1. Field of the Invention
The present invention relates to modeling the structure of subsurface reservoirs, and more particularly to forming models of fracture networks in a reservoir based on pressure transient test measurements obtained from a formation layer of interest in the reservoir.
2. Description of the Related Art
In reservoir engineering, accurate modeling of subsurface reservoirs and formations, and numerical simulation of fluid flow related processes through computer processing, are widely used for accurate oil and gas reservoir management and development plans. Both direct and indirect methods are used to assess the nature of the rock containing hydrocarbon fluids.
Direct methods use direct measuring tools such as well logging tools. However, the ability of such tools to obtain data measurements as a function of depth into the reservoir from the tools is shallow, typically on the order of a few inches. For indirect measurements tools such as pressure gauges are used to record pressure changes due to well rate variations. Indirect measurements involve flowing the well and recording the pressure changes with time. The pressure data obtained are then processed in a number of different ways to describe the reservoir and model the fluid flow processes.
Reservoir modeling is, to a great extent, an art and has its benefits and restraints. There are two main methods to model the reservoirs namely; numerical and analytical. Numerical modeling is flexible, however, it can be inaccurate due to instability of computer processing to solve multiple, multi-variable non-linear differential equations expressing the physical relationships of reservoir rock and fluid phenomena and characteristics. Furthermore, since reservoirs of interest are quite large and there is an increasing need for accuracy, hence, numerical models of a reservoir are organized into a large number of individual cells. The number of cells can be from tens to hundreds of millions for typical reservoirs. Instability in the modeling and the gridding effect make numerical modeling unsuitable to address the more complex cases.
Conversely, analytical methods are exact, accurate, stable solutions and serves as a platform to address more general/complex cases. Moreover, generating Type-Curves for unlimited scenarios is a byproduct of the solution. Although, analytical models are more accurate than numerical models, yet, they are much harder to develop especially with complex geology and well geometries, as the number of variables increase and hence, become hard to solve. Therefore, developers tend to simplify such a complex problem by dividing the problem into segments, replacing the real variables with dimensionless variables and also use mathematical transformations should they need to. This approach results in a set of equations comprising important parameters that are solved analytically or so called semi-analytically.
In current oil production operation ventures, it is becoming increasingly likely to encounter complex geology such as natural and/or man-made fractures. In particular, in transient well test pressure data (derivative plots) from complex fractured carbonate and sandstone reservoirs, a unique flow pattern has been observed indicating complex geology characterized by a fracture flow signature in the flow pattern at early times and a conductive fault indicator in late times. The presence of such complex geology and well geometry in formations of interest is also widely identifiable through the growing number of image and production logs. The identification, characterization and modelling of reservoirs with such pressure signatures have, therefore, become increasingly important. However, so far as is known, there is no analytical solution to interpret such well test data signatures and hence, numerical simulation of the flow has so far been done, which is known to be cumbersome and impractical.
Briefly, the present invention provides a new and improved computer implemented method of determining a model of a subsurface earth formation, having a well intersecting a complex geological network of a fault and a fracture in the formation, based on a pressure transient test of the formation. The computer implemented method obtains a test measure of bottom-hole pressure and also obtains a test pressure derivative at sampled instants of measurement during a pressure transient test of the formation. An estimated reference type-curve set of a plurality of type-curves of well pressures in the well and pressure derivatives for selected test values of reservoir capacity, fracture conductivity, fault conductivity value and distance from the tested well and the formation capacity are received. A model well pressure of the formation is determined based on the test measure of well pressure and an estimated value of fracture conductivity, fault conductivity, distance and the formation capacity. A model pressure derivative is then determined based on the test measure of well pressure and the estimated values in the formation. A model type-curve is then formed of the determined model well pressure of the formation and the model pressure derivative. The model type-curve of the determined model well pressure of the formation and the model pressure derivative are then determined with the plurality of type-curves of the estimated reference type-curve set. If the model type-curve matches one of the plurality of type-curves of the estimated reference type-curve set within an acceptable limit of accuracy, the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation in addition to its proximity and reservoir capacity of the matched type-curve of the estimated reference type-curve set are stored as models of the fracture conductivity and the fault conductivity of the formation. If not, the estimated values are adjusted, and the steps of determining a model well pressure, determining a model pressure derivative, forming a model type-curve and comparing are repeated based on the adjusted estimated value of fracture conductivity, fault conductivity and its remoteness from the tested well along with the formation capacity.
