The kinetics of dilute-acid pretreatment/hydrolysis of the hemicellulose in a mixture of corn cobs and corn stover was investigated. The kinetic data confirmed that the hemicellulose in this feedstock is of a biphasic nature. The kinetic model recognizes the presence of soluble xylose oligomers, xylose monomer, and the decomposition of xylose. The kinetic parameters were determined over the conditions of 120-150 degrees C, and sulfuric acid concentration of 0.44-1.90%. The biphasic nature of the kinetics brings about an additional flexibility in the reactor design and the operation strategy, since different reaction conditions can be applied to each of the two different fractions of hemicellulose in the feedstock. With incorporation of the kinetic data, a percolation reactor operated under various modes, uniform temperature, temperature step change (along with or without flow rate step change), and two-stage reverse-flow operation, was modeled and investigated for its performance. The modeling results affirmed that a step-change/reverse-flow operation is advantageous for biphasic substrates, including agricultural residues. The optimum temperature difference in the step-change operation was determined to be 30 degrees C over a wide range of reaction temperature. Temperature step change alone (without use of reverse-flow mode) increased the product yield by 3-11% (depending on the reaction conditions) over that of uniform temperature operation. The most significant improvement, however, was seen with application of a two-stage reverse-flow reactor arrangement with temperature step change employing different conditions at each stage. This operation essentially doubled the sugar concentration over that of the temperature step change operation.