CN104695928A - Method for evaluating volume transformation capacity of vertical well of fractured tight oil reservoir - Google Patents

Abstract

The invention discloses a method for evaluating the volume transformation capacity of a vertical well of a fractured tight oil reservoir. The method comprises the following steps: forming a transformation fracture network near a well bore, wherein the transformation region is divided into two parts, namely an inner area and an outer area, the inner area is an artificial main fracture transformation region, and the flow conductivity of an artificial main fracture is much higher than external supply, so that the region is assumed to have limited artificial main factures during a model derivation process, the attribute parameters of all factures are consistent, and the seepage of the fluid in a main fracture is linear seepage and follows the Darcy law; under the combined action of artificial fracture extending and reservoir rock brittle shear, the artificial fractures, shear fractures and natural fractures are criss-cross, so that the seepage mode of the region is changed into fracture conductivity primarily; a semi-analytical two-region comprehensive mathematical model which can be used for evaluating the volume transformation capacity of the vertical well is established. The method is applicable to evaluating multi-fracturing of the vertical well of a closed boundary fractured reservoir and the volume transformation of the vertical well of the fractured tight oil reservoir; reference is provided for reasonable development of the tight oil reservoir.

Description

A kind of Fractured compact oil reservoir straight well volume transformation evaluating production capacity method

Technical field

The invention belongs to Fractured compact oil reservoir field, particularly a kind of Fractured compact oil reservoir straight well volume transformation evaluating production capacity method.

Background technology

Hide the overall background of main body replacement strategy at energy source in China unconventionaloil pool under, one of main force that certainly will become in continue resource hidden by the densification oil (gas) that stock number is abundant.Such resource is exploited in success had become the important component part that domestic oil gas " volume increase is stored up " field already.

Sandstone Gas Reservoir hole, throat narrow radii, fluid fluid ability is not good enough, usually need to carry out pressing crack construction to reservoir to greatest extent the man-made fracture having the microcrack of minimum flow conductivity, induced fractures and have a larger flow conductivity is linked together, expand effectively seam net spread space, link up dominant flowing path, fluid is made to flow through the distance of man-made fracture finally to pit shaft from reservoir the shortest, realize " the three-dimensional transformation " of reservoir in length three directions, very big raising reservoir use rate, plays the object increasing ultimate recovery.

Therefore, the evaluating production capacity method that the fine and close oil (gas) of research hides the transformation of straight well volume has become one of core missions that reservoir engineer faces.The method concentrates the advantage of reservoir engineering and modern well test analysis, after building physical model according to mining site actual conditions, transient seepage flow theoretical foundation is set up suitable volume analysis Mathematical Modeling, pilot production oil (gas) well can be analyzed fast and accurately, (gas) well production that produces oil production decline law, effective tracking evaluation is implemented to the working condition of reservoir properties and well.

Volume fracturing renovation technique is the effective means improving hypotonic compact oil reservoir well yield.The fragility compact reservoir that fracture is grown implements repeatedly acid fracturing transformation, and man-made fracture, intrinsic fracture and shear crack are interweaved, and forms the transformation seam net of certain limit near wellbore, thus change Seepage mode, shorten the flowing distance, reduce filtrational resistance, finally realize individual well high yield.Be different from conventional pressure break, how correctly describing pressure-break in the extension of transforming in volume and spread is set up the key that volume fracturing transforms model, lot of domestic and international scholar has done pilot study in this respect: method for numerical simulation application aspect, and Khalid M etc. use fracture network approximate substitution volume transformation region Modling model orthogonal in length and breadth; Arvind Harikesavanallur etc. are in conjunction with microseism result of detection, and matching volume transformation region and transformation degree realize approximate simulation; Changan M etc. use Kazemi double medium model to describe volume transformation region, although method for numerical simulation can tackle complicated Seepage problems, but limit by the own defect of stress and strain model, operation method and software to a great extent, and step is numerous and diverse, uses easy not.Analytic modell analytical model aspect, Liu X. and Lei Xiao uses the fractal straight well volume transformation area fractures that describes of reservoir to distribute, have studied cold heavy oil and take the husky condition of production, Liu Xiong etc. establish the Composite Reservoir model considering the fractal and free-boundary problem of permeability, evaluate compact oil reservoir straight well volume transformation steady state productivity.Although fractal model can describe the spatial in crack preferably, can not objective description pressure propagation behavior and the optimizing research of realization to man-made fracture parameter.Also not can be used for the unstable state evaluating production capacity model of Fractured compact oil reservoir straight well volume transformation up to now.

Summary of the invention

The invention discloses a kind of Fractured compact oil reservoir straight well volume transformation evaluating production capacity method, described method comprises:

Transformation seam net is formed near wellbore, transformation region is two parts: inner region is artificial major fracture transformation region, because artificial major fracture flow conductivity will supply much larger than outside, therefore suppose in model inference process that this district artificial major fracture of limited bar is infinite fluid diversion and every crack property parameters is consistent, the seepage flow of fluid in major fracture is linear seepage flow and follows Darcy's law; Outskirt extends by man-made fracture and under the acting in conjunction of reservoir rock brittle shear, man-made fracture, shear crack and intrinsic fracture are crisscross, change this district's Seepage mode, based on fracture guide,

For evaluating Fractured compact oil reservoir straight well volume transformation production capacity, build Mathematical Modeling as follows:

There is bitesize fracturing reform straight well known circular Fractured compact oil reservoir center, and fixed output quota is produced,

Inner region is the major fracture linear seepage flow stage, and continuity equation is:

$\frac{{\∂}^2{p}_1}{\∂r^2}={\mathrm{\η}}_1^{-1}\frac{\∂p_1}{\∂t}---\left(1\right)$

