EP1630348B1 - Verfahren zur Modellierung der Ölgewinnung aus einer unterirdischen Formation - Google Patents

Verfahren zur Modellierung der Ölgewinnung aus einer unterirdischen Formation Download PDF

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EP1630348B1
EP1630348B1 EP05291700A EP05291700A EP1630348B1 EP 1630348 B1 EP1630348 B1 EP 1630348B1 EP 05291700 A EP05291700 A EP 05291700A EP 05291700 A EP05291700 A EP 05291700A EP 1630348 B1 EP1630348 B1 EP 1630348B1
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model
production
value
point
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EP1630348A1 (de
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Céline Scheidt
Isabelle Zabalza-Mezghani
Dominique Collombier
Mathieu Feraille
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IFP Energies Nouvelles IFPEN
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells

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  • the present invention relates to the study and optimization of the production patterns of oil deposits. It aims at modeling the behavior of an oil field in order to be able to compare several production schemes, and to define an optimal scheme considering a given production criterion (oil recovery, water inflow, production flow rate). ..).
  • the reservoir characterization phase consists in determining a numerical flow model or flow simulator that is compatible with the real data collected in the field. Engineers only have access to a small part of the field they are studying (measurements on cores, logs, well tests, etc.). They must extrapolate these point data over the entire oil field to build the digital simulation model.
  • the production forecasting phase uses the numerical simulation model to estimate future reserves and productions or to improve the production scheme in place. This phase is carried out thanks to the numerical model of simulation constructed from numerous and varied data, but coming from only a tiny part of the deposit. Consequently, the notion of uncertainty must be constantly taken into account.
  • the use of the experimental design method can allow the construction of a simplified model of the flow simulator based on a reduced number of parameters. Experiment plans make it possible to determine the number and spatial location of the parameters of the simulations to be carried out in order to obtain the maximum of relevant information at the lowest possible cost. This simple model translates the behavior of a given response (for example the cumulated oil produced at 10 years) according to some parameters. Its construction requires a reduced number of simulations, defined beforehand thanks to a plan of experiments.
  • the simplified model is used because it is simple and analytical and, therefore, every simulation obtained by this model is immediate. This saves a lot of time.
  • the use of this model allows the reservoir engineer to test as many scenarios as he wishes, regardless of the time required to perform a numerical flow simulation.
  • the present invention proposes to model a petroleum field by making iterative adjustments in order to reproduce the behavior of the oil field, while controlling the number of simulations.
  • the new production value can be selected by taking into account the production gradient at the point associated with the production value with the largest prediction residual.
  • step c) a new value can be selected in step c) and step d) can be performed provided that the largest prediction residue is greater than a previously fixed value.
  • a new value can be selected in step c) and step d) can be performed provided that the prediction residual of the new selected value is greater than a previously fixed value.
  • steps c) and d) can be repeated.
  • step b) one can choose said production values using a plan of experiments.
  • the first model can be adjusted using one of the following approximation methods: approximation by polynomials, neural networks, vector support machines.
  • step d one of the following interpolation methods can be used: kriging method and spline method.
  • the method according to the invention provides the reservoir engineer with a simple and inexpensive formalism in terms of numerical simulations for the management of scenarios and the optimization of production patterns, to help him in his decision-making in order to to minimize the risks.
  • Step 1 Build the tank flow simulator
  • the oil field is modeled using a digital tank simulator.
  • the reservoir simulator or flow simulator makes it possible to calculate the production of hydrocarbons or water over time according to technical parameters such as the number of layers of the reservoir, the permeability of the layers, the strength of the aquifer , the position of oil wells, etc.
  • the flow simulator calculates the derivative of the production value at the point considered.
  • the numerical simulator is built from data characteristic of the oil field.
  • the data is obtained through laboratory measurements of cores and fluids taken from the oil field, by well logs, well tests, and so on.
  • Step 2 Approximation of the flow simulator
  • Parameters influencing the hydrocarbon or water production profiles of the reservoir are selected.
  • the selection of the parameters can be done either with respect to the physical knowledge of the oil field, or by a sensitivity study. For example, it is possible to implement a Student or Fischer statistical test.
  • Parameters may be intrinsic to the oil reservoir. For example, the following parameters may be considered: a permeability multiplier for some layers of the reservoir, the force of the aquifer, the residual oil saturation after a water scan.
  • Parameters may correspond to deposit development options. These parameters can be the position of a well, the level of completion, the drilling technique.
