Method for optimum miscible flooding of reservoirs using a model to determine input profile

Aug. 1, 1967 J P heller 3,333,631

METHOD FOR OPTIMUM MISCIBLE FLOODING OF RESERVOIRS USING A

MODEL TO DETERMINE INPUT PROFILE

Filed Dec. 3, 1964

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FORMATION

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FIG. 3

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FIG. 2

LEGEND

INJECTION WELL PRODUCTION WELL FLUID MOVEMENT

JOHN P. HELLER

INVENTOR.

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ATTORNEY

United States Patent Office

3,333,631

Patented Aug. 1, 1967

3,333,631

METHOD FOR OPTIMUM MISCIBLE FLOODING OF RESERVOIRS USING A MODEL TO DETERMINE INPUT PROFILE

John P. Heller, Dallas, Tex., assignor to Mobil Oil Corporation, a corporation of New York

Filed Dec. 3,1964, Ser. No. 415,640

Claims. (CI. 166—4)

ABSTRACT OF THE DISCLOSURE

This specification describes:

A model is provided representative of a formation, with its injection and production wells, in which miscible flooding is to be used for petroleum recovery. However, the wells employed in the model for injection and production purposes are functionally reversed from those in the formation. Additionally, in the model, the fluids representative of the miscible displacing fluid and the petroleum are also reversed; the former fluid being produced, and the latter fluid being injected, through the wells of the model. Operating this model produces, when breakthrough of the represented displacing fluid occurs, a flood front profile which is the input profile for optimum petroleum recovery in the formation. This input profile is established in the miscible displacing fluid which is injected into the formation in practicing the method for petroleum recovery by which petroleum is produced with optimum recovery.

This invention relates to the recovery of petroleum from a subterranean reservoir and relates more particularly to such recovery by the miscible flooding of the reservoir. In another aspect, the present invention also relates to a method for determining the input profile of a flood front to be established at an injection well for effecting optimum miscible flooding of the reservoir.

Petroleum is recovered from subterranean reservoirs by various methods. Among these methods is the flooding of the formation comprising the reservoir with a fluid miscible with the native petroleum. The fluid miscibly displaces the petroleum from the formation and moves it before a flood front toward a a production well. The method of miscible flooding may be employed initially for the production of petroleum or where further amounts of petroleum are believed to be recoverable from the formation after another procedure has been practiced.

In the method of miscible flooding of the formation for the recovery of petroleum, the successive shapes of the advancing front of the displacing fluid in the formation surrounding each injection well are determined by various factors. Among these factors are included the inhomogeneities of the formation, the number and relative position of the injection nad production wells, the configuration of the gross boundaries of the reservoir, and the fluid properties of the displaced fluid and the displacing fluid. The successive shapes of the area through which the displacement or flood front passes are termed the “sweep patterns” and the ratio of the area within the sweep pattern to the total area at some stage in a displacement program is termed the “sweep efficiency” at that stage of the flood. Obviously, for economic operations, a maximum sweep efficiency is required commensurate with the number of injection and production wells. Usually, the injection and production wells are arranged in regular and uniform geometric patterns. Especially near the edges of a delevolped field, however, the placement of the wells may depart significantly from these patterns. In many instances, high areal sweep efficiencies may be obtained with these well patterns, but for various reasons still higher efficiencies are desired.

One criterion which effects the sweep efficiencies is the shape of the flood front surrounding each injection well. This front shape is determined by various factors which include various geometrical characteristics. These char5 acteristics are the variations in the formation and include inhomogeneities of the porosity, permeability, and native fluid saturation and surface properties of the formation rocks’ matrix. These may be called the formation inhomogeneities, and may include random variations of the jq matrix from microscopic pore-sized dimensions up to large scale trends in the rock properties over the gross dimensions of the formation. They may also be highly ordered variations in the rock parameters, such as a strongly layered structure. Among the geometrical char15 acteristics involved in the determination of the shape of the displacement front are the relative positions of the injection and production wells and the shape of the gross formation boundaries.

In addition to these geometrical factors, the shape of 20 the flood front may also be under the influence of the fluid properties. This is possible if there exists a difference in mobility and density between the displaced fluid and the displacing fluid. Variations in frontal shape may then themselves effect changes in the velocity of fluid move25 ment. Whenever the mobility of the displacing fluid is higher than that of the displaced fluid, the front shape becomes unstable and develops extensions or “fingers.” These fingers may continue to develop during the displacement flooding and will break through into the production 30 well with the resultant dilution of the produced petroleum with displacing fluid. As one result of such breakthrough effects, the lifetime of the field during which petroleum may be produced economically is decreased.

