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Abstract Oil displacement by injection of chemical solutions is a widespread Enhanced Oil Recovery method. Analytical models for one-dimensional displacement of oil by water with chemical components have been developed since the 1960´s. This problem involves complex physical-chemical processes of interphase mass transfer, phase transitions and transport properties changes. The continuous injection of this kind of fluid would be very expensive, so, the injection of chemical slugs is an attractive alternative to improve the recovery of mature oil fields. The continuous injection of chemical solutions is a Riemann problem, easily solved by the introduction of a self-similar variable. Nevertheless, the slug injection is not self-similar, and the problem becomes much more complex from the mathematical point of view. This paper presents the analytical solution of chemical slug injection in an oil reservoir. A flow potential associated with the conservation of the aqueous phase is introduced as a new independent variable instead of time. This change of variables allows the system splitting into one equation (lifting equation) and a thermodynamic system (auxiliary system). The number of auxiliary equations is less than the number of equations in the compositional model by one. In this paper different adsorption isotherms were analyzed. The transport equation solution, or lifting problem solution involves interaction between waves of different families and allows the design of slug sizes in order to obtain the maximum efficiency of this process. Another important application of these solutions is the prediction of chemical flooding regardless of the transport properties (relative permeabilities and viscosities). If the mobility ratio is close to one, this model may be applied in the development of streamlines simulators. Introduction Enhanced Oil Recovery (EOR) methods are applied to increase the recovery from reservoirs whenever a conventional method is not attractive. Among different EOR methods the injection of chemical solutions plays an important role in mature field additional recovery. The chemical methods of enhanced oil recovery include injection of aqueous solutions of several chemical components (polymers, surfactants, salts, etc.) that affect the flow of each phase in porous media (Lake, 1989). Polymer flood consists of adding polymer to the injected water to decrease its mobility. This technique improves reservoir sweep and reduces the amount of injection fluid necessary to recover a given amount of oil. Low concentrations of water-soluble polymers added to the injection water increase the injected fluid viscosity. Displacement of oil by these fluids involves complex physicochemical processes of interphase mass transfer, phase transitions and transport properties changes. These processes can be divided into two main categories: thermodynamical and hydrodynamical ones. They occur simultaneously during the displacement, and are coupled in the modern mathematical models of EOR. One-dimensional displacement of oil by multicomponent chemical solutions taking into account adsorption is described by a hyperbolic system of conservation laws. These systems have been studied since the end of 50's. Fayers and Perrine (1959) were pioneers; they analyzed a 2×2 hyperbolic system considering continuous polymer injection. The problem of one dimensional isothermal multicomponet chromatography with local phase equilibrium without diffusion effects was solved considering the Langmuir's adsorption isotherm. The results showed the fitting between the thermodynamic system and the quasilinear equation theory (Rhee et al, 1970). Entov and Polishchuk (1975) studied the effects of adsorption and diffusion in filtration process through experimental data.
