The solution of chemical process engineering problems often requires the repeated solution of large sparse linear systems of equations that have a highly asymmetric structure. The frontal method can be very efficient for solving such systems on modern computer architectures because, in the innermost loop of the computation, the method exploits dense linear algebra kernels, which are straightforward to vectorize and parallelize. However, unless the rows of the matrix can be ordered so that the frontsize is never very large, frontal methods can be uncompetitive with other sparse solution methods. We review a number of row ordering techniques that use a graph theoretical framework and, in particular, we show that a new class of methods that exploit the row graph of the matrix can be used to significantly reduce the front sizes and greatly enhance frontal solver performance. Comparative results on large-scale chemical process engineering matrices are presented.