A method for predicting dehydration cut-off time based on maximum eigenvalue

Abstract

The present invention relates to the technical field of oil and gas field development, and in particular to a method for predicting dehydration cut-off time based on a maximum eigenvalue. The present invention combines the linear relationship between the transverse relaxation time and the pore throat radius and the capillary force equation, adopts the maximum eigenvalue method to solve the conversion coefficient, and establishes a dehydration cut-off time calculation model based on the maximum eigenvalue method, which provides a new method support for analyzing the gas-water distribution law under different dehydration pressures.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas field development, and in particular to a dehydration cut-off time prediction method based on a maximum eigenvalue. Background Art

[0002] The development of oil and gas reservoirs involves the complex process of gas-water two-phase seepage. Correctly understanding the gas-water distribution law is the premise for well pattern optimization and the formulation of production-enhancing measures. Nuclear magnetic resonance core experiments have been widely used in the study of gas-water distribution laws. By conducting nuclear magnetic resonance experiments on water-saturated cores, and then dehydrating the water-saturated cores by centrifugation or displacement, cores with different water saturations are obtained. Nuclear magnetic resonance experiments are continued on cores with different water saturations to obtain the distribution of transverse relaxation times at different water saturations.

[0003] The fundamental reason for different water saturations is the centrifugal force or displacement pressure, which represents the dehydration pressure. If the dehydration pressure can be converted into the corresponding dehydration cut-off time, the dehydration effect of different dehydration pressures can be analyzed more clearly, which is of great significance for understanding the gas-water distribution law. Summary of the invention

[0004] The present invention aims to solve the above problems and proposes a method for predicting the dehydration cut-off time based on the maximum eigenvalue.

[0005] The technical solution of the present invention is:

[0006] According to the basic principles of nuclear magnetic resonance, the transverse relaxation process of fluid in the pore throat is affected by the combined effects of three mechanisms: free relaxation, diffusion relaxation and surface relaxation. The transverse relaxation time is expressed as:

[0007] 1 / T 2=1 / T 2B +1 / T 2D +1 / T 2S (1)

[0008] Where: T 2 is the transverse relaxation time, with the dimension of ms; T 2B is the transverse free relaxation time, with the dimension of ms; T 2D is the lateral diffusion relaxation time, with the dimension of ms; T 2S is the transverse surface relaxation time, with the dimension of ms.

[0009] When the fluid in the pore throat is a wetting phase, its transverse free relaxation time T2B Much longer than the transverse relaxation time T 2, 1 / in formula (1) T 2B The term can be ignored; when the magnetic field gradient is small and the echo interval is short enough, the transverse diffusion relaxation time T 2D Usually longer, 1 / T 2D The term can be ignored. For NMR experiments, the fluid used in the experiment is usually simulated formation water, the magnetic field is weak and the echo interval is short, so equation (1) can be approximately written as:

[0010] 1 / T 2≈1 / T 2S = r 2 S / V (2)

[0011] Where: r 2 is the transverse surface relaxation intensity, with the dimension of μm / ms; S is the pore throat surface area, dimension is μm 2 ; V is the pore throat volume, dimension is μm 3 ;

[0012] make S / V = F S / r , substituting into formula (2), we get:

[0013] r ≈ r 2 F S T twenty three)

[0014] Where: F S is the pore throat shape factor, dimensionless; r is the pore throat radius, with the dimension of μm.

[0015] Due to ignoring 1 / T 2B and 1 / T 2D 1 / T 2, so both Equation (2) and Equation (3) are approximate equations. For the convenience of solution, it is assumed that the pore throat radius r and transverse relaxation time T The equation relationship between 2 is:

[0016] r= ( r2 F S + d ) T twenty four)

[0017] Where: d is the correction factor of transverse free relaxation time and transverse diffusion relaxation time, with the dimension of μm / ms;

[0018] Introducing into formula (4) d Transform equation (3) into Eq.

[0019] because r 2 F S and d The changing rules of the pore throat radius are unknown and difficult to obtain accurately. r and transverse relaxation time T The correlation between the 2 is unknown.

[0020] If you C = r 2 F S + d , substituting into (4), we get the transverse relaxation time T 2 and pore throat radius C The linear correlation between:

[0021] T 2= r / C (5)

[0022] Where: C is the conversion coefficient, and its dimension is μm / ms.

