## 1 Introduction  
Nitrate contamination in ground water causes human health problems (methemoglobinemia, kidney failure, vomiting, diarea) [1, 2]. Among the several nitrate removal technologies available, adsorption is the most promising in terms of cost and efficiency, as measured by the percentage of nitrate removal, simplicity of design, operation and maintenance and minimising waste production. Experiments in the adsorption process are usually undertaken in a batch operation mode or a column operation mode. The column operation mode is a dynamic and continuous operation process which can be easily related to actual water treatment plants. However, very small size adsorbents which have higher adsorption capacities (due to higher surface area and availability of more adsorption sites) cannot be used in column mode due to the head loss. Furthermore, micro-particles and suspended solids, if present in the influent water, usually clog the column and reduce operating performance.  
The submerged membrane adsorption hybrid system (SMAHS) is an alternative dynamic adsorption system developed during the last two decades to obtain high quality effluent water. In this process, microfiltration (MF) or ultrafiltration (UF) membranes coupled with adsorption technology are used to treat the water. Although the MF or UF do not remove the nitrate, they can remove suspended solids, colloids, micro-organisms and micro-particles from water. The adsorbents are retained in the reactor [3, 4] and kept continuously in suspension via aeration to facilitate increasedadsorption of pollutants. The integrated adsorption and membrane filtration system offers several advantages. Here the adsorbents kept in suspension by the aeration reduce membrane fouling by abrasion and membrane scouring. Consequently, the membrane's operation time and total usable life span increases, which in turn helps to minimise operation and maintenance costs. In addition, this reduces the frequency of membrane cleaning and the membrane cleaning requires smaller amounts of chemicals.  
Another advantage is, unlike in column mode of operation, smaller size adsorbents can be used in SMAHS for higher removal of pollutants and this has been proved in past studies [5; 6]. [PERSON] et al. [5] studied the effect of three particle sizes of granular activated carbon (GAC) on scouring of membrane and dissolved organic carbon removal in SMAHS. They found that the scouring effect was highest for intermediate particle size but DOC removal by adsorption on to GAC was highest for the smallest particle size. The difference in the particle effects were explained by particle settling in the suspension adsorption capacity.  
Most previous SMAHS studies have mainly focused on the removal of metals [7; 8], phosphate [9], colour and reactive dyes [10], and organic micropollutants [11]. Relatively recently, nitrate removal using the SMAHS was reported [12]. The data obtained in the study of [PERSON] et al. [12] was not mathematically modelled. Models have the advantage of simulating the performance of SMAHS at other experimental conditions without expending the time and expense of physical experiments. The model will be helpful to optimise the operating conditions which is important in ground water treatment. The application of mathematical model for SMAHS has not been reported for nitrate. However, a model has been applied for organics removal in the literature [6; 13].  
The objectives of this study were to: (i) compare nitrate adsorption performance of the ion exchange resin, Dowex, iron-coated Dowex (Dowex-Fe), amine grafted (AG) corn cob and AG coconut copra in a SMAHS under four filtration flux; and (ii) simulate the experimental data with a mathematical model. This research is new because to date, in literature, there has been no mathematical model shown to be able to simulate experimental data of nitrate removal from influent water using SMAHS with different adsorbents under different flux conditions.