Patent Publication Number: US-2019196060-A1

Title: Method for modeling a sedimentary basin

Description:
GENERAL TECHNICAL FIELD 
     The present invention relates to a method for modeling a sedimentary basin. 
     PRIOR ART 
     Tools for “modeling basins” that allow the formation of a sedimentary basin to be simulated numerically are known. Mention will be made by way of example of the tool described in patent EP2110686 (U.S. Pat. No. 8,150,669) or in patent applications EP2816377 (US2014/0377872), EP3075947 (US2016/0290107), EP3182176 (US2017/0177764). 
     These computational tools allow all of the sedimentary, tectonic, thermal, hydrodynamic and organic and inorganic chemical processes that are involved in the formation of a sedimentary basin to be simulated in one, two or three dimensions. 
     Numerical modeling of sedimentary basins is an important tool for the exploration of the bedrock and in particular oil and gas exploration. One of its objectives consists in predicting the pressure field at the scale of the sedimentary basin on the basis in particular of geological and geophysical information and of drilling data. In the context of oil and gas exploration, the data that allows such models to be constructed generally originate:
         from appraisals and geological studies for evaluating the oil and gas potential of the sedimentary basin, which are carried out on the basis of available data (outcrops, seismic campaigns, drilling campaigns). Such appraisals aim to:
           better understand the architecture and geological history of the bedrock, and in particular to study whether hydrocarbon migration and maturation processes were able to occur;   identify the regions of the bedrock in which these hydrocarbons could have accumulated;   establish which regions have the best economic potential, evaluated on the basis of the volume and of the nature of the probably trapped hydrocarbons (viscosity, degree of mixture with water, chemical composition, etc.), and their development cost (dependent for example on depth and fluid pressure).   
           exploration wells drilled into the various regions having the best potential, in order to confirm or disprove the potential estimated beforehand, and to acquire new data to feed to new, more precise studies.       

     Conventionally, basin modeling algorithms include three main steps:
         1. a phase of constructing a mesh of the bedrock under an assumption as to its internal architecture and as to the properties that characterize each cell: for example their porosity, their sedimentary nature (clay, sand, etc.) or even their organic material content at the moment of their sedimentation. The construction of this model is based on data acquired via seismic campaigns or well measurements for example. This mesh is structured into layers: a group of cells is assigned to each geological layer of the model basin.   2. a phase of reconstructing the mesh, representing prior states of the architecture of the basin. This step is carried out using, for example, a back stripping method (Steckler, M. S., and A. B. Watts,  Subsidence of the Atlantic - type continental margin off New York,  Earth Planet. Sci. Lett., 41, 1-13, 1978.) or a structural restoration method (see the aforementioned patent application EP2110686 (U.S. Pat. No. 8,150,669)).   3. a step of numerically simulating a selection of physical effects that occur during the evolution of the basin and that contribute to the formation of oil and gas traps. This step is based on a representation of time discretized into “events”, each event being simulated by a succession of time intervals. The start and end of an event correspond to two successive states of the evolution of the architecture of the basin delivered in the preceding step 2. The number of time intervals, which is generally comprised between a few and several hundred, may be set, or vary to match the complexity of the geological and physical mechanisms.       

     It is desirable to use the briefest possible time intervals in order to improve, as much as possible, the quality of the model and its representativeness of reality (this is of major importance to be able subsequently in particular to proceed with oil and gas wells), but such an approach is rapidly limited by the capacity and resources of present-day processors. 
     Even when expensive supercomputers are used, the time required to model a basin is substantial. 
     It would be desirable to improve the computational efficiency of current methods so as to be able to implement them, without loss of quality, on everyday hardware in a reasonable time. 
     The invention aims to improve the situation. 
     DESCRIPTION OF THE INVENTION 
     The invention provides, according to a first aspect, a method for modeling a sedimentary basin, said sedimentary basin having undergone a plurality of geological events defining a sequence of states {A i } of the basin, each of said states extending between two successive geological events, the method comprising the implementation by data processing means of steps of:
         (a) Obtaining measurements of physical quantities of said basin, which are acquired from sensors;   (b) For each of said states A i , constructing a meshed representation of said basin depending on said measurements of physical quantities;   (c) For each of said states A i , and for each cell of said meshed representation,
           1. computing an effective stress applied to the cell at the end of the state A i ;   2. computing an overpressure in the cell at the end of the state A i  depending on said effective stress computed at the end of the state A i .   
               

