Morteza Dejam

Shear dispersion in a capillary tube with a porous wall.

An analytical expression is presented for the shear dispersion during solute transport in a coupled system comprised of a capillary tube and a porous medium. The dispersion coefficient is derived in a capillary tube with a porous wall by considering an accurate boundary condition, which is the continuity of concentration and mass flux, at the interface between the capillary tube and porous medium. A comparison of the obtained results with that in a non-coupled system identifies three regimes including: diffusion-dominated, transition, and advection-dominated. The results reveal that it is essential to include the exchange of solute between the capillary tube and porous medium in development of the shear dispersion coefficient for the last two regimes. The resulting equivalent transport equation revealed that due to mass transfer between the capillary tube and the porous medium, the dispersion coefficient is decreased while the effective velocity in the capillary tube increases. However, a larger effective advection term leads to faster breakthrough of a solute and enhances mass delivery to the porous medium as compared with the classical double-porosity model with a non-coupled dispersion coefficient. The obtained results also indicate that the finite porous medium gives faster breakthrough of a solute as compared with the infinite one. These results find applications in solute transport in porous capillaries and membranes.

The Application of Numerical Laplace Inversion Methods for Type Curve Development in Well Testing: A Comparative Study

Abstract In this work the Fourier series and Zakian and Schapery methods are considered to numerically solve the Laplace transform of a pressure distribution equation for radial flow and to generate the type curves for three different boundary conditions. The results show that the Schapery method leads to approximate solutions for small values of dimensionless time. For large values, however, this method is almost accurate and hence is recommended because it is fast to apply compared to other algorithms. It has been found that the accuracy of the Schapery method for early time prediction can be improved to almost a perfect match with analytical results through multiplying the Schapery relation by a proposed constant coefficient. This coefficient, regardless of the condition in the external boundary, is set to 0.58 when the wellbore storage effect and skin factor are considered. For an infinite acting case, when CD and S are included, and also for constant pressure case, all the methods fail to predict the behavior of the derivative plot accurately at late times, whereas other cases showed acceptable accuracy. At middle times, no analytical solution is available to check the accuracy of numerical methods, but because all the methods discussed here showed identical results, it is reasonable to trust in numerical inversion calculations.

Semi-Analytical Solutions for a Partially Penetrated Well with Wellbore Storage and Skin Effects in a Double-Porosity System with a Gas Cap

We have studied the effect of a constant top pressure on the pressure transient analysis of a partially penetrated well in an infinite-acting fractured reservoir with wellbore storage and skin factor effects. Semi-analytical solutions of a two-dimensional diffusivity equation have been obtained by using successive applications of the Laplace and modified finite Fourier sine transforms. Both pseudo-steady-state and transient exchanges between the matrix and the fractures have been considered. Solutions are presented that can be used to generate type curves for pressure transient analysis or can be used as a forward model in parameter estimation. The presented analysis has applications in well testing of fractured aquifers and naturally fractured oil reservoirs with a gas cap.

Pre-Darcy Flow in Porous Media

Fluid flow in porous media is very important in a wide range of science and engineering applications. The entire establishment of fluid flow application in porous media is based on the use of an experimental law proposed by Darcy (1856). There are evidences in the literature that the flow of a fluid in consolidated and unconsolidated porous media does not follow Darcy law at very low fluxes, which is called pre-Darcy flow. In this paper, the unsteady flow regimes of a slightly compressible fluid under the linear and radial pre-Darcy flow conditions are modeled and the corresponding highly nonlinear diffusivity equations are solved analytically by aid of a generalized Boltzmann transformation technique. The influence of pre-Darcy flow on the pressure diffusion for homogeneous porous media is studied in terms of the nonlinear exponent and the threshold pressure gradient. In addition, the pressure gradient, flux, and cumulative production per unit area are compared with the classical solution of the diffusivity equation based on Darcy flow. The presented results advance our understanding of fluid flow in low-permeability media such as shale and tight formations, where pre-Darcy is the dominant flow regime.

An Experimental Investigation of Fracture Tilt Angle Effects on Frequency and Stability of Liquid Bridges in Fractured Porous Media

Abstract Liquid bridges are believed to play an important role in improving the recovery of fractured reservoirs. However, little is known about the stability of liquid bridges in fractured media at the pore scale. In this work, a glass micromodel representing a stack of two blocks was used at different tilt angles to monitor the frequency and stability of liquid bridges formed during free-fall gravity drainage as a function of tilt angle. It was observed that by increasing the tilt angle, the liquid bridge frequency decreased but its stability increased. This resulted in higher ultimate recovery. In addition, it was found that during the first half of the experiments, the number of bridges was higher but their stability was lower than during the second half of the tests. Moreover, no more than one stable liquid bridge was observed at tilt angles above 20°, and the bridge cross-sectional area was gradually decreased as the stability was maintained. A sequence of bridges that were formed and broken one after the other results in a higher drainage rate than a single bridge with stability equal to the overall stability of the sequence.

