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Quark-hadron duality in the inclusive semileptonic decay $B\to X_c l\nu$ inthe Shifman-Voloshin limit $\Lambda \ll \delta m=m_b - m_c \ll m_b, m_c$ isstudied within a nonrelativistic potential model. The integrated semileptonicdecay rate is calculated in two ways: first, by constructing the OperatorProduct Expansion, and second by a direct summation of the exclusive channels.Sum rules (Bjorken, Voloshin, etc.) for the potential model are derived,providing a possibility to compare the two representations for $\Gamma(B\to X_cl\nu)$. An explicit difference between them referred to as duality-violationeffect is found. The origin of this effect is related to higher charmresonances which are kinematically forbidden in the decay process but arenevertheless picked up by the OPE.  Within the considered $1/m_c^2$ order the OPE and the sum over exclusivechannels match each other, up to the contributions of higher resonances, byvirtue of the sum rules. In particular this is true for the terms of order$\delta m^2/m_c^2$ and $\Lambda \delta m/m_c^2$ which are present in each ofthe decay channels and cancel in the sum of these channels due to the Bjorkenand Voloshin sum rules, respectively. The size of the duality violation effectsis estimated to be of the order $O(\Lambda^{2+b}/m_c^2\delta m^b)$ with $b>0$depending on the details of the potential. Constraints for a better accuracyare discussed.Comment: revtex, 19 pages, a comment on the OPE in the potential model has  been added and several typoes correcte

Semileptonic inclusive heavy meson decay: Duality in a nonrelativistic potential model in the Shifman-Voloshin limit