     The method according to the invention is advantageously completed by the following features, implemented alone or in any technically possible combination thereof:
     the method comprises a step (d) of selecting regions of said basin corresponding to cells of said meshed representation of said basin at the current time containing hydrocarbons;   step (d) comprises developing said basin depending on said selected regions;   step (b) is implemented by backstripping or structural reconstruction;   said effective stress at the end of the state A i  for a cell is computed depending on the effective stress at the end of the preceding state A i-1  and on an additional effective stress on the state A i  dependent on a change in sediment thickness during the state A i ;   step b) comprises, for each cell and each state A i , determining a total vertical stress on the cell, said additional effective stress being computed in step (c) to be the additional total vertical stress A i  with respect to the preceding state A i-1 , minus the hydrostatic pressure equivalent to the change in sediment thickness;   step (c).2 comprises computing a rate of change in the effective stress during the state A i  depending on the effective stress at the end of the state A i  and on the effective stress at the end of the preceding state A i-1 ;   step (c).2 comprises computing a rate of change in a porous volume of the cell during the state A i  while assuming the rate of change in the effective stress during the state A i  to be constant, so as to obtain the overpressure at the end of the state A i  by solving a simplified Darcy equation;   said simplified Darcy equation is given by the formula   

     
       
         
           
             
               
                 
                   
                     
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     C k  the change in void density (porous volume over solid volume) over the change in effective stress under the assumption of hydrostatic pressure,   Vol s,k  the solid volume of the cell k in question,   μ the kinematic viscosity of the fluid,   K the intrinsic permeability of the rock,   Δt the duration of the state in question,   oP i  the overpressure at the end of state A i ,   Δ{tilde over (σ)}ϵ the theoretical additional effective stress.   step (c) comprises a prior step (c).0 of verifying that for at least one of said cells the overpressure has changed during the state A i  by more than at least one preset threshold, and of implementing the rest of step (c) only if this is verified;   step (c).0 comprises computing a value of the theoretical overpressure that would develop in the cell under the assumption of a hydrostatic pressure;   said value of the theoretical overpressure that would develop in the cell under the assumption of a hydrostatic pressure is obtained using formula   

     
       
         
           
             
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     with:
     V the flow speed of the water;   Δ{tilde over (σ)} the effective stress change,   k the permeability   q the Darcy or filtration speed,   oP i  the theoretical overpressure generated during the state A i ,   μ the dynamic viscosity of water,   S the area of the cell normal to the vertical axis,   d the distance between the center of the cell and the center of the top face of the cell,   g the norm of the acceleration due to gravity vector,   Δt the duration of the state in question.   step (c).0 furthermore comprises verifying that for at least one of said cells the overpressure has changed, from the last state A j,j&lt;i  in which the rest of step (c) was implemented, by more than a second preset threshold;   step (c).0 comprises computing, for each cell, an indicator:
       If for each cell the computed value of the theoretical overpressure that would develop in the cell under the assumption of a hydrostatic pressure is lower than said first threshold, each indicator is incremented by the computed value of the theoretical overpressure that would develop in the cell under the assumption of a hydrostatic pressure;
           If for at least one cell the computed value of the theoretical overpressure that would develop in the cell under the assumption of a hydrostatic pressure is higher than said first threshold or the value of the indicator is higher than said second threshold, each indicator is reset to zero.   
           
       

     According to a second aspect, the invention relates to a piece of equipment for modeling a sedimentary basin, said sedimentary basin having undergone a plurality of geological events defining a sequence of states {A i } of the basin, each extending between two successive geological events, the piece of equipment comprising data processing means configured to:
         Obtain measurements of physical quantities of said basin, which are acquired from sensors;   For each of said states A i , construct a meshed representation of the basin depending on said measurements of physical quantities;   For each of said states A i , and for each cell of the meshed representation,
           1. computing an effective stress applied to the cell at the end of the state A i ;   2. computing an overpressure in the cell at the end of the state A i  depending on said effective stress computed at the end of the state A.   
               

     According to a third aspect, the invention relates to a computer program product downloadable from a communication network and/or recorded on a medium that is readable by computer and/or executable by a processor, comprising program code instructions for implementing the method according to the first aspect of the invention, when said program is executed on a computer. 
    
