Asphaltene precipitation modeling through ACE reaping of scaling equations

Precipitation and deposition of asphaltene have undesirable effects on the petroleum industry by increasing operational costs due to reduction of well productivity as well as catalyst poisoning.Herein we propose a reliable model for quantitative estimation of asphaltene precipitation.Scaling equation is the most powerful and popular model for accurate prediction of asphaltene precipitated out of solution in crudes without regard to complex nature of asphaltene.We employed a new mathematical-based approach known as alternating conditional expectation(ACE)technique for combining results of different scaling models in order to increase the accuracy of final estimation.Outputs of three well-known scaling equations,including Rassamdana(RE),Hu(HU),and Ashoori(AS),are input to ACE and the final output is produced through a nonlinear combination of scaling equations.The proposed methodology is capable of significantly increasing the precision of final estimation via a divide-andconquer principle in which ACE functions as the combiner.Results indicate the superiority of the proposed method compared with other individual scaling equation models.

Scaling Equation for Invariant Measure

An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.

Prediction of oil recovery in naturally fractured reservoirs subjected to reinfiltration during gravity drainage using a new scaling equation

By comparing numerical simulation results of single-porosity and dual-porosity models,the significant effect of reinfiltration to naturally fractured reservoirs was confirmed.A new governing equation was proposed for oil drainage in a matrix block under the reinfiltration process.Utilizing inspectional analysis,a dimensionless equation suitable for scaling of recovery curves for matrix blocks under reinfiltration has been obtained.By the design of experiments,test cases with different rock and fluid properties were defined to confirm the scope of the presented equation.The defined cases were simulated using a realistic numerical simulation approach.This method can estimate the oil amount getting into the matrix block through reinfiltration,help simulate the oil drainage process in naturally fractured reservoirs accurately,and predict the recovery rate of matrix block in the early to middle periods of production.Using the defined scaling equation in the dual-porosity model can improve the accuracy of the predicted recovery rate.

The Homoclinic Orbit Solution for Functional Equation

In this paper, some examples, such as iterated functional systems, scaling equation of wavelet transform,and invariant measure system, are used to show that the homoclinic orbit solutions exist in the functional equations too.And the solitary wave exists in generalized dynamical systems and functional systems.