  • Points are selected in the experimental domain for which numerical flow simulations will be performed. These points are used to construct a simplified model that best replicates the deposit flow simulator. These points are chosen by the experimental design method, which makes it possible to determine the number and the location of the simulations to be carried out in order to obtain the maximum information at the lowest possible price and thus to determine a reliable model reflecting at best the production profile. It should be noted that the choice of this experimental device is very important: the initial experimental plan has a primordial role in the development of the modeling of the first model, the results depend strongly on the disposition of the experiments.
  • the first model expresses a criterion of production studied over time, this criterion being expressed as a function of the selected parameters.
  • the production criterion can be oil recovery, water inflow, production flow.
  • the first analytical model is constructed using the previously selected values of this criterion and obtained by means of the flow simulator.
  • Step 3 Adjust the first model
  • the residues are determined at the various simulation points.
  • the residuals correspond to the difference between the response of the first model and the value obtained by the reservoir flow simulator.
  • the residues are interpolated. Any n-dimensional interpolation method may be suitable.
  • the method of kriging or splines can be envisaged. These methods are explained in the book entitled "Statistics for spatial data" by Cressie, N., Wiley, New York 1991 .
  • the residual interpolation structure lends itself well to this sequential approach because it is broken down into two parts: a linear model, which corresponds to the first model determined in step 2, and a term "corrector" which makes it possible to bridge the gap. difference between the prediction of the first model and the simulation point. In the case where the analytical model is satisfactory, it is not necessary to add the term "corrector". In the opposite case, it makes it possible to interpolate the responses and, thus, to take into account the detected non-linearities of the surface.
  • a second adjusted model is determined by adding the results of the interpolation of the residues to the first model determined in step 2.
  • Step 4 Model predictivity test and choice of additional simulation points
  • the second model exactly interpolates the simulations, so the adjustment of the response function is optimal. Since the interpolation method is correct, the "classical" residues are zero. Thus, according to the invention, we are interested in the prediction residues. As a result, the predictivity of the model for out-of-plane points is examined. Predictions should be as precise as possible. Therefore, a model predictivity test is then performed to assess the quality of the approximation to judge the need for improvement by adding new points to the initial plan.
  • the prediction residuals are the residues obtained at a point of the plane by adjusting the first model without this point. Deleting a point and redoing the model estimate will determine if this point (or the area near the point) provides decisive information or not.
  • the calculation of these prediction residues is done for each point of the initial experimental plan. In the neighborhood of the points considered the least predictive of the current plane, that is to say the points having the greatest prediction residue, new points are simulated. To do this, a subsampling zone is defined in the vicinity of the points. The addition of these points may be conditioned by the fact that the residues are greater than a value set by the user.
  • the size of this subsampling area can be defined by using the gradient information of the production at the points and / or the value of the prediction residuals. Indeed, a high gradient value reflects a strong variation of the response. It may therefore be informative to add a new point close to the existing one. On the other hand, a low gradient value in a given direction indicates that there are no irregularities in that direction. Therefore, it is not necessary to investigate a large range of variation in this direction. On the other hand, the variation range for one of the parameters is greater the greater the value of the gradient in this direction. This approach makes it possible to eliminate certain directions (those where the value of the gradient is not significant) and, therefore, to reduce the number of simulations to be performed. This sub-sampling may, for example, result from the construction of a new experimental plan defined on this zone. The choice of this experimental design (factorial plane, composite plane, Latin Hypercube) results from the necessary compromise between the cost and the quality of modeling.
  • pilot point method can be implemented to improve the second model.
  • estimators For a given number of experiments, there are a large number of estimators (exact interpolators) passing through all the experiments and respecting the spatial structure (expectation and covariance) of the process.
  • this class of estimators respecting the data we look for the estimator that maximizes the predictivity a priori.
  • fictitious information that is to say that we add pilot points to the simulated experiments. These pilot points are then considered as data although no simulation has been carried out and will make it possible to browse all the estimators passing through all the experiments.
  • the objective is to select the interpolator that maximizes the predictive coefficient a priori of the model, that is to say that the pilot points are positioned so as to achieve maximum predictivity.
  • pilot points have already been positioned in the uncertain domain and that we are trying to place new pilot points to improve the predictivity of the model.
  • pilot points are chosen to add a number of pilot points less than or equal to the number of actual experiments present, so as not to disturb the model too much.
  • a "fictitious" answer value must be assigned to these points.
