(1) exploration of modeling principle and method: under the gravity of the sedimentary layer itself and the overlying sedimentary layer, the particles are arranged more and more closely, which is a regular phenomenon in the geological history process and is called gravity compaction of the sedimentary layer.
Porosity of sedimentary layer (or acoustic time difference) is the main index to measure the compaction degree of sedimentary layer. In general, with the increase of buried depth, the porosity of sedimentary layer decreases correspondingly, which is irreversible. Even if the overlying sedimentary layer is eroded, its thickness decreases and its load decreases, it cannot rebound. Assuming that the pores of sediments are filled with water (fluid), the change of porosity reflects the change of water (fluid) discharge in pores. Therefore, it is an important way and method to study the regular relationship between porosity and pore water (fluid) excretion in the geological history of sedimentary system.
The quantitative study of gravity compaction, pore volume reduction and pore fluid discharge of sediments is based on the correlation between modern measurement data of sediment porosity (φ) and buried depth (z). Therefore, it is very important to choose which algorithm, explore the correlation between them and establish an approximate and practical mathematical model of compaction.
Since 1980, the former researcher Lin of our institute has studied and counted the modern porosity and buried depth test data of mudstone and sandstone in several sedimentary basins. According to the principle of least square method and curve transformation technology, four curve types, straight line, exponential, power function and logarithm, are used to fit the data in the study area. Comparing various curves with actual data, it is found that fitting with power function and logarithmic curve equation has high correlation coefficient, but low coincidence degree of shallow points, and the deviation of calculated shallow porosity is too large, which shows that these two curve types are not applicable. For sandstone, the shallow porosity calculated by exponential curve fitting is larger, while the linear equation fitting effect is better. For mudstone, the surface porosity calculated by linear equation fitting is obviously low, while the exponential curve fitting effect is better. Accordingly, the relationship curve between mudstone and depth is exponential equation, and the relationship curve between sandstone and depth is linear equation.
(2) Mathematical model of compaction: According to the results of the above modeling methods, the compaction models of mudstone and sandstone can be described as follows.
The mathematical model of mudstone compaction is:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
Where: z-buried depth of mudstone, m;
φm(z)- curve function of mudstone porosity and buried depth;
φφmo——z mudstone porosity when z is 0, decimal;
Cm—— the size constant of mudstone, m- 1.
The mathematical model of sandstone compaction is:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
Where: z-buried depth of sandstone, m;
φs(z)- curve function of sandstone porosity and buried depth;
φφso——z sandstone porosity when z is 0, decimal;
Cs—— the size constant of sandstone, m- 1.
It goes without saying that the quality of the model is related to the amount of porosity data and the uniformity of distribution during modeling. If the test data is correct, and the test points are numerous and evenly distributed, the accuracy of the model can be obviously improved.
(3) Mathematical model of skeleton thickness: The above two compaction models can't give the thickness of mudstone and sandstone in the process of deposition, burial and compaction, and the evolution process of related burial depth and porosity, which is a key problem that must be answered and solved in the paleohydrogeology research of sedimentary basins. How does the evolution of mudstone and sandstone thickness unfold during sedimentary compaction? Therefore, the mathematical model of the thickness of the research layer skeleton is constructed as a scale to consider the compaction degree of the sedimentary layer during the compaction process. With the help of these three mathematical models, the recovery thickness of mudstone and sandstone in any study layer and its corresponding buried depth and porosity can be obtained.
It is assumed that when the pore volume of mudstone and sandstone is 0, it shows that all the water (fluid) stored in mudstone and sandstone has been discharged, and the thickness of mudstone and sandstone becomes the skeleton composed of solid particle aggregates. According to the integral, the mathematical model of rock skeleton thickness can be described as follows:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
Where: hg—— skeleton thickness of study layer, m;
Z 1 —— the depth of the top interface of the study layer, m;
Z2—— the depth of the bottom interface of the study layer, m;
φ (z) —— Porosity-depth curve function of the study layer, with φ m (z) for mudstone and φ s (z) for sandstone.
2. Numerical simulation of sedimentary compaction evolution in the basin.
(1) Technical processing of pre-simulation data: The modern thickness and buried depth of the study layer in each era provided by drilling geological records, because its lithology and thickness are uneven and changeable alternating layers, the continental strata are particularly changeable and complicated. Therefore, gravel, conglomerate, sand and sandstone of various sizes composed of coarse-grained materials are merged into sandstone (hereinafter referred to as sandstone), while clay, mudstone, shale and coal composed of fine-grained materials are merged into mudstone (hereinafter referred to as mudstone), and their cumulative thickness is counted according to each layer group. Due to different exploration degrees and uneven drilling distribution, in areas without drilling geological data, it can be determined by seismic geological data and sedimentary facies map.
