CN106761613A - A kind of well testing of carbon dioxide displacement leading edge determines method - Google Patents

Abstract

The present invention provides a kind of well testing of carbon dioxide displacement leading edge and determines method, including：Step 1, builds WELL TEST INTERPRETATION MODEL, including reservoir model and seepage experiment；Step 2, is linearized, numerical solution WELL TEST INTERPRETATION MODEL by pressure equation；Step 3, according to basic reservoir characteristics test data, by basic well test analysis parameter, is solved with analogy method, obtains the pressure data during drop of pressure/recovery well testing, and is processed, and obtains pressure and pressure semilog or double logarithmic curve；Step 4, using the result for obtaining, is fitted actual pressure and pressure semilog, double logarithmic curve, and calculating target function value；Step 5, the parameter obtained according to step 4 and solution carbon dioxide displacement leading edge relational expression, determine carbon dioxide displacement leading edge.The method considers the own characteristic of various physical property changes and stratum and injection well during carbon dioxide displacement, improves the accuracy of carbon dioxide displacement leading edge determination.

Description

A kind of well testing of carbon dioxide displacement leading edge determines method

Technical field

The present invention relates to oil field development technical field, the well testing for especially relating to a kind of carbon dioxide displacement leading edge determines Method.

Background technology

During carbon dioxide displacement, due to the diffusion of component of mixture during carbon dioxide and crude oil mixed phase, temperature, The characteristics of viscosity change law and stratum and injection well itself, displacing front is difficult to determine, and not yet there is titanium dioxide at present The determination well-logging method of carbon displacing front is proposed.It is this we have invented a kind of determination side of new carbon dioxide displacement leading edge Method, solves above technical problem.

The content of the invention

Various physical property change and stratum and note during considering carbon dioxide displacement it is an object of the invention to provide one kind Enter the own characteristic of well, the well testing that improve the carbon dioxide displacement leading edge of the accuracy of carbon dioxide displacement leading edge determination determines Method.

The purpose of the present invention can be achieved by the following technical measures：The well testing of carbon dioxide displacement leading edge determines method, The well testing of the carbon dioxide displacement leading edge determines that method includes：Step 1, builds WELL TEST INTERPRETATION MODEL, including reservoir model and seepage flow Mathematical Modeling；Step 2, is linearized, numerical solution WELL TEST INTERPRETATION MODEL by pressure equation；Step 3, according to basic oil reservoir thing Property test data, by basic well test analysis parameter, solved with analogy method, obtain drop of pressure/recovery well testing Pressure data in journey, and processed, obtain pressure and pressure semilog or double logarithmic curve；Step 4, using the knot for obtaining Really, actual pressure and pressure semilog, double logarithmic curve, and calculating target function value are fitted；Step 5, obtains according to step 4 Parameter and solution carbon dioxide displacement leading edge relational expression, determine carbon dioxide displacement leading edge.

The purpose of the present invention can also be achieved by the following technical measures：

In step 1, Erecting and improving, meet actual WELL TEST INTERPRETATION MODEL, including reservoir model and seepage flow mathematical modulo Type (shown in formula 1-4)：

K=k^*e^-ε(pi-p) (4)

Wherein, φ porositys；x_uIt is component u molar fractions in liquid phase (oil phase)；y_uIt is component u molar fractions in gas phase；z_u It is component u total moles fractions；S_oIt is oil saturation；S_gIt is gas saturation；

It is the unit volume molal weight flow of u components；p_lIt is phase pressure；p_iIt is original formation pressure；K is that stratum is exhausted To permeability；k_rlIt is relative permeability；k^*It is original permeability；μ_lIt is viscosity；ε is pressure-sensitive coefficient；G_lIt is the startup pressure of each phase Gradient；It is mass density；ρ is molar density；Subscript o, g are represented as oil, gas phase, and l=o, g respectively；α is unit conversion system Number, (darcy unit), α=1 when above-mentioned variable uses hydraulics unit；It is gravity ladder in the x, y and z directions Degree.

