4.1. Overview of Previously Reported Gel Dynamics
To test if these sol-gel transitions can be utilized in the oil field, these functional dynamics were tested at temperatures up to 150 °C and pressures up to 60 MPa. As expected, a rise in temperature leads to a faster rate of gelation for the PHT system, as described in Table 1
. Three 65—5 liquid samples were tested in a Grace M5600, where pressure was maintained at 3.4 MPa and the system was heated to varying temperatures. The data presented in Figure 1
are from small amplitude oscillatory shear experiments, where G’ is the elastic modulus of the materials tested and G” is the viscous modulus. The cross-over points of G’ and G” depict the sol-gel transition. For this 65—5 gel, we see the sol-gel transition times decrease with increasing temperature. At 70, 100, and 150 °C, the sol-gel transitions occur at 350, 200, and 50 min, respectively. The transformation occurring at temperatures up to 150 °C indicates, in part, the suitability for this chemical system under higher temperature wellbore situations.
The 65—5 system was also tested for its sol-gel transition under much higher pressures with rotational rheology, further simulating some of the more extreme conditions found in the oil field. While holding the temperature steady at 70 °C, the 65—5 liquid is pressurized to 20, 35, and 60 MPa and monitored for when the sol-gel transition occurs under rotational shear, as seen in Figure 2
. When the pressure of system is increased while holding temperature constant, the sol-gel transition time of the 65—5 system decreases to 390, 270, and 140 min, respectively. This indicates that pressure has a direct effect on the kinetics of the 65—5 sol-gel transition and accelerates the system towards the condensation pathway of increasingly branched hemiaminal and aminal condensation products. The unique property of the PHT system to make these sol-gel transitions at a wide range of temperatures and pressures shows its versatility for use in oil well completion projects.
4.2. PHT Breakdown with Water
A distinct advantage to using this constitutionally dynamic gel system lies in its reversibility and the ability to remove said gel from wherever it is being placed via a “triggered release”. We previously reported that a PHT gel formed with our original 65—5 formula could “break” under elevated temperatures and pressures using phosphine. However, a more environmentally friendly and easier to use agent for breaking can be achieved by replacing the high molecular weight PPG triamine in the original 65—5 formulation for a smaller weight PEG diamine.
The reversibility of PEG amine PHTs, as compared with PPG amine PHTs, is notably similar in these condensation polymers with the large exception of water being used as a breaker. This is largely because of the high solubility of the 900 Da PEG diamine and the poor solubility of 5 kDa PPG triamine in water. When water is added to an PHT gel of PEG diamine, the system reverts to liquid within minutes. On the other hand, the PPG triamine remains unchanged in the presence of the same quantity of water. The most effective way to revert the PHT gel of the PPG triamine was found to be through the use of a saturated solution (10% wt) of phosphine in NMP, in this case (tris(2-carboxyethyl)phosphine).
4.3. Thermal Stability of PHT
We have previously reported the addition of trivalent metal salts (FeCl3
) gives us the lowest energy and most stabilized products in our PHT scheme, either overtime or in the presence of heat. This led us to evaluate what other metal salts could further stabilize this scheme and to what extent. To evaluate the limits of the thermal stabilities of the HT gels, we assayed a variety of different salts to observe how the salt systems may influence the gel stabilities. A summary of gel thermal stabilities is presented in Table 5
The salts tested are often used in completion brines for such purposes as density adjustment. Interestingly, the various salts influence thermal stability of the gels differently. From our investigations of aluminium chloride, calcium halides, zinc bromide, cesium salts, and sodium bromide, we found that the greatest stability was observed in the case of sodium bromide. In all cases, the gels display superior temperature stability when salt is a component to their compositions. The trend observed is that thermal stability increases from higher (M(III)) to lower oxidation state (M(I)) metal salts (where M is the abbreviation for the metal) and from smaller anions (Cl−) to larger anions (Br−).
4.4. Kinetics with Al(III)
NMR studies of model systems of the dynamic aminal junction in the polymer network reveal the effect of reaction rate enhancement in the presence of aluminium. NMR spectra for these studies are presented in Figure 3
and in the supporting information in Figures S2 through S7
. Because of the apparent lability of the various intermediates in the condensation pathway, with lower molecular weight amines (such as the butyl amine studied in this model), the temperature under which the experiment was monitored was lowered to −25 and 0 °C.