Mathematical Modeling of the Function of Warburg Effect in Tumor Microenvironment

Tumor cells are known for their increased glucose uptake rates even in the presence of abundant oxygen. This altered metabolic shift towards aerobic glycolysis is known as the Warburg effect. Despite an enormous number of studies conducted on the causes and consequences of this phenomenon, little is known about how the Warburg effect affects tumor growth and progression. We developed a multi-scale computational model to explore the detailed effects of glucose metabolism of cancer cells on tumorigenesis behavior in a tumor microenvironment. Despite glycolytic tumors, the growth of non-glycolytic tumor is dependent on a congruous morphology without markedly interfering with glucose and acid concentrations of the tumor microenvironment. Upregulated glucose metabolism helped to retain oxygen levels above the hypoxic limit during early tumor growth, and thus obviated the need for neo-vasculature recruitment. Importantly, simulating growth of tumors within a range of glucose uptake rates showed that there exists a spectrum of glucose uptake rates within which the tumor is most aggressive, i.e. it can exert maximal acidic stress on its microenvironment and most efficiently compete for glucose supplies. Moreover, within the same spectrum, the tumor could grow to invasive morphologies while its size did not markedly shrink.

Magnetically assisted intraperitoneal drug delivery for cancer chemotherapy

Abstract Intraperitoneal (IP) chemotherapy has revived hopes during the past few years for the management of peritoneal disseminations of digestive and gynecological cancers. Nevertheless, a poor drug penetration is one key drawback of IP chemotherapy since peritoneal neoplasms are notoriously resistant to drug penetration. Recent preclinical studies have focused on targeting the aberrant tumor microenvironment to improve intratumoral drug transport. However, tumor stroma targeting therapies have limited therapeutic windows and show variable outcomes across different cohort of patients. Therefore, the development of new strategies for improving the efficacy of IP chemotherapy is a certain need. In this work, we propose a new magnetically assisted strategy to elevate drug penetration into peritoneal tumor nodules and improve IP chemotherapy. A computational model was developed to assess the feasibility and predictability of the proposed active drug delivery method. The key tumor pathophysiology, including a spatially heterogeneous construct of leaky vasculature, nonfunctional lymphatics, and dense extracellular matrix (ECM), was reconstructed in silico. The transport of intraperitoneally injected magnetic nanoparticles (MNPs) inside tumors was simulated and compared with the transport of free cytotoxic agents. Our results on magnetically assisted delivery showed an order of magnitude increase in the final intratumoral concentration of drug-coated MNPs with respect to free cytotoxic agents. The intermediate MNPs with the radius range of 200–300 nm yield optimal magnetic drug targeting (MDT) performance in 5–10 mm tumors while the MDT performance remains essentially the same over a large particle radius range of 100–500 nm for a 1 mm radius small tumor. The success of MDT in larger tumors (5–10 mm in radius) was found to be markedly dependent on the choice of magnet strength and tumor-magnet distance while these two parameters were less of a concern in small tumors. We also validated in silico results against experimental results related to tumor interstitial hypertension, conventional IP chemoperfusion, and magnetically actuated movement of MNPs in excised tissue.

Formation of Traveling Liquid Bridges between Matrix Blocks: Modeling and Simulation

It is widely accepted that under reservoir conditions there exists some degree of block to block interaction that may result in capillary continuity. The formation of liquid bridges causing capillary continuity between blocks will significantly affect ultimate recovery. In this work a mechanistic model with original thought from hydrology for a given steady feeding volumetric flow rate from an upper block (under both gravity and matrix capillary pressure effects) is developed which considers the formation, growth and detachment of pendant liquid droplets perpendicular to the horizontal fracture (assuming to be smooth and parallel walled) between blocks. The length of detached liquid droplet is observed to be weakly related to the flow rate but it increases as the fracture capillary pressure increases. By neglecting the impact of the flow rate, the simple relation is derived for determination of the length of detached pendant droplet which depends on the fracture capillary pressure, liquid density and the gravitational acceleration. Comparison between the horizontal fracture aperture size and the length of detached pendant liquid droplet is then used to evaluate the formation of traveling liquid bridge between upper and lower blocks.