(2) Generalization of lithologic profile: The drilling geology records the interbedded sandstone and mudstone with extremely uneven thickness, and the lithology changes greatly, especially in continental strata. Lithologic profile must be generalized, otherwise it is difficult to calculate. As shown in Figure 4-22, A is the actual lithologic profile, and B and C are the two profiles after generalization. The test results show that:
Whether sandstone or mudstone is placed in the middle of the profile, the calculated recovery thickness is less than the sum of the recovery thicknesses of the upper and lower parts, that is, the compressive strength in the middle is relatively large. In order to eliminate the human error caused by generalization, sandstone and mudstone are placed in the middle when calculating the recovery thickness. The compaction experiment shows that the compacted water discharged from mudstone vertically overlaps and the underlying sandstone migrates under the load, which obviously makes it reasonable to put mudstone in the middle, while the water in sandstone migrates laterally along the river bed under the load.
Figure 4-22 Schematic Diagram of Lithologic Profile Generalization
(3) When there is a sedimentary discontinuity on the sedimentary profile and the sedimentary layer is eroded, it is necessary to restore the original thickness of the denuded layer and then participate in the calculation.
(4) When there are compaction anomalies on the geological section, such as undercompaction zone or ultra-high pressure zone, technical treatment should be carried out or the sweep range of this section should be calculated separately.
3. Selection of calculation method
(1) inversion method: This method follows the principle of sedimentary compaction, based on the modern layered thickness of the basin sedimentary system and its corresponding burial depth and porosity, and according to the era of sedimentary layers from new to old, the geological section is calculated and stripped layer by layer in turn from top to bottom until all the research layers are stripped. The thickness of mudstone and sandstone in different geological periods during the compaction process and their corresponding evolution processes such as buried depth and porosity are restored and calculated. The reverse thinking method dating back to ancient times is called reverse thinking method.
The inversion method includes three assumptions: first, it is assumed that the distribution range of sedimentary layers on the plane is unchanged and only changes in the vertical direction, so the reduction of their volume can be attributed to the reduction of their thickness; Secondly, it is assumed that the skeleton thickness of the sedimentary layer (the thickness when the porosity is 0) is constant during the settlement process, so the decrease of the thickness of the sedimentary layer can be attributed to the decrease of its porosity; Thirdly, assuming that the pores of the sedimentary layer are full of water (fluid), the decrease of the pores of the sedimentary layer can be attributed to the decrease of its water content.
The characteristic of this method is that the calculated parameters are all obtained from the actual measurement, and the calculated results obtained by developing matching application software are consistent with the measured parameter values, so there is no need to correct the parameter values and no human error will be caused. Therefore, we think it is best to use the inversion method for calculation.
(2) Forward simulation method: calculate the original thickness of the stratum according to its modern thickness, modern porosity and original porosity, and then calculate the settlement rate of the stratum according to the original thickness and the corresponding settlement time, so as to restore the settlement and compaction process of the stratum from old to new and from bottom to top, which is called forward simulation method. Like the inversion method, this method also follows the principle of sedimentary compaction and calculates the evolution of formation thickness. Its main disadvantages are that the calculation process is complex, involving many parameters, and it is relatively difficult to determine the settlement time and deposition rate, so it is necessary to adjust the parameter values repeatedly to meet the requirements of calculation accuracy.
4. Methods and steps of inversion simulation calculation
(1) Evaluation of sedimentary skeleton thickness: according to formula (4-18);
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
Because φ (z) (φ m (z) or φ s (z)) and the depth of the top and bottom interfaces of the study layer are known, the skeleton thickness of mudstone or sandstone in any study layer can be obtained.
(2) Evaluation of the recovery thickness of the study layer: the skeleton thickness (hg), the compaction mathematical model (φ (z)) and the buried depth of the top surface of the study layer (Z 1) are all known. Substituting them into the formula (4- 18), we can get the recovery depth of the buried bottom of the study layer.
(3) Estimation of mudstone recovery thickness: Substitute formula (4- 16) into formula (4- 18) and expand to obtain the following nonlinear equation:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
In formula (4- 19), Z 1, φ Mo, Cm and hg are all known quantities, and Z2, Z2-Z 1 obtained by semi-interval search method is the recovery thickness of mudstone in the study layer.