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Chemical flooding methods (1.00)
- Reservoir Description and Dynamics > Fluid Characterization > Fluid modeling, equations of state (1.00)
Abstract The injection of chemical solutions plays an important role in increasing the recovery factor of mature fields. Compositional models considering adsorption phenomena describe polymer/surfactant flooding as a function of the chemical component concentration and salinity of reservoir/injection water. The concentration part of the solution for 1-D multicomponent polymer/surfactant flooding is completely defined by adsorption isotherm and is independent of relative permeabilities and phase viscosities. The one-phase displacement solution has been already developed and it is a well-known problem. The continuous injection of chemical solutions is a Riemann problem solved by introduction of a self-similar variable. In this paper the solution of the two-phase problem for chemical flooding is presented. It is considered the injection of two dissolved components considering adsorption phenomena for two different isotherms: Langmuir and Henry. A flow potential associated with the conservation of the aqueous phase is introduced as a new independent variable instead of time. This change of variables allows the system splitting in one equation and a thermodynamic system. The number of auxiliary equations is less than the number of equations in the compositional model by one. The solution of the thermodynamic part was done by the method of characteristics and it is completely determined by the adsorption isotherm. Once the two-component adsorption problem is solved, the two-phase flow behavior can be predicted. The applications include the choice of the chemical components to be injected for each reservoir, and also evaluate water compatibility. Another important utilization is testing of numerical compositional simulators by checking the independence of compositional dynamics on transport properties and by comparison of the numerical and analytical solutions. The obtained analytical solutions may be used in the development of streamline chemical EOR simulators. Introduction Enhanced Oil Recovery (EOR) methods include injection of different fluids into reservoirs to improve oil displacement. The EOR methods may be classified into the following kinds: chemical methods, solvents methods and thermal methods. The chemical fluids most commonly injected are polymers, surfactants and micellar solutions. Oil displacement by chemical solutions is a widespread Enhanced Oil Recovery method. Analytical models for 1-D displacement of oil by water with chemical compounds have been developed since the 1960's. This problem involves complex physical-chemical processes of inter-phase mass transfer, phase transition and transport properties changes. One-dimensional displacement of oil by an aqueous solution containing several chemicals species considering adsorption is described by an (n+1)×(n+1) hyperbolic system of conservation laws, where n is the number of components in the displacing phase. Continuous polymer injection results in a Riemann problem for this hyperbolic system. The displacement of oil by a polymer slug with water drive is described by an initial and boundary value problem with piecewise constant initial data and results in wave interactions. The Riemann problem for the displacement of oil by hot water is mathematically equivalent to one-component polymer flooding (n=1) for a convex sorption isotherm. Several Riemann solutions for the case n=2 have already been found and a graphical procedure for the solution of this problem was developed. The Riemann solution for n-component polymer flooding was found for the case where the i-th adsorbed concentration depends only on the concentration of the i-th component in the aqueous phase. Exact solutions for non-self-similar slug problems were also published. The Riemann solution for the (n+1)×(n+1) system for two-phase n-component displacement was studied in several papers 9–12 for Langmuir's type adsorption isotherm. The particular case of one-phase n-component flow leads to an (n)×(n) hyperbolic system, which was used for solving the Riemann problem. The projection and lifting procedures developed allow the calculation of any Riemann solution for the two-phase system once the associated one-phase solution is known. The theory developed is based on the fact that the Riemann problem solutions depend on a single parameter, x/t, but this theory cannot be extended to non-self-similar Cauchy/initial-boundary value problems.
Abstract Enhanced Oil Recovery (EOR) methods include injection of different fluids into reservoirs to improve oil displacement. Analytical models for 1-D displacement of oil by gas have been developed during the last 15 years. It was observed from semi-analytical and numerical experiments that several thermodynamic features of the process are not dependent on transport properties. The model for one-dimensional displacement of oil by miscible fluids is analyzed in this paper. The main result is the splitting of thermodynamical and hydrodynamical parts in the EOR mathematical model. The introduction of a potential associated with one of the conservation laws and its use as an independent variable reduces the number of equations. The reduced auxiliary system contains just thermodynamical (equilibrium fractions of each phase, sorption isotherms) variables and the lifting equation contains just hydrodynamical (phases relative permeabilities and viscosities) parameters while the initial EOR model contains both thermodynamical and hydrodynamical functions. So, the problem of EOR displacement was divided into two independent problems: one thermodynamical and one hydrodynamical. Therefore, phase transitions occurring during displacement are determined by the auxiliary system, i.e. they are independent of hydrodynamic properties of fluids and rock. For example, the minimum miscibility pressure (MMP) is independent of relative permeabilities and phases viscosities. The new technique developed permits splitting for both self-similar continuous injection problems and for non-self-similar slug injection problems. Splitting significantly reduces amount of calculations for sensitivity study with respect to transport properties: auxiliary thermodynamic