In step 2, linearized by pressure equation, numerical solution WELL TEST INTERPRETATION MODEL (formula 5)：

In formula, Δ p_o ⁿ⁺¹It is n+1 moment oil phase pressure differentials,Respectively oil, makings metric density；gⁿIt is the n moment Gravity constant, Δ DⁿIt is n moment differences in height；G_l ⁿIt is the free-boundary problem of each phase, l=o, g；S_o,S_gIt is oil, gas saturation；It is oil ingredient and the unit volume molal weight flow of gas component；Δp_cogIt is oil gas capillary force；V is unit volume； T_o ⁿIt is variable unrelated with the time in difference expression；Δ t is time interval；Φ is porosity.

Actual conditions according to oil reservoir develop corresponding numerical well testing simulator.

In step 3, according to basic reservoir characteristics test data, the basic well test analysis parameter of input, with simulator Solved, the pressure data that output pressure lands/recovers during well testing, and processed, obtained pressure and pressure half is right Number or double logarithmic curve.

In step 4, using the pressure and pressure semilog or double logarithmic curve for obtaining, fitting actual pressure and pressure are partly Logarithm, double logarithmic curve, and calculating target function value (formula 6)：

It is least square value,Respectively t_DiMoment edgeThe pressure of the direction of search and initial pressure Power；t(t_Di) it is respectively edgeThe time step and initial time step-length of the direction of search；P is pressure；N is on curve It is discrete to count out.

Using SPSA algorithms in variable-definition domainIn scan for, change relevant parameter (carbon dioxide area Radius R₁, skin factor S, well hole storage coefficient C, mobility ratio M, piezometric conductivity is than η, permeability k and compressibility factor etc.), call Simulator is calculated so that target function value is minimum, obtains final fitting parameter explanation results.

In steps of 5, according to drop of pressure test pressure and pressure semilog plot, felt area is obtained radially by diagram method Stream straight line slope over 10 m_c, felt area radial flow finish time t_end, in combination with well test analysis result, build relational expression (formula 7- 10) carbon dioxide displacement leading edge, is asked for：

X=(R₂/R₁)² (8)

Z=η/M (10)

Wherein, R₂It is carbon dioxide displacement leading-edge radius, m；R₁It is pure carbon dioxide area radius, m；Q is carbon dioxide injection Amount, m³/d；B_gIt is carbon dioxide volume factor；μ_gIt is carbon dioxide viscosity, mPas；The oil reservoir infiltration that k is obtained for well test analysis Rate, 10^-3μm²；H is reservoir thickness, m；η is piezometric conductivity ratio, and M is mobility ratio；X is transition region and CO₂Area's radii ratio it is flat Side, Y is complex parameter expression formula, and Z holds coefficient for storage.

The determination method of the carbon dioxide displacement leading edge in the present invention, result of calculation can be applied to carbon dioxide displacement oil reservoir Evaluation and the establishment of development plan, improve the accuracy of carbon dioxide displacement leading edge determination, are the exploitation of carbon dioxide flooding oil reservoir Accurate formation parameter is provided, and then produces huge economic benefit, with certain promotional value.

Brief description of the drawings

Fig. 1 be carbon dioxide displacement leading edge of the invention well testing determine method a specific embodiment flow chart；

Fig. 2 is the schematic diagram of observed pressure depression curve in a specific embodiment of the invention；

Fig. 3 is the schematic diagram of observed pressure landing semilog plot in a specific embodiment of the invention.

Specific embodiment

It is cited below particularly to go out preferably to implement to enable above and other objects, features and advantages of the invention to become apparent Example, and coordinate institute's accompanying drawings, it is described in detail below.

As shown in figure 1, the well testing that Fig. 1 is carbon dioxide displacement leading edge of the invention determines the flow chart of method.