The flood fronts surrounding injection well just after 35 start of the injection program are relatively smooth in their input profile and reflect the shape of the input boundaries, which are usually the cylindrical bores of the injection wells. This is the case even in floods in which the ratio of fluid mobility of the displaced phase to that 40 of the displacing phase is greater than unity, i.e., an “adverse mobility ratio.” As the miscible flooding proceeds, the flood front develops irregularities corresponding to the effects of the geometrical characteristics mentioned above. These are further amplified by the positive feed45 back or instability engendered by the adverse mobility ratio, and develop further into fingers which reduce the sweep efficiency.

A process evolved for remedying the effects of the fingering in the above-mentioned situations for recover50 ing petroleum is described in a copending application, Ser. No. 309,123, filed Sept. 16, 1963, by the present applicant, and now U.S. Patent No. 3,286,768. In this process, within the formation containing petroleum, one or more instability fingers of the displacing fluid are in55 tentionally created and oriented in directions from the injection well to a production well in which the flow is ordinarily the slowest. These instability fingers produce an input profile in the flood front of the displacing fluid of a shape which counteracts the above undesired effects. ⁶⁰ Various methods for creating selectively oriented instability fingering of the displacing fluid to establish a desired input profile in the flood front may be employed. Preferably, an instability finger is created by injecting the displacing fluid from the injection well into the for65 mation through a directionally oriented void created within the formation from the wall of the well. For example, the injection well is first perforated employing conventional gun perforating means to create a directionally oriented void. Through this void is injected the displac70 ing fluid to create one or more instability fingers which establish the desired input profile in the flood front of the displacing fluid. The influence of these intentionally

3,333,631 produced instability fingers in the input profile on the shape of the flood front is maintained as the front moves away from the injection well by continued control of flow of the injected displacing fluid. Further, an optimum input profile if established at the injection well would provide the flood front of displacing fluid with truly radial flow conditions as it approaches the production well. These radial flow conditions would produce increased sweep efficiency and extend to a maximum the time of recovering petroleum from the production well before unduly large amounts of displacing fluid arrive.

The input profile of the flood front may be created initially adjacent the injection well with a shape to reflect application of instability fingers generally aligned with the direction of the slowest flow of displacing fluid. However, it would be preferred that a more exact method be employed for determining the optimum input profile of the flood front of the displacing fluid immediately adjacent the injection well for effecting optimum recovery of petroleum by the miscible flooding procedure.

It is the principal purpose and object of the present invention to provide a method for recovering petroleum from subterranean reservoirs by miscible flooding procedures employing the determination of the optimum input profile to be established for the displacement flood front at the injection well and establishing the optimum input profile in the flood front of the displacing fluid for effecting the miscible flooding of the formation for the improved recovery of petroleum.

The objects of this invention will be apparent when read in conjunction with the following description, the appended claims, and the attached drawings, wherein:

FIGURE 1 is a plan view of a petroleum reservoir provided with a 5-spot well pattern in the producing formation in which one quadrant is illustrated with the positions and shapes of successive flood fronts of the displacing fluid injected into the centrally disposed injection well in accordance with prior art miscible flooding procedures;

FIGURE 2 is a plan view of a petroleum reservoir model of the formation shown in FIGURE 1; and

FIGURE 3 is the formation in plan view including the same well pattern as in FIGURE 1 but illustrating the positions and shapes of successive flood fronts in the displacing fluid resulting from employing the present invention.

The present invention is based on the modeling of the Darcy flow of fluids through porous materials, and on the principle of reversibility in such flows.

The operation of reservoir models representing a Darcy flow system in the actual operation of the formation is dependent upon certain known principles of dimensional analysis. Various types of hydrodynamic, potentiometric and electrical analog models have been employed in miscible flooding studies of reservoirs and for other purposes. Examples of these models are the conductive cloth models, gelatin models, electrolytic models, sand bed models, and the electrical analog models employing circuits of resistances and capacitances.