problem may be solved once for given reservoir and injected compositions; variation of relative permeabilities and viscosities should be performed just in the solution of one transport equation. In this paper, different analytical solutions for 4-component gas injection problems are analysed. It was considered the injection of nitrogen and hydrocarbon gases into a three-component liquid reservoir fluid. The eigenvalues of the system are related to the propagation velocity of each component in porous media. The existence of elliptic regions (complex eigenvalues) is well known in three-phase flow, but for the first time it is shown that this feature may also occur in two-phase flow. The independence of compositional dynamics on transport properties can be used for testing numerical compositional simulators. If the mobility ratio is close to one, this model may be applied in the development of streamlines simulators. Introduction The injection of fluids not present in reservoirs is the technical definition of Enhanced Oil Recovery (EOR) methods 1. These methods may be classified into three main categories: chemical, solvent and thermal. Solvent methods of EOR may be either miscible or immiscible, depending on the thermodynamic behavior of the mixture of fluids at reservoir temperature and pressure. It was one of the earliest methods used to improve oil recovery. Immiscible solvent displacement reduces oil viscosity and swells reservoir fluid, whereas miscible flooding; besides the characteristics already cited also develops miscible displacement, eliminating interfacial forces. Miscible solvent flooding techniques always involve some mass transfer between phases, like vaporization or condensation of components. The choice of kind and amount of fluid to be injected is strongly dependent on economical aspects. Although liquefied petroleum gas (LPG) has already been the most used solvent injection fluid, now carbon dioxide plays an important role. Usually, a solvent slug is injected into reservoir and driven by a "follow up" fluid.
- Materials > Chemicals > Commodity Chemicals > Petrochemicals (1.00)
- Energy > Oil & Gas > Upstream (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Chemical flooding methods (1.00)
- Reservoir Description and Dynamics > Fluid Characterization > Fluid modeling, equations of state (1.00)
Abstract Among different Enhanced Oil Recovery (EOR) methods, the injection of chemical solutions plays an important role in mature fields additional recovery. Analytical models for 1-D displacement of oil by water with chemical compounds have been developed since the 1960´s. The interfacial activity and mobility control of a chemical flooding process are affected by the concentrations of the ionic species that are present in the water. This problem involves complex physical-chemical processes of interphase mass transfer, phase transition and transport properties changes. The one-phase displacement solution has been already developed and it is a well-known problem. However, its application is limited to already water flooded reservoirs. In this paper the solution of the two-phase problem is presented. A flow potential associated with the conservation of water phase is introduced and used as a new independent variable instead of time. This technique permits splitting the system of equations into a thermodynamic system and one transport equation. It is possible to show from analytical modelling of multi-component polymer/surfactant flood that the concentration "part" of the solution is completely defined by adsorption isotherms (thermodynamic part, called auxiliary system) and does not depend on relative permeabilities and phase viscosities. The number of auxiliary equations is less than the number of equations in the compositional model by one. Once the multi-component adsorption problem is solved, the 2-phase flow behavior can be predicted. This work shows analytical solutions of 1-D oil displacement by water containing two adsorbing cations and one anion for different salt concentrations in injected and formation waters. Electroneutrality and Gapon equilibrium equation are considered. One of the most important applications of these solutions is design of chemical flooding regardless of the water saturation. Introduction Enhanced Oil Recovery (EOR) methods include injection of different fluids into reservoirs to improve oil displacement. The EOR methods may be classified into the following kinds: chemical methods, solvents methods and thermal methods. The chemical fluids most commonly injected are polymers, surfactants and micellar solutions. One-dimensional displacement of oil by an aqueous solution containing several chemicals species considering adsorption is described by an (n+1)´(n+1) hyperbolic system of conservation laws, where n is the number of components in the displacing phase. Continuous polymer injection results in a Riemann problem for this hyperbolic system. The displacement of oil by a polymer slug with water drive is described by an initial and boundary value problem with piecewise constant initial data and results in wave interactions. The Riemann problem for the displacement of oil by hot water is mathematically equivalent to one-component polymer flooding (n=1) for a convex sorption isotherm. Several Riemann solutions for the case n=2have already been found and a graphical procedure for the solution of this problem was developed. The Riemann solution for n-component polymer flooding was found for the case where the i-th adsorbed concentration depends only on the concentration of thei-th component in the aqueous phase. Exact solutions for non-self-similar slug problems were also published. The Riemann solution for the (n+1)´(n+1) system for two-phase n-component displacement was studied in several papers for any arbitrary shape of sorption isotherms. The particular case of one-phase n-component flow leads to an (n)´(n) hyperbolic system, which was used for solving the Riemann problem. The projection and lifting procedures developed allow the calculation of any Riemann solution for the two-phase system once the associated one-phase solution is known. The theory developed is based on the fact that the Riemann problem solutions depend on a single parameter,x/t. Thus, the theory cannot be extended to non-self-similar Cauchy/initial-boundary value problems.