    
     
       DESCRIPTION OF THE FIGURES 
       Other features, aims and advantages of the invention will become apparent from the following description, which is purely illustrative and nonlimiting, and which must be read with reference to the appended drawings, in which: 
         FIG. 1  is a diagram showing the pressure as a function of depth in an exemplary sedimentary medium; 
         FIG. 2 a    schematically shows a known method for modeling a sedimentary basin; 
         FIG. 2 b    schematically shows the method for modeling a sedimentary basin according to the invention; 
         FIG. 2 c    schematically shows the method for modeling a sedimentary basin according to a preferred embodiment of the invention; 
         FIG. 3  illustrates the decoupling between the determination of the effective stress and the determination of the overpressure; 
         FIG. 4  shows a system architecture for implementing the method according to the invention; 
         FIG. 5  shows an example of smoothing of a porosity/stress curve; 
         FIGS. 6 a  and 6 b    show two examples of modeling of a sedimentary basin without and with the method according to the invention. 
     
    
    
     DETAILED DESCRIPTION 
     Principle of the Invention 
     A basin model delivers a predictive map of the bedrock in particular indicating the pressure in the basin (pressure field) over its geological history. 
     To do this, a substantial part of the computing time of the iterative simulating portion is related to the modeling of the effects of water flow in the basin. 
     The equilibrium pressure that is established in the pores of a porous medium if there is a sufficiently permeable path joining the point of study to the surface is referred to as hydrostatic pressure. It is also the pressure that would be obtained in a water column at the same depth. 
     Lithostatic pressure is a generalization to solid rocky media of the concept of hydrostatic pressure, which applies to gaseous and liquid media. It is the pressure that would be obtained in a column of rock at the same depth. 
     The lithostatic and hydrostatic gradients correspond to the variation in the lithostatic and hydrostatic pressures per unit of depth. 
     With reference to  FIG. 1  it may be seen that the fluid pressure observed in the pores of the rock (called observed pore pressure) generally varies in the same way as the hydrostatic pressure. However, under certain geological conditions, the pore pressure may diverge from this normal behavior. 
     The difference between the pore pressure and the hydrostatic pressure is referred to as overpressure/under-pressure (the regions of overpressure and under-pressure are shown in  FIG. 1 ). 
     Specifically, sedimentary basins are, with some notable exceptions, accumulations of gas or hydrocarbons saturated with water. The process of sedimentation and erosion however leads to changes, over the course of geological time, in the vertical load in sedimentary basins. These changes in load induce compaction or expansion of the rocks, effects responsible for the movement of the fluids that they contain, generally relatively brackish water. If the permeability of the rocks allows fluids to flow, the pressure remains at hydrostatic equilibrium, but diverges therefrom in the contrary case. The pore pressure may therefore be higher (overpressure) or lower (under-pressure) than the hydrostatic pressure when, for example, the permeability does not allow water to easily flow within the rock. 
     Various effects may be the origin of overpressures (Grauls, D., Overpressure assessment using a minimum principal stress approach—Overpressures in petroleum exploration; Proc Workshop, Paul, April 1998 —Bulletin du centre de recherche Elf Exploration et Production, Mémoire  22, 137-147, ISSN: 1279-8215, ISBN: 2-901 026-49-4). Major effects for example include:
         Compaction disequilibrium: during a sedimentation episode, the sedimentary field is subjected to an increase in lithostatic stress (due to the increase in the weight of the superjacent rocks). The porosity of the rocks decreases, leading to an increase in the pressure of the fluid present in the porous medium. However, if the fluid is free to flow, it will tend to evacuate in order to return to hydrostatic pressure. There is therefore competition between the speed of expulsion of the fluid and the capacity of the rock to compact. However, the lower the permeability, the greater the diffusion time of the fluid. For a given sedimentation rate, there is therefore a critical permeability below which overpressure is developed.   Expansion of the fluids: Under the effect of a temperature increase, the fluid tends to expand. At constant pore volume, pressure then increases.   A source of internal fluids: certain mineral reactions, such as the conversion of smectite to illite, generate water. Moreover, maturation of the source rock, the origin of hydrocarbons, converts a solid into fluid (organic porosity or secondary porosity is then spoken of). In both these cases, fluid is generated at depth and therefore overpressures develop.       