The present invention also provides a new and improved data processing system for determining a model of a subsurface earth formation, having a well intersecting a complex geological network of a fault and a fracture in the formation, based on a pressure transient test of the formation. The data processing system includes a processor, which obtains a test measure of bottom-hole pressure in the well and also a test pressure derivative at sampled instants of measurement during the pressure transient test of the formation. The processor receives an estimated reference type-curve set of a plurality of type-curves of well pressures in the well and pressure derivatives for selected test values of fracture conductivity fault conductivity in the formation. The processor then determines a model well pressure of the formation based on the test measure of well pressure and an estimated value of fracture conductivity and an estimated value of fault conductivity and its proximity along with the reservoir capacity in the formation, and also determines a model pressure derivative based on the test measure of well pressure and the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation. The processor then forms a model type-curve of the determined model well pressure of the formation and the model pressure derivative. The processor next compares the model type-curve of the determined model well pressure of the formation and the model pressure derivative with the plurality of type-curves of the estimated reference type-curve set. If the model type-curve matches one of the plurality of type-curves of the estimated reference type-curve set within an acceptable limit of accuracy, the processor stores the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation of the matched type-curve of the estimated reference type-curve set as models of the fracture conductivity and the fault conductivity and distance to fault in the formation. If not, the processor adjusts one or all of the estimated value of fracture conductivity, estimated value of fault conductivity and distance to the fault in the formation from the tested well and the quality of formation, and repeats the steps of determining a model well pressure, determining a model pressure derivative, forming a model type-curve and comparing based on the adjusted estimated value of fracture conductivity, fault conductivity and distance of the formation and other values. A memory of the data processing system stores the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation of the matched type-curve of the estimated reference type-curve set as models of the fracture conductivity and the fault conductivity of the formation.
The present invention further provides a new and improved data storage device having stored in a non-transitory computer readable medium computer operable instructions for causing a data processing system to determine a model of a subsurface earth formation, having a well intersecting a complex geological network of a fault and a fracture in the formation, based on a pressure transient test of the formation, the instructions stored in the data storage device causing the data processing system to perform a sequence of processing steps. A test measure of bottom-hole pressure is obtained, and a test pressure derivative is also obtained. An estimated reference type-curve set of a plurality of type-curves of well pressures in the well and pressure derivatives for selected test values of fracture conductivity, fault conductivity and distance with reservoir capacity in the formation are received. A model well pressure of the formation is determined based on the test measure of well pressure and an estimated value of fracture conductivity, fault conductivity, distance and reservoir capacity in the formation. A model pressure derivative is then determined based on the test measure of well pressure and the estimated value of fracture conductivity, the estimated value of fault conductivity and distance with reservoir capacity in the formation. A model type-curve is then formed of the determined model well pressure of the formation and the model pressure derivative based on the determined model well pressure of the formation. The model type-curve of the determined model well pressure of the formation and the model pressure derivative are then determined with the plurality of type-curves of the estimated reference type-curve set. If the model type-curve matches one of the plurality of type-curves of the estimated reference type-curve set within an acceptable limit of accuracy, the estimated value of fracture conductivity and the estimated value of fault conductivity in the formation of the matched type-curve of the estimated reference type-curve set are stored as models of the fracture conductivity and the fault conductivity of the formation. If not, one or both of the estimated value of fracture conductivity, an estimated value of fault conductivity and distance with reservoir capacity in the formation are adjusted, and the steps of determining a model well pressure, determining a model pressure derivative, forming a model type-curve and comparing are repeated based on the adjusted estimated value of fracture conductivity, fault conductivity and distance with reservoir capacity of the formation.
In the drawings,
A fault indicated schematically at 18 is also present in the layer R composed of Region 1, Region 2, and Region 3 nearby the well 10 and the fracture 14. The fault 18 juxtaposes different geometry across a fault between regions identified as Region 2 and Region 3, which are same quality zones in the reservoir. The fault 18 is another component of the complex flow geometry. As indicated at 20, the fault 18 has a fault width Wf.
