UFLUIDLEAKOFF

User subroutine to define the fluid leak-off coefficients for pore pressure cohesive elements.

can be used to define the fluid leak-off coefficients for pore pressure cohesive elements and for slurry cohesive elements;
is called at all material calculation points of elements for which the material definition contains user-defined leak-off coefficients; and
can include material behavior dependent on field variables or state variables.

This page discusses:

Leak-Off Models
Simple Leak-Off Model
Physics-Based Leak-Off Model

Leak-Off Models

Abaqus provides two methods for coding user subroutine UFLUIDLEAKOFF, corresponding to the two models you can use to describe leak-off behavior:

For the simple leak-off model, you define the coefficients that govern the pressure-flow relationship.
For the physics-based leak-off model, you define the leak-off flow rate directly.

Only the simple leak-off model is available in cases without degree of freedom of slurry concentration. You can use both leak-off models for slurry transport analyses (see Defining Slurry Transport and Placement within the Cohesive Element Gap).

Simple Leak-Off Model

You can define the fluid leak-off coefficient as a function of the gap opening, fracture fluid pressure, pore pressure on the top and bottom surfaces, temperature, and field variables.

User Subroutine Interface

      SUBROUTINE UFLUIDLEAKOFF( PERM, PGRAD, DN, P_INT, P_BOT, P_TOP,
     1 ANM, TANG, TIME, DTIME, TEMP, DTEMP, PREDEF, DPRED, C_BOT, C_TOP,
     2 DC_BOT, DC_TOP, STATEV, NSTATV, NOEL, NPT, KSTEP, KINC )
C
      INCLUDE 'ABA_PARAM.INC'
C
      CHARACTER*80 CMNAME
      DIMENSION PERM(2), PGRAD(2), ANM(3), TANG(3,2), TIME(2), PREDEF(1),
     1 DPRED(1), DC_BOT(3), DC_TOP(3), STATEV(NSTATV)
   

      user coding to define C_BOT, C_TOP, DC_BOT, and DC_TOP

      RETURN
      END

Variables to Be Defined

C_BOT: $C_{b o t}$ , fluid leak-off coefficient on the bottom side of a pore pressure cohesive element.
C_TOP: $C_{t o p}$ , fluid leak-off coefficient on the top side of a pore pressure cohesive element.
DC_BOT(1): $\partial C_{b o t} / \partial d$ , where $d$ =DN.
DC_BOT(2): $\partial C_{b o t} / \partial p_{i n t}$ , where $p_{i n t}$ =P_INT.
DC_BOT(3): $\partial C_{b o t} / \partial p_{b o t}$ , where $p_{b o t}$ =P_BOT.
DC_TOP(1): $\partial C_{t o p} / \partial d$ , where $d$ =DN.
DC_TOP(2): $\partial C_{t o p} / \partial p_{i n t}$ , where $p_{i n t}$ =P_INT.
DC_TOP(3): $\partial C_{t o p} / \partial p_{t o p}$ , where $p_{t o p}$ =P_TOP.
STATEV(NSTATV): An array containing the values of the solution-dependent state variables. You define the meaning of these variables. These are passed in as the values at the beginning of the increment and must be returned as the values at the end of the increment. The size of the array is defined as described in Allocating Space for Solution-Dependent State Variables.

Variables Passed in for Information

PERM(1): Fluid permeability.
PERM(2): Derivative of fluid permeability with regard to the opening.
PGRAD(1): First component of internal pressure gradient.
PGRAD(2): Second component of internal pressure gradient.
DN: Relative opening of the element.
P_INT: Internal pressure.
P_BOT: Bottom pressure.
P_TOP: Top pressure.
ANM: Normal vector directed from the bottom face toward the top face.
TANG: Tangent direction vectors.
TIME(1): Value of step time at the beginning of the current increment.
TIME(2): Value of total time at the beginning of the current increment.
DTIME: Time increment.
TEMP: Temperature at the start of the increment.
DTEMP: Increment of temperature.
PREDEF: Array of interpolated values of predefined field variables at this point at the start of the increment, based on the values read in at the nodes.
DPRED: Array of increments of predefined field variables.
NSTATV: Number of solution-dependent state variables that are associated with this material type (defined as described in Allocating Space for Solution-Dependent State Variables).
NOEL: Element number.
NPT: Integration point number.
KSTEP: Step number.
KINC: Increment number.

