Fractional Oil Recovery Research Articles

Application of modified Dykstra-Parsons method to natural bottom-water drive in non-communicating fractured-vuggy reservoir

Universal existence of the filled vug and fracture in carbonate fractured-vuggy reservoir upgrades the complexity of fluid flow as the coexistence of free flow and porous flow. The highly discrete distribution of fracture and vug makes it possible to apply Dykstra-Parsons method in this kind of medium. A modification of Dykstra-Parsons method is proposed to depict the displacement in fracture-vug system, which consists of multiple non-communicating fracture-vug units with each containing fracture, fills, and vug. The displacement front advance equation is derived piecewise corresponding to the position of the front in fracture, fills, and unfilled vug of one unit. The solution to this equation for every fracture-vug unit is used to estimate the production dynamics of the fracture-vug system, including the fractional oil recovery, the water cut, the injected pore volume, and the injectivity ratio. A calculating example with log-normal distribution for fracture aperture is involved to make the sensitivity analysis of gravity number, viscosity ratio, fills properties, and variation of the fracture aperture. In terms of increased oil recovery, decreased water cut, and delayed water breakthrough, it was found that a better performance reached in the condition of weak heterogeneity of fracture, large gravity number, and lower oil//water viscosity ratio; the fills with low permeability and high filling degree is favorable when all vugs are filled identically.

Modified Version of Aronovsky Model for Predicting the Performance of Naturally Fractured Oil Reservoirs

In this work the mathematical model developed by Aronovsky et. al. for predicting rates of free-water imbibition in naturally fractured oil reservoirs has been modified. The proposed model allows prediction of fractional oil recovery by spontaneous water imbibition in core samples with high accuracy.
 The proposed modification involves development of an empirical correlation for the reservoir rock/fluid system-dependent parameter (l) used in Aronofsky model and defined as rate of convergence. The key reservoir rock and fluid physical properties considered in this work include absolute permeability of the rock, porosity, initial water saturation, interfacial tension between oil and water (IFT), viscosity of oil, viscosity of water, and length of core sample.
 The accuracy of the modified model is evaluated using the results of laboratory imbibition tests on nine limestone core samples. All imbibition tests were conducted at 90 ° C. The absolute per cent error based on laboratory versus calculated values of (l) is found to range between 0.334 and 3.88.
 The proposed model may also be applied for predicting fractured reservoir performance on field scale by simply replacing the core length by matrix block length when the block is totally immersed in water. Additional experimental work and/or field observations would be necessary to verify the reliability of the proposed modification.

Mathematical and neural network prediction model of three-phase immiscible recovery process in porous media

Scaling analysis of fluids displacement in porous media is a reliable fast method to evaluate the displacement performance of different oil production processes under various conditions. This paper describes scaling of multiphase flow through permeable media with special attention to three-phase immiscible water alternating gas flooding processes. The procedure of inspectional analysis (IA) was used to determine relevant dimensionless groups. It was found that scaling immiscible water alternative gas (IWAG) displacement in a two-dimensional homogeneous anisotropic medium needs matching of seven dimensionless scaling groups. A series of numerical sensitivity studies were conducted to determine the magnitude of scaling groups and their interaction with recovery factors. None of the dimensionless groups individually could correlate the efficiency of the process in all the circumstances. Two predictor models, a mathematical model and an artificial neural network (ANN) model, were developed to map the effective combinations of the dimensionless scaling groups. For the mathematical model, a new combined dimensionless group which incorporates all the dominant scaling groups has been derived. Functional relationship between the combined group and fractional oil recovery is investigated. This relation has potential application in prediction of displacement efficiency. To prepare the ANN prediction model, scaling groups obtained from fine mesh simulation were used as input parameters. The agreement between the simulation methods and ANN model validate the applicability of the model to predict the recovery factors for the range of the groups which were not included in the simulations. The comparison study of the models showed the superior performance of ANN model compared to the mathematical model. The ANN model can be used to propose a proper development plan for a reservoir and/or to determine the optimal plan of operation.

Effect of operating parameters on mechanical expression of solvent-soaked soybean-grits.