(4) Evaluation of sandstone recovery thickness: Substitute the formula (4- 17) into the formula (4- 18) and simplify it into a quadratic equation:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
In formula (4-20), Z 1, φ s0, CS and hg are all known quantities, and the solution of Z2, z2-z 1 is the recovery thickness of sandstone in the study layer.
According to the above formulas (4- 16) to (4-20), the recovery thickness of each research layer in each research period is solved by the inversion method of stripping from new to old and from top to bottom.
5. Information provided by calculation results of inversion method
The information provided by the inversion calculation results includes the following three aspects:
(1) Direct application information: the thickness of study layer, mudstone and sandstone is calculated quantitatively, and the batch data of thickness, burial depth and porosity recovered by variables such as roof burial depth and porosity in each study period can outline a series of maps of the change process of each variable in the geological history process, which can be used as the basic map of hydrogeological conditions of each study layer in each study period and the working map of paleohydrogeology research process.
(2) One of the indirect application data, the head series diagram of mudstone compaction is restored and drawn: it has been assumed that the pores of sediments are full of water, so the decrease of pore volume caused by compaction in the process of sediment settlement can be attributed to the decrease of sediment water content. The difference between the recovery thickness of the study layer in two adjacent study periods is the compressed thickness of the study layer after compaction in the latter study period. The volume of compressed thickness is numerically equal to the decrease of pore volume in the two research periods, the decrease of pore volume is equal to the amount of compacted water, the volume of compressed thickness is numerically equal to the amount of compacted water, and its unit compressed thickness is numerically equal to the height of compacted water column, that is, the value of compacted head. In this way, the compaction head value can be obtained conveniently, and the series distribution map of compaction head of mudstone in the study layer in each study period can be drawn.
The evaluation of mudstone compaction head mainly includes the following two aspects:
Firstly, the temporal and spatial distribution and evolution of water head of mudstone compaction water reflect the intensity of water circulation in water-bearing system and the amount of mudstone compaction water entering sandstone, which is an important index to restore and calculate the alternating strength of water in research layers in each research period. However, the head and water volume of mudstone compaction water cannot reflect the flow direction of water in permeable sandstone in this study layer. Because, under the same static pressure, if the mudstone thickness in the study layer is large and the sandstone thickness is small, the head of mudstone compaction is large; On the contrary, the head of compacted water is very small. The flow direction of water in permeable sandstone is controlled by the load of overlying sediments.
The second is to study the migration of mature source rocks in the basin. From the hydrogeological point of view, mudstone compaction water is the carrier and driving force of oil and gas migration in source rocks. Therefore, the compacted water discharged from mudstone is beneficial to the primary migration of oil and gas, and the water head value can be used to evaluate the oil and gas migration amount of hydrocarbon-generating rocks, but the water head of compacted water cannot indicate the migration direction and concentrated position of oil and gas in sandstone reservoirs, because the secondary migration or multiple migration of oil and gas in sandstone reservoirs depends on the layered pressure of reservoirs, not the water head of compacted water.
(3) The second information indirectly applied, that is, to resume the calculation of the alternating strength of squeezing water: according to the head or quantity of mudstone compaction water in the study layer, only the alternating situation of sandstone water being replaced by mudstone compaction water in the water-bearing system can be qualitatively displayed, but the alternating strength of mudstone compaction water to sandstone water cannot be proved. Therefore, it is necessary to calculate the water-holding capacity of sandstone while calculating the compacted water quantity of mudstone in each research layer in each research period, and so on, so as to quantitatively restore the alternating strength of squeezed water.
The alternating strength of squeezed water can be calculated by volume method and Monte Carlo method, so as to compare the reliability of the results calculated by the two methods.
The first is the volumetric method, and its calculation method and steps are as follows:
Step 1: Determine the research cycle of the research layer.
Step 2: Delineate the distribution boundary of the study layer. The distribution range of sandstone and mudstone in the study layer is the same in each study period, which means that the calculation area of the study layer can be fixed.
Step 3: Divide the calculation area. The calculation area is divided into several calculation blocks, so that the range of calculation parameters in the same block is as close as possible.
Step 4: Calculate the arithmetic average of sandstone thickness, porosity and mudstone compaction head value (i.e. mudstone compression thickness) in each block according to the sandstone recovery thickness map, roof buried depth map, mudstone compaction head contour map and sandstone compaction mathematical model in the corresponding research period.