At −25 °C, the species in the system without aluminium remain static. However, the addition of aluminium to this system at this temperature affords us a transformation of these species. It is not until raising the temperature of the system up to 0 °C when we begin to see transformation of species in the system without aluminium. Figure 3
a shows the spectral region from 4.92 ppm to 4.72 ppm. 1
H NMR peaks in these regions in a similar model system (with polypropylene glycol amine in place of the butylamine used here) have been previously correlated to R–NH–CH2
–OH functionalities. These transformations occur over approximately 30 min at 0 °C. The depletion of these peaks indicates the conversion of hemiaminal in to aminal (hexahydrotriazine) [11
]. Figure 3
b shows the spectral region from 4.93 to 4.69 ppm where the R–NH–CH2
–OH functionalities of the aluminium catalysed system deplete over 3 h at −25 °C. The depletion of these peaks also indicates the conversion of hemiaminal in to aminal (hexahydrotriazine), but at a lower temperature than the sample without aluminium. In both cases, the temperature was subsequently raised to 0 °C. At this temperature, the aluminium catalysed system displayed relatively little change, whereas the system without aluminium began to evolve new species corresponding to intermediates along the condensation pathway including the final HT product.
4.5. Computational Analysis
The original mechanism of hemi-aminal gel formation proposed by Jones and co-workers [15
] is shown in Scheme 5
with the reaction of methylamine and formaldehyde (R = CH3
). In the Jones mechanism, the rate-determining step (RDS) is described as a concerted loss of water in conjunction with ring formation. The L intermediate (same as in Scheme 2
) is considered in the presence of two explicit water molecules that form a hydrogen bonding network linking the hydroxy group at one end and the secondary amine at the other in a pre-activated conformation readied for cyclization. This network facilitates the loss of water by stabilizing the forming charge of the displacing hydroxide anion during cyclization to form water. Two hydrogen bonds support this anion, while simultaneously removing the proton on the secondary amine that is involved in the ring formation to give the final product, N. This transformation proceeds through a concerted transition-state (TS), [L-N].
Starting from the optimized structure published by Jones (B3LYP), we re-optimized at the B3LYP/6-31+g(d) structural level. We note that Jones’ approach and ours differs only in the use of COSMO in this work compared with the alternative solvent model PCM. We have found that while the proposed transition-state can be localized, our interpretation of its nature is quite different. In examining the imaginary frequency, we find that only small displacements corresponding to ring formation are present, and thus the transition-state proposed in Scheme 4
is not a clean cyclization, as it expresses severe asynchronicity. The transition-state we optimized is dominated by the water loss vibrations with small coupled movements representing ring formation. We also performed a full optimization and frequency analysis including COSMO at each interaction to verify our results, yielding no significant difference in outcome. Thus, we propose the transition-state structure above, [L-M]—(H2
, giving intermediate M—(OH)(H2
is an iminium intermediate stabilized by an internal hydrogen bond, which is thus only slightly endergonic (1.4 kcal/mol) and is obtained through a barrier higher compared with Jones (27.2) at 34.0 kcal/mol. Barriers are determined using the M06-2x/6-31+g(d) single-point with COSMO solvation in water. Furthermore, the subsequent ring closure transition-state was localized [M-N]—(OH)(H2
(small imaginary frequency ca. −80 cm−1
) having a slightly lower barrier relative to the M—(OH)(H2
at 32.0 kcal/mol. Thus, the RDS for the, now stepwise, reaction remains the water loss step, but the ring closure step has been decoupled. This is important for understanding the Al catalysed process. Key structures are presented in Figure 4
In the presence of aluminium, the mechanism alters significantly. The full mechanism is shown in Scheme 6
In this mechanism, the water molecules are effectively replaced by an aluminium atom coordinated to three water molecules. L—Al(H2
is a tridentate complex involving two coordinative bonds from the nitrogen atoms and one coordinative bond from the hydroxyl group. The distal nature of the water molecules hinders their direct involvement in the transition-state as part of a hydrogen bonding network (as above). It was not possible to locate the transition-state [L-N]—Al(H2
leading directly, in a concerted fashion, to the final product in analogy to the Jones mechanism. In the absence of such a TS, we looked extensively for the TS [L-M]—Al(H2
that would represent loss of hydroxyl with the formation of an aluminium hydroxide, this hydroxyl migration process appears to be barrierless at this level of theory. Thus, we believe M—Al(OH)(H2
to be in equilibrium and in roughly equal amounts. Interestingly, the product expresses also a strong hydrogen bond between the iminium methylene group and the aluminium hydroxide group (see Figure 5
When aluminium is present, the RDS now becomes the ring closure step [M-N]—Al(OH)(H2O)3 with a barrier of 22.0 kcal/mol. Thus, aluminium acts as a catalyst with respect to the metal-free process. It should also be noted that the overall process is considerably more exothermic at −14.1 kcal/mol compared with −1.7 kcal/mol for the metal-free.