Oil from soybean is obtained mostly by solvent extraction of soybean flakes. Legislation banning the use of hexane as solvent for extracting edible vegetable oil has forced a search for an alternative solvent and for developing a suitable oil recovery process. Expellers are being used for obtaining vegetable oil by mechanical means (expression) from oil seeds having oil content higher than 20%. It was felt, in view of the stiffness of the soybean matrix, a combination of solvent treatment and expression could be a cheaper alternative; thus an attempt has been made here to develop a two stage process constituting soaking of soybean grits in solvent followed by mechanical compression (hydraulic press) of solvent-soaked grits to recover oil. The present work aimed at studying the effect of various process parameters on oil yield from solvent soaked soybean-grits during soaking as well as pressing stages using the solvents: hexane, ethanol (alternative solvent). The process parameters were identified through holistic approach. The dependant variable was oil recovery (expressed as fraction of initial oil content of soybean) whereas the independent parameters were particle size, solvent-bean mass ratio, soaking time, soaking temperature, applied pressure and pressing time. The effect of each of the above parameters on fractional oil recovery (FOR) was studied. The results of the present study indicate that the above parameters have a significant effect on the fractional oil recovery with particle size, soaking temperature, soaking time and pressing time being the most significant factors. The present study also indicates that ethanol can be used as an alternate solvent to hexane by optimizing the factors as discussed in this paper.

The Modification of the Dykstra-Parsons Method for Inclined Stratified Reservoirs

Summary The Dykstra-Parsons method (Dykstra and Parsons 1950) is used to predict the performance of waterflooding in noncommunicating stratified reservoirs. Much interest has been shown recently in the application of the method to chemical flooding, particularly for the case of polymer injection used for mobility control. The original method assumes that the reservoir layers are horizontal; however, most oil reservoirs exhibit a dip angle, with water being injected in the updip direction. Therefore, it is important to account for the effect of inclination on the performance of the method. A modification of the Dykstra-Parsons equations is obtained to account for reservoir inclination. The developed model includes a dimensionless gravity number that accounts for the effect of the dip angle and the density difference between the displacing and displaced fluids. The derived equation that governs the relative locations of the displacement fronts in different layers is nonlinear, includes a logarithmic term, and requires an iterative numerical solution. This solution is used to estimate the fractional oil recovery, the water cut, the injected pore volume, and the injectivity ratio at the time of water breakthrough in successive layers. Solutions for stratified systems with log-normal permeability distribution were obtained and compared with horizontal systems. The effects of the gravity number, the mobility ratio, and the Dykstra-Parsons permeability-variation coefficient (VDP) on the performance were investigated. Cases of updip and downdip injection are discussed. It was found that for a positive gravity number (updip water injection), performance is enhanced in terms of delayed water breakthrough, increased fractional oil recovery, and decreased water cut as compared with horizontal layers. This occurs for both favorable and unfavorable mobility ratios but is more evident in unfavorable mobility ratios and more-heterogeneous cases. For the case of a negative gravity number (downdip water injection or updip gas injection), the opposite behavior was observed. The results were also compared with the performance of inclined communicating reservoirs with complete crossflow. The effect of communication between layers was found to improve fractional oil recovery for favorable and unit mobility ratios and decrease recovery for unfavorable mobility ratio.

Waterflooding Performance in Inclined Communicating Stratified Reservoirs

Summary A mathematical model is developed for performance prediction of waterflooding performance in communicating stratified reservoirs with a dip angle from the horizontal. The effect of the gravitational force is reflected by a dimensionless gravity number in the fractional flow formula. The gravity number accounts for the dip angle and the density difference between the displacing and displaced fluids. The developed fractional flow formula is used to estimate the fractional oil recovery, the dimensionless time, and the injectivity ratio at times of water breakthrough in the successive layers. The developed model allows for each layer to have its own porosity, endpoint saturations, and endpoint relative permeabilities. Solutions for the waterflooding performance in inclined communicating stratified systems with log-normal permeability distribution were obtained and compared with that of the horizontal systems. The effects of the gravity number, the mobility ratio, and the Dykstra-Parsons permeability-variation coefficient VDP on the performance were investigated. The obtained results showed that the gravity effect of the dip angle enhances the performance in terms of delayed water breakthrough, higher fractional oil recovery, and lower water cut. This improved performance is more significant in the cases of unfavorable mobility ratio and of highly heterogeneous reservoirs. Reservoir dipping does not affect the pseudorelative permeability functions but results in a decrease in the injectivity ratio.

Scaling Immiscible Displacements in Porous Media with Horizontal Wells

Despite the increase in horizontal well applications, scaling fluid displacement in porous medium with horizontal wells is yet to be fully investigated. Determining the conditions under which horizontal wells may lead to better oil recovery is of great importance to the petroleum industry. In this paper, a numerical sensitivity study was performed for several well configurations. The study is performed in order to reveal the functional relationships between the scaling groups governing the displacement and the performance of immiscible displacements in homogeneous reservoirs produced by horizontal wells. These relationships can be used as a quick prediction tool for the fractional oil recovery for any combinations of the scaling groups, thus eliminating the need for the expensive fine-mesh simulations. In addition, they provide the condition under which a horizontal well configuration may yield better recovery performance. These results have potential applications in modeling immiscible displacements and in the scaling of laboratory displacements to field conditions.

