Gradient-based algorithms are widely used in subsurface inverse problems to estimate unknown parameter fields. It requires the first derivatives (sensitivity coefficients) of the loss function with respect to the adjusted parameters. However, the relation between the unknown parameters and the observations is typically governed by partial differential and nonlinear algebraic equations which makes the gradient very expensive to compute for large-scale problems. This work presents an efficient and elegant approach based on the adjoint state to compute the gradient of the loss function. This approach is implemented in a reactive transport code HYTEC, which is based on a sequential iterative approach (SIA). By construction, solving the adjoint problem requires a corresponding SIA structure. Both spatial and time discretization methods should be considered. The discrete adjoint-state derivation accurately represents the gradient showing more consistent results than the continuous derivation. The developed approach is illustrated on a three-dimensional transient saturated flow-transport problem with mineral oxidative dissolution where observations are heads and concentrations. The adjusted parameters can be porosity, effective diffusion/dispersion coefficients, permeability, as well as species concentrations (mobile and immobile).