Abstract:
A fluid flow model is comprised of one cross-flow style core holder and a multitude of standard style core holders, all connected by a concurrent combination of serial and parallel flow paths. The sum of these flow paths yields a fluid flow model that closely approximates a small radial slice of a conventional reservoir. The fluid flow model has particular applicability to estimate the requisite treatment fluid for use in acidizing as well as water control methods.

Description:
[0001]     This application claims the benefit of U.S. patent application Ser. No. 60/717,671, filed on September 16, 2005, herein incorporated by reference. 
     
    
     FIELD OF THE INVENTION  
       [0002]     The present invention relates to a method and apparatus for determining certain fluid flow parameters for any porous media.  
       BACKGROUND OF THE INVENTION  
       [0003]     Acidizing a hydrocarbon formation is the process of reacting an acid in the formation to enhance the flow of hydrocarbons to the wellbore. This can be through the dissolution of existing formation material or through the removal or bypass of blockage, often referred to as “damage to the well” which can be caused by natural or man-made conditions. Acidizing, or acid stimulation, opens up the channels around the wellbore, thereby improving the flow rate. When acid is injected into a formation, permeability is increased, thus enhancing the flow of hydrocarbons to the wellbore. This results in an increase or improvement in production from the formation.  
         [0004]     Prior to introducing fluids into the formation, it is desirable to first determine fluid flow parameters by reservoir modeling techniques. Two key measured properties are porosity and permeability of the reservoir. The porosity of a material is the ratio of the aggregate volume of its void or pore spaces (i.e., pore volume) to its gross bulk volume and, in the case of an oil or gas reservoir, is a measure of the capacity within the reservoir rock which is available for storing oil or gas. The permeability of a material is a measure of the ability of the material to transmit fluids through its pore spaces and is inversely proportional to the flow resistance offered by the material. It is important that such fluid flow parameters be determined by reservoir modeling prior to commencement of treatment.  
         [0005]     Porosity and permeability are determined by taking core samples from the reservoir site and carrying out well-defined measurement techniques on the samples. There are several techniques available for making such measurements. Effective radial modeling is difficult to perform due to constraints imposed by the amount of core material typically available. A true radial model would require very large blocks of reservoir material to effectively model flow patterns and stimulation properties of a given acid system. Since most reservoir coring operations generate 4′ diameter (or smaller) cylindrical cores, obtaining large blocks of intact reservoir is in most cases impossible. Therefore, an improved method of radial stimulation reservoir modeling is desired.  
       SUMMARY OF THE INVENTION  
       [0006]     The fluid flow model device of the invention is comprised of one cross-flow style core holder and a multitude of standard style core holders, all connected by a concurrent combination of serial and parallel flow paths. The sum of these flow paths yields a fluid flow model that closely approximates a small radial slice of a conventional reservoir.  
         [0007]     The results of testing performed with the device of the invention can be scaled-up to simulate real world conditions by using a multiplier value that converts from the slice of reservoir examined to an entire cylinder of revolution around a wellbore. Once the volumes of treatment fluid have been ascertained via the model, actual field treatment volumes may be determined by ascertaining the length of the interval to be treated.  
         [0008]     The fluid flow model of the invention also allows for diversion effectiveness to be evaluated as the test is performed, and can be used with any rigid permeable material. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0009]     In order to more fully understand the drawings referred to in the detailed description of the present invention, a brief description of each drawing is presented, in which:  
         [0010]      FIG. 1  is a side view illustrating the direction of injection flow of a test fluid sample using the inventive reservoir modeling technique;  
         [0011]      FIG. 2  is a side view illustrating the production direction of injection flow of a test fluid sample in accordance with the invention;  
         [0012]      FIG. 3  is a front view of the multi-cell fluid flow assembly of the inventive reservoir modeling technique;  
         [0013]      FIG. 4  is a top view of the fluid flow cell assembly of the invention in operation and depicts the injection direction flow;  
         [0014]      FIG. 5  is a side view of the multi-cell fluid flow assembly of the invention;  
         [0015]      FIG. 6  is a cross-sectional view of a typical reservoir which might be modeled using the invention;  
         [0016]      FIG. 6A  illustrates the relative sizes of the treated area of the model of  FIG. 6 ;  
         [0017]      FIG. 7  is the schematic core holder layout for the modeling set forth in  FIG. 6 ;  
         [0018]      FIG. 8  is a side view illustrating an alternative embodiment of the invention using single core holders wherein the cores of contiguous zones have different diameters; and  
         [0019]      FIG. 9  is a side view illustrating another alternative embodiment of the invention using a radial flow model wherein the cores of contiguous zones have different diameters. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0020]     A design for reservoir modeling is disclosed which is more accurate than the methods of the prior art. In addition, the inventive modeling can be more readily scaled-up to the conditions in the field. The flow modeling test apparatus of the invention renders a more realistic depiction of the amount of treatment fluid needed by the operator, e.g., how much acid is needed to conduct an acidizing operation. The method has particular applicability in the estimation of treatment fluid for use in acidizing (including matrix acidizing and acid diversion) as well as water control treatment methods.  