In step 101, Erecting and improving, meet actual WELL TEST INTERPRETATION MODEL, including reservoir model and seepage flow mathematical modulo Type (shown in formula 1-4)：

K=k^*e^-ε(pi-p) (4)

Wherein, φ porositys；x_uIt is component u molar fractions in liquid phase (oil phase)；y_uIt is component u molar fractions in gas phase；z_u It is component u total moles fractions；s_oIt is oil saturation；s_gIt is gas saturation；It is the unit volume molal weight stream of u components Amount；p_lIt is phase pressure；p_iIt is original formation pressure；K is formation absolute permeability；k_rlIt is relative permeability；k^*It is original infiltration Rate；μ_lIt is viscosity；ε is pressure-sensitive coefficient；G_lIt is the free-boundary problem of each phase；It is mass density；ρ is molar density；Subscript o, G is represented as oil, gas phase, and l=o, g respectively；α is unit conversion coefficient, (is reached when above-mentioned variable uses hydraulics unit Xidan position), α=1；It is gravity gradient in the x, y and z directions.

Flow enters into step 102.

In step 102, linearized by pressure equation, numerical solution WELL TEST INTERPRETATION MODEL (formula 5)：

In formula, Δ p_o ⁿ⁺¹It is n+1 moment oil phase pressure differentials,Respectively oil, makings metric density；gⁿIt is the n moment Gravity constant, Δ DⁿIt is n moment differences in height；G_l ⁿIt is the free-boundary problem of each phase, l=o, g；S_o,S_gIt is oil, gas saturation；It is oil ingredient and the unit volume molal weight flow of gas component；Δp_cogIt is oil gas capillary force；V is unit volume； T_o ⁿIt is variable unrelated with the time in difference expression；Δ t is time interval；Φ is porosity.

Actual conditions according to oil reservoir develop corresponding numerical well testing simulator.Flow enters into step 103.

In step 103, according to basic reservoir characteristics test data, the basic well test analysis parameter of input, with simulator Solved, the pressure data that output pressure lands/recovers during well testing, and processed, obtained pressure and pressure half is right Number or double logarithmic curve.Flow enters into step 104.

In step 104, using the result for obtaining, actual pressure and pressure semilog, double logarithmic curve are fitted, and calculate mesh Offer of tender numerical value (formula 6)：

It is least square value,p(t_Di) it is respectively t_DiMoment edgeThe pressure of the direction of search and initial pressure Power；t(t_Di) it is respectively edgeThe time step and initial time step-length of the direction of search；P is pressure；N is on curve It is discrete to count out.

Using SPSA algorithms in variable-definition domainIn scan for, change relevant parameter (carbon dioxide area Radius R₁, skin factor S, well hole storage coefficient C, mobility ratio M, piezometric conductivity is than η, permeability k and compressibility factor etc.), call Simulator is calculated so that target function value is minimum, obtains final fitting parameter explanation results.Flow enters into step 105.

In step 105, according to drop of pressure test pressure and pressure semilog plot (such as Fig. 2,3), obtained by diagram method Felt area radial flow straight slope over 10 m_c, felt area radial flow finish time t_end, in combination with well test analysis result, build and close It is formula (formula 7-10), asks for carbon dioxide displacement leading edge：

X=(R₂/R₁)² (8)

Z=η/M (10)

Wherein, R₂It is carbon dioxide displacement leading-edge radius, m；R₁It is pure carbon dioxide area radius, m；Q is carbon dioxide injection Amount, m³/d；B_gIt is carbon dioxide volume factor；μ_gIt is carbon dioxide viscosity, mPas；The oil reservoir infiltration that k is obtained for well test analysis Rate, 10^-3μm²；H is reservoir thickness, m；η is piezometric conductivity ratio, and M is mobility ratio；X is transition region and CO₂Area's radii ratio it is flat Side, Y is complex parameter expression formula, and Z holds coefficient for storage.