Outskirt Flow through media with double-porosity continuity equation can be expressed as:

$\frac{1}{r}\frac{\∂}{\∂r}\left(r\frac{\∂p_2}{\∂r}\right)={\mathrm{\η}}_2^{-1}\frac{\∂p_2}{\∂t}-q_m---\left(2\right)$

Wherein:

$q_m=\frac{\mathrm{\γ}{k}_{2m}(p_{2m}-p_2)}{\mathrm{\μ}}=-{\left(\mathrm{\φc}\right)}_{2m}\frac{\∂p_{2m}}{\∂t}$

Primary condition and inner and outer boundary condition:

p ₁(r,0)＝p _i(r _w≤r≤r _f) (3)

p ₂(r,0)＝p _i(r _f≤r≤∞) (4)

$-\mathrm{nb}\frac{k_{1}h}{\mathrm{\μ}}\frac{\∂p_1}{\∂r}=\mathrm{qB},(r=r_w)---\left(5\right)$

$\frac{\∂p_2}{\∂r}=0,(r=r_e)---\left(6\right)$

Coupling place fringe conditions:

p ₁＝p ₂(r＝r _f) (7)

${\mathrm{nbk}}_1\frac{\∂p_1}{\∂r}=2\mathrm{\π}{\mathrm{rk}}_2\frac{\∂p_2}{\∂r},(r=r_f)---\left(8\right)$

All physical quantity dimensionless definition expression formulas:

$p_D=\frac{542.87k_{2}h(p_i-p)}{\mathrm{q\μ}{B}_0};t_D=\frac{3.6k_{2}t}{{\left(\mathrm{\φc}\right)}_2\mathrm{\μ}{r}_f^2};r_D=\frac{r}{r_f};r_c=\frac{r_w}{r_f};r_{\mathrm{eD}}=\frac{r_e}{r_f};$

$\mathrm{\α}=\frac{{\mathrm{\η}}_2}{{\mathrm{\η}}_1}=\frac{k_2{\left(\mathrm{\φc}\right)}_1}{k_1{\left(\mathrm{\φc}\right)}_2};\mathrm{\β}=\frac{{\mathrm{nbk}}_1}{542.87k_2{r}_f};\mathrm{\ω}=\frac{{\left(\mathrm{\φc}\right)}_2}{{\left(\mathrm{\φc}\right)}_2+{\left(\mathrm{\φc}\right)}_{2m}};\mathrm{\λ}=\frac{\mathrm{\γ}{k}_{2m}{r}_f^2}{k_2}$

After formula (1) to formula (8) dimensionless and laplace transform, inner region continuity equation can be rewritten as:

$\frac{{\∂}^2{\tilde{p}}_{1D}}{\∂r_D^2}=\mathrm{\αs}{\tilde{p}}_{1D}---\left(9\right)$

Outskirt continuity equation can be expressed as:

$\frac{{\∂}^2{\tilde{p}}_{2D}}{\∂r_D^2}+\frac{1}{r_D}\frac{\∂{\tilde{p}}_{2D}}{\∂r_D}=s{\tilde{p}}_{2D}-{\tilde{q}}_{\mathrm{mD}}---\left(10\right)$

Formula (10) can be reduced to further:

$\frac{{\∂}^2{\tilde{p}}_{2D}}{\∂r_D^2}+\frac{1}{r_D}\frac{\∂{\tilde{p}}_{2D}}{\∂r_D}=\mathrm{sf}\left(s\right){\tilde{p}}_{2D}---\left(11\right)$

Wherein:

$f\left(s\right)=\frac{\mathrm{\ω}(1-\mathrm{\ω})s+\mathrm{\λ}}{(1-\mathrm{\ω})s+\mathrm{\λ}}$

Inner and outer boundary and coupling place condition Rewriting expression have:

$\frac{\∂{\tilde{p}}_{1D}}{\∂r_D}=\frac{1}{\mathrm{s\β}},(r_D=r_c)---\left(12\right)$

$\frac{d{\tilde{p}}_{2D}(r_{\mathrm{eD}},t_D)}{d{r}_D}=0---\left(13\right)$

${\tilde{p}}_{1D}={\tilde{p}}_{2D},(r_D=1)---\left(14\right)$

$\frac{\∂{\tilde{p}}_{1D}}{\∂r_D}=\frac{1}{\mathrm{\β}}\frac{\∂\widetilde{p_{2D}}}{\∂r_D},(r_D=1)---\left(15\right)$

The general solution of formula (9) and formula (11) is respectively:

${\tilde{p}}_{1D}=A\cosh (\sqrt{\mathrm{s\α}}\×r_D)+B\sinh (\sqrt{\mathrm{s\α}}\×r_D)---\left(16\right)$

${\tilde{p}}_{2D}={\mathrm{CI}}_0(\sqrt{\mathrm{sf}\left(s\right)}\×r_D)+{\mathrm{DK}}_0(\sqrt{\mathrm{sf}\left(s\right)}\×r_D)---\left(17\right)$

Formula (16) and formula (17) are substituted into formula (12), (13), (14), (15), then arrange and can obtain pull-type space pressure expression formula and be:

${\tilde{p}}_{1D}=\frac{\mathrm{X\β}\sqrt{\mathrm{s\α}}\cosh (\sqrt{\mathrm{s\α}}\×(1-r_D))-Y\sqrt{\mathrm{sf}\left(s\right)}\sinh (\sqrt{\mathrm{s\α}}\×(1-r_D))}{\mathrm{s\β}\sqrt{\mathrm{s\α}}\mathrm{\Δ}}---\left(18\right)$