  • pilot points to improve the prior predictivity of the model, we must therefore define the value of pilot points from an objective function that measures this predictivity. Since kriging is an exact interpolation method, "classical" residues are null. They therefore do not provide any information on predictivity, and therefore, the prediction residuals are considered.
  • a priori predictivity we mean the calculation of the prediction residuals in each of the points of the initial experimental plan. The prediction residuals are the residues obtained at a point of the initial experimental plane by adjusting the first model without this point.
  • Deleting a point and re-estimating the model makes it possible to determine whether the point or zone of the experimental domain close to this point provides decisive information or not.
  • the calculation of the prediction residuals is performed in a neighborhood of the pilot point to be optimized. We set initial values for the pilot points and then we consider these data as real and we vary the value of the pilot point to obtain a model that is as predictive as possible, that is, we want to minimize the error mean prediction of the model.
  • the determination of the optimal value of the pilot point is thus performed to minimize the average prediction error of the model over the entire uncertain domain. Likewise, this determination of the optimum value of the pilot point can be carried out so as to minimize the error of local prediction of the model (i.e., in a vicinity of the pilot point, independent of other prediction errors).
  • residues here, we mean, for each pilot point, the difference between the simulated value and the value obtained during the optimization of the pilot points:
  • Confirmation points ie production values obtained by the flow simulator constructed in step 1
  • a criterion for adding simulations can be based on: the value of the derivative of the production values obtained by the flow simulator, the direct identification of points whose maximum production value or identification points whose production value is minimal.
  • a model that approximates the values of the derivatives at the points chosen by the experimental design in step 2 is determined. Then, a new simulation point is added at the point where the response of the derivative model is canceled. provided that this point is sufficiently distant from the simulations already carried out. These confirmation points make it possible to test the predictivity of the second model, in this new investigated zone. If the prediction residuals calculated at the newly selected points exceed a user-defined value, these new points are used to perform a new interpolation phase.
  • Step 5 Build and fit a third model
  • the residues are determined at the new simulation points selected in step 4.
  • the residuals correspond to the difference between the response of the first model and the simulation value obtained by the simulator. flow of the tank.
  • the residues are interpolated. Any n-dimensional interpolation method may be suitable. For example, kriging or splines can be used.
  • the interpolation structure of the residues is divided into two parts: the first model determined in step 2, and a "corrector" term which makes it possible to bridge the gap between the prediction of the first model and the new simulation (s) selected at Step 4.
  • the new simulation makes it possible to interpolate the responses and, thus, to take into account the detected non-linearities of the surface.
  • a second adjusted model is determined by adding the results of the residual interpolation to the first model determined in step 2.
  • Step 6 Finding inflection points
  • Reference B in Figure 2 presents the graph of the estimation of the "camel” function by a linear model obtained from a factorial plane with 4 simulations.
  • Reference C in FIG. 2 represents the graph of the estimation of the "camel” function by a second-order polynomial model obtained from a composite plane centered on 9 simulations.
  • FIG. 3 illustrates the optimization, according to our invention, of the model approaching the "camel" function.
  • the function represented in the unit cube [-1,1] 2 referenced D is obtained by performing steps 2) and 3), from a Latin Hypercube of initial maximin distance containing nine tests.
  • the functions represented in the unit cube [-1,1] 2 referenced E, F and G are obtained by adjusting this function obtained from a Latin Hypercube and adding seven points of simulations. Steps 4) and 5) are repeated three times.

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  • Geology (AREA)
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  • Engineering & Computer Science (AREA)
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Claims (13)

  1. Verfahren zur Simulation der Produktion einer Erdöllagerstätte, wobei die folgenden Schritte ausgeführt werden:
    a) Es wird ein Abfluss-Simulator aus physikalischen Daten konstruiert, die an der Erdöllagerstätte gemessen wurden,
    b) Bestimmen eines ersten analytischen Modells, das die Produktion der Lagerstätte in Abhängigkeit von der Zeit ausdrückt, unter Berücksichtigung der Parameter, die einen Einfluss auf die Produktion der Lagerstätte haben, wobei das erste Modell bestmöglich an eine endliche Zahl von Produktionswerten angepasst wird, die aus dem Abfluss-Simulator erhalten werden,
    c) Auswählen mindestens eines neuen Produktionswerts, der mit einem Punkt assoziiert ist, der in einem Bereich der Lagerstätte liegt, der in Abhängigkeit von der Nichtlinearität der Lagerstättenproduktion in diesem Bereich ausgewählt wird, wobei der neue Wert aus dem Abfluss-Simulator erhalten wird,
    d) Bestimmen eines zweiten Modells, indem das erste Modell so angepasst wird, dass die Antwort des zweiten Modells an dem Punkt dem neuen Produktionswert entspricht.
