Field　experiments　of　solute　transport　through　heterogeneous　porous　and　fractured　media　show　that　the　growth　of　contaminant　plumes　may　convert　between　diffusive　states.　In　this　paper,　we　propose　a　multi-term　time–space　variable-order　fractional　advection–diffusion　model　(MTT-SVO-FADM)　to　describe　the　underlying　transport　dynamics.　We　consider　a　numerical　approach　based　on　the　implicit　numerical　method　for　numerical　solution　of　this　model.　A　fully-discrete　numerical　scheme　is　developed　by　using　the　classical　finite　difference　method.　The　unconditional　stability　and　convergence　of　the　scheme　are　discussed　and　theoretically　proved.　We　use　a　modified　grid　approximation　method　(MGAM)　to　estimate　the　model＇s　parameters.　The　MTT-SVO-FADM　is　then　applied　to　describe　transient　dispersion　observed　at　a　field　tracer　test　and　four　numerical　experiments.　The　results　show　that　this　model　can　simulate　the　experimental　data　more　accurately　and　can　efficiently　quantify　these　transitions.　©　2018　Elsevier　B.V.