${\tilde{p}}_{2D}=\frac{I_0(\sqrt{\mathrm{sf}\left(s\right)}\×r_D)K_1(\sqrt{\mathrm{sf}\left(s\right)}\×r_{\mathrm{eD}})+I_1(\sqrt{\mathrm{sf}\left(s\right)}\×r_{\mathrm{eD}})K_0(\sqrt{\mathrm{sf}\left(s\right)}\×r_D)}{\mathrm{s\Δ}}---\left(19\right)$

Wherein:

$X=I_0\left(\sqrt{\mathrm{sf}\left(s\right)}\right)K_1(\sqrt{\mathrm{sf}\left(s\right)}\×r_{\mathrm{eD}})+I_1(\sqrt{\mathrm{sf}\left(s\right)}\×r_{\mathrm{eD}})K_0\left(\sqrt{\mathrm{sf}\left(s\right)}\right)$

$Y=I_1\left(\sqrt{\mathrm{sf}\left(s\right)}\right)K_1(\sqrt{\mathrm{sf}\left(s\right)}\×r_{\mathrm{eD}})-I_1(\sqrt{\mathrm{sf}\left(s\right)}\×r_{\mathrm{eD}})K_1\left(\sqrt{\mathrm{sf}\left(s\right)}\right)$

$\mathrm{\Δ}=\mathrm{X\β}\sqrt{\mathrm{s\α}}\sinh (\sqrt{\mathrm{s\α}}\×(1-r_c))-Y\sqrt{\mathrm{sf}\left(s\right)}\cosh (\sqrt{\mathrm{s\α}}\×(1-r_c))$

From formula (18), work as r _d=r _ctime, the pull-type space time dependent relational expression of bottom pressure can be expressed as:

${\tilde{p}}_{\mathrm{wD}}\left(s\right)=\frac{\mathrm{X\β}\sqrt{\mathrm{s\α}}\cosh (\sqrt{\mathrm{s\α}}\×(1-r_c))-Y\sqrt{\mathrm{sf}\left(s\right)}\sinh (\sqrt{\mathrm{s\α}}\×(1-r_c))}{\mathrm{s\β}\sqrt{\mathrm{s\α}}\mathrm{\Δ}}---\left(20\right)$

From formula (20), level pressure is produced pull-type space output and fixed output quota and is produced pull-type space bottom pressure and meet following formula:

$\begin{array}{c}{\tilde{q}}_D\left(s\right)=\frac{1}{s^2{\tilde{p}}_{\mathrm{wD}}\left(s\right)}\\ =\frac{\mathrm{\β}\sqrt{\mathrm{s\α}}\mathrm{\Δ}}{s[\mathrm{X\β}\sqrt{\mathrm{s\α}}\cosh (\sqrt{\mathrm{s\α}}\×(1-r_c))-Y\sqrt{\mathrm{sf}\left(s\right)}\sinh (\sqrt{\mathrm{s\α}}\×(1-r_c))]}\end{array}---\left(21\right)$

Based on formula (20) and (21), utilize Stehfest numerical inversion can obtain dimensionless bottom pressure corresponding under fixed output quota working condition and nondimensional time, or the relation curve of corresponding dimensionless output and nondimensional time under level pressure working condition.

Further, piezometric conductivity comparison initial production has impact, and piezometric conductivity is than larger, and initial production is higher; Along with piezometric conductivity continues to increase, the variable quantity of output is relatively much little, and this shows that man-made fracture transformation degree has an optimal value.

Further, the production capacity of fracture conductivity comparison whole production cycle has considerable influence, and along with the increase of β value, initial productivity increases highly significant, namely shows the reconstruction scope improving crack, near wellbore zone, significantly can promote well yield.

Further, the output that the comparison transition flow stage is held in storage has impact, and storage is held than less, and channelling phenomenon is more obvious, and production curve is recessed darker; Interporosity flow coefficient then has impact to matrix-crack channelling stage flow, and interporosity flow coefficient is larger, channelling occur more early.

Further, outskirt pressure break volume spread has impact to later stage production curve, and fracturing reform radius is less, more early enters the energy drain stage, increases the time that crack extension can delay the exhaustion of blowdown producing well greatly.

Remarkable result of the present invention is: the present invention is based on Laplace transform and Stehfest numerical inversion, establish one and can be used for Fractured compact oil reservoir straight well volume transformation semi analytic evaluating production capacity two district composite model, analyze the sensitiveness affecting production capacity correlative factor, depict production decline plate, matching two cause for gossip border producing well data.This model considers the situation that pit shaft many man-made fractures act on simultaneously, the each parameter in reflection crack that can be simple and clear is on the impact of production capacity, the convenient well that adds stores up the parameters such as skin factor, after can providing the transformation of multiple fracture acidizing, reservoir underlying parameter is explained, repeatedly pressure break and the transformation of Fractured compact oil reservoir straight well volume are evaluated, for the optimization of compact oil reservoir reasonable development and volume fracturing transformation provides reference to be applicable to closed boundary fractured reservoir straight well.

Accompanying drawing explanation

Fig. 1 is straight well volume fracturing transformation schematic diagram;

Fig. 2 be piezometric conductivity comparison production capacity affect schematic diagram;

Fig. 3 be fracture conductivity comparison production capacity affect schematic diagram;

Fig. 4 be storage hold comparison production capacity affect schematic diagram;

Fig. 5 is that interporosity flow coefficient affects schematic diagram to production capacity;

Fig. 6 is that volume transformation radius affects schematic diagram to production capacity;

Fig. 7 is 1008 well capacity curve schematic diagrames;

Fig. 8 is 1148 well capacity curve schematic diagrames.

