Method, device, medium and equipment for predicting productivity of gravity gas drive in thick sandstone reservoir

Abstract

The present application relates to a kind of thick sandstone reservoir gravity gas drive productivity prediction method, device, medium and equipment, method includes the following steps: with the Dietz model of inclined gas cap reservoir gas drive oil as the basis, longitudinal with gas-oil displacement front as limit the entire thick sandstone reservoir is divided into unsaturated zone and saturated zone, the volume of remaining oil, residual oil and oil film in two regions is analyzed and calculated, with material balance equation and Jeffreys equation as the basis, material balance relationship is established;Based on material balance relationship and Darcy percolation formula, establish thick sandstone reservoir gravity gas drive productivity prediction mathematical model 1;Combining Kozeny formula, oil and gas J function, establish thick sandstone reservoir gravity gas drive productivity prediction mathematical model 2;Based on mathematical model 1 and mathematical model 2, the size of thick sandstone reservoir gravity gas drive productivity at any time is calculated.The method greatly improves the practicability of thick sandstone reservoir gravity gas drive productivity calculation model.

Description

TECHNICAL FIELD

[0001] The application relates to a method and device for predicting the productivity of gravity gas drive in a thick sandstone reservoir, a medium and equipment, and belongs to the field of oil and gas field development and recovery evaluation. BACKGROUND

[0002] Due to the special oil displacement characteristics of gas, the gas flooding enhanced oil recovery method has been paid more and more attention by major oilfields. Compared with water flooding, gas can enter the pores that water cannot reach under a certain pressure, which can effectively improve the oil displacement efficiency. The conventional gas drive development methods include continuous gas injection (CGI) and water alternating gas (WAG), but due to the adverse gas-oil mobility ratio, both methods have the phenomenon of gas channeling caused by gas overlap in the application process, which is particularly obvious in thick sandstone reservoirs, seriously affecting the development effect, so the key to the success of gas drive is to control gas channeling and expand the swept volume. Gravity gas drive (GAGD) is a new gas flooding enhanced oil recovery method. Its principle is to use the density difference between oil and gas to overcome the limitations of CGI and WAG. The thicker the reservoir, the more obvious the gravity overlap phenomenon, and GAGD uses the overlap of gas to form a secondary gas cap at the top of the reservoir, which gradually presses down and replaces the pore space initially occupied by oil, promoting oil to be displaced into the horizontal production well by gravity. Studies have shown that compared with traditional gas drive methods, gravity gas drive in thick sandstone reservoirs can achieve higher productivity.

[0003] The current mathematical model for predicting the productivity of gravity gas drive still has certain limitations, mainly ignoring the micro oil displacement mechanism of gravity gas drive, that is, considering that the productivity contribution of gravity gas drive mainly comes from the macro oil displacement mechanism - expanding the swept volume, and the micro oil displacement mechanism - oil film flow has a smaller contribution to the productivity. However, in actual application, it is found that gravity gas drive still has great oil production capacity even after gas breakthrough, because at this time gas channeling has been formed, the effect of expanding the swept volume is weak, and therefore the main oil displacement mechanism is oil film flow. When the spreading coefficient is greater than 0, the oil phase can spread between the gas and the pore medium to form an oil film that acts as a drainage path, and under the action of gas and gravity, the remaining oil is produced by relying on oil film flow. Therefore, when predicting the productivity of gravity gas drive, oil film flow is an important factor that must be considered. In summary, there is still a lack of a calculation method for accurately predicting the productivity of gravity gas drive in thick sandstone reservoirs, which is a problem that needs to be solved for efficient development of gravity gas drive in thick sandstone reservoirs. SUMMARY

[0004] In view of the above technical problems, the present application provides a method, device, medium and equipment for predicting the productivity of gravity gas drive in a thick sandstone reservoir, which is based on the Dietz model of gas drive oil in a tilted gas cap reservoir, combines the Jeffreys oil film volume calculation equation, material balance equation, Kozeny formula and oil and gas J function, considers the influence of oil film flow on the productivity of gravity gas drive in the thick sandstone reservoir, establishes a mathematical model for predicting the productivity of gravity gas drive in the thick sandstone reservoir, and realizes fine calculation of data by writing a calculation process, and finally completes the actual production application.