Step 5: Calculate the water storage capacity (Qs) of sandstone in the study layer according to the following formula:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
Where: Qs—— water storage capacity of sandstone in the study layer, m3;
S—— study layer area, m2;
Hs—— the average thickness of sandstone in the study layer, m;
φφs—— the average porosity of sandstone in the study layer, decimal. Step 6: Calculate the compaction water volume (Qm) of mudstone in the study layer according to the following formula:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
Where: Qm—— compaction water of mudstone in the study layer, m3;
S—— study layer area, m2;
Hm—— the average head of mudstone compaction in the study layer, that is, the average compaction thickness of mudstone in two adjacent study periods, m.
Step 7: Study the alternating strength (W pressure) of laminated extruded water and calculate it according to the following formula:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
According to the above method, the alternating intensity of squeezed water is recovered and calculated, and the formation and evolution process of water cycle in each research layer in each research period is revealed.
The second method is Monte Carlo method, and its calculation method and steps are as follows: In view of the fact that the alternating strength of sedimentary water calculated by volume method is an arithmetic average, what is the thickness H and porosity of rock stratum? Are random variables with a certain range. If each parameter is calculated by the distribution function of random variables, the calculation result will be closer to reality. Monte Carlo method is to simulate the probability statistical model of a given problem by using sampling sequences of random variables with different distributions, and put forward the asymptotic statistics of the numerical solution of the problem, also known as statistical simulation method. Therefore, the alternating strength of sedimentary water calculated by this method is compared with that calculated by volume method, which improves the credibility and scientificity.
Step 1: Find the distribution function of random variables: Let random variables be X .. Probability p (x
First, find the maximum Xmax and minimum Xmin in the original data.
Second, find the interval XL = xmax-xmin；;
Thirdly, determine the number m of statistical intervals;
Fourthly, find the separation value of M+ 1 interval:
Xi=Xmin+(XL/M) (i- 1)
i= 1，2，…，M+ 1
Fifth, count the number of original data falling into each interval, find out the corresponding frequency, and then accumulate the frequency values one by one from the maximum side to the minimum side to get the AF(x) values of m intervals.
The random variables Hs and φs in the sandstone water capacity formula QS = s hs φ s are calculated, and the distribution functions AF(Hs) and AF (? S). The area s is a constant.
Step 2: Randomly sample the random variables Hs and φs respectively, and multiply the obtained sampling values Hs 1 and φs 1 by Monte Carlo method to obtain a sample QsS 1 value of the function QS.
In order to realize random sampling, random numbers evenly distributed in the interval of (0, 1) should be taken as the sampling sequence. Here, the mixed congruence method is used to generate uniformly distributed random numbers, and the recursive formula is:
γn+ 1=αγn+β (modulo m)
Where: γn+ 1 and γn are the random numbers of the nth step+1 and the nth step respectively; α is the multiplier coefficient; β is increment; M is a module.
Its mathematical meaning is that the module m can be divisible by [γn+ 1 =-(αγn+β)], that is, γn+ 1 and (αγn+β) are congruent with the module m, and the specific algorithm is as follows:
Ln=αγn+β+M
Nn=Ln-[Ln/M] M
Zn=Nn/M
The values of parameters in the formula are: M=2 19, α=55, β = 3; [ln/m] means that only the integer part of Ln/M is taken; Zn is a random number evenly distributed in the interval of (0, 1).
The specific steps of random sampling are as follows: take the random numbers γh 1 and γ φ 1 obtained by the above algorithm as the probability entrance values of the distribution functions AF(h) and AF(φ) of random variables Hs and φs, and the corresponding probability exit values Hs 1, and? S 1, according to the formula (4-2 1), Qs 1 = hs1(i.e. Monte Carlo multiplication), QS1is the random sample value of the random function Q.
Step 3: Find the distribution function AF(q) of the random function Qs: repeat the random sampling described in step 2 for n times (n can be 5000 ~ 50000, and this time it can be 25000), and then perform the Monte Carlo multiplication for n times according to the formula (4-2 1) to find the random function Q Qs 1, QS2, QS. Then the distribution function AF(q) of the random function Qs is obtained by the frequency distribution method. Therefore, the water capacity of sandstone under different guarantee rates can be given.
Monte Carlo method is the same as the above method to calculate the Qm of mudstone compaction water, so I won't repeat it here.
Step 4: Calculate the alternating strength of water in each study layer in each study period: take the value of sandstone water capacity and mudstone compaction water obtained by Monte Carlo method as the expected value when the guarantee rate is 50%.
(4) Indirect application, recovery calculation and drawing of seepage field formation and evolution series. The third information: Using the calculated data, the hydraulic pressure data of each research layer in each research period are obtained through conversion calculation, and the drawn series of squeezing alternate seepage field is the most important research achievement map finally obtained in paleohydrogeology research.