Detailed description of the invention

Elaborate below in conjunction with the detailed description of the invention of accompanying drawing to a kind of Fractured compact oil reservoir straight well volume transformation evaluating production capacity method disclosed by the invention, and be not used to limit the scope of the invention.

As shown in Figure 1, fragility compact reservoir is after repeatedly acid fracturing is transformed, the transformation seam net of certain volume can be formed near wellbore, transformation region can be subdivided into 2 parts: inner region is artificial major fracture transformation region, because artificial major fracture flow conductivity will supply much larger than outside, therefore, suppose in model inference process that this district artificial major fracture of limited bar is infinite fluid diversion and every crack property parameters is consistent, the seepage flow of fluid in major fracture is linear seepage flow and follows Darcy's law; Outskirt is by under man-made fracture extension and the acting in conjunction of reservoir rock brittle shear, man-made fracture, shear crack and intrinsic fracture are crisscross, change this district's Seepage mode, based on fracture guide, the present invention uses classical Warren-Root model to describe this crack, district spread and fluid neuron network situation.Volume transformation is not subject to man-made fracture transformation impact with exterior domain, and intrinsic fracture can not get effective communication, reservoir permeability ultralow (< 0.1mD), to the supply of volume transformation regional fluid seldom, does not consider.In sum, model basic assumption comprises:

(1) model homogeneous, radially isotropism;

(2) producing well fixed output quota, do not consider well storage impact, fluid, rock are micro-compressible;

(3) be isothermal flow event, fracture guide is main, and seepage flow meets laminar flow characteristic.

Mathematical Modeling and solving:

There is bitesize fracturing reform straight well known circular Fractured compact oil reservoir center, and (in derivation, physical quantity unit follows SI guiding principle standard unit system) is produced in fixed output quota.

Inner region is the major fracture linear seepage flow stage, and continuity equation is:

$\frac{{\&PartialD;}^2{p}_1}{\&PartialD;r^2}={\mathrm{\&eta;}}_1^{-1}\frac{\&PartialD;p_1}{\&PartialD;t}---\left(1\right)$

Outskirt Flow through media with double-porosity continuity equation can be expressed as:

$\frac{1}{r}\frac{\&PartialD;}{\&PartialD;r}\left(r\frac{\&PartialD;p_2}{\&PartialD;r}\right)={\mathrm{\&eta;}}_2^{-1}\frac{\&PartialD;p_2}{\&PartialD;t}-q_m---\left(2\right)$

Wherein:

$q_m=\frac{\mathrm{\&gamma;}{k}_{2m}(p_{2m}-p_2)}{\mathrm{\&mu;}}=-{\left(\mathrm{\&phi;c}\right)}_{2m}\frac{\&PartialD;p_{2m}}{\&PartialD;t}$

Primary condition and inner and outer boundary condition:

p ₁(r,0)＝p _i(r _w≤r≤r _f) (3)

p ₂(r,0)＝p _i(r _f≤r≤∞) (4)

$-\mathrm{nb}\frac{k_{1}h}{\mathrm{\&mu;}}\frac{\&PartialD;p_1}{\&PartialD;r}=\mathrm{qB},(r=r_w)---\left(5\right)$

$\frac{\&PartialD;p_2}{\&PartialD;r}=0,(r=r_e)---\left(6\right)$

Coupling place fringe conditions:

p ₁＝p ₂(r＝r _f) (7)

${\mathrm{nbk}}_1\frac{\&PartialD;p_1}{\&PartialD;r}=2\mathrm{\&pi;}{\mathrm{rk}}_2\frac{\&PartialD;p_2}{\&PartialD;r},(r=r_f)---\left(8\right)$

All physical quantity dimensionless definition expression formulas:

$p_D=\frac{542.87k_{2}h(p_i-p)}{\mathrm{q\&mu;}{B}_0};t_D=\frac{3.6k_{2}t}{{\left(\mathrm{\&phi;c}\right)}_2\mathrm{\&mu;}{r}_f^2};r_D=\frac{r}{r_f};r_c=\frac{r_w}{r_f};r_{\mathrm{eD}}=\frac{r_e}{r_f};$

$\mathrm{\&alpha;}=\frac{{\mathrm{\&eta;}}_2}{{\mathrm{\&eta;}}_1}=\frac{k_2{\left(\mathrm{\&phi;c}\right)}_1}{k_1{\left(\mathrm{\&phi;c}\right)}_2};\mathrm{\&beta;}=\frac{{\mathrm{nbk}}_1}{542.87k_2{r}_f};\mathrm{\&omega;}=\frac{{\left(\mathrm{\&phi;c}\right)}_2}{{\left(\mathrm{\&phi;c}\right)}_2+{\left(\mathrm{\&phi;c}\right)}_{2m}};\mathrm{\&lambda;}=\frac{\mathrm{\&gamma;}{k}_{2m}{r}_f^2}{k_2}$

After formula (1) to formula (8) dimensionless and laplace transform, inner region continuity equation can be rewritten as:

$\frac{{\&PartialD;}^2{\tilde{p}}_{1D}}{\&PartialD;r_D^2}=\mathrm{\&alpha;s}{\tilde{p}}_{1D}---\left(9\right)$

Outskirt continuity equation can be expressed as:

$\frac{{\&PartialD;}^2{\tilde{p}}_{2D}}{\&PartialD;r_D^2}+\frac{1}{r_D}\frac{\&PartialD;{\tilde{p}}_{2D}}{\&PartialD;r_D}=s{\tilde{p}}_{2D}-{\tilde{q}}_{\mathrm{mD}}---\left(10\right)$

