Biogeochemical reaction kinetics are generally established from batch reactors where concentrations are uniform. In natural systems, many biogeochemical processes are characterized by spatially and temporally variable concentration gradients that often occur at scales which are not resolved by field measurements or biogeochemical and reactive transport models. Yet, it is not clear how these sub-scale chemical gradients affect reaction kinetics compared to batch kinetics. Here we investigate this question by studying the paradigmatic case of localized pulses of solute reacting with a solid or a dissolved species in excess. We consider non-linear biogeochemical reactions, representative of mineral dissolution, adsorption and redox reactions, which we quantify using simplified power-law kinetics. The combined effect of diffusion and reaction leads to effective kinetics that differ quantitatively and qualitatively from the batch kinetics. Depending on the nonlinearity (reaction order) of the local kinetics, these effects lead to either enhancement or decrease of the overall reaction rate, and result in a rich variety of reaction dynamics. We derive analytical results for the effective kinetics, which are validated by comparison to direct numerical simulations for a broad range of Damköhler numbers and reaction order. Our findings provide new insights into the interpretation of imperfectly mixed lab experiments, the effective kinetics of field systems characterized by intermittent reactant release and the integration of sub-scale concentration gradients in reactive transport models.

生物地球化学反应动力学通常从浓度均匀的间歇式反应器中建立。在自然系统中，许多生物地球化学过程的特征在于时空变化的浓度梯度，这些梯度通常发生在现场测量或生物地球化学和反应传输模型无法解决的尺度上。然而，与批次动力学相比，尚不清楚这些亚尺度化学梯度如何影响反应动力学。在这里，我们通过研究溶质局部脉冲与固体或过量溶解物质反应的典型案例来研究这个问题。我们考虑非线性生物地球化学反应，代表矿物溶解、吸附和氧化还原反应，我们使用简化的幂律动力学对其进行量化。扩散和反应的综合作用导致在数量和质量上与批次动力学不同的有效动力学。根据局部动力学的非线性（反应顺序），这些影响导致整体反应速率的提高或降低，并导致反应动力学的丰富多样。我们推导出有效动力学的分析结果，通过与广泛范围的 Damköhler 数和反应级数的直接数值模拟进行比较来验证这些结果。我们的发现为解释不完全混合的实验室实验、以间歇性反应物释放为特征的场系统的有效动力学以及反应传输模型中亚尺度浓度梯度的整合提供了新的见解。