Claims (5)

1. the well testing of carbon dioxide displacement leading edge determines method, it is characterised in that the well testing of the carbon dioxide displacement leading edge determines Method includes：

Step 1, builds WELL TEST INTERPRETATION MODEL, including reservoir model and seepage experiment；

Step 2, is linearized, numerical solution WELL TEST INTERPRETATION MODEL by pressure equation；

Step 3, according to basic reservoir characteristics test data, by basic well test analysis parameter, is asked with analogy method Solution, obtains the pressure data during drop of pressure/recovery well testing, and is processed, and obtains pressure and pressure semilog or double Logarithmic curve；

Step 4, using the result for obtaining, is fitted actual pressure and pressure semilog, double logarithmic curve, and calculating target function Value；

Step 5, the parameter obtained according to step 4 and solution carbon dioxide displacement leading edge relational expression, before determining carbon dioxide displacement Edge.

2. the well testing of carbon dioxide displacement leading edge according to claim 1 determines method, it is characterised in that in step 1, The reservoir model and seepage experiment of foundation be：

$\frac{\∂}{\∂t}\[\mathrm{\φ}(x_u{\mathrm{\ρ}}_o{S}_o+y_u{\mathrm{\ρ}}_g{S}_g)\]+\▿\[x_u{\mathrm{\ρ}}_o\stackrel{\‾}{V_o}+y_u{\mathrm{\ρ}}_g\stackrel{\‾}{V_g}\]-\stackrel{\‾}{q_u}=0---\left(1\right)$

$\stackrel{\‾}{V_o}=\left\{\begin{array}{c}-\mathrm{\α}\frac{{\mathrm{kk}}_{ro}}{{\mathrm{\μ}}_o}(\▿p_o-\stackrel{\‾}{{\mathrm{\ρ}}_o}g\▿D-G_o),|\▿p_o-\stackrel{\‾}{{\mathrm{\ρ}}_{o}g}\▿D|>G_o\\ 0,|\▿p_o-\stackrel{\‾}{{\mathrm{\ρ}}_o}g\▿D|\≤G_o\end{array}\right.---\left(2\right)$

$\stackrel{\‾}{V_g}=\left\{\begin{array}{c}-\mathrm{\α}\frac{{\mathrm{kk}}_{rg}}{{\mathrm{\μ}}_g}(\▿p_g-\stackrel{\‾}{{\mathrm{\ρ}}_g}g\▿D-G_g),|\▿p_g-\stackrel{\‾}{{\mathrm{\ρ}}_g}g\▿D|>G_g\\ 0,|\▿p_g-\stackrel{\‾}{{\mathrm{\ρ}}_g}g\▿D|\≤G_g\end{array}\right.---\left(3\right)$

$k=k^{*}{e}^{-\mathrm{\ϵ}(p_i-p)}---\left(4\right)$

Wherein, φ porositys；x_uIt is component u molar fractions in liquid phase (oil phase)；y_uIt is component u molar fractions in gas phase；z_uIt is group Divide u total moles fractions；s_oIt is oil saturation；s_gIt is gas saturation；It is the unit volume molal weight flow of u components； p_lIt is phase pressure；p_iIt is original formation pressure；K is formation absolute permeability；k_rlIt is relative permeability；k^*It is original permeability；μ_l It is viscosity；ε is pressure-sensitive coefficient；G_lIt is the free-boundary problem of each phase；It is mass density；ρ is molar density；Subscript o, g point Oil, gas phase, and l=o, g are not represented as；α is unit conversion coefficient, when above-mentioned variable uses hydraulics unit, i.e. darcy Unit, α=1.It is gravity gradient in the x, y and z directions.