Formula (10) can be reduced to further:

$\frac{{\&PartialD;}^2{\tilde{p}}_{2D}}{\&PartialD;r_D^2}+\frac{1}{r_D}\frac{\&PartialD;{\tilde{p}}_{2D}}{\&PartialD;r_D}=\mathrm{sf}\left(s\right){\tilde{p}}_{2D}---\left(11\right)$

Wherein:

$f\left(s\right)=\frac{\mathrm{\&omega;}(1-\mathrm{\&omega;})s+\mathrm{\&lambda;}}{(1-\mathrm{\&omega;})s+\mathrm{\&lambda;}}$

Inner and outer boundary and coupling place condition Rewriting expression have:

$\frac{\&PartialD;{\tilde{p}}_{1D}}{\&PartialD;r_D}=\frac{1}{\mathrm{s\&beta;}},(r_D=r_c)---\left(12\right)$

$\frac{d{\tilde{p}}_{2D}(r_{\mathrm{eD}},t_D)}{d{r}_D}=0---\left(13\right)$

${\tilde{p}}_{1D}={\tilde{p}}_{2D},(r_D=1)---\left(14\right)$

$\frac{\&PartialD;{\tilde{p}}_{1D}}{\&PartialD;r_D}=\frac{1}{\mathrm{\&beta;}}\frac{\&PartialD;\widetilde{p_{2D}}}{\&PartialD;r_D},(r_D=1)---\left(15\right)$

The general solution of formula (9) and formula (11) is respectively:

${\tilde{p}}_{1D}=A\cosh (\sqrt{\mathrm{s\&alpha;}}\&times;r_D)+B\sinh (\sqrt{\mathrm{s\&alpha;}}\&times;r_D)---\left(16\right)$

${\tilde{p}}_{2D}={\mathrm{CI}}_0(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_D)+{\mathrm{DK}}_0(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_D)---\left(17\right)$

Formula (16) and formula (17) are brought into formula (12), (13), (14), (15) then to arrange and can obtain pull-type space pressure expression formula and be:

${\tilde{p}}_{1D}=\frac{\mathrm{X\&beta;}\sqrt{\mathrm{s\&alpha;}}\cosh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_D))-Y\sqrt{\mathrm{sf}\left(s\right)}\sinh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_D))}{\mathrm{s\&beta;}\sqrt{\mathrm{s\&alpha;}}\mathrm{\&Delta;}}---\left(18\right)$

${\tilde{p}}_{2D}=\frac{I_0(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_D)K_1(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_{\mathrm{eD}})+I_1(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_{\mathrm{eD}})K_0(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_D)}{\mathrm{s\&Delta;}}---\left(19\right)$

Wherein:

$X=I_0\left(\sqrt{\mathrm{sf}\left(s\right)}\right)K_1(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_{\mathrm{eD}})+I_1(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_{\mathrm{eD}})K_0\left(\sqrt{\mathrm{sf}\left(s\right)}\right)$

$Y=I_1\left(\sqrt{\mathrm{sf}\left(s\right)}\right)K_1(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_{\mathrm{eD}})-I_1(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_{\mathrm{eD}})K_1\left(\sqrt{\mathrm{sf}\left(s\right)}\right)$

$\mathrm{\&Delta;}=\mathrm{X\&beta;}\sqrt{\mathrm{s\&alpha;}}\sinh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_c))-Y\sqrt{\mathrm{sf}\left(s\right)}\cosh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_c))$

From formula (18), work as r _d=r _ctime, the pull-type space time dependent relational expression of bottom pressure can be expressed as:

${\tilde{p}}_{\mathrm{wD}}\left(s\right)=\frac{\mathrm{X\&beta;}\sqrt{\mathrm{s\&alpha;}}\cosh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_c))-Y\sqrt{\mathrm{sf}\left(s\right)}\sinh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_c))}{\mathrm{s\&beta;}\sqrt{\mathrm{s\&alpha;}}\mathrm{\&Delta;}}---\left(20\right)$

From formula (20), level pressure is produced pull-type space output and fixed output quota and is produced pull-type space bottom pressure and meet following formula:

$\begin{array}{c}{\tilde{q}}_D\left(s\right)=\frac{1}{s^2{\tilde{p}}_{\mathrm{wD}}\left(s\right)}\\ =\frac{\mathrm{\&beta;}\sqrt{\mathrm{s\&alpha;}}\mathrm{\&Delta;}}{s[\mathrm{X\&beta;}\sqrt{\mathrm{s\&alpha;}}\cosh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_c))-Y\sqrt{\mathrm{sf}\left(s\right)}\sinh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_c))]}\end{array}---\left(21\right)$

Based on formula (20) and (21), utilize Stehfest numerical inversion can obtain dimensionless bottom pressure corresponding under fixed output quota working condition and nondimensional time, or the relation curve of corresponding dimensionless output and nondimensional time under level pressure working condition.

Utilizing typical curve to solve creation data problem analysis is pressure transient well test analysis, particularly, whether pressure transient well test analysis typical curve can be good at showing flow periods feature, and common productivity decline curve clearly can not find out flow periods feature.The people such as Blasingame and McGray (1990,1991) result of study shows to need to redefine dimensionless output and dimensionless material balance pseudotime, draw both sides relation curve can address this problem very well, but it is quite difficult to obtain the dimensionless output expression formula redefined in real space territory.Based on above research, the people such as Agarwal and Gardner (1999) contrast shaft bottom fixed output quota dimensionless pressure inverse (1/P _wD(t _d)) explain curve with Blasingame production decline, result correspondence is relatively good, its asymptotic error increases in time and is tending towards 0 gradually, and precision can meet engineering analysis demand, can utilize the dimensionless bottom pressure inverse (1/P of pressure transient well testing typical curve _wD(t _d)) represent common productivity production decline law.