[0023] The development of gas reservoirs involves complex gas-water two-phase seepage phenomena, and it is particularly important to explore the distribution of gas and water under different water saturation conditions. Nuclear magnetic resonance experiments have shown wide applicability and high efficiency in analyzing the distribution of gas and water. The nuclear magnetic resonance experiment first conducts nuclear magnetic resonance experiments on water-saturated cores, and then obtains cores with different water saturations by changing the centrifugal force or displacement pressure through centrifugation or displacement. Then, nuclear magnetic resonance experiments are conducted again on these cores with different water saturations to obtain the gas-water distribution laws under different water saturation conditions.

[0024] Different centrifugal forces or displacement pressures represent different dehydration pressures. Their essence is to overcome the capillary force to achieve dehydration. Different dehydration pressures correspond to different pore throat radii, representing different dehydration limits. The pore throat radii corresponding to different dehydration pressures are called dehydration radii, which are expressed as r dewater express.

[0025] If the conversion factor is known C According to formula (5), the lateral relaxation time corresponding to the dehydration radius can be obtained. The lateral relaxation time corresponding to the dehydration radius takes into account the physical information represented by the centrifugal force or displacement pressure, which is different from T 2 cutoff value; T 2 The cut-off value is after centrifugation or displacement T 2 distribution is calibrated to obtain the distribution of saturated water. T 2 The cutoff value is obtained without intuitively considering the physical information represented by the centrifugal force or displacement pressure.

[0026] Since NMR saturated water T 2 distribution represents the complete distribution of pore throat radius, in NMR saturated water T 2. Mark the lateral relaxation time corresponding to different dehydration radii on the distribution, and you can clearly judge the dehydration effect of different centrifugal forces or displacement pressures. T 2 cutoff values, so the transverse relaxation time corresponding to the dehydration radius is called the dehydration cutoff time, T 2dewater Indicates. r dewater and T 2dewater Substituting into (5), we get:

[0027] T 2dewater = r dewater / C (6)

[0028] Where: T 2dewater is the dehydration cut-off time, the dimension is ms; r dewater is the dehydration radius, dimension is μm;

[0029] (6) is the dehydration radius r dewater The corresponding dehydration cut-off time T 2dewater The linear correlation between .

[0030] At the same time, the relationship between the pore throat radius and the capillary force satisfies the capillary force equation p c =2 s cos i / r , when the pore throat radius r Value r dewater When capillary force p cDehydration pressure p dewater (centrifugal force or displacement pressure), the dehydration pressure is obtained p dewater Between dehydration radius r dewater The relationship is:

[0031] r dewater =2 s cos i / p dewater (7)

[0032] Where: p dewater is the dehydration pressure, the dimension is MPa; s is the interfacial tension of water, with the dimension of N / m; i is the wetting contact angle of water, with the dimension of °;

[0033] Substituting (7) into (6), we can obtain the dehydration cut-off time: T 2dewater Dehydration stress p dewater The relationship between:

[0034] T 2dewater =2 s cos i / ( C × p dewater ) (8)

[0035] According to formula (8), we only need to know the conversion coefficient C , the dehydration pressure p dewater Convert to dehydration cut-off time T 2dewater .

[0036] Get the conversion factor C There are many methods, and different methods require different calculation parameters. The essence of all methods is to find the transverse relaxation time corresponding to the high-pressure mercury injection pore throat radius based on the correlation between the NMR transverse relaxation time distribution curve and the high-pressure mercury injection pore throat radius distribution curve, so as to obtain the conversion coefficient. C .

[0037] Considering that the distribution curve of high-pressure mercury injection pore throat radius must have a maximum value, the maximum pore throat radius of high-pressure mercury injection can be used as a characteristic value to find the lateral relaxation time corresponding to the maximum pore throat radius of high-pressure mercury injection. Some studies believe that the maximum pore throat radius of high-pressure mercury injection r max(pc) and maximum transverse relaxation time T 2max Correspondingly, it is believed that C = r max (pc) / T 2max This maximum eigenvalue method is very simple, but it does not consider the rationality of the conversion result, resulting in this maximum eigenvalue method being valid only in very few cases.

[0038] Let the transverse relaxation time corresponding to the maximum pore throat radius of high-pressure mercury injection be T 2max # , just find the right T 2max # ,use C = r max (pc) / T 2max # replace C = r max (pc) / T 2max , the accuracy of the maximum eigenvalue method can be increased to 100%. The specific steps are:

[0039] (1) Order T 2max M Representative acquisition T 2max # The intermediate parameter is based on the NMR saturated water T 2 distribution, from T 2max M = T 2max Start using r T2 =( r max (pc) / T 2max M )× T 2. NMR saturated water T 2 Distribution converted to NMR pore throat radius r T2 distribution, and then the NMR pore throat radius r T2 Cumulative volume ratio curve and high-pressure mercury injection pore throat radius r(pc) The cumulative volume ratio curve of the mercury injection pore throat radius is plotted on a graph to determine whether it meets the “high-pressure mercury injection pore throat radius” r (pc) The cumulative volume fraction curve is located at the NMR pore throat radius r T2 The left side of the cumulative volume proportion curve", if satisfied, then the T 2max M As T 2max # ;