In the hydrodynamic model, fluids are flowed through permeable porous media, or within a narrow gap between two flat plates, to represent the Darcy flow system of the formation in a reservoir study. In the potentiometric or electrical analog models, the fluid flows and the permeable porous media of the prototype formation are represented functionally through analogy of the flow of electricity to the Darcy flow system. For example, the use of models in methods for increasing the recovery of petroleum from formations is described in United States Patents 2,867,277 and 2,994,372. The first-identified patent illustrates HeleShaw models, which are hydrodynamic models. For the results of the models representing Darcy flow systems to be transferred practicably to the operation of the formation requires that the two be substantially similar in their Darcy flow systems. For this purpose, the following conditions of similarity must be present in both the model and the formation.

Geometrical similarity

There must be a geometrical similarity of both systems in the microscopic boundary shapes, both internal and external, and in the transitional zone shape at some ref5 erence time of the displacement front. In addition, all known inhomogeneities, including porosity and permeability, should also be scaled such that these values at any point in the model are proportional to their respective values in the formation.

⁴® Dimensionless numbers

The values of certain dimensionless numbers, which are descriptive of the relative strength of the various natural processes shaping the displacement and flow proc15 esses, must be substantially the same in both model and formations. These dimensionless numbers may vary in their precise form and some degree of choice in their selection exists. However, a complete set is as follows:

(A) The mobility ratio M must be the same in both 20 systems. M is in this case, where miscible displacement is effected, the ratio of the viscosity of the displaced fluid to the viscosity of the displacing fluid.

(B) The “Gravity Override Number” must be the same. This function is defined as wherein:

g is the acceleration of gravity;

³⁰ k is the formation permeability;

Δρ is the density difference between the displaced and the displacing fluids;

μ is their mean viscosity; and

W is the Darcy velocity at some characteristic point in the ³⁵ flow system.

This insures that in both systems the effect of gravity on the orientation of the isodensity surfaces will be the same. The scaling of this number is only unnecessary when the 40 overriding effect is negligible.

(C) The “Transverse Dispersion Number” must be the same in both systems. The function is defined as

AW ⁴³ wherein:

D_t is the coefficient of transverse dispersion;

A is a characteristic macroscopic length in the flow length; and ₅₀ W is again the Darcy velocity at some characteristic point in the flow system.

The coefficient D_t is a function of the molecular diffusion coefficient between the fluids used, and also depends on the internal rock geometry and the flow rate.

(D) The “Longitudinal Dispersion Number” must be the same in both systems. This function is defined as

Z\—2l

AW wherein:

A and W have the above definitions; and

Di is the coefficient of longitudinal dispersion of the flow system.

The above characteristics must be present in any model used for determining accurately the displacement front movement in miscible flooding procedures as will be apparent to those skilled in the art. The changes in the shape of the displacement front as mentioned also depend 70 on the geometrical characteristics and on the dimensionless numbers which have been defined. The shape of the displacement front may be denoted by not only the single curve which locates, for example, a mid-concentration line between the displacement and the displacing liquids, 75 but by the entire set of isoconcentration curves specifying

3,333,631 the scalar (concentration) field. Obviously, if the transition zone between the fluids were of zero thickness, then the front would be infinitely sharp since all of the isoconcentration curves would merge into one. In the practical case, however, to be considered, the front is graded and therefore the transition zone occupies an appreciable area.

The time evolution of the shape of the displacement front is dependent on the above set forth dimensionless numbers and this dependence is of two kinds. These kinds are the dispersive changes and the Darcy-changes. The dispersive changes occur due to the process of diffusion and its interaction with the microscopic fluid velocity variations in the formation. By maintaining the two dispersion numbers, the Transverse Dispersion Number, and the Longitudinal Dispersion Number as well as the concentration gardient small in magnitude, the dispersive changes will be negligible in comparison with those frontal shape changes dependent upon the Darcy-changes. These Darcychanges may be classified themselves as those which relate to the shape of the external boundary and those which occur as a result of the feedback situation engendered by viscosity and density differences between the displaced and the displacing fluids.