         [0021]     Typically, each of the referenced core holders discussed herein independently has an inner diameter of approximately 8 inches or less and a length of approximately 12 inches or greater. Typically, each of the cores has a diameter from about 1 to about 8 inches. (As used herein, the term “diameter” in relation to the core is synonymous with the outer diameter of the core.) Cores and core holders of other diameters and/or lengths may be employed. For instance, one or more cores may have a diameter of 2 or 4 inches.  
         [0022]     It will be understood by one of skill in the art that the diameter of a core and the inner diameter of a compatible core holder are numerically the same. For instance, the inner diameter of a core holder for a 1 inch diameter core is 1 inch, a 2 inch inner diameter core holder is compatible for a 2 inch core, a 4 inch inner diameter core holder is compatible for a 4 inch core, etc.  
         [0023]     The multi-cell fluid flow methodology of the invention consists of first introducing a drilling fluid into a primary core zone through a cross flow core holder wherein the drilling fluid is permitted to flow across the face and through the first core and leaking material through the core, by means of a cross-flow style core holder. The cross flow core holder allows for the simulation of filter cake buildup on the exposed core face, thereby modeling actual field conditions during drilling.  
         [0024]     A treatment fluid may then be injected into the primary core zone to remove filter cake from the core face and travel through the first core, stimulating the core as it passes through. Upon exiting from the first core, the treatment fluid passes through a mass flow meter. The fluid is then divided and the divided streams pass, via separate flow lines, into distinct successive or contiguous cores. Treatment fluid is then passed through the secondary core zone and exits the secondary cores. Upon exiting from the secondary cores, one or more of the streams may further be partitioned, after being passed through a mass flow meter, and passed into one or more distinct successive or contiguous tertiary core zones. It is understood that the methodology may be continued to successive or contiguous quaternary core zones and so on depending upon the desires and needs of the operator.  
         [0025]     Referring to  FIG. 1 , a side view showing the direction of injection flow, test core  10  is concentrically placed into a large cylindrical core flow holder  11 . Fluid from oil pump  5 , water pump  6  and/or gas pump  7  is pumped through line  8  into core flow holder  11  via lines SA,  6 A and  7 A, respectively.  
         [0026]     Core holder  11  is ported at intervals along its length. As drawn, three openings are placed equally along the length of the core (about every three to four inches for a core of 12 inch length). As depicted, distinct differential pressure transducers  12 A,  12 B and  12 C are respectively placed over their respective opening and the pressure differential is measured. A fourth differential pressure transducer  12 D is placed at the exit port of the core holder. Fluids are then pumped across the face of core  10  while material is leaked through the core. As the fluid flows across the face of core  10 , the differential pressure creates the build-up of a mud cake from the fluid flow onto the face of the core. This, in turn, simulates reservoir conditions during the drilling operation.  
         [0027]     Upon exiting from test core  10 , the fluid process through mass flow meter  13  which measures the rate of the fluid exiting from core holder  11 . The fluid stream is then partitioned through flow lines  14  and  15  into core holder  21  and  31 , respectively. Core holders  21  and  31  house cores  20  and  30 , respectively. Each of core holders  21  and  31  has four differential pressure transducers equally ( 22 A,  22 B,  22 C and  22 D; and  32 A,  32 B,  32 C and  32 D, respectively) spaced along their length. The effluent from each of cores  20  and  30  then flows through mass flow meters  23  and  33 , respectively.  