  2. Verfahren nach Anspruch 1, wobei in Schritt c) die folgenden Schritte ausgeführt werden:
    - Bestimmen eines Untermodells, das sich bestmöglich an die endliche Zahl der Produktionswerte anpasst, mit Ausnahme eines Testwerts, ausgewählt unter der endlichen Zahl der Produktionswerte,
    - Berechnen eines Vorhersageresiduums, das mit dem Testwert assoziiert ist, indem die Differenz zwischen der Antwort des Untermodells und dem Testwert ausgeführt wird,
    - Berechnen des Vorhersageresiduums, das mit jedem der Vorhersage-Werte assoziiert ist, indem die beiden vorherigen Schritte wiederholt werden, indem nacheinander dem Testwert jeder der Werte zugewiesen wird, die in der endlichen Zahl der Produktionswerte enthalten sind,
    - Auswählen des neuen Produktionswerts in einem Bereich der Lagerstätte, nahe einem Punkt, der mit einem Produktionswert assoziiert ist, der das größte Vorhersageresiduum aufweist.
  3. Verfahren nach Anspruch 2, wobei der neue Produktionswert ausgewählt wird, unter Berücksichtigung des Produktionsgradienten an einem Punkt, der mit dem Produktionswert assoziiert ist, der das größte Vorhersageresiduum hat.
  4. Verfahren nach einem der Ansprüche 2 und 3, wobei in Schritt c) ein neuer Wert ausgewählt wird, und Schritt d) unter der Voraussetzung ausgeführt wird, dass das größte Vorhersageresiduum oberhalb eines zuvor festgelegten Werts liegt.
  5. Verfahren nach Anspruch 1, wobei in Schritt c) die folgenden Schritte ausgeführt werden:
    - Bestimmen einer ersten Kriging-Varianz des ersten Modells für die endliche Zahl der Produktionswerte, die aus dem Abfluss-Simulator erhalten werden,
    - Auswählen eines ersten Kontrollpunkts in der Lagerstätte an der Stelle, an der die erste Kriging-Varianz maximal ist,
    - Bestimmen einer zweiten Kriging-Varianz des ersten Modells für die endliche Zahl der Produktionswerte, die aus dem Abfluss-Simulator und dem ersten Kontrollpunkt erhalten werden,
    - Auswählen eines zweiten Kontrollpunkts in der Lagerstätte an der Stelle, an der die zweite Kriging-Varianz maximal ist,
    - Zuweisen eines Werts jedem der Kontrollpunkte, indem die fünf folgenden Operationen für jeden der Kontrollpunkte ausgeführt werden:
    • Bestimmen eines Untermodells, das sich bestmöglich an die endliche Zahl der Produktionswerte und an den Wert anpasst, der mit einem der Kontrollpunkte assoziiert ist, mit Ausnahme eines Testwerts, ausgewählt unter der endlichen Zahl der Produktionswerte und dem Wert, der mit dem Kontrollpunkt assoziiert ist,
    • Berechnen eines Vorhersageresiduums, das mit dem Testwert assoziiert ist, indem die Differenz zwischen der Antwort des Untermodells und dem Testwert ausgeführt wird,
    • Berechnen des Vorhersageresiduums, das mit jeder der Antworten des Untermodells assoziiert ist, indem die beiden vorherigen Operationen wiederholt werden, indem dem Testwert jeder der Werte nacheinander zugewiesen wird, der in der Gesamtheit, bestehend aus der endlichen Zahl der Produktionswerte und dem Wert, der mit dem Kontrollwert assoziiert ist, enthalten sind,
    • Berechnen der Summe der absoluten Werte der Vorhersageresiduen, die für jeden der Testwerte berechnet werden,
    • Zuweisen des Werts, der diese Summe minimiert, an den Kontrollwert,
    - Bestimmen eines zweiten Untermodells, das sich bestmöglich an die endliche Zahl der Produktionswerte und an die Werte der Kontrollpunkte anpasst,
    - für jeden der Kontrollpunkte wird die Differenz zwischen der Antwort des zweiten Untermodells und die Antwort des ersten Modells ausgeführt,
    - Assoziieren des neuen Produktionswert aus Schritt c) mit dem Kontrollpunkt, für den die Differenz am größten ist,
  6. Verfahren nach Anspruch 5, wobei in Schritt d) das zweite Modell bestimmt wird, indem das erste Modell so angepasst wird, dass die Antwort des zweiten Modells auf den ausgewählten Kontrollpunkt dem neuen Produktionswert entspricht, und außerdem den Werten, die den anderen Kontrollpunkten zugewiesen werden.