Immiscible Displacement of Non-Newtonian Fluids in Communicating Stratified Reservoirs

Summary The displacement of non-Newtonian power-law fluids in communicating stratified reservoirs with a log-normal permeability distribution is studied. Equations are derived for fractional oil recovery, water cut, injectivity ratio, and pseudorelative permeability functions, and the performance is compared with that for Newtonian fluids. Constant-injection-rate and constant-total-pressure-drop cases are studied. The effects of the following factors on performance are investigated: the flow-behavior indices, the apparent mobility ratio, the Dykstra-Parsons variation coefficient, and the flow rate. It was found that fractional oil recovery increases for nw>no and decreases for nw<no, as compared with Newtonian fluids. For the same ratio of nw/no, oil recovery increases as the apparent mobility ratio decreases. The effect of reservoir heterogeneity in decreasing oil recovery is more apparent for the case of nw>no. Increasing the total injection rate increases the recovery for nw>no, and the opposite is true for nw<no. It also was found that the fractional oil recovery for the displacement at constant total pressure drop is lower than that for the displacement at constant injection rate, with the effect being more significant when nw<no.

Dimensionally Scaled Miscible Displacements in Heterogeneous Permeable Media

Understanding and predicting the performance of solvent drives and remediation of contaminated aquifers in heterogeneous reservoirs is of great importance to the petroleum and environmental industries. In this paper, a general method to scale flow through heterogeneous reservoirs is presented for a miscible displacement of oil by a solvent. Results show that scaling miscible displacements in a two-dimensional, heterogeneous, anisotropic vertical cross section requires the matching of 13 dimensionless scaling groups. These groups were derived using a general procedure of inspectional analysis. A detailed numerical sensitivity study was performed to reveal the relationship between the scaling groups and the fractional oil recovery of miscible displacements in heterogeneous reservoirs. This relationship was then mapped using an artificial neural network, which can be used as a quick prediction tool for the fractional oil recovery for any combinations of the scaling groups, thus eliminating the need for the expensive fine-mesh simulations. These results have potential applications in modeling miscible displacements and in the scaling of laboratory displacements to field conditions.

Modelling of Radial Water/Oil Displacement Processes In Water-wet Porous Media: Part II. The Capillary Regime

Abstract The effects of five important operating variables and four dimensionless groups on oil recovery and finger formation during the immiscible radial displacement of oil by water in a consolidated water-wet model porous medium were investigated using statistical model building techniques. Two different approaches were used. In the first approach the operating variables studied included:the flow rate of the injected fluid,the radial distance from the injection point,the viscosity difference between the displaced and displacing phases,the permeability of the porous medium, andthe oil/water interfacial tension. The measured responses were the fractional oil recovery and the number of fingers estimated at breakthrough. The present investigation was confined to the low flow rate (i.e., capillary flow) regime, and it produced results that are potentially useful in practical enhanced oil recovery schemes. It was found that the recovery decreased as the oil/water viscosity ratio increased and this effect became more significant as the flow rate increased. Conversely, as the breakthrough radius or permeability of the cell increased, the recovery increased. The effect of interfacial tension on oil recovery was negative and it also depended on the level of viscosity difference and permeability. In addition, an increase in flow rate, breakthrough radius or the viscosity difference resulted in an increase in the number of fingers, while high permeability reduced the number of fingers. The effect of interfacial tension on the number of fingers was more complex and depended on the value of other operating variables. In the second approach, the operating variables were grouped together in dimensionless terms such as the capillary number and the viscosity ratio among others. The recovery was found to be enhanced with an increase in the ratio of breakthrough radius to the cell thickness. It was, however, reduced as the viscosity ratio increased and this attenuating effect became more significant as the flow rate increased. The effects of the ratio of the cell thickness to the square root of the permeability and of the capillary number depended on the values of the other variables. The number of fingers increased as the values of the above ratios increased, although the actual effects were not always straightforward. The results obtained are in good agreement with previous work and theory. By considering all five variables and their interactions simultaneously, a better understanding of the oil recovery process has been achieved. Introduction Previous analysis of Enhanced Oil Recovery (EOR) processes(1,2) has identified the flow rate of the injection fluid, the viscosity difference between the displaced and displacing fluids (or their ratio), the permeability of the porous medium, the oil/water interfacial tension (IFT), and the breakthrough radius, as the primary operating variables affecting finger formation and oil recovery. However, the underlying mechanisms are not well understood. Investigations to date have been limited to individually examining the influence of only one or two of these variables(3–14). As a result, little information exists as to the joint or interactive effects of all of these important factors.