     To determine the water flow and pressures that result therefrom at the present time, it is necessary to simulate the water flow over the sedimentary history of the basin in the iterative step. 
     To do this, the fluid flows are computed using the conventional Darcy law: 
     
       
         
           
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     with u the speed of movement of the fluid (of the water in the case of modeling of sedimentary basins) in the medium, K the permeability of the medium to the fluid in question, μ the viscosity of the fluid and ρ its density, g the acceleration due to gravity, and P the pore pressure. 
     With reference to  FIG. 2 a   , which shows the sequence of a typical method, the computation of the pressure field in a numerical sedimentary basin model is based on the coupled solution, at the scale of the sedimentary basin, of the variation in the vertical stress, of the variation in the porosity of the rocks, of the variation in their permeability and of the variation in their properties (density and viscosity in particular) and of the volumes of fluids. 
     More precisely, as explained in the introduction, if the set of the states is called  , two states being separated by an event of geological order, then for each state A i  it is necessary to solve the Darcy equation in small time increments (i.e. with a small time interval dt) until the following state A i+1 . 
     Furthermore, while the number of states A i  is in the end relatively limited, it is necessary to have several hundred increments per state in order to obtain a good modeling quality. 
     In order to determine all of the aforementioned properties, the solution of the equations of conservation of mass coupled to the Darcy equation thus requires computational times that may be very long, from a few minutes to several hours, depending on the dimension of the numerical model (number of cells and number of geological events) and depending on the complexity of the physical and geological effects. 
     This problem of the complexity of the solution of the Darcy equation is well known to those skilled in the art familiar with algorithmics. It has moreover been proposed in document US 2010/0223039 to simplify the equations by making assumptions as to the physical effects involved. This is effective but proves to be very complex to manage given the multiplicity of effects and may decrease quality. 
     In contrast, the present method provides an algorithmic trick allowing in every possible case the time interval to be substantially increased (and therefore the number of iterations necessary for each state to be decreased). As will be seen, a single “large” increment may be enough for one state, and in the worst possible case several tens of increments will be enough, thereby decreasing by at least one order of magnitude the number of iterations required for the implementation of the method. 
     The idea is to decouple the deposition and erosion processes (increase or decrease in the sedimentary load) from those of the flow of the fluids (creation/dissipation of the overpressure), as is illustrated in  FIG. 3 , which will be described in more detail below. 
     More precisely, instead of considering the sedimentary load and the overpressure to be two interdependent parameters that it is necessary to solve simultaneously (hence the many increments required in each state), it will be shown that it is possible to determine a priori the change in effective stress between two geological events (and therefore over an entire state A i ), and then, for this state A i , to estimate the overpressure on the basis of the estimated variation in the effective stress. 
     Architecture 
     With reference to  FIG. 2 b   , a method for modeling a sedimentary basin, said sedimentary basin having undergone a plurality of geological events defining a sequence of states {A i } of the basin, each extending between two successive geological events, will now be described. 
     The present method is typically implemented within a piece of equipment such as shown in  FIG. 4  (for example a workstation) equipped with data processing means  21  (a processor) and data storing means  22  (a memory, in particular a hard disk), typically provided with an input/output interface  23  for inputting data and returning the results of the method. 
     The method uses, as explained, data relating to the sedimentary basin to be studied. The latter may for example be obtained from well logging measurements carried out along wells drilled into the studied basin, from the analysis of rock samples for example taken by core drilling, and/or from seismic images obtained following seismic acquisition campaigns. 
     In a step (a), in a known way, the data processing means  21  obtained measurements of physical quantities of said basin, which are acquired from sensors  20 . Nonlimitingly, the sensors  20  may consist of well logging tools, of seismic sensors, of samplers and analyzers of fluid, etc. 
     Given the length and complexity of seismic, stratigraphic and sedimentological measurement campaigns (and geological campaigns generally), said measurements are generally accumulated via dedicated devices  10  allowing such measurements to be gathered from the sensors  20  and stored. 
     These measurements of physical quantities of the basin may be of many types, and mention will in particular be made of water heights, of the deposited types of sediment, of sedimentation or erosion heights, of lateral stresses at the boundary of the field, of lateral flows at the boundary of the field, etc. 
     With regard to the choice of the physical quantities of interest, those skilled in the art may refer to the document “ Contribution de la mécanique ál&#39;étude des bassins sédimentaires: modélisation de la compaction chimique et simulation de la compaction mécanique avec prise en compte d&#39;effets tectonique ”, by Anne-Lise Guilmin, 10, Sep. 2012,  Ecole des Ponts ParisTech.    
     In a step (b), for each of said states A i , the data processing means  21  construct (or reconstruct) a meshed representation of the basin depending on said measurements of physical quantities. The meshed representation models the basin in the form of a set of elementary cells. 
     As will be seen, it is desirable for step (b) to comprise, for each state, the determination of a total vertical stress on each cell of the meshed representation. 
     As is known, those skilled in the art will be able to use known backstripping or structural reconstruction techniques to carry out this step. In the rest of the present description, the example of backstripping will be taken, but the present method is not limited to one particular meshed representation. 
     The present method is very particularly noteworthy in that it comprises, as explained, steps (c).1 and (c).2, which will be implemented recursively for each of the states A. In the rest of the present description, the example of a single time increment per state A i  (i.e. length of the time interval=length of the state) will be taken, this most often being enough; but it will be understood that if the circumstances require it, those skilled in the art will possibly place a plurality of increments in one state (i.e. compute intermediate values of the effective stress and overpressure) if for example it is of a particularly long duration. In practice, the increments will be 5 to 100 times longer, and the number of computational steps divided accordingly. 
     Generally, step (c) then comprises, for each of said states A i , and each cell of the meshed representation:
         1. Computing an effective stress applied to the cell at the end of the state A i ;   2. Computing an overpressure in the cell at the end of the state A i  depending on said effective stress.       

