CORE{sup 2D} V4 is a finite element code for modeling partly or fully saturated water flow, heat transport and multicomponent reactive solute transport under both local chemical equilibrium and kinetic conditions. It can handle coupled microbial processes and geochemical reactions such as acid-base, aqueous complexation, redox, mineral dissolution/precipitation, gas dissolution/exsolution, ion exchange, sorption via linear and nonlinear isotherms, sorption via surface complexation. Hydraulic parameters may change due to mineral precipitation/dissolution reactions. Coupled transport and chemical equations are solved by using sequential iterative approaches. A sequential partly-iterative approach (SPIA) is presented which improves the accuracy of the traditional sequential noniterative approach (SNIA) and is more efficient than the general sequential iterative approach (SIA). While SNIA leads to a substantial saving of computing time, it introduces numerical errors which are especially large for cation exchange reactions. SPIA improves the efficiency of SIA because the iteration between transport and chemical equations is only performed in nodes with a large mass transfer between solid and liquid phases. The efficiency and accuracy of SPIA are compared to those of SIA and SNIA using synthetic examples and a case study of reactive transport through the Llobregat Delta aquitard in Spain. SPIA is found to be as accurate as SIA while requiring significantly less CPU time. In addition, SPIA is much more accurate than SNIA with only a minor increase in computing time. A further enhancement of the efficiency of SPIA is achieved by improving the efficiency of the Newton-Raphson method used for solving chemical equations. Such an improvement is obtained by working with increments of log-concentrations and ignoring the terms of the Jacobian matrix containing derivatives of activity coefficients. A proof is given for the symmetry and non-singularity of the Jacobian matrix. Numerical analyses performed with synthetic examples confirm that these modifications improve the efficiency and convergence of the iterative algorithm.