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In hydraulic fracturing technology, Mini-Fracture Tests (MFTs) which are also known as Diagnostic Fracture Injection Tests (DFITs) have been utilized as an efficient technique to ascertain matrix permeability and closure pressure in petroleum reservoirs. An initial fracture, in Mini-Fracture Tests, is formed by injection of fluid until formation breaks down and the fracture propagates a small remoteness into the reservoir. After shut-in of the injection, the pressure decline is recorded. From the falloff data, the effective permeability of the formation can be estimated by Nolte's G-function, log-log plot, or square root of time analysis. In this paper, case studies are considered by consistently applying analysis method from the G-function, its derivatives, and its relationship to other diagnostic techniques including square-root(time) and log(p wf) − log(t) plots and their appropriate diagnostic derivatives. By analyzing the obtaining results, the commonly applied G-function method yielded approximations of permeability over an order of magnitude higher than the simulated matrix permeability. Errors of permeability which are taken from the G-function and Square Root Time are higher than actual matrix permeability taken from After Closure Analysis.

Freezing is one of the most complicated treatment in food processing due to the dependence of food properties on temperature. In addition, many kinds of food contain a high proportion of water which has some special thermal characteristics. In this study, the freezing process for a fish fillet from Vietnamese catfish fillets is considered using the Finite Element Method. The coupled heat and mass transfer problem is investigated in a discretized computational domain. Numerical results obtained from COMSOL solver then are compared with the experimental data to prove the efficiency of the proposed method.