         [0028]     The fluid exiting from mass flow meter  23  is then partitioned into two additional core holders  41  and  51  which house cores  40  and  50 , respectively. The fluid exiting from mass flow meter  33  may further be partitioned into additional core holders  61  and  71  which house cores  60  and  70 , respectively. Each of core holders  41 ,  51 ,  61 , and  71  is equipped with four differential pressure transducers equally spaced along the length of the core holder. These correspond to transducers  42 A,  42 B,  42 C and  42 D for core holder  41 ; transducers  52 A,  52 B,  52 C and  52 D for core holder  51 ; transducers  62 A,  62 B,  62 C and  62 D for core holder  61 ; and transducers  72 A,  72 B,  72 C and  72 D for core holder  71 .  
         [0029]     Upon exiting from each of test cores  40 ,  50 ,  60  and  70 , the fluid process through mass flow meters  43 ,  53 ,  63  and  73 , respectively; each of which measures the rate of the fluid exiting from the respective core. Data acquisition from each of the mass flow meters is then compared and verified for mass balance as a check of the system (i.e. total mass in is equal to total mass out).  
         [0030]     Unlike core holder  11 , core holders  21 ,  31 ,  41 ,  51 ,  61  and  71  are preferably parallel, versus cross-flow, core holders. Parallel core holders do not allow fluids to be pumped across the core face in a perpendicular flow pattern (normal to the core face) and principally serve to increase the surface area to which the fluid is exposed. The fluids therefore travel parallel to the core holders, through the cores.  
         [0031]     Since each layer of reservoir is simulated by doubling the cross-sectional area available for flow of treatment fluids, the fluid flow model of the invention is closely analogous to a true radial flow model. A true radial model would have increasing core diameter as a function of distance traversed along the longitudinal axis. A true radial model of this nature would be impractical to use, and even more difficult to build. The fluid flow model of the invention approximates the results of a true radial model, while still using core materials actually available in practice.  
         [0032]     Thus, as depicted in  FIG. 1 , fluid is flowed through a total of seven cores. The diameter of each of the cores preferably remains the same. The resultant is analogous to a true radial flow model since the diameter of the cores remains unchanged. The model presents a reasonable simulation of an in-situ radial flow path. The model will predict lower volumes than are really required in practice, because of the constant diameter cores, but that factor can be compensated for when final volumes are calculated. As such, the model may be referred to as a “pseudo-radial flow model.”  
         [0033]     The inventive model is analogous to an in-situ radial flow path since the surface area increases with increasing radius in each distinct core zone though the surface area is constant in each zone. Thus, the fluid flow model of the invention renders an accurate approximation of likely radial flow conditions in-situ.  
         [0034]      FIG. 2  is a side view illustrating the flow in production direction wherein the fluid from oil pump  5 , water pump  6  and/or gas pump  7  is pumped through mass flow meters  5 A,  6 A and  7 A into core holders  80 ,  90 ,  100  and  110 , respectively. The rest of the procedure is the reverse of that illustrated in  FIG. 1 , each of the mass flow meters of  FIG. 1  being capable of dual directional flow.  
         [0035]     The invention is applicable with gases and liquids as well as multi-phase systems. In a preferred mode of operation, no more than two phases are pumped concurrently.  
         [0036]      FIG. 3  illustrates the front view of the cell arrangement with cores  10 ,  20 ,  30 ,  40 ,  50 ,  60  and  70  in each of core holders  11 ,  21 ,  31 ,  41 ,  51 ,  61  and  71 , respectively. The core holders are secured into the illustrated arrangement such that the arrangement is capable of being turned at any angle, horizontally and/or vertically. The entire cell arrangement may be housed in a large temperature chamber  39 , allowing all of the testing to be conducted at elevated temperatures simulating downhole conditions.  
         [0037]      FIG. 4  is a top view of the assembly in operation showing the injection direction flow.  FIG. 5  is a side view of the core testing assembly. All core holders are rigidly connected during testing. This allows testing to be conducted at any desired angle between horizontal and vertical. The entire assembly is housed in a large temperature chamber, which allows the testing to be conducted at any desired temperature as well. Thus, during operation, the assembly may be arranged at the desired angle.  