     As will be seen, the recursive character is due to the fact that the computation of an effective stress applied to the cell at the end of the state A i  advantageously involves the value of the effective stress at the end of the preceding state A i-1 , and the fact that the computation of the overpressure advantageously involves the value of the effective stress at the end of the preceding state A i-1  and of the present state A i  and the value of the overpressure in the cell at the end of the preceding state A i-1 . 
     This may be summarized as follows:
         1. computation of an effective stress applied to the cell at the end of the state A i  on the basis of the effective stress applied to the cell at the end of the preceding state A i-1 ;   2. computation of an overpressure in the cell at the end of the state A i  depending on the effective stresses applied to the cell at the end of the state A i  and at the end of the preceding state A i-1 , and on the overpressure in the cell at the end of the preceding state A i-1 .       

     Step (c).1 is a step of computing effective stresses applied to the basin. More precisely, said effective stress at the end of the state A i  is computed for each cell of the meshed representation, and for each state A. 
     Step (c).1 thus allows the change in effective stress between two geological events (i.e. during a state A i ) to be determined a priori. Knowing the effective stress in each cell of the model at the start of the state A i  in question (equal to that at the end of the preceding state A i-1 ), denoted σ initial , an additional effective stress denoted σ eff   _   add  is computed, which is added to the stress σ initial  in order to obtain σ eff . According to one embodiment of the invention, the effective stress corresponds to the lithostatic stress. The vertical stress corresponding to the weight of the superjacent rocks is called the lithostatic stress. The additional lithostatic stress thus corresponds to the variation in the weight of the superjacent rocks during the state A i , i.e. to the deposition or erosion. In the case of lithostatic stress, the rocks are considered to be nonporous, or in other words the lithostatic stress does not comprise the weight of the fluids present in the pores of the superjacent rocks. 
     According to one embodiment of the invention, the effective stress corresponds to the total stress. The total stress corresponds to the weight of the superjacent rocks, the rocks being considered to be a porous medium able to contain fluids such as water. The additional total stress thus corresponds to the variation in the weight of the superjacent rocks during the state A i , i.e. to the deposition or erosion. 
     The thickness of sediment deposited or eroded during the same state A i  is also known. Consequently:
         In the case of a sedimentary deposition, step (b) delivers the additional total vertical stress Δσ v  (difference between the total vertical stresses at the end of the state A i  in question and the preceding state A i-1 , respectively) and the theoretical additional effective stress M under the assumption that these additional sediments are at hydrostatic pressure (this generally being the case because these freshly deposited sediments are generally very porous and very permeable).   In the case of an erosion, the additional total vertical stress Δσ v  and the theoretical additional effective stress Δ{tilde over (σ)} of the removed portion of the sedimentary column are known by virtue of the computation carried out in the preceding state A i-1 .       

