Patent Application
20130282286
The present invention pertains in general to computation methods and more particularly to a computer system and computer-implemented method for calibrating permeability for use in reservoir modeling.
A number of conventional models and methodologies are used to compute or simulate flow of fluids in a rock formation for reservoir forecasting of hydrocarbon production. For example, three dimensional (3D) geocellular reservoir model of porosity and permeability using statistics can be employed for reservoir forecasting of hydrocarbon production. However, permeabilities in such a geocellular reservoir model are generally not predictive for hydrocarbon forecasting unless dynamic data is used to calibrate permeabilities measured in core plugs with permeabilities assigned to geocellular model cells. The permeabilities of geocellular model cells are, naturally, orders of magnitude larger in size than the permeabilities obtained from core plugs.
One conventional method for performing this calibration process is by applying permeability multipliers during reservoir simulation to match production data in a process known as history matching. However, this method is time consuming and resource intensive. In addition, this calibration process is often performed at the end of building a reservoir model and without involving the reservoir model. As a result, the model is not “corrected” or enhanced by the calibration process.
Therefore, there is a need for a calibration method that cures these and other deficiencies in the conventional methods.
An aspect of the present invention is to provide a computer-implemented method for calibrating a reservoir characteristic including a permeability of a rock formation. The method includes inputting a measured product KH of a measured permeability K and a flowing zone thickness H over a plurality of corresponding zones in one or more wells and inputting porosity logs for each measured product KH in each of the plurality of corresponding zones obtained from the one or more wells. The method further includes reading a porosity-permeability cloud of data points; calculating, for each zone, a predicted product KH from the porosity log using the porosity-permeability cloud of data points; determining one or more weighting coefficients between the predicted KH and the measured KH corresponding to each zone, and calibrating the measured permeability corresponding to each zone using the one or more coefficients.
Another aspect of the present invention is to provide a system for calibrating a permeability of a rock formation. The system includes a computer readable memory configured to store input data comprising a measured product KH of a measured permeability K and a flowing zone thickness H over a plurality of corresponding zones in one or more wells, and porosity logs for each measured product KH in each of the plurality of zones obtained from the one or more wells. The system further includes a computer processor in communication with the computer readable memory, the computer processor being configured to: read a porosity-permeability cloud of data points; calculate, for each zone, a predicted product KH from the porosity log using the porosity-permeability cloud of data points; determine a weighting coefficient between the predicted KH and the measured KH corresponding to each zone; and calibrate the measured permeability corresponding to each zone using the one or more weighting coefficients.
A further aspect of the present invention is to provide a computer implemented method for calibrating a permeability of a rock formation. The method includes inputting, into the computer, a measured product KH of a measured permeability K by a flowing zone thickness H over a plurality of corresponding zones in one or more wells; and inputting, into the computer, permeability logs for each measured product KH in each of the plurality of zones obtained from the one or more wells. The method further includes calculating, by the computer, for each zone, a predicted product KH from the permeability log; determining, by the computer, one or more weighting coefficients between the predicted KH and the measured KH corresponding to each zone; and calibrating the measured permeability corresponding to each zone using the one or more weighting coefficients.
Yet another aspect of the present invention is to provide a system for calibrating a permeability of a rock formation. The system includes a computer readable memory configured to store input data comprising a measured product KH of a measured permeability K and a flowing zone thickness H over a plurality of corresponding zones in one or more wells, and permeability logs for each measured product KH in each of the plurality of zones obtained from the one or more wells. The system further includes a computer processor in communication with the computer readable memory, the computer processor being configured to: calculate, for each zone, a predicted product KH from the permeability log; determine a weighting coefficient between the predicted KH and the measured KH corresponding to each zone; and calibrate the measured permeability corresponding to each zone using the one or more weighting coefficients.
Although the various steps of the method according to one embodiment of the invention are described in the above paragraphs as occurring in a certain order, the present application is not bound by the order in which the various steps occur. In fact, in alternative embodiments, the various steps can be executed in an order different from the order described above or otherwise herein. For example, it is contemplated to transform from, the first model to the second model, or vice versa; or to transform from the third model to the second model, or vice versa; or yet to transform from the third model to the first model, or vice versa.
These and other objects, features, and characteristics of the present invention, as well as the methods of operation and functions of the related elements of structure and the combination of parts and economies of manufacture, will become more apparent upon consideration of the following description and the appended claims with reference to the accompanying drawings, all of which form a part of this specification, wherein like reference numerals designate corresponding parts in the various figures. In one embodiment of the invention, the structural components illustrated herein are drawn to scale. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the invention. As used in the specification and in the claims, the singular form of “a”, “an”, and “the” include plural referents unless the context clearly dictates otherwise.