         [0038]     An exemplary fluid flow methodology of the invention as it applies to a typical hydrocarbon bearing reservoir in accordance with the invention is illustrated in  FIG. 6  (not drawn to scale) wherein the view illustrated is representative of the viewer looking longitudinally down the axis of the wellbore. The concentric circles in  FIG. 6  depict three sections of the reservoir surrounding a 12′ diameter drilled wellbore. Each of the concentric circles represents a core zone wherein “X” represents the primary core zone, “Y” represents the secondary core zone and “Z” represents the tertiary core zone. Each zone has a radius that is 12′ larger than its adjacent section. For instance, where the drilled hole is 12′ in diameter, the core zones have radii of 18′ (primary core zone), 30′ (secondary core zone) and 42′ (tertiary core zone), respectively. While no metal casing is illustrated, it is understood that a cased hole system could also be simulated.  
         [0039]     The figure illustrates what each of the cores would represent in the targeted  25  reservoir. The primary core zone of  FIG. 6  uses only core modeling core  100  to model the behavior of core zone X. The secondary core zone use modeling cores  200  and  300  to simulate the next segment of cylinder Y. Finally, the tertiary core zone uses modeling cores  400 ,  500 ,  600  and  700 . The schematic core holder layout is set forth in  FIG. 7 .  
         [0040]     Assuming the objective is to predict the amount of treatment fluid needed for a  12  inch inner diameter wellbore, Table I illustrates the core methodology of the invention using a 2 inch outer diameter core for the primary, secondary and tertiary zones depicted in  FIG. 6 .  
                                                         TABLE 1                                               Square root           Core   Core   Total   of total           Diameter,   Area,   Treated   treated area           inches   in 2     Area, in 2     (in inches)                                    x-section core 1 - Zone ‘X’   2   3.14   3.14   1.77       x-section core 2 - Zone ‘Y’   2   3.14       x-section core 3 - Zone ‘Y’   2   3.14   6.28   2.51       x-section core 4 - Zone ‘Z’   2   3.14       x-section core 5 - Zone ‘Z’   2   3.14       x-section core 6 - Zone ‘Z’   2   3.14       x-section core 7 - Zone ‘Z’   2   3.14   12.57   3.54                  
 
         [0041]      FIG. 6A  represents the relative sizes of the treated area as though they were converted from cylinders into squares. The numbers represent the dimension (in inches) of the sides of the square blocks of reservoir rock. In this way, square blocks of rock representing the reservoir could be laid like bricks into the configuration shown in  FIG. 6  to allow for calculation of the radial flow values illustrated in Table 2.  
         [0042]     Assuming the methodology is for a 12′ core length, Table 2 illustrates calculation of the multipliers required to complete each zone:  
                                                           TABLE 2                           Assuming a 12″ hole is drilled into the reservoir                    Treated area                   Circumference   square   Effectively   Radial       Radius of Zone   of various radii   Dimension   swept arc   multiplier       (in inches)   (in inches)   (in inches)   (in degrees)   value                    Zone ‘X’ 6   37.70   1.77   16.9   21.30       Zone ‘Y’   113.10   2.51   8.0   45.12       18       Zone ‘Z’   188.50   3.54   6.8   53.17       30                  
 
 The small triangles, e.g., the triangle between core  400  and  700  of the tertiary zone, in  FIG. 6  illustrate the degree which the inventive model deviates from a true radial flow model. 
 
         [0043]     The designated arcs represent a portion of the reservoir. For instance, the primary core zone is characterized by a 16.9° (1.77/37.70×360° ) arc. The multiplier thus of the primary core zone is 21.27 (16.9×21.27=360°, a full circle). Using this information, the scale-up of acid needed for an acidizing job of a 12′ inner diameter wellbore may be estimated.  
         [0044]     An exemplary process for estimating total acid required to stimulate a zone could consist of establishing a core flow model assembly with seven fresh cores, such as, as set forth in  FIG. 6 , a primary core zone containing one core; a secondary core zone containing two cores and a tertiary core zone containing four cores. Each of the cores could then be flooded with a reactive treatment fluid. The treatment fluid effluent from the cores from the tertiary zone could be monitored for reactivity, until such time as reactive fluids are found in abundance. The volume of fluid would be noted at that point in time. Calculations could then be made to determine the quantity of treatment fluid required by the actual reservoir.  