[0005] To achieve the above object, the present application adopts the following technical solutions:

[0006] A method for predicting the productivity of gravity gas drive in a thick sandstone reservoir, comprising the following steps:

[0007] Based on the Dietz model of gas drive oil in a tilted gas cap reservoir, the entire thick sandstone reservoir is divided into an unsaturated zone and a saturated zone in the vertical direction with the gas-oil displacement front as the boundary, the volumes of remaining oil, residual oil and oil film in the two zones are analyzed and calculated, and the material balance relationship is established based on the material balance equation and Jeffreys equation;

[0008] Based on the material balance relationship and Darcy seepage formula, the mathematical relationship between the seepage velocity of the oil phase in the saturated zone and the fluid properties, reservoir parameters, oil and gas front migration distance and displacement time is derived, and mathematical model 1 for predicting the productivity of gravity gas drive in the thick sandstone reservoir is established; combined with the Kozeny formula and oil and gas J function, mathematical model 2 for predicting the productivity of gravity gas drive in the thick sandstone reservoir is established; and each physical parameter in the mathematical models 1 and 2 is dimensionless processed to obtain dimensionless mathematical models 1 and 2;

[0009] A small increment is taken from 0, substituted into the dimensionless mathematical model 1, the pushing distance increment of the limit between the saturated zone and the unsaturated zone is calculated, and the unsaturated limit at different displacement times is calculated by iteration with the increment as the initial value; the unsaturated limit at different displacement times calculated is substituted into the dimensionless mathematical model 2, and the size of the productivity of gravity gas drive in the thick sandstone reservoir at any time is calculated.

[0010] The method for predicting the productivity of gravity gas drive in the thick sandstone reservoir is preferably based on the following assumptions: the existence of reservoir heterogeneity and fractures is not considered, the permeability distribution is uniform; the thickness of the oil layer is constant; the displacement mode is piston displacement; the compressibility of rock and fluid and the influence of oil and gas capillary force are ignored; the gas is injected into the oil layer from the top, and the oil and gas are vertically instantaneously balanced, and the oil and gas interface is stable at any time, that is, the forces and speeds of each point on the oil and gas interface are the same.

[0011] The thick sandstone reservoir gravity gas drive productivity prediction method, preferably, the material balance relationship, the specific formula is as follows:

[0012]

[0013] In the formula, V t is the total displacement volume, m 3 ; L is the reservoir thickness, m; z d is the oil and gas front migration distance, m; A is the oil-bearing area of the reservoir, m 2 ; b is the oil film width, m; t is the displacement time, d; S or and S oi are residual oil saturation and initial oil saturation, respectively, %; Δρ is the oil and gas density difference, kg / m 3 ; μ is the oil viscosity, mP·s; g is the gravitational acceleration, m / s 2 ; φ is the porosity, dimensionless.

[0014] The thick sandstone reservoir gravity gas drive productivity prediction method, preferably, the specific formula of the mathematical model 1 is as follows:

[0015]

[0016] In the formula, k is the absolute permeability, mD; k ro is the oil phase relative permeability, dimensionless; μ o is the oil phase viscosity, mP·s; α is the reservoir dip angle, rad; ρ o is the oil phase density, kg / m 3 ; p o is the oil phase pressure, MPa; z is the oil and gas interface migration distance, m.

[0017] The thick sandstone reservoir gravity gas drive productivity prediction method, preferably, the specific formula of the mathematical model 2 is as follows:

[0018]

[0019] In the formula, F S is the correction factor of the Kozeny equation, dimensionless; S g is the gas phase saturation, %; σ is the oil and gas interfacial tension, mN / m; S o is the oil phase saturation, %; f(S g ) is the flow equation; J(S o )' is the derivative of the oil and gas J function.

[0020] The thick sandstone reservoir gravity gas drive productivity prediction method, preferably, the specific formula of the dimensionless mathematical model is as follows:

[0021]

[0022]

[0023] In the formula, T D , Z D are dimensionless time and dimensionless displacement distance respectively; K is absolute permeability, mD; K ro is relative permeability of oil phase, dimensionless; M is oil-gas mobility ratio, dimensionless; is porosity, dimensionless; R is recovery, %; t D is dimensionless displacement time, dimensionless.

[0024] The gravity gas drive productivity prediction method of the thick sandstone reservoir is preferably used to calculate the size of the gravity gas drive productivity of the thick sandstone reservoir at any time by using the mathematical model 1 and the mathematical model 2, and specifically as follows:

[0025] The initial value of time and the initial value of the unsaturated limit are 0, the time increment Δt D is a small value, the formula t Dold =t Dold +Δt D is substituted into the first formula of claim 6 and Z Dnew =Z Dnew +ΔZ D is calculated, the initial value of the unsaturated limit of the second time step is the calculation result of the first time step, the time increment is unchanged, the unsaturated limit of the second time step is calculated, and the unsaturated limits of time steps are calculated by using the method of continuous iteration, the saturation limit of each time step is substituted into the second formula of claim 6 to calculate the size of the productivity of each time step, and the productivity curve is drawn by taking the time step as the horizontal coordinate and taking the productivity corresponding to each time step as the vertical coordinate.

[0026] The second aspect of the present application provides a gravity gas drive productivity prediction device for a thick sandstone reservoir, comprising:

[0027] The first processing unit is used to divide the entire thick sandstone reservoir into an unsaturated area and a saturated area by taking the Dietz model of the oil reservoir gas drive of the inclined gas cap as the basis and taking the gas-oil displacement front as the limit in the vertical direction, analyze and calculate the volumes of remaining oil, residual oil and oil film in the two areas, and establish the material balance relationship based on the material balance equation and the Jeffreys equation.

