Moisture loss due to internal evaporation and its relationship to nonuniformity of heating in microwave reheating of high moisture solid foods was studied. A simple heat and mass transfer model was developed that excluded diffusional limitations of moisture movement. Microwave absorption and some dielectric and thermal properties were measured as input parameters to the model. Effect of varying microwave penetration with moisture level and temperature was included. For smaller total moisture loss, typical for a reheating application, predictions of total moisture loss and temperatures matched well with experimental data. Most of the moisture loss occurred from the edges due to higher temperature at these locations. Uniformity of heating to achieve a given average temperature is the key variable controlling total moisture loss. When starting from a frozen material, heating is much more nonuniform, leading to a greater moisture loss. As surface area increases for a given volume, uniformity of heating increases and the total moisture loss reduces. This simple model can be an effective tool in computer‐aided optimization of food products and processes.

Summary A systematic study of permeability modification of Berea sandstone by the injection of alternate slugs of polymer and aluminum citrate is described. The research included brine permeabilities from 10 to 300 md. Results of treatments with Pusher 700TM showed that permeability reduction was limited to the front end of the core (0 to 4 in. [0 to 10 cm]). The effective mobility of the treated region was so low that in-depth treatment of the remainder of the core was prevented. The amount and distribution of permeability reduction is related to both polymer and aluminum retention. The retention of aluminum was found to be a nonequilibrium process, varying with flow rate and thus residence time in the core. Aluminum was retained in large quantities in Berea core in the absence of polymer. Changing the treatment sequence to aluminum citrate/brine/polymer/brine yielded in-depth treatment of cores 12 to 48 in. [30 to 121 cm] in length. Both magnitude and persistence of permeability reduction were comparable to or better than those obtained with the combination process. Permeability increased with distance from the core inlet Permeability increased with distance from the core inlet in most runs. This is believed to be caused by nonuniform distribution of retained aluminum. Introduction Reservoir heterogeneity is the major cause of low volumetric sweep efficiency in many waterfloods because injected fluids flow through high-permeability intervals, bypassing oil in tighter regions of the reservoir. Several processes have been developed that reduce rock permeability by injecting polymer solutions into the permeability by injecting polymer solutions into the high-permeability regions. One class of processes relies on in-situ gelation of polymers. Gelation is accomplished by crosslinking poly-acrylamide or polysaccharide with a metal ion, usually chromium. poly-acrylamide or polysaccharide with a metal ion, usually chromium. Polymer concentrations of 2,000 to 5,000 ppm are required to form Polymer concentrations of 2,000 to 5,000 ppm are required to form gels in most systems. Because these systems are viscous, depth of penetration at practical injection rates and pressures is probably penetration at practical injection rates and pressures is probably limited to the region within 50 to 75 ft [15 to 23 m] of the wellbore. Deeper penetration may occur if high permeability is a result of fractures. In-depth penetration is desired in reservoirs where crossflow between layers would reduce the effectiveness of a near-wellbore treatment. In 1974, Needham et al. described a process that seemed to provide in-depth reduction of rock permeability. The process, called the combination process, involves contacting a process, called the combination process, involves contacting a porous rock with a dilute polymer solution to obtain an adsorbed porous rock with a dilute polymer solution to obtain an adsorbed layer of polymer on the rock surface. The polymer solution is displaced by an aluminum citrate solution to enable aluminum ions to interact with adsorbed polymer. Finally, the aluminum citrate solution was displaced by a polymer solution and then brine. Reduction in brine permeability after treatment ranged from factors of 3 to 4,170 for several sandstones when 250-ppm polymer concentrations were used. This permeability reduction was more resistant to elution than that obtained with a single polymer treatment. Results for treatment of Berea core by sequential injection of 250-ppm polymer/aluminum citrate/250-ppm polymer/brine produced permeability reductions by factors of 12 to 42 in cores where produced permeability reductions by factors of 12 to 42 in cores where brine permeability at