     To use yet other words, knowing the solid volume of the additional load, the backstripping (step (b)) gives its porosity under the assumption of hydrostatic pressure. The additional total load (additional stress) is therefore known and the additional effective stress (total load—hydrostatic pressure equivalent to the sedimented thickness) σ eff   _   add  is deduced therefrom. 
     It is then possible to compute, from the effective stress, in step (c).2, the overpressure, because, at each point of the sedimentary column, the variation in the effective stress is then the sum of Δ{tilde over (σ)}, which is uniform over the entire column (formed by the current cell and the underlying cells), and of the change in overpressure at the point in question (which therefore corresponds to the divergence from the hydrostatic pressure). 
     In this step (c).2, the data processing means  21  thus estimate the overpressure at the end of the geological state A i  in question on the basis of the change in effective stress estimated in the preceding step. 
     According to one highly preferred embodiment of the invention, the curve of the variation in the porosity as a function of the load is linearized locally, as may be seen in  FIG. 5 . This is the key point that allows the Darcy equation to be solved for a large time interval (of as large as the entire length of the state A i ), and not in small increments of movement over this curve. 
     The underlying assumption is that the rate of change in the porous volume is constant during the state A i  and thus a linear variation in the porous volume with respect to the overpressure is obtained. This allows the latter to be rapidly estimated with a “simplified” Darcy equation directly relating the overpressure at the start and end of the state A i , according to the following formula: 
     
       
         
           
             
               
                 
                   
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     With: 
     C k  the change in void density (porous volume over solid volume) over the change in effective stress under the assumption of hydrostatic pressure, 
     Vol s,k  the solid volume of the cell k in question, 
     μ the kinematic viscosity of the fluid, 
     K the intrinsic permeability of the rock, 
     Δt the duration of the state in question, 
     oP i  the overpressure at the end of the state A i , 
     Δ{tilde over (σ)}ϵ The theoretical additional effective stress under the assumption that these additional sediments have a hydrostatic pressure. 
     In summary, step (c).2 advantageously comprises computing a rate of change in the effective stress during the state A i  depending on the effective stress at the end of the state A i  and on the effective stress at the end of the preceding state A i-1 . 
     Conventionally, step (c) will possibly moreover comprise the numerical imulation (where appropriate over a shorter time interval) of at least one physical effect so as to estimate, apart from the overpressure, any quantity of the sedimentary basin that could possibly be of interest to those skilled in the art, such as fluid saturations, temperatures, etc. 
     Preferred Embodiment 
     According to one very advantageous embodiment, the present method proposes to avoid implementing the computation of the overpressure of step (c).2 if said computation is not necessary. 
     Specifically, in the earliest phases of the geological history of a sedimentary basin, the pressure field is often in hydrostatic equilibrium, i.e. the overpressure is zero at every point in the basin. It is then possible to directly determine the pressure at every point in the basin without solving the Darcy equation or even the simplified equation presented above. It is enough to apply the formula: 
         P   z   =P   atm +ρ gz,  
 