Based on underlying parameter α=0.1, β=10, ω=0.05, λ=0.0001, r _c=0.001, r _eD=1000, adopt control variate method, draw the relation curve with nondimensional time reciprocal of dimensionless bottom pressure under different parameters, analyze piezometric conductivity ratio, ratio is held in fracture conductivity ratio, storage, interporosity flow coefficient, volume transform the factors such as radius to the affecting laws of production capacity.

As shown in Figure 2, which show (α=0.1,0.5 under different piezometric conductivity ratio, 0.9) relation curve of dimensionless bottom pressure inverse and nondimensional time, as can be seen from the figure: piezometric conductivity comparison initial production has impact, piezometric conductivity is than larger, and initial production is higher; Piezometric conductivity is than when changing to 0.5 from 0.1, initial production increase is comparatively obvious, and when changing to 0.9 from 0.5, this variable quantity is relatively much little, visible man-made fracture transformation degree has an optimal value, in transformation given volume situation, the flow conductivity blindly increasing the artificial major fracture of near wellbore there is no need.

As shown in Figure 3, which show (β=0.1 under different fracture conductivity ratio, 1,10) dimensionless bottom pressure inverse and the relation curve of nondimensional time, can obtain from curve: the production capacity of fracture conductivity comparison whole production cycle has considerable influence, along with the increase of β value, initial productivity increases highly significant, it can thus be appreciated that, improve the reconstruction scope in crack, near wellbore zone, significantly can promote well yield, this transformation was all highly profitable to the whole production cycle.In addition, fracture conductivity increases than β, impels individual well high yield simultaneously, also can, with obvious compound boundary stream, later stage output be increased progressively not obvious.The analysis of comprehensive piezometric conductivity ratio, should note transformation degree and the reasonably optimizing of transformation volume, ensure maximum production.

As shown in Figure 4 and Figure 5, it sets forth different storage appearance than (ω=0.05,0.5,0.9) and different interporosity flow coefficient (λ=1 × 10 ^-5, 1 × 10 ^-4, 1 × 10 ^-3) under the dimensionless bottom pressure relation curve with nondimensional time reciprocal, can very clearly find out from figure: similar to common double dense media, storage hold than and interporosity flow coefficient affect degree and the time of channelling generation respectively.The output that the comparison transition flow stage is held in storage has impact, and storage is held than less, and channelling phenomenon is more obvious, and production curve is recessed darker; Interporosity flow coefficient then has impact to matrix-crack channelling stage flow, and interporosity flow coefficient is larger, channelling occur more early.

Volume transformation radius major embodiment outskirt pressure break spread volume is on the impact of production capacity.Fig. 6 gives different volumes transformation radius (r _eD=100,300,500) relation curve of dimensionless bottom pressure inverse and nondimensional time under, as can be seen from curve: outskirt pressure break volume spread has impact to later stage production curve, fracturing reform radius is less, more early enter the energy drain stage, increase the time that crack extension can delay the exhaustion of blowdown producing well greatly.

From production capacity affecting parameters sensitivity analysis above: fracture conductivity has impact than β to early metaphase production capacity; Piezometric conductivity only has impact to early stage deliverability curve than α; Chu Rong affects the recessed degree of curve in mid-term and time of origin respectively than ω and interporosity flow coefficient λ; Volume transformation radius r _eDthen affect later stage production curve.Therefore when matching actual production data and curves, adopt control variate method, first adjust fracture conductivity than β value, secondly regulate piezometric conductivity than α, last matching storage is held than ω, interporosity flow coefficient λ and volume transformation radius r _eD.

Research block is low porosity and low permeability, the Triassic system chiltern Conglomerate Reservoir that non-homogeneity is extremely strong, and crack is grown not.1008 well finishing drilling well depth 2300m, oil well blowing is produced, and front and back are through 3 pressure breaks, and also carried out acidifying transformation afterwards, core permeability is 2.731 × 10 ^-3μm ², be low permeability reservoir.Before test, day production fluid 30m ³.As shown in Figure 7, trying to achieve interpretation parameters has: k for pressure data and matching dimensionless bottom pressure reciprocal curve ₁=23.38 × 10 ^-3μm ², k ₂=14.03 × 10 ^-3μm ², nb=0.094m, ω=0.025, λ=0.05, r _e=143m.As can be seen from interpretation parameters, 1008 well transformation situations are better, so initial production is high, but be subject to the impact on outer closure border, well control area is little, and later stage production declining is very fast.

1148 wells are multiple fracturing production, and oil pumping is produced, and done acidifying transformation afterwards, free from flaw core permeability is 0.05 × 10 ^-3μm ², be compact reservoir.Before test, well daily fluid production rate 3.4m ³, this test lasts 169.5h.As shown in Figure 8, trying to achieve interpretation parameters has: k for creation data and matching dimensionless bottom pressure reciprocal curve ₁=1.15 × 10 ^-3μm ², k ₂=0.69 × 10 ^-3μm ², nb=0.022m, ω=0.25, λ=0.018, r _e=400m, can find out that inner region transformation situation is not as good as 1008 wells from 1148 well interpretation parameters, initil output is not high, but fracture extension and connection situation are better, and the nearly 400m of volume transformation radius, ensure that the campaign that this well is longer.

The parameter interpretation result of two mouthfuls of wells is coincide actual geological condition all substantially, demonstrates this model and is evaluating the applicability of band closed boundary fractured reservoir straight well repeatedly in fracturing reform and the transformation of Fractured compact oil reservoir straight well volume and practicality.