Referring now to FIGURE 1, the Darcy-changes and their results will be described in reference to a petroleum reservoir consisting of formation 10 having uniform isotropic geometrical characteristics and in which a conventional miscible flooding procedure is practiced. In the formation 10, injection well 11 and production wells 12, 13, 14, and 15 are provided in a 5-spot uniform and regular geometric well pattern. The increased fingering of successive fronts created by injecting a displacing fluid, such as propane or liquefied petroleum gases, denoted hereinafter as LPG, into the injection well 11 clearly displays in the upper right quadrant of formation 10 the response to the existing geometrical characteristics. These sweep patterns behind these fronts are typical of a 5-spot displacement with a moderately adverse mobility ratio and with the flood front graded sufficiently to suppress the development of high wave number instability fingers. They do show the growth of the dominant instability pattern of wave number 4, which is initiated by the fourfold symmetry of the 5-spot pattern. The front 16 has a circular shape representative of radial flow conditions from the injection well 11. The degree to which the “nosing” of each of the successive fronts 17, 18, 19, and 20 protrudes, as well as rate at which the shape change by fingering occurs, is dependent on the viscosity ratio of the displacing and the displaced fluids. The front 20 illustrates breakthrough of the displacing fluid at a time when a substantial amount of petroleum or crude oil remains within the confines of the 5-spot symmetry unit. Both of these Darcychanges in frontal shape are reversible in time. It is on this time reversibility that the present method is based, and by which a model is employed, wherein the positive time direction in the formation is represented by negative time direction in the model.

Referring now to FIGURE 2, the method of the present invention will be described wherein a model is employed of the formation 10 which by prior art flooding procedures produces the undesired fingering effects in the successive fronts shown in FIGURE 1. FIGURE 2 represents a model 21 of the formation 10 portrayed in FIGURE 1. This model 21 may be constructed in any conventional manner. It also will be helpful to match dispersion numbers with the reservoir, however.

In the model employed, whether of the hydrodynamic or any other known types, it is to be understood that the reservoir model is arranged to have represented functionally the same Darcy flow system including geometrical similarity and dimensionless numbers, and the same arrangement pattern for well means employed for injection and production purposes as in the formation. Also, fluid flows as functionally employed in the model bear a cer6 tain mobility ratio relationship to their counterparts in the formation.

The model construction described in the aforementioned United States Patent 2,867,277 for a hydrodynamic model 5 in providing the model 21 is employed for illustrative and descriptive purposes. The model 21 is arranged to have functionally the same Darcy flow system as the formation of the formation 10. However, the production well 13 in the formation 10 is represented by injection well 22 ₁₀ in the model 21, and the injection well 11 in the formation 10 is represented by a production well 23 in the model 21.

The model 21 is now operated with displaced and displacing fluids having a mobility ratio M equal to the 15 reciprocal of the ratio of the viscosity of the displaced fluid to the viscosity of the displacing fluid associated with the prototype formation 10.

In a particular embodiment the displacing and displaced fluids employed in the model 21 may be the displaced 20 and displacing fluids, respectively, associated with the formation 10. More particularly, and as one example, the native petroleum of the formation 10 is introduced via the injection well 22 into the model 21 and the displacing fluid injected into the formation 10, such as LPG, 25 ^ls the displaced fluid native to the model which fluid is produced from the production well 23. However, other fluid flows of displacing and displaced fluids as functionally employed in the model 21 may be used representing the displacing and displaced fluids associated with the forma30 tion 10 but with the reciprocal mobility ratio relationship.

Introduction of the displacing fluid through the injection well 22 into the model 21 results in successive fronts 24, 25, 26, 27 and 28 being created in progression toward the production well 23 from which displaced fluid is pro35 duced. Obviously, these fronts 24 to 28, inclusive, are successively formed positive in time direction relative to the model 21 but negative in time direction when compared to the formation 10 of FIGURE 1. It is apparent that whereas the displacement fronts 16 to 20, inclusive, 40 are unstable and result in the fourth-order fingering into the formation 10 of FIGURE 1, the fronts 24 to 28, inclusive, are superstable in the model 21 portrayed in FIGURE 2. Thus, the fronts 24, 25, and 26 adjacent the injection well 22 correspond to radial flow conditions 45 with flow velocity independent of azimuth angle and thusly are circular. Each of the successive fronts 27 and 28 toward the production well 23 undergoes transition from a circular shape as the influence of the production well 23 overcomes eventually the superstability resulting 50 from the favorable mobility ratio. Of particular notice is the shape or the profile of the front 28 immediately adjacent the production well 23 in the model 21. Since fluid movements in the model 21 in FIGURE 2 are negative in time direction relative to their counterparts in 55 the formation 10 shown in FIGURE 1, the profile of the flood front 28 adjacent the production well 23 in FIGURE 2 is of the desired shape for the injection front to be established by any suitable means at the injection well 11 in the formation 10 shown in FIGURES 60 1 and 3. Obviously, the sequence of flood front configurations in the model 21 in FIGURE 2 will be the same as that desired for the formation 10 except for a reversal of their order in time and direction of movement. The method of determining the input profile has many uses 65 besides in the following described method for recovering petroleum. For example, such input profiles may be determined in studies for the best placement of wells in a reservoir.