     with P z  the pressure at the depth z, P atm  atmospheric pressure, ρ w  the density of water, g the acceleration due to gravity. 
     In order to generate a pressure that diverges from hydrostatic equilibrium, it is necessary for the volume of fluid to be moved because of changes in geological conditions to be larger than the volume of water that the flow properties allow to be made to flow. Assuming a purely vertical flow of water, it is possible to compute, during each state A i , in each of the cells of the geological model, the difference between the volume of fluid to be moved and the volume that may actually flow because of the permeability of the rock. It is then possible to determine whether there exists a possible source of abnormal pressure. If no source of abnormal pressure exists (or if the source term is lower than a criterion) during the duration of a state A i , the basin is then considered to be in hydrostatic equilibrium. The calculation of this balance being far rapider than the solution of the Darcy equation, it is possible to completely solve the Darcy equation, even as presently simplified, only when this proves to be necessary and thus to drastically decrease computation times. Thus, with reference to  FIG. 2 c   , step (c) preferably comprises a prior step (c).0 of verifying that, for at least one of said cells, the overpressure has changed during the state A i  by more than at least one preset threshold, and, at the end of which, the rest of step (c) is implemented only if this is verified. Alternatively, if this is not verified, the pressure field is in hydrostatic equilibrium and it is possible to apply the formula: P z =P atm +ρ w gz (i.e. the overpressure is zero everywhere). 
     As will be seen, advantageously two preset thresholds are used: a first threshold is used for each cell, and if this first threshold is verified everywhere, a second “cumulative error” threshold is tested. Those skilled in the art are perfectly able to determine the values of these thresholds, depending on the expected precision of the estimation of the overpressures. 
     To implement this verification procedure, a balance between the volume of fluid to be moved and the volume of mobile fluid is carried out for each state A i . Generally, step (c).0 comprises computing a value of the theoretical overpressure that would develop in the cell under the assumption of a hydrostatic pressure. 
     It must be understood that the verifying step does not compute the overpressure in the cell at the end of the state A i , nor even its actual change during the state A i , but only estimates a theoretical change therein (by virtue of the assumption of a hydrostatic pressure). This theoretical value proves easy to compute and is representative of the actual value. This is thus a reliable test of the need or not to solve an equation of the Darcy equation type. 
     As explained, a second cumulative error threshold (or total error threshold) may be used. In other words, step (c).0 advantageously furthermore comprises verifying that for at least one of said cells the overpressure has changed, from the last state A j,j&lt;i  in which the rest of step (c) was implemented, by more than a second preset threshold. It must be understood that the two verifications are cumulative: if at least one of the tests is verified (single error above the first threshold OR cumulative error above the second threshold), the Darcy equation is solved, and if none of the tests is verified (single error below the first threshold AND cumulative error below the second threshold) the Darcy equation is not solved. 
     In a particularly preferred way, for this total error test “indicators” associated with each of the cells, which indicators will be described below, are used. These indicators allow the small theoretical overpressures that are ignored to be summed so as to force the Darcy equation to be solved at the end of a certain time when the total error is no longer acceptable. More precisely, if for all the cells the rest of step (c) is not implemented (i.e. if a computed theoretical overpressure value is lower than said first threshold) then the indicator is incremented, and if it is implemented for at least one cell, the indicators are reset to 0. 
     In summary, step (c).0 advantageously comprises computing, for each cell, an indicator:
         If for each cell the computed value of the theoretical overpressure that would develop in the cell under the assumption of a hydrostatic pressure is lower than said first threshold, each indicator is incremented by the computed value of the theoretical overpressure that would develop in the (corresponding) cell under the assumption of a hydrostatic pressure;   If for at least one cell the computed value of the theoretical overpressure that would develop in the cell under the assumption of a hydrostatic pressure is lower than said first threshold or the value of the indicator (associated with the cell) is higher than said second threshold, each indicator is reset to zero.       

     To use yet other words, step (c) comprises, for each of said states A i , and for each cell of said meshed representation, the verification that, for at least one of said cells, an overpressure has changed during the state A i  by more than a first preset threshold (and advantageously the additional verification that for at least one of said cells the overpressure has changed, from the last state A j,j&lt;i  in which the rest of step (c) was implemented, by more than a second preset threshold), and if (and only if) this (at least one of the two verifications) is verified, the overpressure in the cell at the end of the state A i  is computed in step (c).2. 
     According to one particularly preferred embodiment:
         a. In the first state A 0 , the indicator that will be used to determine the method used to compute the pressure term (hydrostatic pressure or by actual solution of an equation of the Darcy equation type) is initialized to 0 in each cell.   b. For each state A i :
           i. The volume of fluid that must flow because of changes in the geological conditions in the cell in order to preserve a medium saturated with fluid is first computed for each cell of the model. This value corresponds to the difference in volume of the cell during the duration of the state A i , for example determined by the backward structural restoration method (backstripping method for the implementation of step (b)). This volume is negative in the case where the volume of the cell increases.   ii. A value of the overpressure, oP i , that would develop in the cell if the latter followed exactly the variation in volume given by the backward computation (i.e. under the assumption of a hydrostatic pressure) is estimated.   
               

     
       
         
           