[0028] The second processing unit is used for deducing the mathematical relationship between the seepage velocity of the oil phase in the saturated area and the fluid properties, reservoir parameters, oil and gas front migration distance, and displacement time based on the material balance relationship and the Darcy seepage formula, and establishing a gravity gas drive productivity prediction mathematical model 1 of the thick sandstone reservoir; the mathematical model 2 of the gravity gas drive productivity prediction of the thick sandstone reservoir is established by combining the Kozeny formula and the oil and gas J function; and the dimensionless processing is performed on each physical parameter in the mathematical models 1 and 2 to obtain the dimensionless mathematical models 1 and 2.

[0029] The third processing unit is used for taking a small increment from 0 based on time, substituting into the dimensionless mathematical model 1, calculating the pushing-down distance increment of the limit between the saturated area and the unsaturated area, taking the limit between the saturated area and the unsaturated area at different displacement times as the initial value, and iteratively calculating the unsaturated limit at different displacement times; and the unsaturated limit at different displacement times is substituted into the dimensionless mathematical model 2 to calculate the gravity gas drive productivity of the thick sandstone reservoir at any time.

[0030] The third aspect of the present application provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to realize the steps of the gravity gas drive productivity prediction method of the thick sandstone reservoir.

[0031] The fourth aspect of the present application provides a computer device, which comprises a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor realizes the steps of the gravity gas drive productivity prediction method of the thick sandstone reservoir when executing the computer program.

[0032] The present application has the following advantages due to the above technical solutions:

[0033] 1. The present application is based on the Dietz model of the gas drive oil in the inclined gas cap reservoir, combines the Jeffreys equation, the material balance equation, the Kozeny formula, and the oil and gas J function, considers the influence of the oil film flow on the gravity gas drive productivity of the thick sandstone reservoir, establishes the gravity gas drive productivity prediction mathematical model of the thick sandstone reservoir, and completes the establishment of the calculation method by programming the calculation process.

[0034] 2. The traditional mathematical model is oriented to the seepage / displacement process, and the model is established based on the motion / seepage equation, but there is currently a lack of seepage equation for accurately describing the oil film flow, and the model establishment has difficulty. The mathematical model of the present application is oriented to the displacement result, and is based on the material balance relationship, avoids the establishment of the complex oil film seepage equation while considering the oil film flow, and improves the rationality and accuracy of the gravity gas drive productivity prediction result of the thick sandstone reservoir.

[0035] 3、The present application considers the oil film effect, eliminates the oil film thickness which is an undetermined physical parameter in practical application through a series of derivations, and greatly improves the practicability of the gravity gas drive productivity calculation model of the thick sandstone reservoir. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 is a schematic diagram of a method for predicting and calculating the gravity gas drive productivity of a thick sandstone reservoir provided by an embodiment of the present application;

[0037] Figure 2 is a schematic diagram of a Dietz model for gas drive oil of a tilted gas cap reservoir provided by the embodiment of the present application;

[0038] Figure 3 is a schematic diagram of a gravity gas drive productivity calculation process of a thick sandstone reservoir provided by the embodiment of the present application;

[0039] Figure 4 is a flow chart of a full-diameter core displacement experiment provided by the embodiment of the present application;

[0040] Figure 5 is an oil and gas J function distribution diagram provided by the embodiment of the present application;

[0041] Figure 6 is a comparison diagram of the model prediction result and the actual production result provided by the embodiment of the present application. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical scheme and advantages of the present application clearer, the technical scheme in the present application is described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0043] The mathematical model for predicting the productivity of gravity gas drive still has certain limitations, mainly showing that the micro oil displacement mechanism of gravity gas drive is ignored, that is, it is considered that the productivity contribution of gravity gas drive mainly comes from the macro oil displacement mechanism, that is, the expansion of swept volume, and the micro oil displacement mechanism, that is, oil film flow, has smaller contribution to the productivity. However, it is found in actual application that gravity gas drive still has great oil production capacity even after gas breakthrough, because the effect of expanding sweep is weak due to the formation of gas channeling, and therefore the oil film flow plays a main oil displacement role. When the spreading coefficient is greater than 0, the oil phase can spread between the gas and the pore medium to form an oil film acting as a drainage path, and under the action of gas and gravity, the remaining oil is produced by relying on the oil film flow. Therefore, when predicting the productivity of gravity gas drive, the oil film flow is an important factor that must be considered. At present, there is still a lack of a calculation method for accurately predicting the productivity of gravity gas drive in a thick sandstone reservoir. In order to solve this problem, the present application provides a method for predicting the productivity of gravity gas drive in a thick sandstone reservoir, which is based on the Dietz model of gas drive oil in an inclined gas cap reservoir, combines the Jeffreys oil film volume calculation equation, the material balance equation, the Kozeny formula and the oil and gas J function, considers the influence of oil film flow on the productivity of gravity gas drive in a thick sandstone reservoir, establishes a mathematical model for predicting the productivity of gravity gas drive in a thick sandstone reservoir, and realizes fine calculation of data by writing a calculation process, and finally completes the actual production application.