To overcome the aforementioned difficulties, the present invention provides a computer implemented methodology of modeling of subsurface reservoirs and formations, and reservoir simulation of such models. The present invention provides improvements to the existing technological processes of characterizing and modeling of subsurface hydrocarbon reservoirs, where complex flow geometry with fractures and faults are present in order to evaluate their development. The present invention is also potentially capable of improving the functioning of computers in performance of reservoir simulation, by reducing the processing time lost due to instability in the simulator processing of the reservoir model.
Set forth below are nomenclature and the major working equations of the analytical solution, also interchangeably referred to as the model, which are used in calculating pressures and pressure derivatives. In this model, the well is considered to be producing at a constant rate of g STB/d, while the pressures and pressure derivatives and the crossflow rates are determined for the three regions. The Laplace and Fourier transforms have been performed on the equations governing the two dimensional flow in these three regions. These transformations are with respect to dimensionless time (t), in terms of transform parameters (s) and a space variable (x) in terms of transform parameter (p), respectively. The equations (with the associated boundary conditions) are solved in the Laplace space and inverted numerically using a Gaver-Stehfest numerical inversion, such as that described in Villinger, H., “Solving Cylindrical Geothermal Problems Using Gaver-Stehfest Inverse Laplace Transform,” Geophysics, (1985).
a=Distance from origin, ft
B=Formation volume factor, RB/STB
C=Wellbore storage, bbls/psi
cf Formation compressibility, psi−1
ct=Total compressibility, psi−1
dF=Distance to fault, ft
FCDf=Dimensionless fracture conductivity
FCF=Dimensional fracture conductivity, md-ft
FCDF=Dimensionless fault conductivity
FCF=Dimensional fault conductivity, md-ft
k=Matrix permeability, md
kf=Fracture permeability, md
kF=Fault permeability, md
kd=Dimensionless matrix permeability, md
kdf=Dimensionless fracture permeability, md
kf·wf=Fracture conductivity, md-ft
fr=Reference permeability, and
kn=(n) reservoir permeability, md
Pi=Initial formation pressure, psi
P1=Region-1 pressure, psi
P2=Region-2 pressure, psi
Pf=Fracture pressure, psi
Pwf=Flowing BHP, psi
Pd=dimensionless pressure
Pd1=Dimensionless Region-1 pressure
Pd2=Dimensionless Region-2 pressure
Pdf=Dimensionless fracture pressure
Pdwf=Dimensionless well flowing pressure
q=Flow rate at surface, STB/D
rw=Wellbore radius, ft
r=Distance from the center of wellbore, ft
s=Laplace parameter
tD=Dimensionless time
tDf=Fracture dimensionless time
wf=Fracture width, ft
xf=Fracture half-length, ft
xd=Dimensionless x-coordinates
yd=Dimensionless y-coordinates
Δp=Pressure change since start of transient test, psi
Δt=Time elapsed since start of test, hours
η=0.0002637 k/φμct, hydraulic diffusivity, ft2/hr
ηDF=Fault hydraulic diffusivity, dimensionless
ηDf=Fracture hydraulic diffusivity, dimensionless
ηD=Matrix hydraulic diffusivity, dimensionless
μ=Viscosity, cp
φ=Porosity, fraction
ρ=Fourier parameter
Subscripts
C=Conductivity
D=Dimensionless
F=Fault
f=Fracture
w=Wellbore
The formation two dimensional flow illustrated in
Where the qualities of Region 1, 2 & 3 are identical.