residual oil varied from 10 to 27 md. Comparable reductions in permeability were reported for Berea cores without residual oil saturation (ROS). Similar reductions in brine permeability were observed when the polymer and aluminum citrate solutions were separated by a large polymer and aluminum citrate solutions were separated by a large brine slug. Because of this, in-situ mixing of these solutions was not believed to cause the permeability reduction. Instead, permeability reduction was thought to occur in a sequential process. permeability reduction was thought to occur in a sequential process. Aluminum ion was retained by the polymer adsorbed during the first polymer cycle. Permeability reduction occurs when polymer is polymer cycle. Permeability reduction occurs when polymer is retained during the second polymer cycle by crosslinking with aluminum ions to form a layered structure. The findings of Needham et al. were supported by Thomas, who conducted experiments with this process in capillary tubes. He concluded that the reduction in water permeability occurred in sequence, with the polymer forming an adsorbed layer on the capillary wall, the aluminum ion interacting with the adsorbed polymer, and then another layer of polymer attaching to the metal polymer, and then another layer of polymer attaching to the metal ion. Buildup of his polymer/metal-ion/polymer network reduced the size of the capillaries and inhibited the flow of water. The research described in this paper was undertaken to correlate permeability reduction obtained from the combination process, as permeability reduction obtained from the combination process, as well as the extent and persistence of the treatment, with process variables. During initial experiments, we discovered that permeability reduction was limited to a short distance near the entrance permeability reduction was limited to a short distance near the entrance of a core. The research program was expanded to investigate mechanisms responsible for uneven permeability distribution. Methods and Materials Experimental work was done with Berea sandstone cores obtained from Cleveland Quarry in 2-in. [5.1 -cm] -diameter, 4-ft [ 122-cm] -long or 2 X2-in. [5.1 X5.1-cm] -square, 4-ft [122-cm] -long cross sections. Cores were cut to specific lengths, and Lucite TM caps were tacked on each end. Spacing between the endcap and the core was about the thickness of a sheet of paper. Each core was coated with alternating layers of epoxy and gauze in a rotating apparatus and dried. Pressure ports were installed at selected positions along the core by drilling a 5/32-in. [0.39-cm] pilot hole near the core surface. Final tapping was done with a flat mill bit. During tapping, the core was pressurized with air to a few psi to minimize penetration of the bit into the core and to clear debris from the port. A few experiments were run on short cores 1 in. [2.54 cm] in diameter. The stock brine of Needham et al. was used to saturate the core and to prepare most of the solutions used in the displacement experiments. This brine contained 910 ppm NaCl, 239 ppm CaCl2, and 50 ppm MgCl2. The core was saturated byflushing the core with CO, to displace all air,evacuating the core to 400 m Hg, and (i) measuring the volume of brine drawn into the core when the inlet line was opened to a brine reservoir. In most cases, the core was weighed before and after saturation to check the PV. Porosity was calculated from the PV and bulk volume. Porosity was calculated from the PV and bulk volume. Berea cores were used as received. The stock brine contained sufficient dissolved solids to prevent mobilization of clays.

Comparl son of the isoperms obtained by the parametric method with the isoperms plotted byWith the advent of enhanced oil recovery the graphical contouringtechnique show that: (1) (EOR) methods such as chemical flooding, miscible the parametric method gives a more reliable fit gas displacementand thermal methods, thrf?e-phase to the data points than manual techniques, relative permeabilitydata are needed to predict because it is based on mathematicaloptimization performances of field applications. Complexity and therefore eliminates subjective bias and (2) of experimental and calculation procedures for the graphical contouring method reveals the three-phaserelative permeabilitymeasurements is fluctuation in the original data points and a primary reason why published data in this area possible smaller scale trends that may be ire limited. Furthermore,arbitrarymethods used significant. The functional form presented in ior analysis and graphical representation of this paper can be used to estimate three-phase these experimental data are affected to some relative permeabilityfrom displacement (unsteady extent by subjectivebias. state) core flood experimentalresults.

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