipitating conditions are exactly those used to form a 1.4:1 precipitate mixture at variable pH above (see Figure 3). The micromodel was then eluted with deionized water at a flow rate of 0.05 cm3/min and an elution curve was generated by analyzing effluent samples for HEDP concentration. A comparison of this elution curve with those previously obtained from the 1:1 precipitate and 2:1 precipitate, respectively, is illustrated in Figure 11. This figure shows that the elution curve resulting from the
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variable pH precipitate dissolution lies between those obtained from the two distinct precipitates, indicating that this curve has dissolution characteristics of each precipitate. This observation becomes more apparent when time lapse photographs from the micromodel are studied. The initial precipitate region under study contains both the 1:1 fibrous precipitate and the 2:1 spherical precipitate, as shown in Figure 12. After the elution was begun, the time lapse photographs in Figure 12 show that all of the 1:1 precipitate dissolves quickly while the 2:1 precipitate remains, seemingly unaffected. Hence, the initial shape of the elution curve was governed by 1:1 precipitate dissolution while the subsequent long tail results from dissolution of the 2:1 precipitate. Factors Affecting the Dissolution Rates of Each Distinct Precipitate. The time lapse micromodel photographs illustrating the release of a 1.4:1 precipitate mixture clearly show that the 1:1 precipitate dissolves much more rapidly than the 2:1 precipitate. The difference in the HEDP solubility limit between the distinct precipitates helps to explain why the 1:1 precipitate dissolves faster than the 2:1 precipitate. Because the solubility limit for the 1:1 precipitate (1380 ppm) was experimentally determined to be 2 orders of magnitude greater than that for the 2:1 precipitate (12.2 ppm), the concentration driving force between the surface and bulk solution, (Cs-C), was also 2 orders of magnitude greater, resulting in faster precipitate dissolution rates. The reason why the 1:1 precipitate has a higher solubility limit than the 2:1 precipitate, in turn, is related to the molecular structure of each precipitate. The molecular structure of the 1:1 precipitate potentially contains one stable five molecule ring and two hydroxide groups while the 2:1 molecular structure potentially contains two stable five molecule rings with no hydroxide groups (see Figure 1). The fact that the 2:1 precipitate has two highly stable five molecule rings (as opposed to
Figure 12. Sequential release of 1.4:1 calcium-HEDP precipitate from a micromodel.
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one five molecule ring in the 1:1 precipitate) increases the stability of its molecule structure which, in turn, will decrease its solubility in an aqueous media.7 In addition, the solubility of a metal chelate is dependent upon the hydrophilicity of its side groups present in its molecular structure.7,12 The 1:1 precipitate contains two hydroxide groups that are extremely hydrophilic while the 2:1 precipitate replaced its hydroxide groups with a stable five molecule ring containing calcium, further suggesting that the 2:1 precipitate is less soluble than the 1:1 precipitate. However, a more complete investigation of the molecular structures of the two precipitates needs to be performed in order to verify these hypotheses. Conclusions 1. The reaction of calcium with HEDP can form two distinct precipitates: a soluble 1:1 calcium-HEDP precipitate that is comprised of fibrous spindles and an insoluble 2:1 calcium-HEDP precipitate that is made up of spherical particles. In addition, at conditions of varying pH, mixtures of the two distinct precipitates are capable of forming. 2. SEM photographs and XRD measurements of calcium-HEDP precipitates revealed that 1:1 calciumHEDP precipitates were crystalline in nature while the 2:1 calcium-HEDP precipitates were amorphous rather than crystalline. (12) Martell, A. E.; Motekaitis, R. J. Determination and Use of Stability Constants; VCH Publishing: New York, 1992.
Browning and Fogler
3. The formation of calcium-HEDP precipitates at different (but constant) pH values and calcium/HEDP molar ratios indicate that “critical” pH values exist that define the conditions in which each distinct precipitate can form. At a calcium to HEDP molar ratio of 1:1, the critical pH value was determined to be approximately 4.7 while in the series of titrations carried out at a molar ratio of 10:1, the critical pH value was found to be approximately 3.9. 4. Standard acid-base titrations with HEDP showed that the presence of calcium significantly alters the resulting titration curve by reducing the effective pKa value of the third deprotonating hydrogen. 5. The releases of 1:1 and 2:1 calcium-HEDP precipitates from ceramic cores differ significantly. The 1:1 precipitate dissolves much faster than the 2:1 precipitate. 6. The release of a precipitate mixture containing both 1:1 and 2:1 calcium-HEDP from a micromodel showed that the resulting elution curve fell between those of the 1:1 and 2:1 precipitates. This phenomenon was due, in large part, to the fast initial dissolution of the 1:1 precipitate followed by the slow 2:1 precipitate dissolution. Acknowledgment. The authors recognize Michelle Moceri for her significant contribution in obtaining the experimental data as she performed many of the experiments. We thank the Industrial Affiliates Program at the University of Michigan for their financial support. LA9603277