As has been described above, Laplace and Fourier transformations are applied to the five equations above governing the two dimensional flow in these three regions, fracture and fault. These mathematical transformations were with respect to dimensionless time (tD), in terms of transformed parameter (s) and a space variable (xd), in terms of the transformed parameter (φ, respectively. The equations (with the associated boundary conditions) were solved in the Laplace space and inverted numerically. The final equation for the wellbore pressure in Laplace domain is set forth in Equation (2) below:
where:
ηD, ηDf and ηDF are the dimensionless hydraulic diffusivity of matrices, fracture and fault, respectively, as defined:
where:
n=1,2,3,f&F
FCDf is the dimensionless fracture conductivity described by
the region's reference permeability is: kr=1.0 md,
and
is the matrix dimensionless permeability,
and the dimensionless pressure is:
the dimensionless coordinates written as:
with the dimensionless time being expressed as:
A comprehensive computer implemented methodology of modeling to characterize fractures network in homogeneous petroleum reservoirs according to the present invention is illustrated schematically in
The flow chart T (
The flow chart T of
As shown at step 40, processing according to the present invention begins with data regarding the formation rock, fluid and geometric properties of the layer R and well 10 being stored in memory of a data processing system D (
During step 44, model values of the pressure derivative are obtained by the data processing system D based on a specified input value of dimensional fracture conductivity FCf and dimensional fault conductivity FCF and the pressure transient test data obtained for the region of interest. The derivative is calculated using a computer code that multiplies the dimensionless time (tD), in terms of Laplace transform parameter (s), by the change in well pressure with respect to time to produce the well test derivative and plot it in a log-log scale. In step 46, the model values of the pressure derivative for the specified input value of dimensional fracture conductivity FCf and dimensional fault conductivity FCF during step 44 are stored in memory of the data processing system D, together with the input value of dimensional fracture conductivity FCf and dimensional fault conductivity FCF.
As indicated schematically at step 48, the values of fracture conductivity and fault conductivity are adjusted as required for a range of postulated values deemed likely to be present based on the pressure transient test data, and additional model values of pressure derivative obtained as described above in step 44 and stored in memory of the data processing system D. In this way a set of model values for type-curves are stored in the data processing system D and are available as indicated at step 50 for presentation as output displays from the data processing system D for analysis by reservoir engineers and analysts.
The flow chart F of
During step 66, actual values for well pressure and pressure derivative are obtained according to actual measured well pressure transient tests data according to Equation (1) above in the data processing system D. During step 68, model pressure and derivative plots based on actual pressure transient testing are generated and then made ready to compare with the model pressure and derivative of the data obtained during step 62. The well pressure and pressure derivative values determined during step 68 are also formatted in a form for storage and subsequent display in log-log plots, and are available in that format for output display by data processing system D.
During step 70, the values for well pressure and pressure derivative determined from actual pressure transient test data results during step 66 are compared with the model values of well pressure and pressure derivative in the log-plot format resulting from step 62. This comparison is done by super-imposing of pressure data from the actual pressure transient test data results on the proposed type curve or reservoir model.
Step 72 involves an evaluation of the results of comparison step 72. If the well pressure and pressure derivative values obtained during step 68, which are compared with model values during step 70 indicate that the generated actual values being compared do correspond within a specified acceptable degree to the model data, an acceptable value of well pressure and pressure derivative is indicated.
It is a common practice to leave the criteria of determining the closeness between the generated values form actual pressure transient tests and the model values up to the experience and judgment of the user analyst or engineer. Such a process involves minimizing the standard deviation between the measured pressure and pressure derivatives based on postulated fracture and fault conductivity values and the model pressure and pressure and pressure derivative values to a preset criterion value (for example, 0.1). Once such a preset criterion value is satisfied in step 72, the user is thus satisfied to call the model as the reasonably well matched one for the fracture and fault conductivity values
Then, as indicated at step 74 the fracture and fault parameters indicated by the model are reported as those for the layer being analyzed. During step 76, the fracture and fault parameters are displayed as results from the data processing system D.
If the results of step 72 indicate an unacceptable match between pressure or pressure derivative, or both of them, in the measured data and that of the model values being compared, the value of either or both of the dimensional fracture conductivity FCf and dimensional fault conductivity FCF are adjusted during step 78. The distance to fault dF and matrix permeability k may also be adjusted during step 78. Processing returns to step 66 for processing of the actual well data based on the adjusted values of fracture and/or fault conductivity. Processing continues for further iterations until during step 72 an acceptable agreement is achieved between the measured data and the model data. This indicates, as noted, that the dimensional fracture conductivity and dimensional fault conductivity values of the current iteration are proper indications of the complex flow geometry.
As illustrated in
The processor 102 is, however, typically in the form of a personal computer having a user interface 106 and an output display 108 for displaying output data or records of processing of force measurements performed according to the present invention. The output display 108 includes components such as a printer and an output display screen capable of providing printed output information or visible displays in the form of graphs, data sheets, graphical images, data plots and the like as output records or images.