[0044] As shown in Figure 1 The method for predicting the productivity of gravity gas drive in a thick sandstone reservoir provided by the present application comprises the following steps:

[0045] 1) The construction of the prediction calculation method is based on the following basic assumptions: the existence of reservoir heterogeneity and fractures is not considered, the permeability distribution is uniform; the thickness of the oil layer is constant; the displacement mode is piston displacement; the compressibility of rock and fluid and the influence of oil and gas capillary force are ignored; the gas is injected from the top of the oil layer, and the oil and gas vertically reach equilibrium at any time, that is, the forces and velocities of each point on the oil and gas interface are the same.

[0046] 2) Based on the Dietz model of gas drive oil in an inclined gas cap reservoir, the entire reservoir is divided into an unsaturated zone and a saturated zone in the vertical direction with the gas-oil displacement front as the boundary, the volumes of remaining oil, residual oil and oil film in the two zones are analyzed and calculated, the material balance relationship is established based on the material balance equation and the Jeffreys equation, and Figure 2 is a schematic diagram of the Dietz model of gas drive oil in an inclined gas cap reservoir, and the establishment process of the material balance relationship is as follows:

[0047] According to the assumed conditions, gas is injected into the oil layer from the top, and oil and gas reach vertical instantaneous equilibrium, and the oil and gas interface is stable at any time, i.e. the forces and speeds of each point at the oil and gas interface are the same. The total displacement volume in the gravity gas displacement process is denoted as V t The displacement swept area is divided into a saturated area V s and an unsaturated area V us . The saturated area is an unswept area, and the unsaturated area is a swept area. The unsaturated area is divided into a remaining oil volume V r and an oil film volume V f。 . According to the material balance relationship, there are:

[0048] V t = V s + V us (1)

[0049] V us = V r + V f (2)

[0050] Assuming that the initial oil saturation and the residual oil saturation are S oi and S or , respectively, there are:

[0051] V s = S oi φA(L-z d ) (3)

[0052] V r = S or φAz d (4)

[0053] V t = S oi φAL (5)

[0054] The volume of the oil film phase can be estimated by Jeffreys equation, i.e.:

[0055]

[0056] By combining equations (1), (2), (3), (4), (5), and (6), there are:

[0057]

[0058] In equations (3)-(7), L is the reservoir thickness, m; z d is the oil and gas front migration distance, m; A is the oil-bearing area of the reservoir, m 2 ; b is the oil film width, m; t is the displacement time, d; S or and S oiSor and Soi are residual oil saturation and initial oil saturation, respectively, %; p g ρg is gas density, kg / m 3 ; μg is gas viscosity, mPa·s; g is gravity acceleration, m / s g ; φ is porosity, dimensionless; Δρ is oil-gas density difference, kg / m 2 ; μ is oil phase viscosity, mPa·s. 3 ; φ is porosity, dimensionless; Δρ is oil-gas density difference, kg / m o ; μ is oil phase viscosity, mPa·s.

[0059] 3) Based on the material balance relationship and Darcy's law established in step 2), the mathematical relationship between the seepage velocity of the oil phase in the saturated area and the fluid properties, reservoir parameters, oil-gas front migration distance, and displacement time is derived, and a mathematical model 1 for predicting the productivity of the giant thick sandstone reservoir under gravity gas drive is established. The establishment process of the model is as follows:

[0060] The Darcy's law velocity of the saturated area is:

[0061]

[0062] Deriving equation (8) with respect to time gives:

[0063]

[0064] Substituting equation (9) into equation (8) gives:

[0065]

[0066] According to Darcy's law, the seepage velocity of the oil phase in the saturated area under the action of gravity is:

[0067]

[0068] Substituting equation (11) into equation (10) gives:

[0069]

[0070] In equations (8)-(12), v o is the oil phase seepage velocity, m 3 / h; v s is the Darcy's law velocity of the saturated area, m 3 ·s -1 / m 2 ; k is the absolute permeability, mD; k rg is the relative permeability of the gas phase, dimensionless; k ro is the relative permeability of the oil phase, dimensionless; α is the reservoir dip angle, rad; p o is the oil phase pressure, MPa; ρ o is the oil density, kg / m 3 ; μ owhere v is the oil viscosity, mPa-s; z is the oil-gas interfacial migration distance, m.