  7. Verfahren nach einem der Ansprüche 1 bis 6, wobei in Schritt c) die folgenden Schritte ausgeführt werden:
    - Bestimmen eines analytischen Modells, das den Differenzialquotienten der Produktion der Lagerstätte in Abhängigkeit von der Zeit ausdrückt, wobei das Modell bestmöglich an die Differenzialquotienten an den Punkten angepasst wird, die mit den Produktionswerten assoziiert sind, die in Schritt b) verwendet werden,
    - aus dem Modell, das den Differenzialquotienten ausdrückt, wird mindestens ein neuer Produktionswert ausgewählt, der mit einem Punkt assoziiert ist, an dem die Antwort des Modells, das den Differenzialquotienten ausdrückt, null ist.
  8. Verfahren nach Anspruch 7, wobei in Schritt c) ein neuer Wert ausgewählt wird und Schritt d) unter der Voraussetzung ausgeführt wird, dass das Vorhersageresiduum des neuen ausgewählten Werts oberhalb eines zuvor festgelegten Werts liegt.
  9. Verfahren nach einem der Ansprüche 7 und 8, wobei nach Schritt d) die folgenden Schritte ausgeführt werden:
    - Bestimmen eines dritten analytischen Modells, das den Differenzialquotienten der Produktion der Lagerstätte in Abhängigkeit von der Zeit ausdrückt, wobei das dritte Modell bestmöglich an die Differenzialquotienten an den Punkten angepasst wird, die mit der endlichen Zahl der Produktionswerte assoziiert sind, die in Schritt c) ausgewählt werden,
    - wenn die Antwort des dritten analytischen Modells auf den in Schritt c) ausgewählten Punkt größer null ist, Bestimmen eines Punkts, der mit dem maximalen Wert der Antwort des zweiten Modells nahe dem in Schritt c) ausgewählten Werts assoziiert ist,
    - wenn die Antwort des dritten analytischen Modells auf den in Schritt c) ausgewählten Punkt kleiner null ist, Bestimmen eines Punkts, der mit dem minimalen Wert der Antwort des zweiten Modells nahe dem in Schritt c) ausgewählten Werts assoziiert ist,
    - Bestimmen eines neuen Produktionswerts durch den Abfluss-Simulator an dem Punkt, der mit dem zuvor bestimmten minimalen oder maximalen Wert assoziiert ist,
    - Bestimmen eines vierten Modells, indem das zweite Modell so angepasst wird, dass die Antwort des vierten Modells dem neuen Wert entspricht, der in dem vorherigen Schritt bestimmt wurde.
  10. Verfahren nach einem der vorhergehenden Ansprüche, wobei die Schritte c) und d) wiederholt werden.
  11. Verfahren nach einem der vorhergehenden Ansprüche, wobei in Schritt b) die Produktionswerte gewählt werden, indem ein Versuchsplan verwendet wird.
  12. Verfahren nach einem der vorhergehenden Ansprüche, wobei in Schritt b) das erste Modell unter Verwendung eines der folgenden Näherungsverfahren angepasst wird: polynomiale Näherung, neuronale Netze, Support-Vector-Maschinen.
  13. Verfahren nach einem der vorhergehenden Ansprüche, wobei in Schritt d) eines der folgenden Interpolationsverfahren verwendet wird. Kriging-Verfahren und Spline-Verfahren.
EP05291700A 2004-08-30 2005-08-08 Verfahren zur Modellierung der Ölgewinnung aus einer unterirdischen Formation Expired - Lifetime EP1630348B1 (de)

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DE602005001737D1 (de) 2007-09-06
US20060047489A1 (en) 2006-03-02
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FR2874706A1 (fr) 2006-03-03
FR2874706B1 (fr) 2006-12-01
ATE368167T1 (de) 2007-08-15
US7788074B2 (en) 2010-08-31
NO20053858L (no) 2006-03-01
CA2515324A1 (fr) 2006-02-28
CA2515324C (fr) 2015-04-21
NO335452B1 (no) 2014-12-15

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