A method for the production of an additive for a high concentration carbonaceous solid-water slurry which comprises mixing a water soluble low molecular copolymer (a) made from 0.2 to 20 mol % of the nonionic monomer (A), 50 to 99.8 mol % of at least one anionic monomer (B), and 0 to 49.8 mol % of the other monomer (C), having a weight-average molecular weight in a range of from 1000 to 39,000, an adsorption ratio relative to carbonaceous solids in a range of from 5 to 50%, and an adsorption ratio relative to clayish mineral particles in a range of from 5 to 40% and a water soluble high molecular copolymer (b) made from 0.2 to 20 mol % of the nonionic monomer (A), 50 to 99.8 mol % of at least one anionic monomer (B), and 0 to 49.8 mol % of the other monomer (C), having a weight-average molecular weight in a range not less than 40000, an adsorption ratio relative to carbonaceous solids in a range not less than 50%, and an adsorption ratio relative to clayish mineral particles in a range not less than 40% at a weight ratio of copolymer (a)/copolymer(b), in the range of from 10/90 to 99/1 by weight, said low molecular copolymer (a) and said high molecular copolymer (b) severally being one or more members selected from the group of water-soluble copolymers obtained by polymerizing the monomer components,
- (A) from 0.2 to 20 mol % of a nonionic monomer represented by the formula (I):
- ##STR13## wherein R.sup.1 stands for --CH.sub.2 --, --(CH.sub.2).sub.2 --, --(CH.sub.2).sub.3 --, --C(CH.sub.3).sub.2 --, --CO--, or --CH.sub.2 CO--,
- A.sup.1, A.sup.2, and A.sup.3 independently stand for a hydrogen atom or a methyl group where R.sup.1 is --CH.sub.2 --, --(CH.sub.2).sub.2 --, --(CH.sub.2).sub.3 --, or --C(CH.sub.3).sub.2 -- or A.sup.1 and A.sup.2 independently stand for a hydrogen atom, a methyl group, or --COOX and A.sup.1 and A.sup.2 do not simultaneously stand for --COOX and A.sup.3 stands for a hydrogen atom, a methyl group, --COOX, or --CH.sub.2 COOX where R.sup.1 is CO or --CH.sub.2 CO and A.sup.1 and A.sup.2 independently stand for a hydrogen atom or a methyl group where A.sup.3 is --COOX or --CH.sub.2 COOX, wherein
- X stands for a hydrogen atom, an alkali metal atom, an alkaline earth metal atom, an ammonium group, or an organic amine group,
- R.sup.2 stands for an alkylene group of 2 to 4 carbon atoms,
- n stands for a number of an average in the range of from 1 to 100,
- R.sup.3 stands for an alkyl group of 1 to 30 carbon atoms, an alkenyl group, an aryl group, an aralkyl group, a cyclic alkyl group, or a cyclic alkenyl group, or a monovalent organic group derived from a heterocyclic compound,
- (B) from 50 to 99.8 mol % of at least one anionic monomer selected from the group consisting of (B-1) an unsaturated carboxylic acid monomer represented by the formula (II):
- ##STR14## wherein R.sup.4 and R.sup.5 independently stand for a hydrogen atom, a methyl group, or --COOM and R.sup.4 and R.sup.5 do not simultaneously stand for --COOM,
- R.sup.6 stands for a hydrogen atom, a methyl group, or --CH.sub.2 COOM, providing that R.sup.4 and
- R.sup.5 independently stand for a hydrogen atom or methyl group where R.sup.6 is --CH.sub.2 COOM, and
- M stands for a hydrogen atom, an alkali metal atom, an alkaline earth metal atom, an ammonium group, or an organic amine group and (B-2) a sulfoalkyl(meth)acrylate type monomer represented by the formula (III):
- ##STR15## wherein R.sup.7 stands for a hydrogen atom or a methyl group, Z stands for an alkylene group of 1 to 4 carbon atoms, and
- Y stands for a hydrogen atom, an alkali metal atom, an alkaline earth metal atom, an ammonium group, or an organic amine group, and
- (C) from 0 to 49.8 mol % of an other monomer copolymerizable with any of the monomers (A), (B-1) or (B-2)' selected from the group consisting of:
- methacrylic acid alkyl esters;
- vinyl sulfonic acid, styrene sulfonic acid, allyl sulfonic acid, methallyl sulfonic acid, and 2-acrylamide-2-methylpropane sulfonic acid, and the monovalent metal salts, divalent metal salts, ammonium salts, and organic amine salts of the said acids;
- hydroxyl group containing (meth)acrylates;
- (meth)acrylamides;
- styrene and p-methyl styrene;
- vinyl acetate, propenyl acetate, and vinyl chloride;
- and mixtures thereof,
- provided the total of the monomers of (A), (B-1), (B-2), and (C) is 100 mol %.