[0071] 4) Combined with Kozeny formula and oil-gas J function, a mathematical model 2 for predicting the productivity of gravity gas drive in thick sandstone reservoirs was established; each physical parameter in the mathematical model was dimensionless processed to obtain dimensionless mathematical models 1 and 2, and the establishment process of the model was as follows:

[0072] The J function formula between the oil phase and the gas phase is:

[0073]

[0074] Combined with formula (11) and formula (13), we have:

[0075]

[0076] In formula (14), p

[0077] In formula (13) and formula (14), p c is the displacement pressure, MPa; p g is the gas phase pressure, MPa; S g is the gas phase saturation, %; σ is the interfacial tension, mN / m; S o is the oil phase saturation, %; f(S g ) is the flow fraction equation; J(S o )' is the derivative of J function; J(S o ) is the J function.

[0078] The width of the oil film is b, and according to the Kozeny formula, we have:

[0079]

[0080] The oil saturation at any time is:

[0081]

[0082] By combining formula (1), formula (3), formula (4), formula (5) and formula (6), we have:

[0083]

[0084]

[0085] Taking the derivative of formula (17) with respect to the migration distance and substituting formula (14), we have:

[0086]

[0087] Substituting formula (19) into formula (12), we have:

[0088]

[0089] F in formula (15)-(20) s is the correction factor of Kozeny formula, dimensionless.

[0090] In order to simplify the expression, dimensionless number T D and Z D are introduced, i.e.

[0091]

[0092]

[0093] Substitute formula (21) and formula (22) into formula (18) and (20), and arrange to get the dimensionless form of mathematical model 1 and 2:

[0094]

[0095]

[0096] In the formula, T D , Z D are dimensionless time and dimensionless migration distance respectively; K is absolute permeability, mD; K ro is the relative permeability of oil phase, dimensionless; M is the mobility ratio of oil and gas, dimensionless; is porosity, %; R is recovery, %; t D is dimensionless displacement time, dimensionless.

[0097] 5) Write the calculation process of the model: take a small increment (such as 0.001) from 0 for time, substitute it into mathematical model 2 established in step 4) to calculate the downward pushing distance increment of the saturation and unsaturated zone limit, i.e. the increment of oil and gas front migration distance, take this as the initial value, and calculate the unsaturated limit at different displacement times through continuous iteration; substitute the calculated unsaturated limit at different displacement times into mathematical model 1 established in step 3) to calculate the gravity gas drive productivity of the thick sandstone reservoir at any time. The specific process is as follows:

[0098] The calculation method of the model: take 0 for the initial value of time and the initial value of unsaturated limit, take a small value (such as 0.001) for time increment△t D , substitute formula (25) into formula (23) and (26) to calculate the unsaturated limit at the first time step:

[0099] t Dold = t Dold +△t D (25)

[0100] Z Dnew = ZDnew + ΔZ D (26)

[0101]

[0102] In formula (25)-(27), t Dold is dimensionless displacement time, dimensionless; Z Dnew is dimensionless oil-gas interface migration distance, dimensionless.

[0103] The initial value of the second time step and the unsaturated limit initial value take the calculation result of the first time step, the time increment is unchanged, and the unsaturated limit of the second time step is calculated. In this way, the unsaturated limit of each time step is calculated by using the method of continuous iteration. The saturation limit of each time step is substituted into formula (24) to calculate the productivity of each time step. The time step is taken as the horizontal coordinate, and the productivity corresponding to each time step is taken as the vertical coordinate to draw the productivity curve. The values of some parameters need to be specially explained during calculation. For the reservoir without measured oil and gas J function, formula (27) is the Corey function, which can be used to replace the J function, and the correction factor F s of the Kozeny formula s This parameter is difficult to define, and the value is usually 0.5; for the reservoir with partial production data, F s can take the initial value 0.5 for calculation. If the error between the calculation result and the actual result is greater than the set value, the value of F s is optimized and recalculated, and the best F s value is obtained by iteration.

[0104] The prediction method of the present application will be described in detail below in combination with specific application examples.

[0105] The method of the present application is described by taking a terrestrial thick glutenite reservoir natural core experiment as an example. The reservoir lithology is mainly fine sandstone, followed by siltstone and medium sandstone, and the bottom is conglomerate and gravel-containing sandstone. The rock types are mainly quartz sandstone and feldspar quartz sandstone. The reservoir space is mainly secondary pore, followed by primary pore, the pore throat diameter is 0.2-24 μm, and the average pore throat radius is 3-4 μm, which is a medium-low porosity and low permeability reservoir. Full-diameter natural cores of the reservoir are selected for gravity gas drive experiment to verify the calculation method proposed by the present application.

[0106] 1. Experimental method

[0107] The experimental model needs to be long enough to meet the experimental requirements. The length of a natural full-diameter core is often insufficient. Therefore, a core splicing method is required to create a longer experimental core. In this experiment, the core end faces are ground smooth to ensure that the fluoropolymer sleeve will not break due to surface irregularities during the confining pressure process. Three layers of filter paper are placed between the contacting core ends to effectively reduce the end-face effect caused by capillary forces, resulting in more accurate experimental results. A 60cm long experimental model was obtained through this core splicing method.