3. the well testing of carbon dioxide displacement leading edge according to claim 1 determines method, it is characterised in that in step 2, The formula of numerical solution WELL TEST INTERPRETATION MODEL is：

$\begin{array}{c}\mathrm{\Δ}\[{T_o}^n\left({{\mathrm{\Δp}}_o}^{n+1}-{\stackrel{\‾}{{\mathrm{\ρ}}_o}}^n{g}^n{\mathrm{\ΔD}}^n-{G_o}^n\right)+{T_g}^n\left({\mathrm{\Δp}}_o+{\mathrm{\Δp}}_{cog}-{\stackrel{\‾}{{\mathrm{\ρ}}_g}}^n{g}^n{\mathrm{\ΔD}}^n-{G_g}^n\right)\\ +q_o^n+q_g^n=\frac{V}{\mathrm{\Δ}t}\[{\mathrm{\φ}}^{n+1}{\left({\mathrm{\ρ}}_o{S}_o+{\mathrm{\ρ}}_g{S}_g\right)}^{n+1}-{\mathrm{\φ}}^n{\left({\mathrm{\ρ}}_o{S}_o+{\mathrm{\ρ}}_g{S}_g\right)}^n\]\end{array}---\left(5\right)$

In formula, Δ p_o ⁿ⁺¹It is n+1 moment oil phase pressure differentials,Respectively oil, makings metric density；gⁿFor n moment gravity is normal Number, Δ DⁿIt is n moment differences in height；G_l ⁿIt is the free-boundary problem of each phase, l=o, g；S_o,S_gIt is oil, gas saturation； It is oil ingredient and the unit volume molal weight flow of gas component；Δp_cogIt is oil gas capillary force；V is unit volume；T_o ⁿIt is difference The variable unrelated with the time in expression formula；Δ t is time interval；Φ is porosity.

4. the well testing of carbon dioxide displacement leading edge according to claim 1 determines method, it is characterised in that in step 4, The formula of calculating target function value is：

$D\left(\stackrel{\→}{x}\right)=\underset{i=1}{\overset{n}{\Σ}}{\[p\left(\stackrel{\→}{x},t_{Di}\right)-p\left(t_{Di}\right)\]}^2+\underset{i=1}{\overset{n}{\Σ}}{\[dp/d\ln t\left(\stackrel{\→}{x},t_{Di}\right)-dp/d\ln t\left(t_{Di}\right)\]}^2---\left(6\right)$

It is least square value,p(t_Di) it is respectively t_DiMoment edgeThe pressure and initial pressure of the direction of search；t(t_Di) it is respectively edgeThe time step and initial time step-length of the direction of search；P is pressure；N be curve on from Scatterplot number.

With SPSA algorithms in variable-definition domainIn scan for, change relevant parameter, including carbon dioxide area radius R₁, skin factor S, well hole storage coefficient C, mobility ratio M, piezometric conductivity than η, permeability k and compressibility factor, be simulated meter Calculate so that target function value is minimum, obtains final fitting parameter explanation results.

5. the well testing of carbon dioxide displacement leading edge according to claim 1 determines method, it is characterised in that in steps of 5, According to drop of pressure test pressure and pressure semilog plot, felt area radial flow straight slope over 10 m is obtained by diagram method_c, ripple And area's radial flow finish time t_end, in combination with well test analysis result, relational expression is built, ask for carbon dioxide displacement leading edge：

$X=\frac{XY+Z-1}{Z}---\left(7\right)$

X=(R₂/R₁)² (8)

$XY=7\×{10}^5\frac{{\mathrm{qB}}_g{\mathrm{\μ}}_g}{{\mathrm{\πkhm}}_c{t}_{end}}---\left(9\right)$

Z=η/M (10)

Wherein, R₂It is carbon dioxide displacement leading-edge radius, m；R₁It is pure carbon dioxide area radius, m；Q is carbon dioxide injection amount, m³/d；B_gIt is carbon dioxide volume factor；μ_gIt is carbon dioxide viscosity, mPas；The Reservoir Permeability that k is obtained for well test analysis, 10^-3μm²；H is reservoir thickness, m；η is piezometric conductivity ratio, and M is mobility ratio；X is transition region and CO₂Area's radii ratio square, Y It is complex parameter expression formula, Z holds coefficient for storage.