The foregoing is only the preferred embodiments of the present invention, the numerical value mentioned in the description of above-mentioned manual and number range are not limited to the present invention, just for the invention provides preferred embodiment, be not limited to the present invention, for a person skilled in the art, the present invention can have various modifications and variations.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (5)

1. a Fractured compact oil reservoir straight well volume transformation evaluating production capacity method, described method comprises:

Transformation seam net is formed near wellbore, transformation region is two parts: inner region is artificial major fracture transformation region, because artificial major fracture flow conductivity will supply much larger than outside, therefore suppose in model inference process that this district artificial major fracture of limited bar is infinite fluid diversion and every crack property parameters is consistent, the seepage flow of fluid in major fracture is linear seepage flow and follows Darcy's law; Outskirt extends by man-made fracture and under the acting in conjunction of reservoir rock brittle shear, man-made fracture, shear crack and intrinsic fracture are crisscross, change this district's Seepage mode, based on fracture guide,

For evaluating Fractured compact oil reservoir straight well volume transformation production capacity, build Mathematical Modeling as follows:

There is bitesize fracturing reform straight well known circular Fractured compact oil reservoir center, and fixed output quota is produced,

Inner region is the major fracture linear seepage flow stage, and continuity equation is:

$\frac{{\&PartialD;}^2{p}_1}{\&PartialD;r^2}={\mathrm{\&eta;}}_1^{-1}\frac{{\&PartialD;p}_1}{\&PartialD;t}---\left(1\right)$

Outskirt Flow through media with double-porosity continuity equation can be expressed as:

$\frac{1}{r}\frac{\&PartialD;}{\&PartialD;r}\left(r\frac{\&PartialD;p_2}{\&PartialD;r}\right)={\mathrm{\&eta;}}_2^{-1}\frac{{\&PartialD;p}_2}{\&PartialD;t}-q_m---\left(2\right)$

Wherein:

$q_m=\frac{\mathrm{\&gamma;}{k}_{2m}(p_{2m}-p_2)}{\mathrm{\&mu;}}=-{\left(\mathrm{\&phi;c}\right)}_{2m}\frac{{\&PartialD;p}_{2m}}{\&PartialD;t}$

Primary condition and inner and outer boundary condition:

p ₁(r,0)＝p _i(r _w≤r≤r _f) (3)

p ₂(r,0)＝p _i(r _f≤r≤∞) (4)

$-\mathrm{nb}\frac{k_{1}h}{\mathrm{\&mu;}}\frac{{\&PartialD;p}_1}{\&PartialD;r}=\mathrm{qB},(r=r_w)---\left(5\right)$

$\frac{{\&PartialD;p}_2}{\&PartialD;r}=0,(r=r_e)---\left(6\right)$

Coupling place fringe conditions:

p ₁＝p ₂(r＝r _f) (7)

${\mathrm{nbk}}_1\frac{{\&PartialD;p}_1}{\&PartialD;r}=2\mathrm{\&pi;r}{k}_2\frac{{\&PartialD;p}_2}{\&PartialD;r},(r=r_f)---\left(8\right)$

All physical quantity dimensionless definition expression formulas:

$p_D=\frac{542.87k_{2}h(p_i-p)}{\mathrm{q\&mu;}{B}_0};t_D=\frac{3.6k_{2}t}{{\left(\mathrm{\&phi;c}\right)}_2{\mathrm{\&mu;r}}_f^2};r_D=\frac{r}{r_f};r_c=\frac{r_w}{r_f};r_{\mathrm{eD}}=\frac{r_e}{r_f};$

$\mathrm{\&alpha;}=\frac{{\mathrm{\&eta;}}_2}{{\mathrm{\&eta;}}_1}\frac{k_2{\left(\mathrm{\&phi;c}\right)}_1}{k_1{\left(\mathrm{\&phi;c}\right)}_2};\mathrm{\&beta;}=\frac{{\mathrm{nbk}}_1}{542.87k_2{r}_f};\mathrm{\&omega;}=\frac{{\left(\mathrm{\&phi;c}\right)}_2}{{\left(\mathrm{\&phi;c}\right)}_2+{\left(\mathrm{\&phi;c}\right)}_{2m}};\mathrm{\&lambda;}=\frac{\mathrm{\&gamma;}{k}_{2m}{r}_f^2}{k_2}$

After formula (1) to formula (8) dimensionless and laplace transform, inner region continuity equation can be rewritten as:

$\frac{{\&PartialD;}^2{\tilde{p}}_{1D}}{\&PartialD;r_D^2}=\mathrm{\&alpha;}{s\tilde{p}}_{1D}---\left(9\right)$

Outskirt continuity equation can be expressed as:

$\frac{{\&PartialD;}^2{\tilde{p}}_{2D}}{\&PartialD;r_D^2}+\frac{1}{r_D}\frac{\&PartialD;{\tilde{p}}_{2D}}{\&PartialD;r_D}=s{\tilde{p}}_{2D}-{\tilde{q}}_{\mathrm{mD}}---\left(10\right)$

Formula (10) can be reduced to further:

$\frac{{\&PartialD;}^2{\tilde{p}}_{2D}}{\&PartialD;r_D^2}+\frac{1}{r_D}\frac{\&PartialD;{\tilde{p}}_{2D}}{\&PartialD;r_D}=\mathrm{sf}\left(s\right){\tilde{p}}_{2D}---\left(11\right)$ Wherein:

$f\left(s\right)=\frac{\mathrm{\&omega;}(1-\mathrm{\&omega;})s+\mathrm{\&lambda;}}{(1-\mathrm{\&omega;})s+\mathrm{\&lambda;}}$

