In this talk I extend the study of Heffter arrays and the biembedding of graphs on orientable surfaces, first discussed by D. Archdeacon in 2014. I begin with the definitions of Heffter systems and Heffter arrays and their relationship to orientable biembeddings through current graphs. I then focus on two specific cases. I first prove the existence of embeddings for every complete graph K_6n+1 in which every edge is on a face of size 3 and a face of size n. I next present partial results for biembedding K_10n+1 with every edge on a face of size 5 and a face of size n. Finally, I address the more general question of ordering subsets of Z_n \ {0}. I conclude with some open conjectures and further explorations.