[0108] Before conducting the experiment, follow the instructions in the appendix. Figure 4 The experimental procedure is shown below. First, the assembled core is loaded. Due to the length and weight of the core, it is easy to break during loading. Therefore, a combination of support rings and tie rods is used for loading the core, effectively protecting the pressure measurement points and preventing the core assembly from bending. To facilitate loading, the core assembly is loaded into the cylinder from the outside. To address the influence of displacement pressure and temperature changes on the tightness of the core assembly, a three-axis piston structure is installed at one end of the device, which clamps the core according to changes in axial pressure. After loading, the airtightness of the device is checked.

[0109] After the airtightness test was completed, the core was saturated with fluid. First, the core was evacuated, then saturated with water. Due to the large size of the model, conventional self-absorption saturation methods are prone to insufficient saturation, affecting subsequent experiments. In this study, self-absorption saturation was performed for 24 hours, followed by water flooding at a rate of 1 mL / min. The injected and produced volumes were recorded, and water injection was stopped when the produced water reached 1000 mL. The porosity of the experimental model was calculated by combining the self-absorption volume, the injected volume, and the produced water volume.

[0110] Calculate permeability. After saturation with water, permeability is measured on the core sample. Different injection rates are selected to measure the pressure values ​​when the system pressure is stable. These values ​​are plotted on the same coordinate system, and the slope is calculated. The numerical conversion relationship between the slope and permeability is calculated using Darcy's formula to obtain an accurate water-measured permeability value.

[0111] When saturating the oil, first saturate at a low speed of 0.1 mL / min. After the injected pore volume reaches 0.7 PV, increase the saturation speed to 1 mL / min. The purpose of this is to allow the oil phase to enter the small pores better, thereby ensuring high oil saturation and low bound water saturation.

[0112] After saturation with oil, the core samples were aged in a constant temperature environment of 90℃ for 24 hours. Following aging, gravity gas drive was performed at a 10° inclination angle and an extremely low gas injection rate (0.01 mL / min). During the experiment, both confining pressure and back pressure were monitored by an automatic tracking pump to ensure system pressure stability. The experiment was stopped once gas was observed at the outlet. The fluid parameters used in the verification experiment are shown in Table 1.

[0113] 2. Experimental results and calculation model verification

[0114] The oil and gas J function in the calculation model proposed by the present application is difficult to obtain through displacement core experiments, so the Corey type function is selected for the J function, and the results are shown in the attached Figure 5 The selection of the correction factor of the Kozeny formula in the calculation model is difficult to define, and the present application selects the value as 0.5 and 1, respectively calculates the model calculation values in the two cases, and compares with the actual experimental data, and the comparison of the model calculation results with the actual experimental data is shown in the attached Figure 6 .

[0115] Table 1 Verification of experimental fluid parameters

[0116]

[0117] Correction factor F of Kozeny formula s The size has a great influence on the prediction results. F s Affects the size of the oil film effect, F s The greater, the greater the width of the oil film, the stronger the role it plays. Therefore, F s When the value is larger, the prediction of the model is more ideal, that is, the reason for the error is related to the selection of the parameters, including the corresponding J function and F s The value, etc. The selection of these parameters restricts the accuracy of the model calculation results. Under the conditions of the J function and F s The value given in this section, the calculation method proposed by the present application has certain differences in predicting the recovery rate of each time step of the actual experimental results, but the error is within 10%, which basically meets the requirements, that is, the reliability of the gravity gas drive productivity calculation method for thick sandstone reservoirs provided by the present application is verified.

[0118] The second aspect of the present application provides a gravity gas drive productivity prediction device for a thick sandstone reservoir, comprising:

[0119] The first processing unit is used to divide the entire thick sandstone reservoir into an unsaturated area and a saturated area based on the Dietz model of the inclined gas cap oil reservoir gas drive oil displacement front in the vertical direction, analyze and calculate the volumes of remaining oil, residual oil and oil film in the two areas, and establish a material balance relationship based on the material balance equation and the Jeffreys equation.

[0120] The second processing unit is used for deducing the mathematical relationship between the seepage velocity of the oil phase in the saturated area and the fluid properties, reservoir parameters, oil and gas front migration distance, displacement time based on the material balance relationship and Darcy seepage formula, and establishing a gravity gas drive productivity prediction mathematical model 1 of the thick sandstone reservoir; the mathematical model 2 of the gravity gas drive productivity prediction of the thick sandstone reservoir is established by combining the Kozeny formula and the oil and gas J function; the dimensionless processing is performed on each physical parameter in the mathematical model 1 and 2 to obtain the dimensionless mathematical model 1 and 2;

[0121] The third processing unit is used for taking a small increment from 0 based on time, substituting into the dimensionless mathematical model 1, calculating the pushing down distance increment of the limit between the saturated area and the unsaturated area, taking the limit between the saturated area and the unsaturated area at different displacement times as the initial value, and iteratively calculating the unsaturated limit at different displacement times; and the unsaturated limit at different displacement times calculated is substituted into the dimensionless mathematical model 2 to calculate the size of the gravity gas drive productivity of the thick sandstone reservoir at any time.

