*3.2.3 Cross-linked phosphate esters*

Several studies report the attempts made to gel light hydrocarbon gas (LPG) using phosphorus-based esters cross-linked with polyvalent metal ions (**Figure 10**) for dry hydraulic fracturing applications [90, 92–95]. These techniques use phosphate mono-/diesters linked to alkyl tails. Typically, a hydrocarbon liquid agent solution is formed by combining two low-viscosity liquid reactants (i.e. a solution containing the phosphate ester and one containing a polyvalent metal ion crosslinking agent) together in the fluid that is being thickened. The two low-viscosity liquids quickly dissolve in the hydrocarbon fluid (e.g. light alkane) without the need of heating and/or cooling cycles. The polyvalent metal ion bound more tightly to phosphate esters than to the ligand, which leads the phosphate ester to quickly chelate with metal ion and form long micellar and a supramolecular structure as shown in **Figure 11**. If this long micellar structure remains soluble in the solvent, then it can significantly improve the solution viscosity. Rapid dissolution of the phosphate ester system in the solvent and the rapid viscosity enhancement kinetics could make these molecular structures attractive for use with NGL in EOR applications [88, 89].

There are a few studies reporting the use of oil-soluble phosphate mono-/ diesters, dialkyl phosphinic acids, or alkyl phosphonic acid ester cross-linked with polyvalent metal ions including Fe3+, Mg2+, Al3+, Zn2+, and Ti4+ at concentrations of 0.2–2.5 wt% to increase the viscosity of hydrocarbon oils (e.g. diesel and kerosene) by 2–100-fold [93, 94, 97]. Furthermore, phosphate-based esters could be used as gel agents for CO2 and hydrocarbon liquid mixtures [98, 99]. Lee and Dhuwe et al. [82, 88, 89] studied blends of cross-linked phosphate esters (CPE) (phosphate ester (HGA 70-C6) and cross-linker (HGA 65)) with NGL components (ethane, propane, and butane) at temperatures ranging from 298 to 373 K and pressures ranging from 13.8 to 62 MPa. They found that phosphate ester and the cross-linked solution are soluble in ethane, propane, and butane at concentrations of 0.25–1 wt% and temperatures of 298–333 K. However, the cross-linked solution was slightly hazy due to small droplets of CPE suspended in the solution. This mixture (phosphate ester + cross-linker) achieved a modest viscosity increase in ethane, while greater increases occurred in propane and butane. For example, at a concentration of 1 wt% at 333 K and 20.68 MPa, the viscosity of ethane increased by a factor of 1.45-fold, and the viscosity of propane and butane increased by 2.6- and 3.2-fold, respectively. This mixture cannot form a single phase in the NGL components due to the suspension of very small droplets of CPE in the solution and because its suitability for injection into porous media is limited [88] (**Table 2**).