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                     V 
                     
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                   oP 
                 
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                     k 
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                       oP 
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     It will in particular be noted that if k (the permeability in m 2  of the cell at the start of the state) is very small, it is indeed true that oP=Δ{tilde over (σ)}, 
     With: 
     V the flow speed of the water (m/s), 
     Δ{tilde over (σ)} the effective stress change (Pa), 
     k the permeability (m 2 ), 
     q the Darcy or filtration speed (m/s), 
     oP i  the theoretical overpressure generated during the state (kg/m/s 2 ) (the latter may be negative when the difference in volume is negative). 
     μ the dynamic viscosity (kg/m/s) of water, 
     S the area of the cell normal to the vertical axis (in m 2 ), 
     d the distance between the center of the cell and the center of the top face of the cell (in m), 
     g the norm of the acceleration due to gravity vector (m/s 2 ), 
     Δt the duration of the state (in s).
             iii. The term oP i  is compared, for each cell of the model, with said first preset threshold. This threshold corresponds to the acceptable error in the estimation of the overpressure between two states of the sedimentary basin.
               1. If no cell exceeds the criterion, i.e. the absolute value of oP i  remains lower than or equal to the first threshold, then the value of the indicator in each of the cells is incremented by oP i . The indicator is then compared with the (empirical) second preset threshold corresponding to the total “acceptable” error.
                   a. If this second threshold is not exceeded, the pressure is not computed by solving an equation of the Darcy equation type. It is assumed that during this state A i  the overpressure has not varied from the preceding state A i-1 . Specifically, this situation expresses the fact that the geological conditions allow the changes in volume of rock in the basin to be handled without a priori modification of the overpressure (depending on the criteria used).   
                   2. If at least one of the two thresholds is not respected in at least one of the cells of the model, it is necessary to solve the Darcy equation (step (c).2) in order to determine the overpressure distribution in the sedimentary basin. The value of the indicator is then reset to 0 in all of the model.   
                       

     Return 
     At the end of step (c), which is repeated for each cell and for each state A i , at least the value of the overpressure in each cell at the current time is obtained. 
     Furthermore, depending on the basin simulator used to implement the invention, additional information may be obtained on the formation of the sedimentary layers, their compaction under the effect of the weight of superjacent sediments, the heating thereof during their burial, the formation of hydrocarbons by thermal generation, the movement of these hydrocarbons in the basin under the effect of floatability, of capillary action, of differences in the pressure gradients and/or of subterranean flows, and/or the amount of hydrocarbons produced by thermal generation in the cells of said meshed representation of said basin 
     On the basis of such information, it is possible to identify regions of said basin, corresponding to cells of said meshed representation at the current time of said basin, containing hydrocarbons, and the content, the nature and the pressure of the hydrocarbons that are trapped therein. Those skilled in the art will then be able to select the regions of the studied basin having the best oil and gas potential. 
     The development of the basin for oil and gas purposes may then take a number of forms, in particular:
         exploration wells may be drilled into the various regions selected as having the best potential, in order to confirm or disprove the potential estimated beforehand, and to acquire new data to feed to new, more precise studies,   development wells (production or injection wells) may be drilled in order to recover hydrocarbons present within the sedimentary basin in regions selected as having the best potential.       

     The method thus preferably comprises a step (d) of selecting regions of said basin corresponding to cells of said meshed representation of said basin at the current time containing hydrocarbons, and/or of development of said basin depending on said selected regions. 
     Alternatively or in addition, step (d) may comprise the return to the interface  23  of information on the well, such as a visual representation as will now be described. 
     Result 
     Purely by way of illustration,  FIGS. 6 a  and 6 b    show the models of a sedimentary basin (the overpressure value computed for each cell is shown) obtained by implementing a conventional method and a method according to the invention. 
     The modeling qualities may be seen to be similar (identical patterns have been generated) whereas the simulation times were very different: in the case of the conventional method ( FIG. 6 a   ), this time was 24 minutes 31 seconds, whereas only 3 minutes 26 seconds were required in the case of the method according to the invention ( FIG. 6 b   ). With the same computational resources and modeling quality, a time-saving of a factor of 7 was observed. 
     Piece of Equipment and Computer Program Product 
     According to a second aspect, the piece of equipment  14  for implementing the present method for modeling a sedimentary method is provided. 
     This piece of equipment  14  comprises, as explained, data processing means  21 , and advantageously data storing means  22 , and an interface  23 . 
     The data processing means  21  are configured to:
         Obtain measurements of physical quantities of said basin, which are acquired from sensors  20 ;   For each of said states A i , construct a meshed representation of the basin depending on said measurements of physical quantities;   For each of said states A i , and for each cell of the meshed representation,
           1. computing an effective stress applied to the cell at the end of the state A i ;   2. computing an overpressure in the cell at the end of the state A i  depending on said effective stress computed at the end of the state A i .   
               

     According to a third aspect, the invention also relates to a computer program product downloadable from a communication network and/or recorded on a medium that is readable by computer and/or executable by a processor, comprising program code instructions for implementing the method according to the first aspect, when said program is executed on a computer.