A method for separating oil and water phases of an oil-water dispersion or emulsion derived from petroleum industry operations, comprising providing to the oil-water emulsion 1 to 10,000 ppm of an anionic polymer comprising: A) 15-80 % by weight of at least one C 3 -C 8 α,β-ethylenically unsaturated carboxylic acid monomer of the formula: where R is H, and R' is H, C 1 -C 4 alkyl, or --CH 2 COOX; R is --COOX and R' is H or --CH 2 COOX; or R is CH 3 and R' is H; and X is H or C 1 -C 4 alkyl; B) 15-80 % by weight of at least one nonionic, copolymerizable α,β-ethylenically unsaturated monomer of the formula: CH 2 =CYZ where Y is H and Z is --COOR, --C 6 H 4 R', CN, Cl, or -CH=CH 2; Y is CH 3 and Z is --COOR, --C 6 H 4 R', CN or -CH=CH 2; or Y and Z are Cl; and R is C 1 -C 8 alkyl or C 2 -C 8 hydroxyalkyl; R' is H, Cl, Br, or C 1 -C 3 alkyl; and R" is C 1 -C 8 alkyl; C) 1-50% by weight of one or more of the following monomers: at least one nonionic vinyl surfactant ester of the formula: where R is H or CH 3, each R' is C 1 -C 4 alkyl, R" is C 8 -C 20 alkyl or C 8 -C 16 alkylphenyl, n is an average number from 6-100, and m is an average number from 0-50 provided that n≥m and (n+m) is 6-100; and at least one nonionic, copolymerizable α,β-ethylenically unsaturated monomer having longer polymer chains than monomer B) and selected from lauryl methacrylate, stearyl methacrylate, ethylhexyl methacrylate, cinnamyl methacrylate, oleyl methacrylate, ricinoleyl methacrylate, t-butylstyrene, vinyl decanoate, vinyl stearate, vinyl laurate, vinyl oleate, vinyl iso-octyl ether, vinyl β-naphthyl ether, and combinations thereof; and at least one nonionic urethane monomer which is the urethane reaction product of a monohydric non-ionic surfactant with a monoethylenically unsaturated monoisocyanate; and D) 0-5 % by weight of at least one crosslinker, wherein all weight percents total 100 percent and are based on the total weight of the anionic polymer. A) 15-80 % by weight of at least one C 3 -C 8 α,β-ethylenically unsaturated carboxylic acid monomer of the formula: where R is H, and R' is H, C 1 -C 4 alkyl, or --CH 2 COOX; R is --COOX and R' is H or --CH 2 COOX; or R is CH 3 and R' is H; and X is H or C 1 -C 4 alkyl; where R is H, and R' is H, C 1 -C 4 alkyl, or --CH 2 COOX; R is --COOX and R' is H or --CH 2 COOX; or R is CH 3 and R' is H; and X is H or C 1 -C 4 alkyl; B) 15-80 % by weight of at least one nonionic, copolymerizable α,β-ethylenically unsaturated monomer of the formula: CH 2 =CYZ where Y is H and Z is --COOR, --C 6 H 4 R', CN, Cl, or -CH=CH 2; Y is CH 3 and Z is --COOR, --C 6 H 4 R', CN or -CH=CH 2; or Y and Z are Cl; and R is C 1 -C 8 alkyl or C 2 -C 8 hydroxyalkyl; R' is H, Cl, Br, or C 1 -C 3 alkyl; and R" is C 1 -C 8 alkyl; Y is H and Z is --COOR, --C 6 H 4 R', CN, Cl, or -CH=CH 2; Y is CH 3 and Z is --COOR, --C 6 H 4 R', CN or -CH=CH 2; or Y and Z are Cl; and R is C 1 -C 8 alkyl or C 2 -C 8 hydroxyalkyl; R' is H, Cl, Br, or C 1 -C 3 alkyl; and R" is C 1 -C 8 alkyl; C) 1-50% by weight of one or more of the following monomers: at least one nonionic vinyl surfactant ester of the formula: where R is H or CH 3, each R' is C 1 -C 4 alkyl, R" is C 8 -C 20 alkyl or C 8 -C 16 alkylphenyl, n is an average number from 6-100, and m is an average number from 0-50 provided that n≥m and (n+m) is 6-100; and at least one nonionic, copolymerizable α,β-ethylenically unsaturated monomer having longer polymer chains than monomer B) and selected from lauryl methacrylate, stearyl methacrylate, ethylhexyl methacrylate, cinnamyl methacrylate, oleyl methacrylate, ricinoleyl methacrylate, t-butylstyrene, vinyl decanoate, vinyl stearate, vinyl laurate, vinyl oleate, vinyl iso-octyl ether, vinyl β-naphthyl ether, and combinations thereof; and at least one nonionic urethane monomer which is the urethane reaction product of a monohydric non-ionic surfactant with a monoethylenically unsaturated monoisocyanate; and at least one nonionic vinyl surfactant ester of the formula: where R is H or CH 3, each R' is C 1 -C 4 alkyl, R" is C 8 -C 20 alkyl or C 8 -C 16 alkylphenyl, n is an average number from 6-100, and m is an average number from 0-50 provided that n≥m and (n+m) is 6-100; and R is H or CH 3, each R' is C 1 -C 4 alkyl, R" is C 8 -C 20 alkyl or C 8 -C 16 alkylphenyl, n is an average number from 6-100, and m is an average number from 0-50 provided that n≥m and (n+m) is 6-100; and at least one nonionic, copolymerizable α,β-ethylenically unsaturated monomer having longer polymer chains than monomer B) and selected from lauryl methacrylate, stearyl methacrylate, ethylhexyl methacrylate, cinnamyl methacrylate, oleyl methacrylate, ricinoleyl methacrylate, t-butylstyrene, vinyl decanoate, vinyl stearate, vinyl laurate, vinyl oleate, vinyl iso-octyl ether, vinyl β-naphthyl ether, and combinations thereof; and at least one nonionic urethane monomer which is the urethane reaction product of a monohydric non-ionic surfactant with a monoethylenically unsaturated monoisocyanate; and D) 0-5 % by weight of at least one crosslinker, wherein all weight percents total 100 percent and are based on the total weight of the anionic polymer.