In the accompanying drawings:
As will be described in detail in the following paragraphs, in one embodiment, a calibration method is described in which dynamic measures of permeability K from well-tests or measures of the product KH of permeability K with a flowing zone thickness H, are used to dynamically recalibrate a porosity-permeability cloud data points transform that is used in geostatistics so as to create a geocellular model of permeability. In one embodiment, the calibration method can be applied on sedimentary facies for use in facies-based geocellular modeling. In one embodiment, the calibration method may also account for uncertainty in the product KH. Distributions, such as, but not limited to, P10, P50 and P90, in porosity-permeability can be used in combination with other factors to estimate uncertainty of oil-in-place (OIP), for example, and thus estimate a recovery factor in an oil field being modeled.
The method further includes, optionally determining a relative score range for an accuracy of the measured value OKHm and a lower limit and an upper limit for each measured value OKHm (OKH1, OKH2, etc.), at S12. In one embodiment, the lower and upper limit for a given well-test depends on whether the well-test is run for a long period of time enough to reach ‘infinite-acting’ time or steady state. The lower and upper limit for the well-test also depends if a pressure decline data in the well-test is well-matched by an analytical or numerical model and any other factors deemed relevant by a reservoir engineer.
The accuracy score range is a qualitative measure of the well-test in which, for example, a higher score is assigned the well-test if the well-test is conducted in a well and zone within the well in which complicating geological factors such as, for example, nearby faults or stratigraphic pinch outs are not thought to be present. The scoring is qualitative in nature as it involves a confidence level that a geologist or engineer has on the measured data from the well-test. In one embodiment, one possible implementation of a score range is to use numerical values between 0 and 10, for example. Hence, if a measurement A in a well-test is given a score range between 0 and 5, and a measurement B in the a well-test is given a score range between 5 and 10, for example. These score ranges imply that measurement A pessimistically has no value at all and optimistically has the same value as measurement B when measurement B has a pessimistic score.
The method further includes, at S14, inputting porosity logs for each measured value OKHm (i.e., for each zone or interval) obtained from the one or more well-tests. The method may further include optionally inputting, at S16, an index log representing one or more facies of the rock formation for a certain geological area of interest. A facies is a qualitative attribute that is assigned to a rock formation. For example, the facies of rock formation may be referred to as being “clean sand” (i.e., a sand having a relatively small proportion of clay in it) or may be referred to as being clay (i.e., a rock which is essentially clay), etc. Hence, a facies defines in general terms the rock type within the rock formation. A facies can also be seen as a statistical description or a statistical characterization of a rock volume. For example, a facies of rock formation can be described as being approximately 90% sand and 10% clay or vice versa, 90% of clay and 10% of sand, etc.
Therefore, in one embodiment, a three-dimensional data representing porosity logs for each KH zone or interval and for each facies index log are used as inputs in the calibrating method. In one embodiment, for each facies log index, a two-dimensional data representing a logarithm (log) of the measured permeability K or logarithm (log) of the measured product KH (OKHm) versus the porosity P or vice-versa, the porosity P versus the log of the measured permeability or log of the measured product KH (OKHm) can be plotted on a graph. The obtained graph is a plurality of data points representing the relationship between the log of the measured K or KH and porosity P.
The method further includes, at S18, reading a porosity-permeability cloud of data points (also referred to as the porosity-permeability cloud transform) as a set of n porosity-permeability pairs (Pn,Kn). In one embodiment, the porosity-permeability pairs (Pn,Kn) can be sorted by porosity, for example, sorted by increasing porosity or sorted by decreasing porosity. In one embodiment, the porosity-permeability cloud of data points can originate from core data and can be obtained, for example, in the laboratory, when analyzing core plugs, for example using mercury injection and other techniques. In another embodiment, instead of or in addition to a porosity-permeability cloud of data points, a theoretical relationship between porosity P and permeability K can be used. In one embodiment, the porosity-permeability cloud of data points can be used to calculate a permeability log and a porosity log. In another embodiment, instead of a porosity-permeability cloud of data points, a permeability log can be obtained directly over the plurality of intervals m in which case the step of calculating the permeability log and porosity log from porosity-permeability cloud transform can be eliminated.
The method further includes, at S20, for each facies, and for each interval or zone m, calculating a predicted KH for that facies from the porosity log using the permeability-porosity cloud of data points (permeability-porosity cloud transform). The average permeability for any depth in the interval m with a log porosity P is determined by the average permeability of all pairs Pn,Kn such that the porosity Pn are within a cumulative probability tolerance of porosity P. The tolerance is derived from the number of bins in the porosity permeability cloud data points.
A log KH for a given facies f (LKHf) is equal to a sum of the product of the average permeability K by the sample spacing interval H over data samples j that are within the given facies f. This can be expressed by the following equation (1):
where
For example, for the sake of illustration, if there are two facies f1 and f2, equation (1) can be written as equation (2):
for facies f1, where
for facies f2, where
Next, a determination is made as to whether uncertainty analysis is needed or not, at S21. In the case where no uncertainty analysis is needed and there is more than one facies, i.e., a plurality of facies (for example, facies f1 and f2), a non-affine multiple linear regression can be used to determine, at S22, the weighting coefficient Wf for each facies from the over-determined system of equations and summed over each facies, for each zone m to obtain the observed or measured OKHm. This can be expressed by the following equation (4):
For example, if there are two facies (e.g., facies f1 corresponding to clean sand and facies f2 corresponding to dirty sand), a weighting factor or coefficient W1 can be assigned to rock with facies f1 and a weighting factor or coefficient W2 can be assigned to rock with facies f2. Similarly, a permeability log LKH1 can be assigned to rock with facies f1 and a permeability log LKH2 can be assigned to rock with facies f2. In this case, equation (4) can be rewritten as equation (5):
W
1
×LKH
1
+W
2
×LKH
2
=OKH
m (5)
By using a simple regression, the weights W1 and W2 can be determined. In general, by using a regression method, the weights Wf corresponding to each facies can be determined.
