Mixing ratios of sublimating gases from ices in porous bodies in the solar system are important, observable phenomena. Surface erosion and dust build-up on a comet nucleus and coma formation are processes attributable to the flux of sublimating gases. Our computer simulations focus on the gas flux from volatile, icy components in the surface layer of a porous, Jupiter-family comet in order to relate quantitatively the observed relative molecular abundances in the coma with those in the nucleus. We assume a porous body containing dust and up to four components of chemically different ices (e.g. H₂O, CO, CO₂, CH₄) and solve the mass and energy equations for the different volatiles simultaneously. The model includes inflowing and outflowing gas within the body, dust mantle build-up, depletion of the most volatile ices in outer layers, and recondensation of gases in deeper layers. The model calculations start with a homogeneously mixed body at a constant temperature and a constant mass density at aphelion of an orbit. Due to insolation and conduction the internal heat of the body increases, and as a result of sublimation of the minor, more volatile components, the initially homogeneous body differentiates into a multi-layered body. For example a dust, H₂O, CO₂, and CO ice body differentiates into a four-layer body in which the deepest layer has the original composition and the higher layers are successively more depleted of volatiles. The boundaries between the layers are sublimation fronts of the corresponding volatile phases. The depths of the sublimation fronts change with time and are on the order of tens of meters. From the calculations we obtain temperature, relative chemical abundance, porosity, and pore size distributions as a function of depth, and the gas flux into the interior and into the coma for each of the volatiles at various positions of the comet in its orbit. In this paper we explore some early steps on the way to a more comprehensive model for comet nuclei. In order to understand the consequences of processes better we have made some simplifying assumptions. To investigate the effects of dust, we have modeled the nucleus with and without dust. We find that a dust layer at the surface of the nucleus drastically reduces the sublimation flux of H₂O at heliocentric distances, r<3 AU. The ratio of the gas flux of minor volatiles to that of H₂O in the coma varies by several orders of magnitude from aphelion to perihelion. We developed a two-dimensional model for heat and mass transfer to investigate inhomogeneities (e.g. boundaries between active and inactive surface layers), surfaces with different shapes, and surface structures. For the first test calculations we assumed that some area is exposed to sunlight and an adjacent area is shaded from sunlight. We present results for the temperature and gas abundance distributions on adjacent shadowed and exposed surface layers as a function of orbital position. The computer simulations may be useful for comet modeling and to produce engineering models of a comet nucleus for spacecraft missions and subsequently for the interpretation and understanding of in situ results.