Referring now to FIGURE 3, there is shown the forma70 tion 10 with the injection well 11 and production well 13 as priorly described with reference to FIGURE 1, and wherein the shape of the flood front 28 obtained with the model 21 of FIGURE 2 is established as the input profile, adjacent the injection well 11, in a flood front 29 of in75 jected displacing fluid. The displacing fluid may be any

3,333,631 fluid employed for the miscible displacement of petroleum, and one example is LPG. It will be seen that the continued injection of the displacing fluid into the injection well 11 at the flow conditions employed for establishing the desired input profile displaces the petroleum toward, and to be produced from, the production well 13 on the formation 10 shown in FIGURE 3. This action will produce successive displacement fronts 30, 31, 32, and 33 having configurations exactly as they appear in the model 21 of FIGURE 2 in the fronts 27, 26, 25, and 24, respectively. The only difference between these successive displacement fronts in FIGURES 2 and 3 is that they are reversed in their order in time and direction of movement. Thus, the successive fronts 31, 32, and 33 have a circular configuration representing radial flow conditions for some distance from the production well 33. These radial flow conditions produce a substantial increase in the sweep efficiency of the displacement fronts in the miscible flooding procedure. As one result, a greater amount of petroleum is produced from the formation 10 than could be obtained in the formation 10 by conventional methods as represented in FIGURE 1.

As previously mentioned, the process of dispersion causes the frontal thickness to become progressively greater in the positive direction of tiime in both the model 21 of FIGURE 2 and the formation 10 of FIGURE 3. This, of course, limits the time reversal modeling method of this invention to situations in which the dispersive effects are small. However, it will be seen that these situations are precisely those to which modeling is limited by other considerations as well. Additionally, it is desired to reduce to a great degree the growth of instability fingers in the displacement fronts 29 to 33 of high-wave numbers in the unstable displacement front configuration of the formation 10 shown in FIGURE 3. The formation of the high-wave number fingers in the displacement fronts may be restricted where the front has a relatively broad transition zone, that is, one with a large grading distance. In this case, the growth rates of the high-wave number fingers are much reduced, while the growth rates of the lower order wave perturbations, such as the fourth (which is dominant when -a 5-spot geometric well pattern is employed) are relatively unaffected. By employment of large grading distances in the model 21, as well as in the formation 10, the undesired effects of dispersion and of the formation of highwave number fingerings are avoided. Generally, an appropriate grading length will depend upon the value ot the mobility ratio. Preferably, the higher the mobility ratio M, the greater will be the required grading length. However, this is true in all models employed in miscible displacement flooding procedures.

Thus, in summary, the shape of the flood front 28 in the model 21 is determined from the last of the successive flood fronts 24 to 28 as has been described. The shape of the flood front 28 may be recorded in any suitable manner for future use, if desired. This shape is utilized as the input profile of the flood front 29 to be established adjacent the injection well 11 of the formation 10. The input profile of the flood front 29 can be established by the injection of the displacing fluid in any suitable manner from the injection well 11. For example, the selective formation of instability fingers by directional perforation may be used. Continuing injection of the miscible displacing fluid, such as LPG, into -the injection well 11 produces the successive fronts 30, 31, 32, and 33 until the breakthrough occurs into the production well 13. The displaced petroleum is produced or recovered from the production well 13 under radial flow conditions which extend therefrom a substantial distance toward the injection well 11.

Obviously, by the foregoing steps, greater sweep efficiency by the displacing fluid is obtained along with -an extension of the time over which petroleum can be pro8 duced from the production well 13 without undue collateral production of the displacing fluid. These results mean an improved production of petroleum through utilization of the method of this invention.

From the foregoing it will be -apparent that a method is disclosed which accomplishes all of the stated objects of this invention. Various modifications of the disclosed method may be made by those skilled in the art without departing from -the spirit of this invention. For this and ₁₀ other reasons, the present description is intended to be illustrative of this invention, -and only the appended claims -are to be considered -as limitative of the invention.