[0122] The third aspect of the present application provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to realize the steps of the gravity gas drive productivity prediction method of the thick sandstone reservoir.

[0123] The fourth aspect of the present application provides a computer device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, and the processor realizes the steps of the gravity gas drive productivity prediction method of the thick sandstone reservoir when executing the computer program.

[0124] The present application is described in terms of flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to the specific implementations. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as combinations of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus produce a device that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in the flow or multiple flows and / or blocks Figure 1 The functions specified in the flow or multiple flows and / or blocks

[0125] These computer program instructions can also be stored in a computer readable memory capable of guiding the computer or other programmable data processing apparatus to work in a specific way, so that the instructions stored in the computer readable memory produce a product including instruction devices, which implement the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in the flow or multiple flows and / or blocks Figure 1 The functions specified in the flow or multiple flows and / or blocks

[0126] These computer program instructions can also be loaded into a computer or other programmable data processing devices, so that a series of operational steps are performed on the computer or other programmable data processing devices to generate computer-implemented processes, thus the instructions executed on the computer or other programmable data processing devices provide the function of implementing the processes specified in the flowcharts Figure 1 one flow or multiple flows and / or the functions specified in one block or multiple blocks. Figure 1 one flow or multiple flows and / or the functions specified in one block or multiple blocks.

[0127] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application, and not to limit it; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand: it can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method of predicting deliverability of a massive sandstone reservoir by gravity gas drive, characterized by, The method comprises the following steps: Based on the Dietz model of gas drive oil in a tilted gas cap reservoir, the entire thick sandstone reservoir is divided into an unsaturated zone and a saturated zone in the vertical direction with the gas-oil displacement front as the boundary, the volumes of remaining oil, residual oil and oil film in the two zones are analyzed and calculated, and a material balance relationship is established based on the material balance equation and the Jeffreys equation; Based on the material balance relationship and the Darcy seepage formula, a mathematical relationship between the seepage velocity of the oil phase in the saturated zone and fluid properties, reservoir parameters, oil-gas front migration distance and displacement time is derived, a mathematical model 1 for predicting the productivity of the thick sandstone reservoir under gravity gas drive is established, Kozeny formula and oil-gas J function are combined to establish a mathematical model 2 for predicting the productivity of the thick sandstone reservoir under gravity gas drive, and each physical parameter in the mathematical models 1 and 2 is processed in a dimensionless manner to obtain dimensionless mathematical models 1 and 2; A small increment is taken from 0 for time, substituted into the dimensionless mathematical model 1, and the pushing-down distance increment of the boundary between the saturated zone and the unsaturated zone is calculated, the unsaturated boundary at different displacement times is calculated by iteration with the increment as the initial value, the unsaturated boundary at different displacement times is substituted into the dimensionless mathematical model 2, and the productivity of the thick sandstone reservoir under gravity gas drive at any time is calculated; The specific formulas of the dimensionless mathematical models 1 and 2 are as follows: where Z D is the dimensionless oil-gas interfacial displacement distance; T D is the dimensionless displacement time; K is the absolute permeability; K ro is the relative permeability of the oil phase; M is the oil-gas mobility ratio; φ is the porosity; R is the recovery efficiency; t D is the dimensionless displacement time; μ o is the viscosity of the oil phase; S o is the saturation of the oil phase; J(S o )′ is the derivative of the oil-gas J function; L is the reservoir thickness; S or and S oi are the residual oil saturation and the initial oil saturation, respectively; F S is the correction factor of the Kozeny equation; Δρ is the oil-gas density difference; and α is the reservoir dip.

2. The method of predicting deliverability of a massive sandstone reservoir by gas gravity drive according to claim 1, characterized in that, The productivity prediction method of the thick sandstone reservoir under gravity gas drive is based on the following assumptions: the existence of reservoir heterogeneity and fractures is not considered, the permeability distribution is uniform, the thickness of the oil layer is constant, the displacement mode is piston displacement, the compressibility of rock and fluid and the influence of oil and gas capillary force are ignored, gas is injected into the oil layer from the top, oil and gas vertically reach equilibrium at any time, and the oil-gas interface is stable, that is, the forces and velocities of each point on the oil-gas interface are the same.

