RESEARCH NOTES Extension of an Artiﬁcial Neural Network Algorithm for Estimating Sulfur Content of Sour Gases at Elevated Temperatures and Pressures Mehdi Mehrpooya, † Amir H. Mohammadi,* ,‡ and Dominique Richon ‡ Chemical Engineering Department, Faculty of Engineering, Tehran UniVersity, Tehran, Iran, and MINES ParisTech, CEP/TEP-Centre E ´ nerge ´tique et Proce ´de ´s, 35 Rue Saint Honore ´, 77305 Fontainebleau, France In this communication, we report an extended artiﬁcial neural network algorithm to estimate sulfur content of sour/acid gases. The main advantage of this algorithm is that it eliminates any need for characterization parameters, due to the tendency of sulfurs to react, required in thermodynamic models. To develop this tool, reliable experimental data found in the literature on sulfur content of various gases are used. To estimate the sulfur content of a gas, the information on temperature, pressure, gravity of acid gas free gas, and the concentrations of hydrogen sulﬁde and carbon dioxide in the gas are required. The developed algorithm is then used to predict independent experimental data (not used in its development). It is shown that the artiﬁcial neural network algorithm can be used as an efﬁcient tool to estimate sulfur content of various gases. 1. Introduction Sulfur deposition is a serious problem that can affect sour natural gas production, transportation and processing. 1-29 Deposition of sulfur can block production facilities and cause a substantial and drastic reduction in the permeability of the formation near the wellbore. 1,2 The occurrence of sulfur precipitation has also been reported in natural gas transportation and processing. 1-5 Accurate knowledge of sulfur + sour/acid gas phase behavior is therefore important to avoid sulfur deposition problems. 1 One of the main difﬁculties in describing the phase behavior of sulfur-containing systems is the lack of suitable characterization parameters as the tendency of sulfurs to react takes their characterization difﬁcult. 1-29 Sulfur may exist as a number of polymeric species ranging up to S 8 in the gas and combines with other gases to produce polysulﬁdes or sulfanes such as H 2 S 9 . 1,14,15 The amount of each molecule depends both on pressure and temperature. 1,10-13 Modeling sulfur + sour/acid gas phase equilibrium by conventional thermodynamic models therefore requires the use of many unknown parameters considering the above-mentioned reactions should be taken into account. 1-29 The various thermodynamic models reported in the literature typically use the Peng-Robinson equation of state (PR- EoS) 30 and concern ranges of pressure, temperature, and hydrogen sulﬁde amount at gas production conditions typically greater than those of gas transportation and processing conditions. Artiﬁcial neural network (ANN) algorithms are known to be effective to model complex systems. These tools are ﬁrst subjected to a set of training data consisting of input data together with corresponding outputs. 1,31,32 After a sufﬁcient number of training iterations, the neural network learns the patterns in the data fed to it and creates an internal model, which is used to make predictions for new inputs. 1 The aim of this work is to extend a previously reported feed- forward (back-propagation) neural network (FNN) algorithm 1 for estimating the sulfur content of hydrogen sulﬁde to various sour gases. In this method, the sulfur content of a gas is estimated from the information on temperature, pressure, acid gas free gas gravity, and concentrations of hydrogen sulﬁde and carbon dioxide in the gas. The optimization algorithm chosen in this work is a modiﬁed Levenberg-Marquardt algorithm 33,34 with Bayesian regularization technique, which is specially indicated to optimize ANNs using small learning sample size. The reliable experimental data reported in the literature are used to develop and then validate this model. 2. Feed-Forward Neural Network Algorithm Feed-forward neural networks are the most frequently used and are designed with one input layer, one output layer, and hidden layers. 1,31,32,35-39 The number of neurons in the input and output layers is equal to the number of inputs and outputs, respectively. 1,31,32,35-39 The accuracy of the model representa- tion depends on the architecture and parameters of the neural network. 1,31,32,35-39 In the FNN algorithm, the input layer of the network receives all the input data and introduces scaled data to the network. 1,39 The data from the input neurons are propagated through the network via weighted interconnections. 1,39 Every i neuron in a k layer is connected to every neuron in adjacent layers. 1,39 The i neuron within the hidden k layer performs the following tasks: summation of the arriving weighted inputs and propagations of the resulting summation through an activation function, f, to the adjacent neurons of the next hidden layer or to the output neuron(s). In this work, the activation function is tangent sigmoid: 1,39 where x stands for parameter of activation function. A bias term, b, is associated with each interconnection in order to introduce a supplementary degree of freedom. The expression of the weighted sum, S, to the ith neuron in the kth layer (k g 2) is 1,39 where w is the weight parameter between each neuron-neuron interconnection and I i ) [I i,1 , ..., I i,N k -1 ] represents an input * To whom correspondence should be addressed. E-mail: amir- hossein.mohammadi@ensmp.fr. Tel.: +(33) 1 64 69 49 70. Fax: +(33) 1 64 69 49 68. † Tehran University. ‡ CEP/TEP-Centre E ´ nerge ´tique et Proce ´de ´s. f(x) ) 1 - e -x 1 + e -x x ∈ [-∞, +∞] and f(x) ∈ [-1, +1] (1) S k,i ) ∑ j)1 N k-1 [(w k-1,j,i I k-1,j ) + b k,i ] (2) Ind. Eng. Chem. Res. 2010, 49, 439–442 439 10.1021/ie900399b CCC: $40.75  2010 American Chemical Society Published on Web 11/19/2009