Physics-Based Leak-Off Model

You can define the leak-off flux rate as a function of the gap opening, fracture fluid pressure, pore pressure on the top and bottom surfaces, slurry concentration, pressure gradients, temperature, and field variables.

User Subroutine Interface

      SUBROUTINE UFLUIDLEAKOFF( PERM, PGRAD, DN, P_INT, P_BOT, P_TOP,
     1 ANM, TANG, TIME, DTIME, TEMP, DTEMP, PREDEF, DPRED, Q_BOT, Q_TOP,
     2 DQ_BOT, DQ_TOP, STATEV, NSTATV, NOEL, NPT, KSTEP, KINC )
C
      INCLUDE 'ABA_PARAM.INC'
C
      CHARACTER*80 CMNAME
      DIMENSION PERM(2), PGRAD(2), DN(2), ANM(3), TANG(3,2), TIME(2),
     1 PREDEF(1), DPRED(1), DQ_BOT(6), DQ_TOP(6), STATEV(NSTATV)
   

      user coding to define C_BOT, C_TOP, DC_BOT, and DC_TOP

      RETURN
      END

Variables to Be Defined

Q_BOT: $q_{b o t}$ , leak-off flow rate into the bottom crack surface.
Q_TOP: $q_{t o p}$ , leak-off flow rate into the top crack surface.
DQ_BOT(1): $\partial q_{b o t} / \partial d$ , where $d$ =DN(1).
DQ_BOT(2): $\partial q_{b o t} / \partial p_{i n t}$ , where $p_{i n t}$ =P_INT.
DQ_BOT(3): $\partial q_{b o t} / \partial p_{b o t}$ , where $p_{b o t}$ =P_BOT.
DQ_BOT(4): $\partial q_{b o t} / \partial C_{v}$ , where $C_{v}$ =DN(2).
DQ_BOT(5): $\partial q_{b o t} / (\partial p_{i n t} / \partial x)$ , where $\partial p_{i n t} / \partial x$ =PGRAD(1).
DQ_BOT(6): $\partial q_{b o t} / (\partial p_{i n t} / \partial y)$ , where $\partial p_{i n t} / \partial y$ =PGRAD(2).
DQ_TOP(1): $\partial q_{t o p} / \partial d$ , where $d$ =DN.
DQ_TOP(2): $\partial q_{t o p} / \partial p_{i n t}$ , where $p_{i n t}$ =P_INT.
DQ_TOP(3): $\partial q_{t o p} / \partial p_{t o p}$ , where $p_{t o p}$ =P_TOP.
DQ_TOP(4): $\partial q_{t o p} / \partial C_{v}$ , where $C_{v}$ =DN(2).
DQ_BOT(5): $\partial q_{t o p} / (\partial p_{i n t} / \partial x)$ , where $\partial p_{i n t} / \partial x$ =PGRAD(1).
DQ_TOP(6): $\partial q_{t o p} / (\partial p_{i n t} / \partial y)$ , where $\partial p_{i n t} / \partial y$ =PGRAD(2).
STATEV(NSTATV): An array containing the values of the solution-dependent state variables. You define the meaning of these variables, which are passed in as the values at the beginning of the increment and must be returned as the values at the end of the increment. The size of the array is defined as described in Allocating Space for Solution-Dependent State Variables.

Variables Passed in for Information

PERM(1): Fluid permeability.
PERM(2): Derivative of fluid permeability with regard to the opening.
PGRAD(1): First component of internal pressure gradient.
PGRAD(2): Second component of internal pressure gradient.
DN(1): Relative opening of the element.
DN(2): Slurry concentration.
P_INT: Internal pressure.
P_BOT: Bottom pressure.
P_TOP: Top pressure.
ANM: Normal vector directed from the bottom face toward the top face.
TANG: Tangent direction vectors.
TIME(1): Value of step time at the beginning of the current increment.
TIME(2): Value of total time at the beginning of the current increment.
DTIME: Time increment.
TEMP: Temperature at the start of the increment.
DTEMP: Increment of temperature.
PREDEF: Array of interpolated values of predefined field variables at this point at the start of the increment, based on the values read in at the nodes.
DPRED: Array of increments of predefined field variables.
NSTATV: Number of solution-dependent state variables that are associated with this material type (defined as described in Allocating Space for Solution-Dependent State Variables).
NOEL: Element number.
NPT: Integration point number.
KSTEP: Step number.
KINC: Increment number.