The user interface 106 of computer 100 also includes a suitable user input device or input/output control unit 110 to provide a user access to control or access information and database records and operate the computer 100.
Data processing system D further includes a database 114 stored in memory, which may be internal memory 114, or an external, networked, or non-networked memory as indicated at 116 in an associated database server 118. The database 114 also contains various data including the time and pressure data obtained during pressure transient testing of the layer under analysis, as well as the rock, fluid and geometric properties of layer R and well 10, and other formation properties, physical constants, parameters, data measurements identified above with respect to
The data processing system D includes program code 120 stored in a data storage device, such as memory 104 of the computer 100. The program code 120, according to the present invention is in the form of computer operable instructions causing the data processor 102 to perform the methodology of modeling to characterize fractures network in homogeneous petroleum reservoirs as shown in
It should be noted that program code 120 may be in the form of microcode, programs, routines, or symbolic computer operable languages that provide a specific set of ordered operations that control the functioning of the data processing system D and direct its operation. The instructions of program code 120 may be stored in non-transitory memory 104 of the computer 100, or on computer diskette, magnetic tape, conventional hard disk drive, electronic read-only memory, optical storage device, or other appropriate data storage device having a computer usable medium stored thereon. Program code 120 may also be contained on a data storage device such as server 118 as a non-transitory computer readable medium, as shown.
The processor 102 of the computer 100 accesses the pressure transient testing data and other input data measurements as described above to perform the logic of the present invention, which may be executed by the processor 102 as a series of computer-executable instructions. The stored computer operable instructions cause the data processor computer 100 to develop type-curves of pressure and pressure derivatives as functions of time for different fracture and fault conductivities according to the methodology of
The type-curves displayed in
The type-curves of
The pressure derivative type-curves of
A synthetic numerically-built model of simulated flow geometry with a well intersecting a fracture network, was constructed and the pressure data were generated by a backward modelling of the given well rate, fluid, reservoir, fracture and fault parameters and properties. The pressure data for the simulated flow geometry of the model were then analyzed in a commercial well-test package (i. e. ECRIN of KAPPA Associates). The results obtained for the numerical model are shown at 250 in
Heavy lines 280 and 282 have been added in
A well model case example form an actual well in a producing field provided a data set for comparison with processing results according to the present invention. The well model corresponds to a vertical well intersecting a fracture network in a tight homogenous reservoir. The case example was to evaluate results according to the present invention in comparison with an existing example of data from an actual well. Pressure transient testing of the actual well has determined the well to exhibit a flow which is dominated by a fracture bi-linear flow regime for both pressure type-curve at 298 and pressure derivative type-curve at 256 in
Heavy lines 296 and 298 have been added in
Dimensional Fracture Conductivity,
Dimensionless Fracture Conductivity,
Distance to. Fault, dF
Dimensional Fault Conductivity, FCf=kF·kwf
Dimensionless Fault Conductivity,
From the foregoing, it can be seen that the present invention provides a new methodology where pressure transient data is processed so that a complex flowing geometry with flow from fractures and faults is rigorously described based on values of fracture conductivities and fault conductivities which are determined. Thus, the present invention provides models of the complex flow geometry which conforms to both numerical models and actual field data. The present invention provides reliable reservoir models based on the pressure transient testing of a reservoir.
Type-curves such as those shown in
The present invention thus provides accurate semi-analytical solutions for a well intersecting fractures network in homogenous reservoir(s). This is of considerable value in view of increasing activities in production from naturally faulted geological settings and unconventional reservoirs. The developed present invention offers more flexible schemes to easily carry out modelling with increasing certainty and larger positive impact on the management decisions of such reservoirs.
The invention has been sufficiently described so that a person with average knowledge in the field of reservoir modeling and simulation may reproduce and obtain the results mentioned in the invention herein. Nonetheless, any skilled person in the field of technique, subject of the invention herein, may carry out modifications not described in the request herein, to apply these modifications to a determined structure and methodology, or in the use and practice thereof, requires the claimed matter in the following claims; such structures and processes shall be covered within the scope of the invention.
It should be noted and understood that there can be improvements and modifications made of the present invention described in detail above without departing from the spirit or scope of the invention as set forth in the accompanying claims.