3. The method of predicting deliverability of a massive sandstone reservoir by gas gravity drive according to claim 1, characterized in that, The specific formula of the material balance relationship is as follows: where V t is the total displacement volume; L is the reservoir thickness; z d is the oil-gas front migration distance; A is the oil-bearing area of the reservoir; b is the oil film width; t is the displacement time; S or and S oi are the residual oil saturation and the initial oil saturation, respectively; Δρ is the oil-gas density difference; μ is the crude oil viscosity; g is the gravitational acceleration; and φ is the porosity.

4. The method of predicting deliverability of a massive sandstone reservoir by gas gravity drive according to claim 1, characterized in that, The specific formula of the mathematical model 1 is as follows: where k is the absolute permeability; k ro is the relative permeability of the oil phase; μ o is the viscosity of the oil phase; α is the reservoir dip; ρ o is the density of the oil phase; p o is the pressure of the oil phase; and z is the oil-gas interface migration distance.

5. The method of predicting deliverability of a massive sandstone reservoir by gas gravity drive according to claim 4, characterized in that, The specific formula of the mathematical model 2 is as follows: where F S is a correction factor for the Kozeny equation; S g is the gas phase saturation; σ is the oil-gas interfacial tension; S o is the oil phase saturation; f(S g ) is the fractional flow equation; and J(S o )' is the derivative of the oil-gas J-function.

6. The method of predicting deliverability of a massive sandstone reservoir by gas gravity drive according to claim 1, wherein, The productivity of the thick sandstone reservoir under gravity gas drive at any time is calculated by using the mathematical model 1 and the mathematical model 2, and the calculation is as follows: The initial values ​​for time and the unsaturated threshold are both set to 0, and the time increment is Δt. D Take the smallest value, and express the equation t Dold =t Dold +Δt D , t Dold For dimensionless displacement time, substitute into dimensionless mathematical model 1 and Z Dnew =Z Dnew +ΔZ D Z Dnew To calculate the dimensionless oil and gas interface migration distance, the unsaturated limit for the first time step is calculated. The initial values ​​for the second time step and the initial values ​​for the unsaturated limit are taken from the calculation results of the first time step, with the time increment remaining unchanged. The unsaturated limit for the second time step is then calculated, and so on. The unsaturated limit for each time step is calculated using an iterative method. The saturation limit for each time step is then substituted into the dimensionless mathematical model 2 to calculate the production capacity for each time step. The production capacity curve is plotted with the time step as the horizontal axis and the production capacity corresponding to each time step as the vertical axis.

7. A device for predicting the deliverability of a massive sandstone reservoir under gravity gas drive, characterized in that it comprises: It comprises: The first processing unit is used for dividing the entire thick sandstone reservoir into an unsaturated zone and a saturated zone in the vertical direction with the gas-oil displacement front as the boundary based on the Dietz model of gas drive oil in a tilted gas cap reservoir, analyzing and calculating the volumes of remaining oil, residual oil and oil film in the two zones, and establishing a material balance relationship based on the material balance equation and the Jeffreys equation; The second processing unit is used for deriving a mathematical relationship between the seepage velocity of the oil phase in the saturated zone and fluid properties, reservoir parameters, oil-gas front migration distance and displacement time based on the material balance relationship and the Darcy seepage formula, establishing a mathematical model 1 for predicting the productivity of the thick sandstone reservoir under gravity gas drive, combining Kozeny formula and oil-gas J function to establish a mathematical model 2 for predicting the productivity of the thick sandstone reservoir under gravity gas drive, and processing each physical parameter in the mathematical models 1 and 2 in a dimensionless manner to obtain dimensionless mathematical models 1 and 2; The specific formulas of the dimensionless mathematical models 1 and 2 are as follows: where Z D is the dimensionless oil-gas interfacial displacement distance; T D is the dimensionless displacement time; K is the absolute permeability; K ro is the relative permeability of the oil phase; M is the oil-gas mobility ratio; φ is the porosity; R is the recovery; t D is the dimensionless displacement time; μ o is the viscosity of the oil phase; S o is the saturation of the oil phase; J(S o )′ is the derivative of the oil-gas J function; L is the reservoir thickness; S or and S oi are the residual oil saturation and the initial oil saturation, respectively; F S is the correction factor for the Kozeny equation; Δρ is the oil-gas density difference; and α is the reservoir dip angle. The third processing unit is used for taking a tiny increment from 0 based on time, substituting into the dimensionless mathematical model 1, calculating the pushing-down distance increment of the limit between the saturated zone and the unsaturated zone, taking the increment as an initial value, and calculating the unsaturated limit at different displacement times through continuous iteration; and substituting the calculated unsaturated limit at different displacement times into the dimensionless mathematical model 2 to calculate the size of the gravity gas drive productivity of the thick sandstone reservoir at any time.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program, when executed by a processor, implements the steps of the method for predicting the gravity gas drive productivity of the thick sandstone reservoir according to any one of claims 1-6.

9. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor, when executing the computer program, implements the steps of the method for predicting the gravity gas drive productivity of the thick sandstone reservoir according to any one of claims 1-6.

Images