Inner and outer boundary and coupling place condition Rewriting expression have:

$\frac{\&PartialD;{\tilde{p}}_{1D}}{\&PartialD;r_D}=\frac{1}{\mathrm{s\&beta;}},(r_D=r_c)---\left(12\right)$

$\frac{d{\tilde{p}}_{2D}(r_{\mathrm{eD}},t_D)}{{\mathrm{dr}}_D}=0---\left(13\right)$

${\tilde{p}}_{1D}={\tilde{p}}_{2D},(r_D=1)---\left(14\right)$

$\frac{\&PartialD;{\tilde{p}}_{1D}}{\&PartialD;r_D}=\frac{1}{\mathrm{\&beta;}}\frac{\&PartialD;{\tilde{p}}_{2D}}{\&PartialD;r_D},(r_D=1)---\left(15\right)$

The general solution of formula (9) and formula (11) is respectively:

${\tilde{p}}_{1D}=A\cosh (\sqrt{\mathrm{s\&alpha;}}\&times;r_D)+B\sinh (\sqrt{\mathrm{s\&alpha;}}\&times;r_D)---\left(16\right)$

${\tilde{p}}_{2D}={\mathrm{CI}}_0(\sqrt{\mathrm{sf}\left(s\right)}\&times;f_D)+{\mathrm{DK}}_0(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_D)---\left(17\right)$

Formula (16) and formula (17) are substituted into formula (12), (13), (14), (15), then arrange and can obtain pull-type space pressure expression formula and be:

${\tilde{p}}_{1D}=\frac{\mathrm{X\&beta;}\sqrt{\mathrm{s\&alpha;}}\cosh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_D))-Y\sqrt{\mathrm{sf}\left(s\right)}\sinh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_D))}{\mathrm{s\&beta;}\sqrt{\mathrm{s\&alpha;}}\mathrm{\&Delta;}}---\left(18\right)$

${\tilde{p}}_{2D}=\frac{I_0(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_D)K_1(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_{\mathrm{eD}})+I_1(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_{\mathrm{eD}})K_0(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_D)}{\mathrm{s\&Delta;}}---\left(19\right)$ Wherein:

$X=I_0\left(\sqrt{\mathrm{sf}\left(s\right)}\right)K_1(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_{\mathrm{eD}})+I_1(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_{\mathrm{eD}})K_0\left(\sqrt{\mathrm{sf}\left(s\right)}\right)$

$Y=I_1\left(\sqrt{\mathrm{sf}\left(s\right)}\right)K_1(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_{\mathrm{eD}})-I_1(\sqrt{\mathrm{sf}\left(s\right)}\&times;r_{\mathrm{eD}})K_1\left(\sqrt{\mathrm{sf}\left(s\right)}\right)$

$\mathrm{\&Delta;}=\mathrm{X\&beta;}\sqrt{\mathrm{s\&alpha;}}\sinh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_c))Y\sqrt{\mathrm{sf}\left(s\right)}\cosh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_c))$

From formula (18), work as r _d=r _ctime, the pull-type space time dependent relational expression of bottom pressure can be expressed as:

${\tilde{p}}_{\mathrm{wD}}\left(s\right)=\frac{\mathrm{X\&beta;}\sqrt{\mathrm{s\&alpha;}}\cosh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_c))-Y\sqrt{\mathrm{sf}\left(s\right)}\sinh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_c))}{\mathrm{s\&beta;}\sqrt{\mathrm{s\&alpha;}}\mathrm{\&Delta;}}---\left(20\right)$

From formula (20), level pressure is produced pull-type space output and fixed output quota and is produced pull-type space bottom pressure and meet following formula:

$\begin{array}{c}{\tilde{q}}_D\left(s\right)=\frac{1}{s^2{\tilde{p}}_{\mathrm{wD}}\left(s\right)}\\ =\frac{\mathrm{\&beta;}\sqrt{\mathrm{s\&alpha;}}\mathrm{\&Delta;}}{s[\mathrm{X\&beta;}\sqrt{\mathrm{s\&alpha;}}\mathrm{coh}(\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_c))-Y\sqrt{\mathrm{sf}\left(s\right)\sinh (\sqrt{\mathrm{s\&alpha;}}\&times;(1-r_c))}]}\end{array}---\left(21\right)$

Based on formula (20) and (21), utilize Stehfest numerical inversion can obtain dimensionless bottom pressure corresponding under fixed output quota working condition and nondimensional time, or the relation curve of corresponding dimensionless output and nondimensional time under level pressure working condition.

2. method according to claim 1, is characterized in that, piezometric conductivity comparison initial production has impact, and piezometric conductivity is than larger, and initial production is higher; Along with piezometric conductivity continues to increase, the variable quantity of output is relatively much little, and this shows that man-made fracture transformation degree has an optimal value.

3. method according to claim 1, is characterized in that, the production capacity of fracture conductivity comparison whole production cycle has considerable influence, along with the increase of β value, initial productivity increases highly significant, namely shows the reconstruction scope improving crack, near wellbore zone, significantly can promote well yield.

4. method according to claim 1, is characterized in that, the output that the comparison transition flow stage is held in storage has impact, and storage is held than less, and channelling phenomenon is more obvious, and production curve is recessed darker; Interporosity flow coefficient then has impact to matrix-crack channelling stage flow, and interporosity flow coefficient is larger, channelling occur more early.

5. method according to claim 1, it is characterized in that, outskirt pressure break volume spread has impact to later stage production curve, and fracturing reform radius is less, more early enter the energy drain stage, increase the time that crack extension can delay the exhaustion of blowdown producing well greatly.