EVALUATION OF MODIFIED STARCHES FOR IMPROVED OIL RECOVERY

Hydrolyzed polyacrylamides (HPAM) products have been widely used as selective relative permeability modifiers in recovery processes. Limitations to these traditional products have prompted a search for cheaper, more stable, and environmentally friendly alternatives. This article describes rheological, chemical, and physical properties of selected modified starches and evaluates their effectiveness in oil recovery applications. Waxy corn and tapioca starches were used in concentrations ranging from 0.2 to 3% (m/v), prepared in 0 to 6% NaCl concentrations, heated to 95°C and tested at various temperatures (25, 40, 60, 75, and 90°C). An empirical rheological model to characterize the viscosity of the starches was developed, and results were used in a simulation model for performance testing. Injectivity studies were used to quantify polymer retention and adsorption. Simulations studies indicate that modified starch flooding showed an increase of 6 to 8% in cumulative oil production over a commercial polyacrylamide flooding. In addition, the results show superior performance and economic benefits in using modified starch rather than polyacrylamides in the simulated reservoir conditions. Benefits in increased fractional oil recovery and reduced water-oil ratio will lead to lower material costs, reduced water treatment and handling costs, and a better process efficiency.

An Analytical Model Of One-Dimensional Miscible Displacement In Porous Media

Abstract A mathematical model having an analytical solution that is valid both for stable and unstable one-dimensional first-contact miscible displacement in homogeneous and heterogeneous porous media has not been reported in the literature. This paper's main objective is to present such a definitive model. This model is described by the diffusion-convection equation for which an approximate parametric solution is found to be a one parameter family of curves. Furthermore, simple formulae for cumulative oil recovery, solvent effluent concentration and oil cut are derived and then successfully matched with numerous published experimental data. All the matches are excellent and definitely superior to those obtained from alternative models. Many new results are obtained and some conclusions from previous investigators corroborated. Introduction The first contact miscible displacement process has been discussed in many excellent texts, and will not be reviewed here(3,12,14). Instead, the mathematical simulation of this process will be discussed. With varying degrees of success(3,5,7,12), a number of different mathematical models have been used to describe one-dimensional first-contact stable miscible displacement which occurs for a favorable solvent oil mobility ratio (M < 1) in homogeneous porous media. The solutions of the partial differential equations governing this displacement are either numerical or analytical in form. In the latter case, they are given in terms of the error function for a variety of initial and boundary conditions(3,5,7,12,13). However, the utility of these solutions is limited because there is often a lack of agreement between these solutions and experimental data. Miscible displacement in heterogeneous media is much more difficult to model because it is less tractable physically, and invariably does not lend itself to a simple mathematical formulation. This formulation is further complicated in the case of unstable miscible displacement (M> 1) which is accompanied by viscous fingering. No mathematical model which can accurately describe this problem and has an analytical solution has been reported. The only known model to have an analytical solution(11) (Koval's Method) is an analogy of the immiscible displacement theory of Buckley and Leverett. Indeed, Koval's formula for fractional solvent flow and oil recovery are identical to those derived for unstable immiscible displacement and commonly used in waterflood calculations(8), provided that Koval's factor K is substituted by the water-oil mobility ratio M. Thus, his solution satisfies the 1-D immiscible equation and not the diffusion-convection equation. This approach cannot be accurate because it neglects the important miscible phenomena of diffusion and dispersion. Nevertheless, Koval obtained satisfactory agreement with experimental data from miscible displacement tests in which diffusion and dispersion had little influence on the formation of viscous fingering(14). When this influence is not negligible, which was the case for part of the data given in Koval's paper, his method fails. Furthermore, it cannot be used to match time-dependent data; thus, its application is quite limited. The model presented here will be shown to be a superior alternative to Koval's model and all other known models.

The Effect of Crossflow on Waterflooding of Stratified Reservoirs

Abstract A mathematical model is developed for waterflooding performance in linear stratified systems for both cases of non-communicating layers with no crossflow and communicating layers with complete crossflow. The model accounts for variation of porosity and saturation in addition to permeability of the different layers. The model predicts the fractional oil recovery, the water cut, the total volume injected, and the change in the total pressure drop, or the change in injection rate at the water breakthrough in the successive layers. A systematic procedure for ordering of layers and performing calculations is outlined. A procedure for combining layers to avoid instability in the case of low mobility ratio is introduced. The developed model is applied to different examples of stratified reservoirs. The effects of mobility ratio and crossflow between layers are discussed. The effects of variable porosity and fluid saturation are discussed also. It was found that crossflow between layers enhances the oil recovery for systems with favorable mobility ratios (λw/λo < 1) and retards oil recovery for systems with unfavorable mobility ratios. It was found also that crossflow causes the effect of the mobility ratio on oil recovery to become more pronounced. The variation of porosity and fluid saturation with permeability is found to increase oil recovery over that for the case of uniform porosity and saturation for both favorable and unfavorable mobility ratios.