         [0045]     For instance, 1 gallon of reactive fluid may be injected into the flow setup, at which point, reactive fluids would be noted at the effluent end of the tertiary cores. Using the model set forth in  FIG. 6 , the largest radial multiplier value of 53.17 would overestimate the total acid required to achieve equivalent radial penetration distance in the actual reservoir. To calculate the required volume of reactive fluid when using the largest radial multiplier value, one would use the square root of the area covered by the tertiary cores (3.54′) to determine the volume of acid required to treat one linear foot of reservoir. The linear footage multiplier would equal 12′/3.55′=3.39. The total volume per foot of zone would be calculated as 53.17×3.39=180.24 gallons/foot of zone of reactive fluid required to treat one linear foot of reservoir to a depth of penetration of 42′. Total job volume would then be obtained by multiplying the total linear footage of the zone of interest by the volume factor of 180.24 gallons/foot of zone. The resulting volume would be the total required to treat the zone of interest.  
         [0046]     In another variant, the cores of contiguous zones may be characterized by increasing diameter. Likewise, the core holders of contiguous zones may be characterized by increasing inner diameter. In practice, this model, in some circumstances, may be more predictable of volumes of treatment fluid actually required in the field.  
         [0047]     Referring to  FIG. 8 , this fluid flow model may contain fluid pump  805  for introduction of the treatment fluid into the single core zone holder. The fluid enters primary core zone  810  in primary cross-flow core holder  811  of specified diameter, such as 1 inch. The diameter of secondary core zone  820  in core holder  821  would then be greater than the diameter of core  810 . For instance, where the diameter of core  810  is 1 inch, the diameter of core  820  may be 2 or 4 inches. The tertiary core  830  within core holder  831  would then have a diameter of greater size than the diameter of secondary core zone  820 . For instance, the diameter of tertiary core  830  may be 6 to 8 inches or greater. The primary core zone would be connected by serial flow path  815  to secondary core  820  which would, in turn, be connected by serial flow path  825  to tertiary core  830 . Calculations could then be made consistent with those above having a constant diameter.  
         [0048]      FIG. 9  is a further embodiment of the invention wherein the fluid flow model of the invention is closely analogous to a true radial flow model. Referring to  FIG. 9 , a side view showing the direction of injection flow, core  910  is concentrically placed into cylindrical core flow holder  911 . Fluid from the pump is pumped through line  908  into core flow holder  911  and material is leaked through the core. As the fluid flows across the face of core  910 , the differential pressure creates the build-up of a mud cake from the fluid flow onto the face of the core. This, in turn, simulates reservoir conditions during the drilling operation.  
         [0049]     Upon exiting from test core  910 , the fluid process through mass flow meter  913  which measures the rate of the fluid exiting from core holder  911 . The fluid stream is then partitioned through flow lines  914  and  915  into core holder  921  and  931 , respectively. Core holders  921  and  931  house cores  920  and  930 , respectively. Secondary cores  920  and  930  have a diameter greater than the diameter of the primary core holder  910 . For instance, the diameter of the primary core  910  could be 1 inch whereas the diameter of each of the secondary cores  920  and  930  could be between from about 2 to about 4 inches. The effluent from each of cores  920  and  930  then flows through mass flow meters  923  and  933 , respectively.  
         [0050]     The fluid exiting from mass flow meter  923  is then partitioned into two additional core holders  941  and  951  which house cores  940  and  950 , respectively. The fluid exiting from mass flow meter  933  may further be partitioned into additional cores  960  and  970  which are housed by core holders  961  and  971 , respectively. The diameter of each of cores  940 ,  950 ,  960  and  970  is greater than the diameter of the secondary cores  920  and  930 . For instance, the diameter of the tertiary cores  940 ,  950 ,  960  and  970  could be between from about 6 and about 8 inches and could even be greater than 8 inches.  
         [0051]     Upon exiting from each of test cores  940 ,  950 ,  960  and  970 , the fluid process through mass flow meters  943 ,  953 ,  963  and  973 , respectively; each of which measures the rate of the fluid exiting from the respective core. Calculations could then be made consistent with those above having a constant diameter.  
         [0052]     The foregoing disclosure and description of the invention is illustrative and explanatory thereof, and various changes in the size, shape, and materials, as well as in the details of illustrative construction and assembly, may be made without departing from the spirit of the invention.