A numerical method for computing hydrometallurgical activity-activity diagrams

Kwadwo Asare Osseo-Asare, Thomas H. Brown

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


A modification of the DIAGRAM computer program has been developed to facilitate graphical representation of hydrometallurgical equilibria. The method is based on dissociation equations with corresponding log equilibrium constants, K i , and log reaction quotients, Q i ; K i equals Q i at equilibrium. The ith dissociation equation is written in terms of Q i , the log activity of the ith metallic species (P i ), and a certain set of variables (V j ), representing the log activities of species whose stability fields are not to be plotted (e.g., log{Me 2+ }, log{e}, log{H + }): Q i = B i P i + ∑ j=i nC ij V j where B i is the reaction coefficient of the ith metallic species in the ith dissociation equation, and C ij is the reaction coefficient of the jth variable in the ith dissociation equation. One of the variables is designated the balancing variable and allows comparison of the relative stability of any two metallic species to be made in terms of a single equation. By means of the balancing variable, the program generates internally the m(m-1)/2 relative stability equations linking pairs of the m metal-containing species. The stability region of each metallic species is then determined by a systematic scanning of the plotting area using the criterion (K L >Q L ?). DIAGRAM can calculate and plot stability diagrams using any two of the system variables. Thus not only Eh-pH diagrams, but additional plots of log {Metal}-pH, log{Metal}-Eh, log{NH 2 + NH 4 + }-pH, etc. can be generated readily. The numerical and thermodynamic bases of the program are described and the capability of DIAGRAM is illustrated with some selected hydrometallurgical examples.

Original languageEnglish (US)
Pages (from-to)217-232
Number of pages16
Issue number3
StatePublished - Jan 1 1979

All Science Journal Classification (ASJC) codes

  • Industrial and Manufacturing Engineering
  • Metals and Alloys
  • Materials Chemistry


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