Abstract Enhanced Oil Recovery (EOR) methods include injection of different fluids into reservoirs to improve oil displacement. These processes can be divided into two main categories: thermodynamical and hydrodynamical ones. Analytical models for 1-D displacement of oil by gas have been developed during the last 15 years. It was observed from semi-analytical and numerical experiments that several thermodynamic features of the process (MMP, key tie lines, etc) are not dependent of transport properties. The model for one-dimensional displacement of oil by miscible fluids is analyzed in this paper. The main result is the splitting of thermodynamical and hydrodynamical parts in the EOR mathematical model. The introduction of a potential associated with one of the conservation laws and its use as an independent variable reduces the number of equations. The reduced auxiliary system contains just thermodynamical (equilibrium fractions of each phase, sorption isotherms) variables and the lifting equation contains just hydrodynamical (phases relative permeabilities and viscosities) parameters while the initial EOR model contains both thermodynamical and hydrodynamical functions. So, the problem of EOR displacement was divided into two independent problems: one thermodynamical and one hydrodynamical. Therefore, phase transitions occurring during displacement are determined by the auxiliary system, i.e. they are independent of hydrodynamic properties of fluids and rock. For example, the minimum miscibility pressure (MMP) is independent of relative permeabilities and phases viscosities. The splitting technique may be used for the solution of Riemann problems and for non-self-similar displacement of oil by rich gas solvent slug with lean gas drive considering ideal behavior of the fluids, i.e. constant distribution coefficients. For 3-D displacements, the splitting is valid if and only if the total mobility is constant. It allows the application of the obtained 1-D analytical solutions in streamline simulators. The technique reduces significantly the amount of calculations for sensitivity study of gasflooding processes with respect to transport properties: auxiliary thermodynamic problem may be solved once for given reservoir and injected compositions; variation of relative permeabilities and viscosities should be performed just in the solution of one transport equation. Introduction The injection of different gases (methane, rich hydrocarbon gases, carbon dioxide, nitrogen and various combinations) in order to improve displacement by mass exchange between oleic and gas phases is the basis of the solvent methods of enhanced oil recovery[1]. One dimensional displacement of oil by gas in large scale approximation is described by (n-1)x(n-1) hyperbolic system of conservation laws, where n is the number of components[2–5]. Continuous gas injection results in a Riemann problem for this hyperbolic system. Displacement of oil by a gas slug with another gas drive is described by the initial and boundary value problem with piece-wise initial data[6]. The elementary hyperbolic waves in the 2x2 system for two-phase three-component displacement can be described both analytically and graphically[7]. It may be used to find several exact solutions for Riemann problems of continuous gas injection. Analytical 1D models for different types of ternary phase diagrams and boundary conditions related to injection of different fluids were developed using the same technique[1,8–10]. The semi-analytical solutions for n-component gas flooding obtained by numerical combination of shocks and rarefactions waves allow thermodynamic analysis, minimum miscibility pressure (MMP) calculations and recovery estimates[2–5]. The technique was developed for any number of components. A hyperbolic system for gas flooding is similar to the one of polymer flooding. The observation that concentration waves in 2-phase environment can be obtained from one phase multi component flow was used for the development of a semi-analytical Riemann problem solver for two-phase n components polymer flooding[11]. The exact solutions for this problem with adsorption governed by Langmuir isotherm were obtained using 1 phase solution[11,12]. This technique cannot be extended for non-self-similar problems of oil displacement by polymer slugs.
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Gas-injection methods (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Chemical flooding methods (1.00)