Page 268 - PVT Property Correlations

234 PVT Property Correlations

pressure, reservoir pressure, API, and temperature. The number of input
nodes to their ANN were therefore 24. They used one hidden layer.
Ikiensikimama and Azubuike (2012) used 802 data points collected from
Niger Delta region of Nigeria to build an ANN model for oil formation vol-
ume factor. They used the usual four inputs in the nodes of the input layer
and one hidden layer.
Shateri et al. (2015) used a dataset of 978 data points to develop an ANN
model for gas compressibility factor. Their model was compared to nine
empirical correlations and five equations of state. The model predicted the
compressibility factor of natural gases with an average absolute percent rela-
tive error of 2.3%. Their network had two input nodes and one hidden layer.
Back propagation technique was used with the Wilcoxon generalized radial
basis function network (WGRBFN).
Adeeyo (2016) developed models for prediction of bubble point pressure
and formation volume factor at bubble point pressure for Nigerian crude oils.
The data sets consisted of 2114 bubble point pressure and 2024 oil formation
volume factor values at bubble point pressure. One hidden layer was used.
The number of neurons in the hidden layer was varied until stable results
were obtained. Comparison was made of the ANN models with other pub-
lished correlations, and the ANN models were concluded to be superior.
A variety of ANN models were developed for prediction of PVT proper-
ties for oils and gases from basic inputs. The models used data sets of differ-
ent sizes, with the majority using the back propagation technique. In
addition, the majority of the models developed have only one hidden layer,
with several ANN models having two hidden layers.

ARTIFICIAL NEURAL NETWORK MODELS DESIGN

The basic ANN model structure includes an input layer with a number of
input nodes (determined by the number of input variables). The ANN also
contains an output layer with defined output nodes in addition to a user-
defined arbitrary number of hidden layers (with each hidden layer consisting
of an arbitrary number of nodes) determined by the problem size. The fol-
lowing problem illustrates typical calculations of an ANN model.

Problem 1—Simple Artificial Neural Network Calculations

Assume the basic ANN structure in Fig. 10.6 to be an example of a
single-layer neural network with two input nodes, one hidden layer with
two nodes, and two output nodes. The hidden layer is connected to a bias
node (B1), and the output layer is connected to another bias node (B2).
The initialization and output values for the ANN training are given in