[0040] (2) If not satisfied, gradually reduce T 2max M Take value, use r T2 =( r max (pc) / T 2max C )× T 2. NMR saturated water T 2 Distribution converted to NMR pore throat radius r T2 distribution, and then the NMR pore throat radius r T2 Cumulative volume ratio curve and high-pressure mercury injection pore throat radius r (pc) The cumulative volume ratio curve of the mercury injection pore throat radius is plotted on a graph to determine whether it meets the “high-pressure mercury injection pore throat radius” r (pc) The cumulative volume fraction curve is located at the NMR pore throat radius r T2 The left side of the cumulative volume proportion curve is ", then the T 2max M As T 2max # ;

[0041] Get T 2max # After that, C = r max (pc) / T 2max # Substituting into (8), we can obtain the dehydration cut-off time based on the maximum eigenvalue method: T 2dewater Computational model:

[0042] T 2dewater =(2 s cos i × T 2max # ) / ( r max (pc) × p dewater ) (9)

[0043] Where: T 2max # is the transverse relaxation time corresponding to the maximum pore throat radius of high-pressure mercury injection, with the dimension of ms;

[0044] r max (pc) is the maximum pore throat radius of high-pressure mercury injection, with the dimension of μm;

[0045] Since simulated formation water is used in the NMR experiment, s =0.07275N / m, i =0°, 2 s cos i =0.1455, so formula (9) becomes:

[0046] T 2dewater =(0.1455× T 2max # ) / ( r max (pc) × p dewater ) (10).

[0047] The technical effects of the present invention are:

[0048] The present invention combines the linear relationship between the transverse relaxation time and the pore throat radius and the capillary force equation, adopts the maximum eigenvalue method to solve the conversion coefficient, and establishes a dehydration cut-off time calculation model based on the maximum eigenvalue method, which provides a new method support for analyzing the gas-water distribution law under different dehydration pressures. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 for r (pc) Cumulative volume share distribution curve.

[0050] Figure 2 For NMR saturated waterT 2 Cumulative volume share distribution curve.

[0051] Figure 3 for T 2max M = 1445.10ms, a schematic diagram for judging whether the judgment condition is met.

[0052] Figure 4 for T 2max M = 649.53 ms, a schematic diagram for judging whether the judgment condition is met. DETAILED DESCRIPTION

[0053] A method for predicting the dehydration cut-off time based on the maximum eigenvalue is as follows:

[0054] Step 1: Conduct high-pressure mercury injection and nuclear magnetic resonance experiments on water-saturated cores to draw r (pc) The cumulative volume distribution curve of r max (pc) ; Draw the NMR of saturated water T 2 Cumulative volume share distribution curve, obtain T 2max ; Dehydrate the water-saturated core to obtain the centrifugal force or displacement pressure during the dehydration process;

[0055] Step 2: Get T 2max # ; The specific process is:

[0056] (1) Definition T 2max M ;

[0057] (2) Construct judgment conditions: r (pc) Are all the cumulative volume proportion curves located in r T2 The left side of the cumulative volume share curve;

[0058] (3) T 2max M = T 2max Start using r T2 =( r max (pc) / T 2maxM )× T 2. NMR saturated water T 2 The cumulative volume share distribution curve is converted to r T2 The cumulative volume ratio curve of T 2max M As T 2max # On the contrary, it decreases T 2max M Take the value and re-judge whether the judgment condition is met until the value that meets the judgment condition is T 2max M As T 2max # ;

[0059] Step 3: Calculate the dehydration cut-off time using formula (10) T 2dewater .

[0060] Specific experimental cases

[0061] A method for predicting the dehydration cut-off time based on the maximum eigenvalue is as follows:

[0062] Step 1: Carry out high-pressure mercury injection and nuclear magnetic resonance experiments on the water-saturated core. The results of the high-pressure mercury injection experiments are shown in Table 1. r (pc) The cumulative volume distribution curve of Figure 1 ), get r max (pc) = 0.4003μm; the NMR experimental results of saturated water are shown in Table 2, and the NMR of saturated water is plotted. T 2 Cumulative volume share distribution curve ( Figure 2 ), get T 2max =1445.10ms; the water-saturated core was dehydrated by displacement method, and the displacement pressure and water saturation in the displacement process were obtained as shown in Table 3. The displacement pressure of 0 in Table 3 represents the saturated water state;

[0063] Table 1 High pressure mercury injection test results

[0064] ;

[0065] Table 2 NMR of saturated water T 2 Distribution

[0066] ;

[0067] Table 3 Displacement pressure and water saturation during displacement

[0068] .

