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.　(C)　2018　Elsevier　B.V.　All　rights　reserved.