If one or more of the weights Wf associated with one or more facies f is/are negative, that negative weight value can be replaced by a positive but relatively small weight. For example, in the example above, if the determined W1 is negative for some reason, W1 can be assigned a relatively small value close to zero to resolve the linear regression equations.
In one embodiment, the number m of zones is selected to be larger or equal to the number facies f. Alternatively, the number of facies can be selected to be smaller than the number of zones. To ensure this condition, the facies f types may be lumped together to reduce the number of facies f.
In another embodiment, when no uncertainty analysis is needed and there is only one facies (e.g., clean sand), a power law calibration can be implemented, at S22, that optimizes parameters a and b to fit the following equation (6):
a×LKH
m
b
=OKH
m (6)
If uncertainty analysis is needed then a Monte Carlo approach can be used, at S24 in the weighted non-affine multiple regression or weighted power law fit above. In the Monte Carlo approach, the different weights for each observed or measured KH interval are randomly drawn from a relative accuracy score range for that well test described in the above paragraphs and the observed or measured KH is randomly drawn between the lower and upper limits also described in the above paragraphs.
In this case, a dynamic distribution (e.g., P10, P50 and P90) of cloud transforms can be created, at S26, from the Monte Carlo results using a ranking method, such as for example ranking by average, of the permeability for each run.
Therefore, as it can be appreciated from the above paragraphs, the method includes determining a weighting coefficient (one or more weighting coefficient associated with one or more facies) between the predicted product KH and the measured product KH. In one embodiment, the method further includes calibrating the measured permeability corresponding to each zone using the one or more weighting coefficients.
In one embodiment, the P10, P50, P90 calibrated porosity-permeability cloud transforms created, at S26, or in another embodiment P10, P50, and P90 calibrated permeability logs, can be used by geostatistical methods to create reservoir models suitable for flow simulation. A suite of flow simulation experiments can be used to predict the distribution of expected recoverable hydrocarbon volumes because the permeability used in the models has already been calibrated with dynamic flow information obtained from well tests.
In one embodiment, the method or methods described above can be implemented as a series of instructions which can be executed by a computer. As it can be appreciated, the term “computer” is used herein to encompass any type of computing system or device including a personal computer (e.g., a desktop computer, a laptop computer, or any other handheld computing device), or a mainframe computer (e.g., an IBM mainframe), or a supercomputer (e.g., a CRAY computer), or a plurality of networked computers in a distributed computing environment.
For example, the method(s) may be implemented as a software program application which can be stored in a computer readable medium such as hard disks, CDROMs, optical disks, DVDs, magnetic optical disks, RAMs, EPROMs, EEPROMs, magnetic or optical cards, flash cards (e.g., a USB flash card), PCMCIA memory cards, smart cards, or other media.
Alternatively, a portion or the whole software program product can be downloaded from a remote computer or server via a network such as the internet, an ATM network, a wide area network (WAN) or a local area network.
Alternatively, instead or in addition to implementing the method as computer program product(s) (e.g., as software products) embodied in a computer, the method can be implemented as hardware in which for example an application specific integrated circuit (ASIC) can be designed to implement the method.
As can be appreciated from the above description, the computer readable memory 100 can be configured to store input data having a measured product KH of permeability K by flowing zone thickness H over a plurality of zones in one or more wells, and porosity logs for each measured product KH in each of the plurality of zones obtained from the one or more wells. The computer processor 120 in communication with the computer readable memory 130 can be configured to: (a) read a porosity-permeability cloud of data points; (b) calculate, for each zone, a predicted product KH from the porosity log using the porosity-permeability cloud of data points; (c) determine a weighting coefficient between the predicted product KH and the measured product KH corresponding to each zone; and (d) calibrate the measured permeability corresponding to each zone using the one or more weighting coefficients.
Although the invention has been described in detail for the purpose of illustration based on what is currently considered to be the most practical and preferred embodiments, it is to be understood that such detail is solely for that purpose and that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover modifications and equivalent arrangements that are within the spirit and scope of the appended claims. For example, it is to be understood that the present invention contemplates that, to the extent possible, one or more features of any embodiment can be combined with one or more features of any other embodiment.
Furthermore, since numerous modifications and changes will readily occur to those of skill in the art, it is not desired to limit the invention to the exact construction and operation described herein. Accordingly, all suitable modifications and equivalents should be considered as falling within the spirit and scope of the invention.