[0069] Step 2: Get T 2max # ; The specific process is:

[0070] (1) Definition T 2max M ;

[0071] (2) Construct judgment conditions: r (pc) Is the cumulative volume ratio curve located at r T2 The left side of the cumulative volume share curve;

[0072] (3) T 2max M = T 2max =1445.10ms, using r T2 =( r max (pc) / T 2max M )× T 2. NMR saturated water T 2 The cumulative volume share distribution curve is converted to r T2 The cumulative volume ratio curve of r T2 The cumulative volume ratio curve of r (pc) The cumulative volume share curves of Figure 3 ;from Figure 3 It can be seen that r (pc) The cumulative volume share curve is not located at r T2 The left side of the cumulative volume proportion curve, that is, the judgment condition is not met;

[0073] Reduce T 2max M Take the value, and then judge the condition; until T 2max M = 649.53 ms, using rT2 =( r max (pc) / T 2max M )× T 2=0.00062× T 2. NMR saturated water T 2 The cumulative volume share distribution curve is converted to r T2 The cumulative volume ratio curve of r T2 The cumulative volume ratio curve of r (pc) The cumulative volume share curves of Figure 4 ;according to Figure 4 It can be seen that r (pc) The cumulative volume ratio curve and r T2 The cumulative volume ratio curve meets the judgment condition; therefore, T 2max M As T 2max # ,get T 2max # = T 2max M =649.53 ms.

[0074] Step 3: Calculate the dehydration cut-off time using formula (10) T 2dewater , dehydration cut-off time T 2dewater The calculation results are shown in Table 4;

[0075] Table 4 Dehydration cut-off time T 2dewater

[0076] .

Claims

1. A method for predicting the dehydration deadline based on the maximum eigenvalue, characterized in that: By solving the following formula (10): T 2dewater =(0.1455× T 2max # ) / ( r max (pc) × p dewater ) （10） in, T 2max # The specific solution process is: (1) Definition T 2max M ; (2) Construct judgment conditions: r (pc) Are all the cumulative volume proportion curves located in r T2 The left side of the cumulative volume share curve; (3) T 2max M = T 2max Start using r T2 =( r max (pc) / T 2max M )× T 2. NMR saturated water T 2 The cumulative volume share distribution curve is converted to r T2 The cumulative volume ratio curve of T 2max M As T 2max # On the contrary, it decreases T 2max M The value is taken, and the judgment condition is re-judged until the judgment condition is satisfied. T 2max M As T 2max # ; in: T 2dewater is the dehydration cut-off time, the dimension is ms; T 2max # is the transverse relaxation time corresponding to the maximum pore throat radius of high-pressure mercury injection, with the dimension of ms; r max (pc) is the maximum pore throat radius of high-pressure mercury injection, with the dimension of μm; p dewater is the dehydration pressure, the dimension is MPa; r (pc) is the high-pressure mercury injection pore throat radius, with the dimension of μm; r T2 is the NMR pore throat radius, dimension is μm; T 2 is the transverse relaxation time, with the dimension of ms; T 2max is the maximum transverse relaxation time, with the dimension of ms; T 2max M It is an intermediate parameter with the dimension of ms.

2. The method for predicting the dehydration deadline based on the maximum eigenvalue according to claim 1, characterized in that: The dehydration pressure includes centrifugal force and / or displacement pressure.

3. The method for predicting the dehydration deadline based on the maximum eigenvalue according to claim 1, characterized in that: The high pressure mercury injection pore throat radius r (pc) and the maximum pore throat radius of high-pressure mercury injection r max (pc) Obtained through high-pressure mercury injection experiment.

4. The method for predicting the dehydration deadline based on the maximum eigenvalue according to claim 1, characterized in that: The NMR of saturated water T 2 Cumulative volume fraction distribution curve and maximum transverse relaxation time T 2max Saturated water by NMR T 2 distribution obtained.

5. The method for predicting the dehydration cut-off time based on the maximum eigenvalue according to claim 1, characterized in that: The reduction T 2max M The value varies with the NMR saturated water T 2 distribution correspondingly decreases.

6. The method for predicting the dehydration deadline based on the maximum eigenvalue according to claim 4 or 5, characterized in that: The NMR of saturated water T 2 distribution was obtained by NMR experiments on saturated water.

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